diff --git a/master/api/rocq-runtime/Coq_checklib/Mod_checking/index.html b/master/api/rocq-runtime/Coq_checklib/Mod_checking/index.html index a0773566d6..78397183b7 100644 --- a/master/api/rocq-runtime/Coq_checklib/Mod_checking/index.html +++ b/master/api/rocq-runtime/Coq_checklib/Mod_checking/index.html @@ -1,2 +1,2 @@ -Mod_checking (rocq-runtime.Coq_checklib.Mod_checking)

Module Coq_checklib.Mod_checking

val set_indirect_accessor : (Opaqueproof.opaque -> Opaqueproof.opaque_proofterm) -> unit
exception BadConstant of Names.Constant.t * Pp.t
\ No newline at end of file +Mod_checking (rocq-runtime.Coq_checklib.Mod_checking)

Module Coq_checklib.Mod_checking

val set_indirect_accessor : (Opaqueproof.opaque -> Opaqueproof.opaque_proofterm) -> unit
exception BadConstant of Names.Constant.t * Pp.t
\ No newline at end of file diff --git a/master/api/rocq-runtime/Declarations/index.html b/master/api/rocq-runtime/Declarations/index.html index 2bcbd37987..23b9cd8fa0 100644 --- a/master/api/rocq-runtime/Declarations/index.html +++ b/master/api/rocq-runtime/Declarations/index.html @@ -3,4 +3,4 @@ ... with In (params) : Un := cn1 : Tn1 | ... | cnpn : Tnpn

Record information: If the type is not a record, then NotRecord If the type is a non-primitive record, then FakeRecord If it is a primitive record, for every type in the block, we get:

The kernel does not exploit the difference between NotRecord and FakeRecord. It is mostly used by extraction, and should be extruded from the kernel at some point.

type record_info =
| NotRecord
| FakeRecord
| PrimRecord of (Names.Id.t * Names.Label.t array * Sorts.relevance array * Constr.types array) array
type regular_inductive_arity = {
mind_user_arity : Constr.types;
mind_sort : Sorts.t;
}
type inductive_arity = (regular_inductive_arity, template_arity) declaration_arity
type squash_info =
| AlwaysSquashed
| SometimesSquashed of Sorts.Quality.Set.t(*

A sort polymorphic inductive I@{...|...|...} : ... -> Type@{ s|...} is squashed at a given instantiation if any quality in the list is not smaller than s.

NB: if s is a variable SometimesSquashed contains SProp ie non ground instantiations are squashed.

*)
type one_inductive_body = {
mind_typename : Names.Id.t;(*

Name of the type: Ii

*)
mind_arity_ctxt : Constr.rel_context;(*

Arity context of Ii. It includes the context of parameters, that is, it has the form paramdecls, realdecls_i such that Ui (see above) is forall realdecls_i, si for some sort si and such that Ii has thus type forall paramdecls, forall realdecls_i, si. The context itself is represented internally as a list in reverse order [realdecl_i{r_i};...;realdecl_i1;paramdecl_m;...;paramdecl_1].

*)
mind_arity : inductive_arity;(*

Arity sort and original user arity

*)
mind_consnames : Names.Id.t array;(*

Names of the constructors: cij

*)
mind_user_lc : Constr.types array;(*

Types of the constructors with parameters: forall params, Tij, where the recursive occurrences of the inductive types in Tij (i.e. in the type of the j-th constructor of the i-th types of the block a shown above) have the form Ind ((mind,0),u), ..., Ind ((mind,n-1),u) for u the canonical abstract instance associated to mind_universes and mind the name to which the inductive block is bound in the environment.

*)
mind_nrealargs : int;(*

Number of expected real arguments of the type (no let, no params)

*)
mind_nrealdecls : int;(*

Length of realargs context (with let, no params)

*)
mind_squashed : squash_info option;(*

Is elimination restricted to the inductive's sort?

*)
mind_nf_lc : (Constr.rel_context * Constr.types) array;(*

Head normalized constructor types so that their conclusion exposes the inductive type. It includes the parameters, i.e. each component of the array has the form (decls_ij, Ii params realargs_ij) where decls_ij is the concatenation of the context of parameters (possibly with let-ins) and of the arguments of the constructor (possibly with let-ins). This context is internally represented as a list [cstrdecl_ij{q_ij};...;cstrdecl_ij1;paramdecl_m;...;paramdecl_1] such that the constructor in fine has type forall paramdecls, - forall cstrdecls_ij, Ii params realargs_ij with params referring to the assumptions of paramdecls and realargs_ij being the "indices" specific to the constructor.

*)
mind_consnrealargs : int array;(*

Number of expected proper arguments of the constructors (w/o params)

*)
mind_consnrealdecls : int array;(*

Length of the signature of the constructors (with let, w/o params)

*)
mind_recargs : wf_paths;(*

Signature of recursive arguments in the constructors

*)
mind_relevance : Sorts.relevance;
mind_nb_constant : int;(*

number of constant constructor

*)
mind_nb_args : int;(*

number of no constant constructor

*)
mind_reloc_tbl : Vmvalues.reloc_table;
}

Datas specific to a single type of a block of mutually inductive type

type recursivity_kind =
| Finite(*

= inductive

*)
| CoFinite(*

= coinductive

*)
| BiFinite(*

= non-recursive, like in "Record" definitions

*)
Datas associated to a full block of mutually inductive types
type mutual_inductive_body = {
mind_packets : one_inductive_body array;(*

The component of the mutual inductive block

*)
mind_record : record_info;(*

The record information

*)
mind_finite : recursivity_kind;(*

Whether the type is inductive, coinductive or non-recursive

*)
mind_ntypes : int;(*

Number of types in the block

*)
mind_hyps : Constr.named_context;(*

Section hypotheses on which the block depends

*)
mind_univ_hyps : UVars.Instance.t;(*

Section polymorphic universes.

*)
mind_nparams : int;(*

Number of expected parameters including non-uniform ones (i.e. length of mind_params_ctxt w/o let-in)

*)
mind_nparams_rec : int;(*

Number of recursively uniform (i.e. ordinary) parameters

*)
mind_params_ctxt : Constr.rel_context;(*

The context of parameters (includes let-in declaration)

*)
mind_universes : universes;(*

Information about monomorphic/polymorphic/cumulative inductives and their universes

*)
mind_template : template_universes option;
mind_variance : UVars.Variance.t array option;(*

Variance info, None when non-cumulative.

*)
mind_sec_variance : UVars.Variance.t array option;(*

Variance info for section polymorphic universes. None outside sections. The final variance once all sections are discharged is mind_sec_variance ++ mind_variance.

*)
mind_private : bool option;(*

allow pattern-matching: Some true ok, Some false blocked

*)
mind_typing_flags : typing_flags;(*

typing flags at the time of the inductive creation

*)
}
type mind_specif = mutual_inductive_body * one_inductive_body
Rewrite rules
type quality_pattern = Sorts.Quality.pattern =
| PQVar of int option
| PQConstant of Sorts.Quality.constant
type instance_mask = UVars.Instance.mask
type sort_pattern = Sorts.pattern =
| PSProp
| PSSProp
| PSSet
| PSType of int option
| PSQSort of int option * int option
type 'arg head_pattern =
| PHRel of int
| PHSort of sort_pattern
| PHSymbol of Names.Constant.t * instance_mask
| PHInd of Names.inductive * instance_mask
| PHConstr of Names.constructor * instance_mask
| PHInt of Uint63.t
| PHFloat of Float64.t
| PHString of Pstring.t
| PHLambda of 'arg array * 'arg
| PHProd of 'arg array * 'arg

Patterns are internally represented as pairs of a head-pattern and a list of eliminations Eliminations correspond to elements of the stack in a reduction machine, they represent a pattern with a hole, to be filled with the head-pattern

type pattern_elimination =
| PEApp of pattern_argument array
| PECase of Names.inductive * instance_mask * pattern_argument * pattern_argument array
| PEProj of Names.Projection.Repr.t
and head_elimination = pattern_argument head_pattern * pattern_elimination list
and pattern_argument =
| EHole of int
| EHoleIgnored
| ERigid of head_elimination
type rewrite_rule = {
nvars : int * int * int;
lhs_pat : instance_mask * pattern_elimination list;
rhs : Constr.constr;
}
Representation of rewrite rules in the kernel
type rewrite_rules_body = {
rewrules_rules : (Names.Constant.t * rewrite_rule) list;
}

(c, { lhs_pat = (u, elims); rhs }) in this list stands for (PHSymbol (c,u), elims) ==> rhs

Module declarations
type mod_body = [
| `ModBody
]
type mod_type = [
| `ModType
]
type (_, 'v) when_mod_body =
| ModBodyVal : 'v -> (mod_body, 'v) when_mod_body
| ModTypeNul : (mod_type, 'v) when_mod_body

Functor expressions are forced to be on top of other expressions

type ('ty, 'a) functorize =
| NoFunctor of 'a
| MoreFunctor of Names.MBId.t * 'ty * ('ty, 'a) functorize

The fully-algebraic module expressions : names, applications, 'with ...'. They correspond to the user entries of non-interactive modules. They will be later expanded into module structures in Mod_typing, and won't play any role into the kernel after that : they are kept only for short module printing and for extraction.

type 'uconstr with_declaration =
| WithMod of Names.Id.t list * Names.ModPath.t
| WithDef of Names.Id.t list * 'uconstr
type 'uconstr module_alg_expr =
| MEident of Names.ModPath.t
| MEapply of 'uconstr module_alg_expr * Names.ModPath.t
| MEwith of 'uconstr module_alg_expr * 'uconstr with_declaration
type 'uconstr functor_alg_expr =
| MENoFunctor of 'uconstr module_alg_expr
| MEMoreFunctor of 'uconstr functor_alg_expr

A module expression is an algebraic expression, possibly functorized.

type module_expression = (Constr.constr * UVars.AbstractContext.t option) functor_alg_expr

A component of a module structure

type structure_field_body =
| SFBconst of constant_body
| SFBmind of mutual_inductive_body
| SFBrules of rewrite_rules_body
| SFBmodule of module_body
| SFBmodtype of module_type_body

A module structure is a list of labeled components.

Note : we may encounter now (at most) twice the same label in a structure_body, once for a module (SFBmodule or SFBmodtype) and once for an object (SFBconst or SFBmind)

and structure_body = (Names.Label.t * structure_field_body) list

A module signature is a structure, with possibly functors on top of it

and module_signature = (module_type_body, structure_body) functorize
and module_implementation =
| Abstract(*

no accessible implementation

*)
| Algebraic of module_expression(*

non-interactive algebraic expression

*)
| Struct of structure_body(*

interactive body living in the parameter context of mod_type

*)
| FullStruct(*

special case of Struct : the body is exactly mod_type

*)
and 'a generic_module_body = {
mod_mp : Names.ModPath.t;(*

absolute path of the module

*)
mod_expr : ('a, module_implementation) when_mod_body;(*

implementation

*)
mod_type : module_signature;(*

expanded type

*)
mod_type_alg : module_expression option;(*

algebraic type

*)
mod_delta : Mod_subst.delta_resolver;(*

quotiented set of equivalent constants and inductive names

*)
mod_retroknowledge : ('a, Retroknowledge.action list) when_mod_body;
}

For a module, there are five possible situations:

and module_body = mod_body generic_module_body

A module_type_body is just a module_body with no implementation and also an empty mod_retroknowledge. Its mod_type_alg contains the algebraic definition of this module type, or None if it has been built interactively.

and module_type_body = mod_type generic_module_body
type 'a module_retroknowledge = ('a, Retroknowledge.action list) when_mod_body

Extra invariants :

\ No newline at end of file + forall cstrdecls_ij, Ii params realargs_ij with params referring to the assumptions of paramdecls and realargs_ij being the "indices" specific to the constructor.

*)mind_consnrealargs : int array;(*

Number of expected proper arguments of the constructors (w/o params)

*)mind_consnrealdecls : int array;(*

Length of the signature of the constructors (with let, w/o params)

*)mind_recargs : wf_paths;(*

Signature of recursive arguments in the constructors

*)mind_relevance : Sorts.relevance;mind_nb_constant : int;(*

number of constant constructor

*)mind_nb_args : int;(*

number of no constant constructor

*)mind_reloc_tbl : Vmvalues.reloc_table;}

Datas specific to a single type of a block of mutually inductive type

type recursivity_kind =
| Finite(*

= inductive

*)
| CoFinite(*

= coinductive

*)
| BiFinite(*

= non-recursive, like in "Record" definitions

*)
Datas associated to a full block of mutually inductive types
type mutual_inductive_body = {
mind_packets : one_inductive_body array;(*

The component of the mutual inductive block

*)
mind_record : record_info;(*

The record information

*)
mind_finite : recursivity_kind;(*

Whether the type is inductive, coinductive or non-recursive

*)
mind_ntypes : int;(*

Number of types in the block

*)
mind_hyps : Constr.named_context;(*

Section hypotheses on which the block depends

*)
mind_univ_hyps : UVars.Instance.t;(*

Section polymorphic universes.

*)
mind_nparams : int;(*

Number of expected parameters including non-uniform ones (i.e. length of mind_params_ctxt w/o let-in)

*)
mind_nparams_rec : int;(*

Number of recursively uniform (i.e. ordinary) parameters

*)
mind_params_ctxt : Constr.rel_context;(*

The context of parameters (includes let-in declaration)

*)
mind_universes : universes;(*

Information about monomorphic/polymorphic/cumulative inductives and their universes

*)
mind_template : template_universes option;
mind_variance : UVars.Variance.t array option;(*

Variance info, None when non-cumulative.

*)
mind_sec_variance : UVars.Variance.t array option;(*

Variance info for section polymorphic universes. None outside sections. The final variance once all sections are discharged is mind_sec_variance ++ mind_variance.

*)
mind_private : bool option;(*

allow pattern-matching: Some true ok, Some false blocked

*)
mind_typing_flags : typing_flags;(*

typing flags at the time of the inductive creation

*)
}
type mind_specif = mutual_inductive_body * one_inductive_body
Rewrite rules
type quality_pattern = Sorts.Quality.pattern =
| PQVar of int option
| PQConstant of Sorts.Quality.constant
type instance_mask = UVars.Instance.mask
type sort_pattern = Sorts.pattern =
| PSProp
| PSSProp
| PSSet
| PSType of int option
| PSQSort of int option * int option
type 'arg head_pattern =
| PHRel of int
| PHSort of sort_pattern
| PHSymbol of Names.Constant.t * instance_mask
| PHInd of Names.inductive * instance_mask
| PHConstr of Names.constructor * instance_mask
| PHInt of Uint63.t
| PHFloat of Float64.t
| PHString of Pstring.t
| PHLambda of 'arg array * 'arg
| PHProd of 'arg array * 'arg

Patterns are internally represented as pairs of a head-pattern and a list of eliminations Eliminations correspond to elements of the stack in a reduction machine, they represent a pattern with a hole, to be filled with the head-pattern

type pattern_elimination =
| PEApp of pattern_argument array
| PECase of Names.inductive * instance_mask * pattern_argument * pattern_argument array
| PEProj of Names.Projection.Repr.t
and head_elimination = pattern_argument head_pattern * pattern_elimination list
and pattern_argument =
| EHole of int
| EHoleIgnored
| ERigid of head_elimination
type rewrite_rule = {
nvars : int * int * int;
lhs_pat : instance_mask * pattern_elimination list;
rhs : Constr.constr;
}
Representation of rewrite rules in the kernel
type rewrite_rules_body = {
rewrules_rules : (Names.Constant.t * rewrite_rule) list;
}

(c, { lhs_pat = (u, elims); rhs }) in this list stands for (PHSymbol (c,u), elims) ==> rhs

Module declarations
type mod_body = [
| `ModBody
]
type mod_type = [
| `ModType
]
type (_, 'v) when_mod_body =
| ModBodyVal : 'v -> (mod_body, 'v) when_mod_body
| ModTypeNul : (mod_type, 'v) when_mod_body

Functor expressions are forced to be on top of other expressions

type ('ty, 'a) functorize =
| NoFunctor of 'a
| MoreFunctor of Names.MBId.t * 'ty * ('ty, 'a) functorize

The fully-algebraic module expressions : names, applications, 'with ...'. They correspond to the user entries of non-interactive modules. They will be later expanded into module structures in Mod_typing, and won't play any role into the kernel after that : they are kept only for short module printing and for extraction.

type 'uconstr with_declaration =
| WithMod of Names.Id.t list * Names.ModPath.t
| WithDef of Names.Id.t list * 'uconstr
type 'uconstr module_alg_expr =
| MEident of Names.ModPath.t
| MEapply of 'uconstr module_alg_expr * Names.ModPath.t
| MEwith of 'uconstr module_alg_expr * 'uconstr with_declaration
type 'uconstr functor_alg_expr =
| MENoFunctor of 'uconstr module_alg_expr
| MEMoreFunctor of 'uconstr functor_alg_expr

A module expression is an algebraic expression, possibly functorized.

type module_expression = (Constr.constr * UVars.AbstractContext.t option) functor_alg_expr

A component of a module structure

type ('mod_body, 'mod_type) structure_field_body =
| SFBconst of constant_body
| SFBmind of mutual_inductive_body
| SFBrules of rewrite_rules_body
| SFBmodule of 'mod_body
| SFBmodtype of 'mod_type

A module structure is a list of labeled components.

Note : we may encounter now (at most) twice the same label in a structure_body, once for a module (SFBmodule or SFBmodtype) and once for an object (SFBconst or SFBmind)

and ('mod_body, 'mod_type) structure_body = (Names.Label.t * ('mod_body, 'mod_type) structure_field_body) list
\ No newline at end of file diff --git a/master/api/rocq-runtime/Declareops/index.html b/master/api/rocq-runtime/Declareops/index.html index 8c94cf02a6..1c132e674a 100644 --- a/master/api/rocq-runtime/Declareops/index.html +++ b/master/api/rocq-runtime/Declareops/index.html @@ -1,2 +1,2 @@ -Declareops (rocq-runtime.Declareops)

Module Declareops

Operations concerning types in Declarations : constant_body, mutual_inductive_body, module_body ...

Arities
val map_decl_arity : ('a -> 'c) -> ('b -> 'd) -> ('a, 'b) Declarations.declaration_arity -> ('c, 'd) Declarations.declaration_arity
Constants
val subst_const_body : Mod_subst.substitution -> Declarations.constant_body -> Declarations.constant_body

Is there a actual body in const_body ?

val constant_has_body : ('a, 'b) Declarations.pconstant_body -> bool
val constant_polymorphic_context : ('a, 'b) Declarations.pconstant_body -> UVars.AbstractContext.t
val constant_is_polymorphic : ('a, 'b) Declarations.pconstant_body -> bool

Is the constant polymorphic?

Return the universe context, in case the definition is polymorphic, otherwise the context is empty.

val is_opaque : ('a, 'b) Declarations.pconstant_body -> bool
Inductive types
val eq_recarg : Declarations.recarg -> Declarations.recarg -> bool
val pr_recarg : Declarations.recarg -> Pp.t
val pr_wf_paths : Declarations.wf_paths -> Pp.t
val mk_norec : Declarations.wf_paths
val dest_subterms : Declarations.wf_paths -> Declarations.wf_paths list array
val recarg_length : Declarations.wf_paths -> int -> int
val subst_mind_body : Mod_subst.substitution -> Declarations.mutual_inductive_body -> Declarations.mutual_inductive_body
val inductive_polymorphic_context : Declarations.mutual_inductive_body -> UVars.AbstractContext.t
val inductive_is_polymorphic : Declarations.mutual_inductive_body -> bool

Is the inductive polymorphic?

Is the inductive cumulative?

val inductive_is_cumulative : Declarations.mutual_inductive_body -> bool

Is the inductive cumulative?

val inductive_make_projection : Names.inductive -> Declarations.mutual_inductive_body -> proj_arg:int -> Names.Projection.Repr.t * Sorts.relevance

Anomaly when not a primitive record or invalid proj_arg

val inductive_make_projections : Names.inductive -> Declarations.mutual_inductive_body -> (Names.Projection.Repr.t * Sorts.relevance) array option
Modules
Kernel flags

A default, safe set of flags for kernel type-checking

Hash-consing

Here, strictly speaking, we don't perform true hash-consing of the structure, but simply hash-cons all inner constr and other known elements

val hcons_const_body : ?hbody:(Constr.t -> Constr.t) -> ('a, 'b) Declarations.pconstant_body -> ('a, 'b) Declarations.pconstant_body
val hcons_generic_module_body : 'a Declarations.generic_module_body -> 'a Declarations.generic_module_body
val hcons_module_body : Declarations.module_body -> Declarations.module_body
\ No newline at end of file +Declareops (rocq-runtime.Declareops)

Module Declareops

Operations concerning types in Declarations : constant_body, mutual_inductive_body, module_body ...

Arities
val map_decl_arity : ('a -> 'c) -> ('b -> 'd) -> ('a, 'b) Declarations.declaration_arity -> ('c, 'd) Declarations.declaration_arity
Constants
val subst_const_body : Mod_subst.substitution -> Declarations.constant_body -> Declarations.constant_body

Is there a actual body in const_body ?

val constant_has_body : ('a, 'b) Declarations.pconstant_body -> bool
val constant_polymorphic_context : ('a, 'b) Declarations.pconstant_body -> UVars.AbstractContext.t
val constant_is_polymorphic : ('a, 'b) Declarations.pconstant_body -> bool

Is the constant polymorphic?

Return the universe context, in case the definition is polymorphic, otherwise the context is empty.

val is_opaque : ('a, 'b) Declarations.pconstant_body -> bool
Inductive types
val eq_recarg : Declarations.recarg -> Declarations.recarg -> bool
val pr_recarg : Declarations.recarg -> Pp.t
val pr_wf_paths : Declarations.wf_paths -> Pp.t
val mk_norec : Declarations.wf_paths
val dest_subterms : Declarations.wf_paths -> Declarations.wf_paths list array
val recarg_length : Declarations.wf_paths -> int -> int
val subst_mind_body : Mod_subst.substitution -> Declarations.mutual_inductive_body -> Declarations.mutual_inductive_body
val inductive_polymorphic_context : Declarations.mutual_inductive_body -> UVars.AbstractContext.t
val inductive_is_polymorphic : Declarations.mutual_inductive_body -> bool

Is the inductive polymorphic?

Is the inductive cumulative?

val inductive_is_cumulative : Declarations.mutual_inductive_body -> bool

Is the inductive cumulative?

val inductive_make_projection : Names.inductive -> Declarations.mutual_inductive_body -> proj_arg:int -> Names.Projection.Repr.t * Sorts.relevance

Anomaly when not a primitive record or invalid proj_arg

val inductive_make_projections : Names.inductive -> Declarations.mutual_inductive_body -> (Names.Projection.Repr.t * Sorts.relevance) array option
Kernel flags

A default, safe set of flags for kernel type-checking

Hash-consing

Here, strictly speaking, we don't perform true hash-consing of the structure, but simply hash-cons all inner constr and other known elements

val hcons_const_body : ?hbody:(Constr.t -> Constr.t) -> ('a, 'b) Declarations.pconstant_body -> ('a, 'b) Declarations.pconstant_body
\ No newline at end of file diff --git a/master/api/rocq-runtime/Environ/Globals/index.html b/master/api/rocq-runtime/Environ/Globals/index.html index 1e155dd69e..9499226951 100644 --- a/master/api/rocq-runtime/Environ/Globals/index.html +++ b/master/api/rocq-runtime/Environ/Globals/index.html @@ -1,2 +1,2 @@ -Globals (rocq-runtime.Environ.Globals)

Module Environ.Globals

type t
val view : t -> view
\ No newline at end of file +Globals (rocq-runtime.Environ.Globals)

Module Environ.Globals

type t
val view : t -> view
\ No newline at end of file diff --git a/master/api/rocq-runtime/Environ/index.html b/master/api/rocq-runtime/Environ/index.html index 6da1aea189..36779378c8 100644 --- a/master/api/rocq-runtime/Environ/index.html +++ b/master/api/rocq-runtime/Environ/index.html @@ -1,2 +1,2 @@ -Environ (rocq-runtime.Environ)

Module Environ

Unsafe environments. We define here a datatype for environments. Since typing is not yet defined, it is not possible to check the informations added in environments, and that is why we speak here of ``unsafe'' environments.

Environments have the following components:

Linking information for the native compiler

type key = int CEphemeron.key option Stdlib.ref
type constant_key = Declarations.constant_body * (link_info Stdlib.ref * key)
type mind_key = Declarations.mutual_inductive_body * link_info Stdlib.ref
module Globals : sig ... end
type named_context_val = private {
env_named_ctx : Constr.named_context;
env_named_map : Constr.named_declaration Names.Id.Map.t;(*

Identifier-indexed version of env_named_ctx

*)
env_named_idx : Constr.named_declaration Range.t;(*

Same as env_named_ctx but with a fast-access list.

*)
}
type rel_context_val = private {
env_rel_ctx : Constr.rel_context;
env_rel_map : Constr.rel_declaration Range.t;
}
type env = private {
env_globals : Globals.t;
env_named_context : named_context_val;
env_rel_context : rel_context_val;
env_universes : UGraph.t;
env_qualities : Sorts.QVar.Set.t;
symb_pats : Declarations.rewrite_rule list Names.Cmap_env.t;
env_typing_flags : Declarations.typing_flags;
vm_library : Vmlibrary.t;
retroknowledge : Retroknowledge.retroknowledge;
rewrite_rules_allowed : bool;(*

Allow rewrite rules (breaks e.g. SR)

*)
env_nb_rel : int;
irr_constants : Sorts.relevance Names.Cmap_env.t;(*

irr_constants is a cache of the relevances which are not Relevant. In other words, const_relevance == Option.default Relevant (find_opt con irr_constants).

*)
irr_inds : Sorts.relevance Names.Indmap_env.t;(*

irr_inds is a cache of the relevances which are not Relevant. cf irr_constants.

*)
constant_hyps : Names.Id.Set.t Names.Cmap_env.t;(*

Cache section variables depended on by each constant. Not present -> depends on nothing.

*)
inductive_hyps : Names.Id.Set.t Names.Mindmap_env.t;(*

Cache section variables depended on by each inductive. Not present -> depends on nothing.

*)
}
type rewrule_not_allowed =
| Symb
| Rule
exception RewriteRulesNotAllowed of rewrule_not_allowed
val oracle : env -> Conv_oracle.oracle
val set_oracle : env -> Conv_oracle.oracle -> env
val eq_named_context_val : named_context_val -> named_context_val -> bool
val empty_env : env
val universes : env -> UGraph.t
val rel_context : env -> Constr.rel_context
val named_context : env -> Constr.named_context
val named_context_val : env -> named_context_val
val set_universes : UGraph.t -> env -> env
val typing_flags : env -> Declarations.typing_flags
val is_impredicative_set : env -> bool
val type_in_type : env -> bool
val deactivated_guard : env -> bool
val indices_matter : env -> bool
val is_impredicative_sort : env -> Sorts.t -> bool
val is_impredicative_family : env -> Sorts.family -> bool
val empty_context : env -> bool

is the local context empty

Context of de Bruijn variables (rel_context)
val nb_rel : env -> int
val push_rel : Constr.rel_declaration -> env -> env
val push_rel_context : Constr.rel_context -> env -> env
val push_rec_types : Constr.rec_declaration -> env -> env
val push_rel_context_val : Constr.rel_declaration -> rel_context_val -> rel_context_val
val set_rel_context_val : rel_context_val -> env -> env
val empty_rel_context_val : rel_context_val
val lookup_rel : int -> env -> Constr.rel_declaration

Looks up in the context of local vars referred by indice (rel_context) raises Not_found if the index points out of the context

val evaluable_rel : int -> env -> bool
val env_of_rel : int -> env -> env
Recurrence on rel_context
val fold_rel_context : (env -> Constr.rel_declaration -> 'a -> 'a) -> env -> init:'a -> 'a
Context of variables (section variables and goal assumptions)
val named_context_of_val : named_context_val -> Constr.named_context
val val_of_named_context : Constr.named_context -> named_context_val
val empty_named_context_val : named_context_val
val ids_of_named_context_val : named_context_val -> Names.Id.Set.t

map_named_val f ctxt apply f to the body and the type of each declarations. *** /!\ *** f t should be convertible with t, and preserve the name

val push_named : Constr.named_declaration -> env -> env
val push_named_context : Constr.named_context -> env -> env

Looks up in the context of local vars referred by names (named_context) raises Not_found if the Id.t is not found

val evaluable_named : Names.variable -> env -> bool
val named_type : Names.variable -> env -> Constr.types
val named_body : Names.variable -> env -> Constr.constr option
Recurrence on named_context: older declarations processed first
val fold_named_context : (env -> Constr.named_declaration -> 'a -> 'a) -> env -> init:'a -> 'a
val match_named_context_val : named_context_val -> (Constr.named_declaration * named_context_val) option
val fold_named_context_reverse : ('a -> Constr.named_declaration -> 'a) -> init:'a -> env -> 'a

Recurrence on named_context starting from younger decl

val reset_context : env -> env

This forgets named and rel contexts

val reset_with_named_context : named_context_val -> env -> env

This forgets rel context and sets a new named context

val pop_rel_context : int -> env -> env

This removes the n last declarations from the rel context

val fold_constants : (Names.Constant.t -> Declarations.constant_body -> 'a -> 'a) -> env -> 'a -> 'a

Useful for printing

val fold_inductives : (Names.MutInd.t -> Declarations.mutual_inductive_body -> 'a -> 'a) -> env -> 'a -> 'a
Global constants
Add entries to global environment
val add_constant_key : Names.Constant.t -> Declarations.constant_body -> link_info -> env -> env
val lookup_constant_key : Names.Constant.t -> env -> constant_key
val lookup_constant : Names.Constant.t -> env -> Declarations.constant_body

Looks up in the context of global constant names raises an anomaly if the required path is not found

val evaluable_constant : Names.Constant.t -> env -> bool
val mem_constant : Names.Constant.t -> env -> bool
val add_rewrite_rules : (Names.Constant.t * Declarations.rewrite_rule) list -> env -> env
val polymorphic_constant : Names.Constant.t -> env -> bool

New-style polymorphism

val polymorphic_pconstant : Constr.pconstant -> env -> bool
val type_in_type_constant : Names.Constant.t -> env -> bool
...

constant_value env c raises NotEvaluableConst Opaque if c is opaque, NotEvaluableConst NoBody if it has no body, NotEvaluableConst IsProj if c is a projection, NotEvaluableConst (IsPrimitive p) if c is primitive p and an anomaly if it does not exist in env

type const_evaluation_result =
| NoBody
| Opaque
| IsPrimitive of UVars.Instance.t * CPrimitives.t
| HasRules of UVars.Instance.t * bool * Declarations.rewrite_rule list
exception NotEvaluableConst of const_evaluation_result
val constant_value_and_type : env -> Names.Constant.t UVars.puniverses -> Constr.constr option * Constr.types * Univ.Constraints.t

The universe context associated to the constant, empty if not polymorphic

val constant_context : env -> Names.Constant.t -> UVars.AbstractContext.t

The universe context associated to the constant, empty if not polymorphic

val constant_value_in : env -> Names.Constant.t UVars.puniverses -> Constr.constr
val constant_type_in : env -> Names.Constant.t UVars.puniverses -> Constr.types
val constant_opt_value_in : env -> Names.Constant.t UVars.puniverses -> Constr.constr option
val is_symbol : env -> Names.Constant.t -> bool
val is_primitive : env -> Names.Constant.t -> bool
val get_primitive : env -> Names.Constant.t -> CPrimitives.t option
val is_array_type : env -> Names.Constant.t -> bool
val is_int63_type : env -> Names.Constant.t -> bool
val is_float64_type : env -> Names.Constant.t -> bool
val is_string_type : env -> Names.Constant.t -> bool
val is_primitive_type : env -> Names.Constant.t -> bool
Primitive projections
val lookup_projection : Names.Projection.t -> env -> Sorts.relevance * Constr.types

Checks that the number of parameters is correct.

val get_projection : env -> Names.inductive -> proj_arg:int -> Names.Projection.Repr.t * Sorts.relevance

Anomaly when not a primitive record or invalid proj_arg.

val get_projections : env -> Names.inductive -> (Names.Projection.Repr.t * Sorts.relevance) array option
val lookup_mind_key : Names.MutInd.t -> env -> mind_key

Inductive types

val add_mind_key : Names.MutInd.t -> mind_key -> env -> env

Looks up in the context of global inductive names raises an anomaly if the required path is not found

val mem_mind : Names.MutInd.t -> env -> bool
val mind_context : env -> Names.MutInd.t -> UVars.AbstractContext.t

The universe context associated to the inductive, empty if not polymorphic

val polymorphic_ind : Names.inductive -> env -> bool

New-style polymorphism

val polymorphic_pind : Constr.pinductive -> env -> bool
val type_in_type_ind : Names.inductive -> env -> bool
val template_polymorphic_ind : Names.inductive -> env -> bool

Old-style polymorphism

val template_polymorphic_pind : Constr.pinductive -> env -> bool
Changes of representation of Case nodes

Given an inductive type and its parameters, builds the context of the return clause, including the inductive being eliminated. The additional binder array is only used to set the names of the context variables, we use the less general type to make it easy to use this function on Case nodes.

val expand_branch_contexts : Declarations.mind_specif -> UVars.Instance.t -> Constr.constr array -> (Names.Name.t Constr.binder_annot array * 'a) array -> Constr.rel_context array

Given an inductive type and its parameters, builds the context of the return clause, including the inductive being eliminated. The additional binder array is only used to set the names of the context variables, we use the less general type to make it easy to use this function on Case nodes.

instantiate_context u subst nas ctx applies both u and subst to ctx while replacing names using nas (order reversed). In particular, assumes that ctx and nas have the same length.

Name quotients
module type QNameS = sig ... end
module QConstant : QNameS with type t = Names.Constant.t
module QMutInd : QNameS with type t = Names.MutInd.t
module QInd : QNameS with type t = Names.Ind.t
module QConstruct : QNameS with type t = Names.Construct.t
module QProjection : sig ... end
module QGlobRef : QNameS with type t = Names.GlobRef.t
Modules
val add_modtype : Declarations.module_type_body -> env -> env
val shallow_add_module : Declarations.module_body -> env -> env

shallow_add_module does not add module components

val lookup_module : Names.ModPath.t -> env -> Declarations.module_body
Universe constraints
val add_constraints : Univ.Constraints.t -> env -> env

Add universe constraints to the environment.

  • raises UniverseInconsistency.
val check_constraints : Univ.Constraints.t -> env -> bool

Check constraints are satifiable in the environment.

val push_context : ?strict:bool -> UVars.UContext.t -> env -> env

push_context ?(strict=false) ctx env pushes the universe context to the environment.

  • raises UGraph.AlreadyDeclared

    if one of the universes is already declared.

val push_context_set : ?strict:bool -> Univ.ContextSet.t -> env -> env

push_context_set ?(strict=false) ctx env pushes the universe context set to the environment. It does not fail even if one of the universes is already declared.

val push_floating_context_set : Univ.ContextSet.t -> env -> env

Same as above but keep the universes floating for template. Do not use.

val push_subgraph : Univ.ContextSet.t -> env -> env

push_subgraph univs env adds the universes and constraints in univs to env as push_context_set ~strict:false univs env, and also checks that they do not imply new transitive constraints between pre-existing universes in env.

val set_typing_flags : Declarations.typing_flags -> env -> env
val set_impredicative_set : bool -> env -> env
val set_type_in_type : bool -> env -> env
val set_allow_sprop : bool -> env -> env
val sprop_allowed : env -> bool
val allow_rewrite_rules : env -> env
val rewrite_rules_allowed : env -> bool
val update_typing_flags : ?typing_flags:Declarations.typing_flags -> env -> env

update_typing_flags ?typing_flags may update env with optional typing flags

val universes_of_global : env -> Names.GlobRef.t -> UVars.AbstractContext.t
Sets of referred section variables

global_vars_set env c returns the list of id's occurring either directly as Var id in c or indirectly as a section variable dependent in a global reference occurring in c

val global_vars_set : env -> Constr.constr -> Names.Id.Set.t
val vars_of_global : env -> Names.GlobRef.t -> Names.Id.Set.t
val really_needed : env -> Names.Id.Set.t -> Names.Id.Set.t

closure of the input id set w.r.t. dependency

like really_needed but computes a well ordered named context

Unsafe judgments.

We introduce here the pre-type of judgments, which is actually only a datatype to store a term with its type and the type of its type.

type ('constr, 'types) punsafe_judgment = {
uj_val : 'constr;
uj_type : 'types;
}
val on_judgment : ('a -> 'b) -> ('a, 'a) punsafe_judgment -> ('b, 'b) punsafe_judgment
val on_judgment_value : ('c -> 'c) -> ('c, 't) punsafe_judgment -> ('c, 't) punsafe_judgment
val on_judgment_type : ('t -> 't) -> ('c, 't) punsafe_judgment -> ('c, 't) punsafe_judgment
type unsafe_judgment = (Constr.constr, Constr.types) punsafe_judgment
val make_judge : 'constr -> 'types -> ('constr, 'types) punsafe_judgment
val j_val : ('constr, 'types) punsafe_judgment -> 'constr
val j_type : ('constr, 'types) punsafe_judgment -> 'types
type ('types, 'sorts) punsafe_type_judgment = {
utj_val : 'types;
utj_type : 'sorts;
}
type unsafe_type_judgment = (Constr.types, Sorts.t) punsafe_type_judgment
exception Hyp_not_found

apply_to_hyp sign id f split sign into tail::(id,_,_)::head and return tail::(f head (id,_,_) (rev tail))::head. the value associated to id should not change

val is_polymorphic : env -> Names.GlobRef.t -> bool
val is_template_polymorphic : env -> Names.GlobRef.t -> bool
val is_type_in_type : env -> Names.GlobRef.t -> bool
VM and native
val vm_library : env -> Vmlibrary.t
val set_vm_library : Vmlibrary.t -> env -> env
val lookup_vm_code : Vmlibrary.index -> env -> Vmemitcodes.to_patch

Native compiler

val set_retroknowledge : env -> Retroknowledge.retroknowledge -> env

Primitives

\ No newline at end of file +Environ (rocq-runtime.Environ)

Module Environ

Unsafe environments. We define here a datatype for environments. Since typing is not yet defined, it is not possible to check the informations added in environments, and that is why we speak here of ``unsafe'' environments.

Environments have the following components:

Linking information for the native compiler

type key = int CEphemeron.key option Stdlib.ref
type constant_key = Declarations.constant_body * (link_info Stdlib.ref * key)
type mind_key = Declarations.mutual_inductive_body * link_info Stdlib.ref
module Globals : sig ... end
type named_context_val = private {
env_named_ctx : Constr.named_context;
env_named_map : Constr.named_declaration Names.Id.Map.t;(*

Identifier-indexed version of env_named_ctx

*)
env_named_idx : Constr.named_declaration Range.t;(*

Same as env_named_ctx but with a fast-access list.

*)
}
type rel_context_val = private {
env_rel_ctx : Constr.rel_context;
env_rel_map : Constr.rel_declaration Range.t;
}
type env = private {
env_globals : Globals.t;
env_named_context : named_context_val;
env_rel_context : rel_context_val;
env_universes : UGraph.t;
env_qualities : Sorts.QVar.Set.t;
symb_pats : Declarations.rewrite_rule list Names.Cmap_env.t;
env_typing_flags : Declarations.typing_flags;
vm_library : Vmlibrary.t;
retroknowledge : Retroknowledge.retroknowledge;
rewrite_rules_allowed : bool;(*

Allow rewrite rules (breaks e.g. SR)

*)
env_nb_rel : int;
irr_constants : Sorts.relevance Names.Cmap_env.t;(*

irr_constants is a cache of the relevances which are not Relevant. In other words, const_relevance == Option.default Relevant (find_opt con irr_constants).

*)
irr_inds : Sorts.relevance Names.Indmap_env.t;(*

irr_inds is a cache of the relevances which are not Relevant. cf irr_constants.

*)
constant_hyps : Names.Id.Set.t Names.Cmap_env.t;(*

Cache section variables depended on by each constant. Not present -> depends on nothing.

*)
inductive_hyps : Names.Id.Set.t Names.Mindmap_env.t;(*

Cache section variables depended on by each inductive. Not present -> depends on nothing.

*)
}
type rewrule_not_allowed =
| Symb
| Rule
exception RewriteRulesNotAllowed of rewrule_not_allowed
val oracle : env -> Conv_oracle.oracle
val set_oracle : env -> Conv_oracle.oracle -> env
val eq_named_context_val : named_context_val -> named_context_val -> bool
val empty_env : env
val universes : env -> UGraph.t
val rel_context : env -> Constr.rel_context
val named_context : env -> Constr.named_context
val named_context_val : env -> named_context_val
val set_universes : UGraph.t -> env -> env
val typing_flags : env -> Declarations.typing_flags
val is_impredicative_set : env -> bool
val type_in_type : env -> bool
val deactivated_guard : env -> bool
val indices_matter : env -> bool
val is_impredicative_sort : env -> Sorts.t -> bool
val is_impredicative_family : env -> Sorts.family -> bool
val empty_context : env -> bool

is the local context empty

Context of de Bruijn variables (rel_context)
val nb_rel : env -> int
val push_rel : Constr.rel_declaration -> env -> env
val push_rel_context : Constr.rel_context -> env -> env
val push_rec_types : Constr.rec_declaration -> env -> env
val push_rel_context_val : Constr.rel_declaration -> rel_context_val -> rel_context_val
val set_rel_context_val : rel_context_val -> env -> env
val empty_rel_context_val : rel_context_val
val lookup_rel : int -> env -> Constr.rel_declaration

Looks up in the context of local vars referred by indice (rel_context) raises Not_found if the index points out of the context

val evaluable_rel : int -> env -> bool
val env_of_rel : int -> env -> env
Recurrence on rel_context
val fold_rel_context : (env -> Constr.rel_declaration -> 'a -> 'a) -> env -> init:'a -> 'a
Context of variables (section variables and goal assumptions)
val named_context_of_val : named_context_val -> Constr.named_context
val val_of_named_context : Constr.named_context -> named_context_val
val empty_named_context_val : named_context_val
val ids_of_named_context_val : named_context_val -> Names.Id.Set.t

map_named_val f ctxt apply f to the body and the type of each declarations. *** /!\ *** f t should be convertible with t, and preserve the name

val push_named : Constr.named_declaration -> env -> env
val push_named_context : Constr.named_context -> env -> env

Looks up in the context of local vars referred by names (named_context) raises Not_found if the Id.t is not found

val evaluable_named : Names.variable -> env -> bool
val named_type : Names.variable -> env -> Constr.types
val named_body : Names.variable -> env -> Constr.constr option
Recurrence on named_context: older declarations processed first
val fold_named_context : (env -> Constr.named_declaration -> 'a -> 'a) -> env -> init:'a -> 'a
val match_named_context_val : named_context_val -> (Constr.named_declaration * named_context_val) option
val fold_named_context_reverse : ('a -> Constr.named_declaration -> 'a) -> init:'a -> env -> 'a

Recurrence on named_context starting from younger decl

val reset_context : env -> env

This forgets named and rel contexts

val reset_with_named_context : named_context_val -> env -> env

This forgets rel context and sets a new named context

val pop_rel_context : int -> env -> env

This removes the n last declarations from the rel context

val fold_constants : (Names.Constant.t -> Declarations.constant_body -> 'a -> 'a) -> env -> 'a -> 'a

Useful for printing

val fold_inductives : (Names.MutInd.t -> Declarations.mutual_inductive_body -> 'a -> 'a) -> env -> 'a -> 'a
Global constants
Add entries to global environment
val add_constant_key : Names.Constant.t -> Declarations.constant_body -> link_info -> env -> env
val lookup_constant_key : Names.Constant.t -> env -> constant_key
val lookup_constant : Names.Constant.t -> env -> Declarations.constant_body

Looks up in the context of global constant names raises an anomaly if the required path is not found

val evaluable_constant : Names.Constant.t -> env -> bool
val mem_constant : Names.Constant.t -> env -> bool
val add_rewrite_rules : (Names.Constant.t * Declarations.rewrite_rule) list -> env -> env
val polymorphic_constant : Names.Constant.t -> env -> bool

New-style polymorphism

val polymorphic_pconstant : Constr.pconstant -> env -> bool
val type_in_type_constant : Names.Constant.t -> env -> bool
...

constant_value env c raises NotEvaluableConst Opaque if c is opaque, NotEvaluableConst NoBody if it has no body, NotEvaluableConst IsProj if c is a projection, NotEvaluableConst (IsPrimitive p) if c is primitive p and an anomaly if it does not exist in env

type const_evaluation_result =
| NoBody
| Opaque
| IsPrimitive of UVars.Instance.t * CPrimitives.t
| HasRules of UVars.Instance.t * bool * Declarations.rewrite_rule list
exception NotEvaluableConst of const_evaluation_result
val constant_value_and_type : env -> Names.Constant.t UVars.puniverses -> Constr.constr option * Constr.types * Univ.Constraints.t

The universe context associated to the constant, empty if not polymorphic

val constant_context : env -> Names.Constant.t -> UVars.AbstractContext.t

The universe context associated to the constant, empty if not polymorphic

val constant_value_in : env -> Names.Constant.t UVars.puniverses -> Constr.constr
val constant_type_in : env -> Names.Constant.t UVars.puniverses -> Constr.types
val constant_opt_value_in : env -> Names.Constant.t UVars.puniverses -> Constr.constr option
val is_symbol : env -> Names.Constant.t -> bool
val is_primitive : env -> Names.Constant.t -> bool
val get_primitive : env -> Names.Constant.t -> CPrimitives.t option
val is_array_type : env -> Names.Constant.t -> bool
val is_int63_type : env -> Names.Constant.t -> bool
val is_float64_type : env -> Names.Constant.t -> bool
val is_string_type : env -> Names.Constant.t -> bool
val is_primitive_type : env -> Names.Constant.t -> bool
Primitive projections
val lookup_projection : Names.Projection.t -> env -> Sorts.relevance * Constr.types

Checks that the number of parameters is correct.

val get_projection : env -> Names.inductive -> proj_arg:int -> Names.Projection.Repr.t * Sorts.relevance

Anomaly when not a primitive record or invalid proj_arg.

val get_projections : env -> Names.inductive -> (Names.Projection.Repr.t * Sorts.relevance) array option
val lookup_mind_key : Names.MutInd.t -> env -> mind_key

Inductive types

val add_mind_key : Names.MutInd.t -> mind_key -> env -> env

Looks up in the context of global inductive names raises an anomaly if the required path is not found

val mem_mind : Names.MutInd.t -> env -> bool
val mind_context : env -> Names.MutInd.t -> UVars.AbstractContext.t

The universe context associated to the inductive, empty if not polymorphic

val polymorphic_ind : Names.inductive -> env -> bool

New-style polymorphism

val polymorphic_pind : Constr.pinductive -> env -> bool
val type_in_type_ind : Names.inductive -> env -> bool
val template_polymorphic_ind : Names.inductive -> env -> bool

Old-style polymorphism

val template_polymorphic_pind : Constr.pinductive -> env -> bool
Changes of representation of Case nodes

Given an inductive type and its parameters, builds the context of the return clause, including the inductive being eliminated. The additional binder array is only used to set the names of the context variables, we use the less general type to make it easy to use this function on Case nodes.

val expand_branch_contexts : Declarations.mind_specif -> UVars.Instance.t -> Constr.constr array -> (Names.Name.t Constr.binder_annot array * 'a) array -> Constr.rel_context array

Given an inductive type and its parameters, builds the context of the return clause, including the inductive being eliminated. The additional binder array is only used to set the names of the context variables, we use the less general type to make it easy to use this function on Case nodes.

instantiate_context u subst nas ctx applies both u and subst to ctx while replacing names using nas (order reversed). In particular, assumes that ctx and nas have the same length.

Name quotients
module type QNameS = sig ... end
module QConstant : QNameS with type t = Names.Constant.t
module QMutInd : QNameS with type t = Names.MutInd.t
module QInd : QNameS with type t = Names.Ind.t
module QConstruct : QNameS with type t = Names.Construct.t
module QProjection : sig ... end
module QGlobRef : QNameS with type t = Names.GlobRef.t
Modules
val add_modtype : Mod_declarations.module_type_body -> env -> env
val shallow_add_module : Mod_declarations.module_body -> env -> env

shallow_add_module does not add module components

Universe constraints
val add_constraints : Univ.Constraints.t -> env -> env

Add universe constraints to the environment.

  • raises UniverseInconsistency.
val check_constraints : Univ.Constraints.t -> env -> bool

Check constraints are satifiable in the environment.

val push_context : ?strict:bool -> UVars.UContext.t -> env -> env

push_context ?(strict=false) ctx env pushes the universe context to the environment.

  • raises UGraph.AlreadyDeclared

    if one of the universes is already declared.

val push_context_set : ?strict:bool -> Univ.ContextSet.t -> env -> env

push_context_set ?(strict=false) ctx env pushes the universe context set to the environment. It does not fail even if one of the universes is already declared.

val push_floating_context_set : Univ.ContextSet.t -> env -> env

Same as above but keep the universes floating for template. Do not use.

val push_subgraph : Univ.ContextSet.t -> env -> env

push_subgraph univs env adds the universes and constraints in univs to env as push_context_set ~strict:false univs env, and also checks that they do not imply new transitive constraints between pre-existing universes in env.

val set_typing_flags : Declarations.typing_flags -> env -> env
val set_impredicative_set : bool -> env -> env
val set_type_in_type : bool -> env -> env
val set_allow_sprop : bool -> env -> env
val sprop_allowed : env -> bool
val allow_rewrite_rules : env -> env
val rewrite_rules_allowed : env -> bool
val update_typing_flags : ?typing_flags:Declarations.typing_flags -> env -> env

update_typing_flags ?typing_flags may update env with optional typing flags

val universes_of_global : env -> Names.GlobRef.t -> UVars.AbstractContext.t
Sets of referred section variables

global_vars_set env c returns the list of id's occurring either directly as Var id in c or indirectly as a section variable dependent in a global reference occurring in c

val global_vars_set : env -> Constr.constr -> Names.Id.Set.t
val vars_of_global : env -> Names.GlobRef.t -> Names.Id.Set.t
val really_needed : env -> Names.Id.Set.t -> Names.Id.Set.t

closure of the input id set w.r.t. dependency

like really_needed but computes a well ordered named context

Unsafe judgments.

We introduce here the pre-type of judgments, which is actually only a datatype to store a term with its type and the type of its type.

type ('constr, 'types) punsafe_judgment = {
uj_val : 'constr;
uj_type : 'types;
}
val on_judgment : ('a -> 'b) -> ('a, 'a) punsafe_judgment -> ('b, 'b) punsafe_judgment
val on_judgment_value : ('c -> 'c) -> ('c, 't) punsafe_judgment -> ('c, 't) punsafe_judgment
val on_judgment_type : ('t -> 't) -> ('c, 't) punsafe_judgment -> ('c, 't) punsafe_judgment
type unsafe_judgment = (Constr.constr, Constr.types) punsafe_judgment
val make_judge : 'constr -> 'types -> ('constr, 'types) punsafe_judgment
val j_val : ('constr, 'types) punsafe_judgment -> 'constr
val j_type : ('constr, 'types) punsafe_judgment -> 'types
type ('types, 'sorts) punsafe_type_judgment = {
utj_val : 'types;
utj_type : 'sorts;
}
type unsafe_type_judgment = (Constr.types, Sorts.t) punsafe_type_judgment
exception Hyp_not_found

apply_to_hyp sign id f split sign into tail::(id,_,_)::head and return tail::(f head (id,_,_) (rev tail))::head. the value associated to id should not change

val is_polymorphic : env -> Names.GlobRef.t -> bool
val is_template_polymorphic : env -> Names.GlobRef.t -> bool
val is_type_in_type : env -> Names.GlobRef.t -> bool
VM and native
val vm_library : env -> Vmlibrary.t
val set_vm_library : Vmlibrary.t -> env -> env
val lookup_vm_code : Vmlibrary.index -> env -> Vmemitcodes.to_patch

Native compiler

val set_retroknowledge : env -> Retroknowledge.retroknowledge -> env

Primitives

\ No newline at end of file diff --git a/master/api/rocq-runtime/Global/index.html b/master/api/rocq-runtime/Global/index.html index 34130d2516..9073a3cb97 100644 --- a/master/api/rocq-runtime/Global/index.html +++ b/master/api/rocq-runtime/Global/index.html @@ -1,2 +1,2 @@ -Global (rocq-runtime.Global)

Module Global

This module defines the global environment of Rocq. The functions below are exactly the same as the ones in Safe_typing, operating on that global environment. add_* functions perform name verification, i.e. check that the name given as argument match those provided by Safe_typing.

val safe_env : unit -> Safe_typing.safe_environment
val env : unit -> Environ.env
val universes : unit -> UGraph.t
val named_context_val : unit -> Environ.named_context_val
val named_context : unit -> Constr.named_context
Enriching the global environment
val set_impredicative_set : bool -> unit

Changing the (im)predicativity of the system

val set_indices_matter : bool -> unit
val set_typing_flags : Declarations.typing_flags -> unit
val set_check_guarded : bool -> unit
val set_check_positive : bool -> unit
val set_check_universes : bool -> unit
val typing_flags : unit -> Declarations.typing_flags
val set_allow_sprop : bool -> unit
val sprop_allowed : unit -> bool
val set_rewrite_rules_allowed : bool -> unit
val rewrite_rules_allowed : unit -> bool

Variables, Local definitions, constants, inductive types

val push_named_assum : (Names.Id.t * Constr.types) -> unit
val push_named_def : (Names.Id.t * Entries.section_def_entry) -> unit
val push_section_context : UVars.UContext.t -> unit
val fill_opaque : Safe_typing.opaque_certificate -> unit
val add_rewrite_rules : Names.Id.t -> Declarations.rewrite_rules_body -> unit
val add_constraints : Univ.Constraints.t -> unit

Extra universe constraints

val push_context_set : Univ.ContextSet.t -> unit

Non-interactive modules and module types

Sections

val open_section : unit -> unit

poly is true when the section should be universe polymorphic

val close_section : Summary.Interp.frozen -> unit

Close the section and reset the global state to the one at the time when the section what opened.

val sections_are_opened : unit -> bool

Interactive modules and module types

val start_module : Names.Id.t -> Names.ModPath.t
val start_modtype : Names.Id.t -> Names.ModPath.t
Queries in the global environment
val exists_objlabel : Names.Label.t -> bool
val constant_of_delta_kn : Names.KerName.t -> Names.Constant.t
val mind_of_delta_kn : Names.KerName.t -> Names.MutInd.t
type indirect_accessor = {
access_proof : Opaqueproof.opaque -> Opaqueproof.opaque_proofterm option;
}
val body_of_constant : indirect_accessor -> Names.Constant.t -> (Constr.constr * unit Opaqueproof.delayed_universes * UVars.AbstractContext.t) option

Returns the body of the constant if it has any, and the polymorphic context it lives in. For monomorphic constant, the latter is empty, and for polymorphic constants, the term contains De Bruijn universe variables that need to be instantiated.

val body_of_constant_body : indirect_accessor -> Declarations.constant_body -> (Constr.constr * unit Opaqueproof.delayed_universes * UVars.AbstractContext.t) option

Same as body_of_constant but on constant_body.

Compiled libraries
val start_library : Names.DirPath.t -> Names.ModPath.t
Misc

Function to get an environment from the constants part of the global * environment and a given context.

val env_of_context : Environ.named_context_val -> Environ.env
val is_joined_environment : unit -> bool
val is_curmod_library : unit -> bool
val is_polymorphic : Names.GlobRef.t -> bool
val is_template_polymorphic : Names.GlobRef.t -> bool
val is_type_in_type : Names.GlobRef.t -> bool
Retroknowledge
val register_inline : Names.Constant.t -> unit
val register_inductive : Names.inductive -> 'a CPrimitives.prim_ind -> unit
Oracle
val set_strategy : Conv_oracle.evaluable -> Conv_oracle.level -> unit
Conversion settings
val set_share_reduction : bool -> unit
val set_VM : bool -> unit
val set_native_compiler : bool -> unit
val current_modpath : unit -> Names.ModPath.t
val current_dirpath : unit -> Names.DirPath.t
val with_global : (Environ.env -> Names.DirPath.t -> 'a Univ.in_universe_context_set) -> 'a
val global_env_summary_tag : Safe_typing.safe_environment Summary.Dyn.tag
\ No newline at end of file +Global (rocq-runtime.Global)

Module Global

This module defines the global environment of Rocq. The functions below are exactly the same as the ones in Safe_typing, operating on that global environment. add_* functions perform name verification, i.e. check that the name given as argument match those provided by Safe_typing.

val safe_env : unit -> Safe_typing.safe_environment
val env : unit -> Environ.env
val universes : unit -> UGraph.t
val named_context_val : unit -> Environ.named_context_val
val named_context : unit -> Constr.named_context
Enriching the global environment
val set_impredicative_set : bool -> unit

Changing the (im)predicativity of the system

val set_indices_matter : bool -> unit
val set_typing_flags : Declarations.typing_flags -> unit
val set_check_guarded : bool -> unit
val set_check_positive : bool -> unit
val set_check_universes : bool -> unit
val typing_flags : unit -> Declarations.typing_flags
val set_allow_sprop : bool -> unit
val sprop_allowed : unit -> bool
val set_rewrite_rules_allowed : bool -> unit
val rewrite_rules_allowed : unit -> bool

Variables, Local definitions, constants, inductive types

val push_named_assum : (Names.Id.t * Constr.types) -> unit
val push_named_def : (Names.Id.t * Entries.section_def_entry) -> unit
val push_section_context : UVars.UContext.t -> unit
val fill_opaque : Safe_typing.opaque_certificate -> unit
val add_rewrite_rules : Names.Id.t -> Declarations.rewrite_rules_body -> unit
val add_constraints : Univ.Constraints.t -> unit

Extra universe constraints

val push_context_set : Univ.ContextSet.t -> unit

Non-interactive modules and module types

Sections

val open_section : unit -> unit

poly is true when the section should be universe polymorphic

val close_section : Summary.Interp.frozen -> unit

Close the section and reset the global state to the one at the time when the section what opened.

val sections_are_opened : unit -> bool

Interactive modules and module types

val start_module : Names.Id.t -> Names.ModPath.t
val start_modtype : Names.Id.t -> Names.ModPath.t
Queries in the global environment
val exists_objlabel : Names.Label.t -> bool
val constant_of_delta_kn : Names.KerName.t -> Names.Constant.t
val mind_of_delta_kn : Names.KerName.t -> Names.MutInd.t
type indirect_accessor = {
access_proof : Opaqueproof.opaque -> Opaqueproof.opaque_proofterm option;
}
val body_of_constant : indirect_accessor -> Names.Constant.t -> (Constr.constr * unit Opaqueproof.delayed_universes * UVars.AbstractContext.t) option

Returns the body of the constant if it has any, and the polymorphic context it lives in. For monomorphic constant, the latter is empty, and for polymorphic constants, the term contains De Bruijn universe variables that need to be instantiated.

val body_of_constant_body : indirect_accessor -> Declarations.constant_body -> (Constr.constr * unit Opaqueproof.delayed_universes * UVars.AbstractContext.t) option

Same as body_of_constant but on constant_body.

Compiled libraries
val start_library : Names.DirPath.t -> Names.ModPath.t
Misc

Function to get an environment from the constants part of the global * environment and a given context.

val env_of_context : Environ.named_context_val -> Environ.env
val is_joined_environment : unit -> bool
val is_curmod_library : unit -> bool
val is_polymorphic : Names.GlobRef.t -> bool
val is_template_polymorphic : Names.GlobRef.t -> bool
val is_type_in_type : Names.GlobRef.t -> bool
Retroknowledge
val register_inline : Names.Constant.t -> unit
val register_inductive : Names.inductive -> 'a CPrimitives.prim_ind -> unit
Oracle
val set_strategy : Conv_oracle.evaluable -> Conv_oracle.level -> unit
Conversion settings
val set_share_reduction : bool -> unit
val set_VM : bool -> unit
val set_native_compiler : bool -> unit
val current_modpath : unit -> Names.ModPath.t
val current_dirpath : unit -> Names.DirPath.t
val with_global : (Environ.env -> Names.DirPath.t -> 'a Univ.in_universe_context_set) -> 'a
val global_env_summary_tag : Safe_typing.safe_environment Summary.Dyn.tag
\ No newline at end of file diff --git a/master/api/rocq-runtime/Mod_declarations/.dummy b/master/api/rocq-runtime/Mod_declarations/.dummy new file mode 100644 index 0000000000..e69de29bb2 diff --git a/master/api/rocq-runtime/Mod_declarations/index.html b/master/api/rocq-runtime/Mod_declarations/index.html new file mode 100644 index 0000000000..3c1e107dd5 --- /dev/null +++ b/master/api/rocq-runtime/Mod_declarations/index.html @@ -0,0 +1,2 @@ + +Mod_declarations (rocq-runtime.Mod_declarations)

Module Mod_declarations

type 'a generic_module_body
type module_body = Declarations.mod_body generic_module_body

For a module, there are five possible situations:

type module_type_body = Declarations.mod_type generic_module_body

A module_type_body is just a module_body with no implementation and also an empty mod_retroknowledge. Its mod_type_alg contains the algebraic definition of this module type, or None if it has been built interactively.

type structure_field_body = (module_body, module_type_body) Declarations.structure_field_body
type structure_body = (module_body, module_type_body) Declarations.structure_body

A module signature is a structure, with possibly functors on top of it

type module_implementation =
| Abstract(*

no accessible implementation

*)
| Algebraic of Declarations.module_expression(*

non-interactive algebraic expression

*)
| Struct of structure_body(*

interactive body living in the parameter context of mod_type

*)
| FullStruct(*

special case of Struct : the body is exactly mod_type

*)
type 'a module_retroknowledge = ('a, Retroknowledge.action list) Declarations.when_mod_body

Extra invariants :

Accessors
val mod_type_alg : 'a generic_module_body -> Declarations.module_expression option
val mod_retroknowledge : module_body -> Retroknowledge.action list
Builders
val make_module_body : Names.ModPath.t -> module_signature -> Mod_subst.delta_resolver -> Retroknowledge.action list -> module_body
val strengthen_module_body : src:Names.ModPath.t -> dst:Names.ModPath.t option -> module_signature -> Mod_subst.delta_resolver -> module_body -> module_body
val replace_module_body : structure_body -> Mod_subst.delta_resolver -> module_body -> module_body
val module_type_of_module : module_body -> module_type_body
val module_body_of_type : Names.ModPath.t -> module_type_body -> module_body
val functorize_module : (Names.MBId.t * module_type_body) list -> module_body -> module_body
Setters
val set_implementation : module_implementation -> module_body -> module_body
val set_retroknowledge : module_body -> Retroknowledge.action list -> module_body
Mapping
val functor_smart_map : ('a -> 'a) -> ('b -> 'b) -> ('a, 'b) Declarations.functorize -> ('a, 'b) Declarations.functorize
Substitution
Hashconsing
val hcons_generic_module_body : 'a generic_module_body -> 'a generic_module_body
val hcons_module_body : module_body -> module_body
val hcons_module_type : module_type_body -> module_type_body
Cleaning a module expression from bounded parts

For instance: functor(X:T)->struct module M:=X end) becomes: functor(X:T)->struct module M:=<content of T> end)

val clean_structure : Names.MBIset.t -> structure_body -> structure_body
\ No newline at end of file diff --git a/master/api/rocq-runtime/Mod_typing/index.html b/master/api/rocq-runtime/Mod_typing/index.html index 48890486dd..b03dc4747b 100644 --- a/master/api/rocq-runtime/Mod_typing/index.html +++ b/master/api/rocq-runtime/Mod_typing/index.html @@ -1,2 +1,2 @@ -Mod_typing (rocq-runtime.Mod_typing)

Module Mod_typing

Main functions for translating module entries

type 'a vm_handler = {
vm_handler : Environ.env -> Declarations.universes -> Constr.t -> 'a -> 'a * Vmlibrary.indirect_code option;
}
type 'a vm_state = 'a * 'a vm_handler

translate_module produces a module_body out of a module_entry. In the output fields:

translate_modtype produces a module_type_body whose mod_type_alg cannot be None (and of course mod_expr is Abstract).

From an already-translated (or interactive) implementation and an (optional) signature entry, produces a final module_body

translate_mse_incl translate the mse of a module or module type given to an Include

\ No newline at end of file +Mod_typing (rocq-runtime.Mod_typing)

Module Mod_typing

Main functions for translating module entries

type 'a vm_handler = {
vm_handler : Environ.env -> Declarations.universes -> Constr.t -> 'a -> 'a * Vmlibrary.indirect_code option;
}
type 'a vm_state = 'a * 'a vm_handler

translate_module produces a module_body out of a module_entry. In the output fields:

translate_modtype produces a module_type_body whose mod_type_alg cannot be None (and of course mod_expr is Abstract).

From an already-translated (or interactive) implementation and an (optional) signature entry, produces a final module_body

translate_mse_incl translate the mse of a module or module type given to an Include

\ No newline at end of file diff --git a/master/api/rocq-runtime/Modops/index.html b/master/api/rocq-runtime/Modops/index.html index 6de960b9a4..e417d0a014 100644 --- a/master/api/rocq-runtime/Modops/index.html +++ b/master/api/rocq-runtime/Modops/index.html @@ -1,2 +1,2 @@ -Modops (rocq-runtime.Modops)

Module Modops

Various operations on modules and module types

Functors

val is_functor : ('ty, 'a) Declarations.functorize -> bool
val destr_functor : ('ty, 'a) Declarations.functorize -> Names.MBId.t * 'ty * ('ty, 'a) Declarations.functorize
val destr_nofunctor : Names.ModPath.t -> ('ty, 'a) Declarations.functorize -> 'a

Conversions between module_body and module_type_body

val module_body_of_type : Names.ModPath.t -> Declarations.module_type_body -> Declarations.module_body
val check_modpath_equiv : Environ.env -> Names.ModPath.t -> Names.ModPath.t -> unit
val annotate_struct_body : Declarations.structure_body -> Declarations.module_signature -> Declarations.module_signature
Substitutions
Adding to an environment

adds a module and its components, but not the constraints

same as add_module, but for a module whose native code has been linked by the native compiler. The linking information is updated.

same, for a module type

Strengthening
val strengthen_and_subst_module_body : Declarations.module_body -> Names.ModPath.t -> bool -> Declarations.module_body
Building map of constants to inline
Cleaning a module expression from bounded parts

For instance: functor(X:T)->struct module M:=X end) becomes: functor(X:T)->struct module M:=<content of T> end)

Errors
type signature_mismatch_error =
| InductiveFieldExpected of Declarations.mutual_inductive_body
| DefinitionFieldExpected
| ModuleFieldExpected
| ModuleTypeFieldExpected
| NotConvertibleInductiveField of Names.Id.t
| NotConvertibleConstructorField of Names.Id.t
| NotConvertibleBodyField
| NotConvertibleTypeField of Environ.env * Constr.types * Constr.types
| CumulativeStatusExpected of bool
| PolymorphicStatusExpected of bool
| NotSameConstructorNamesField
| NotSameInductiveNameInBlockField
| FiniteInductiveFieldExpected of bool
| InductiveNumbersFieldExpected of int
| InductiveParamsNumberField of int
| RecordFieldExpected of bool
| RecordProjectionsExpected of Names.Name.t list
| NotEqualInductiveAliases
| IncompatibleUniverses of UGraph.univ_inconsistency
| IncompatiblePolymorphism of Environ.env * Constr.types * Constr.types
| IncompatibleConstraints of {
got : UVars.AbstractContext.t;
expect : UVars.AbstractContext.t;
}
| IncompatibleVariance
| NoRewriteRulesSubtyping
type subtyping_trace_elt =
| Submodule of Names.Label.t
| FunctorArgument of int
type module_typing_error =
| SignatureMismatch of subtyping_trace_elt list * Names.Label.t * signature_mismatch_error
| LabelAlreadyDeclared of Names.Label.t
| NotAFunctor
| IsAFunctor of Names.ModPath.t
| IncompatibleModuleTypes of Declarations.module_type_body * Declarations.module_type_body
| NotEqualModulePaths of Names.ModPath.t * Names.ModPath.t
| NoSuchLabel of Names.Label.t * Names.ModPath.t
| NotAModuleLabel of Names.Label.t
| NotAConstant of Names.Label.t
| IncorrectWithConstraint of Names.Label.t
| GenerativeModuleExpected of Names.Label.t
| LabelMissing of Names.Label.t * string
| IncludeRestrictedFunctor of Names.ModPath.t
exception ModuleTypingError of module_typing_error
val error_existing_label : Names.Label.t -> 'a
val error_incompatible_modtypes : Declarations.module_type_body -> Declarations.module_type_body -> 'a
val error_signature_mismatch : subtyping_trace_elt list -> Names.Label.t -> signature_mismatch_error -> 'a
val error_no_such_label : Names.Label.t -> Names.ModPath.t -> 'a
val error_not_a_module_label : Names.Label.t -> 'a
val error_not_a_constant : Names.Label.t -> 'a
val error_incorrect_with_constraint : Names.Label.t -> 'a
val error_generative_module_expected : Names.Label.t -> 'a
val error_no_such_label_sub : Names.Label.t -> string -> 'a
val error_include_restricted_functor : Names.ModPath.t -> 'a
\ No newline at end of file +Modops (rocq-runtime.Modops)

Module Modops

Various operations on modules and module types

Functors

val is_functor : ('ty, 'a) Declarations.functorize -> bool
val destr_functor : ('ty, 'a) Declarations.functorize -> Names.MBId.t * 'ty * ('ty, 'a) Declarations.functorize
val destr_nofunctor : Names.ModPath.t -> ('ty, 'a) Declarations.functorize -> 'a

Conversions between module_body and module_type_body

val module_body_of_type : Names.ModPath.t -> Mod_declarations.module_type_body -> Mod_declarations.module_body
val check_modpath_equiv : Environ.env -> Names.ModPath.t -> Names.ModPath.t -> unit
val annotate_struct_body : Mod_declarations.structure_body -> Mod_declarations.module_signature -> Mod_declarations.module_signature
Substitutions
Adding to an environment

adds a module and its components, but not the constraints

same as add_module, but for a module whose native code has been linked by the native compiler. The linking information is updated.

same, for a module type

val add_retroknowledge : Retroknowledge.action list -> Environ.env -> Environ.env
Strengthening
val strengthen_and_subst_module_body : Mod_declarations.module_body -> Names.ModPath.t -> bool -> Mod_declarations.module_body
Building map of constants to inline
Cleaning a module expression from bounded parts

For instance: functor(X:T)->struct module M:=X end) becomes: functor(X:T)->struct module M:=<content of T> end)

Errors
type signature_mismatch_error =
| InductiveFieldExpected of Declarations.mutual_inductive_body
| DefinitionFieldExpected
| ModuleFieldExpected
| ModuleTypeFieldExpected
| NotConvertibleInductiveField of Names.Id.t
| NotConvertibleConstructorField of Names.Id.t
| NotConvertibleBodyField
| NotConvertibleTypeField of Environ.env * Constr.types * Constr.types
| CumulativeStatusExpected of bool
| PolymorphicStatusExpected of bool
| NotSameConstructorNamesField
| NotSameInductiveNameInBlockField
| FiniteInductiveFieldExpected of bool
| InductiveNumbersFieldExpected of int
| InductiveParamsNumberField of int
| RecordFieldExpected of bool
| RecordProjectionsExpected of Names.Name.t list
| NotEqualInductiveAliases
| IncompatibleUniverses of UGraph.univ_inconsistency
| IncompatiblePolymorphism of Environ.env * Constr.types * Constr.types
| IncompatibleConstraints of {
got : UVars.AbstractContext.t;
expect : UVars.AbstractContext.t;
}
| IncompatibleVariance
| NoRewriteRulesSubtyping
type subtyping_trace_elt =
| Submodule of Names.Label.t
| FunctorArgument of int
type module_typing_error =
| SignatureMismatch of subtyping_trace_elt list * Names.Label.t * signature_mismatch_error
| LabelAlreadyDeclared of Names.Label.t
| NotAFunctor
| IsAFunctor of Names.ModPath.t
| IncompatibleModuleTypes of Mod_declarations.module_type_body * Mod_declarations.module_type_body
| NotEqualModulePaths of Names.ModPath.t * Names.ModPath.t
| NoSuchLabel of Names.Label.t * Names.ModPath.t
| NotAModuleLabel of Names.Label.t
| NotAConstant of Names.Label.t
| IncorrectWithConstraint of Names.Label.t
| GenerativeModuleExpected of Names.Label.t
| LabelMissing of Names.Label.t * string
| IncludeRestrictedFunctor of Names.ModPath.t
exception ModuleTypingError of module_typing_error
val error_existing_label : Names.Label.t -> 'a
val error_incompatible_modtypes : Mod_declarations.module_type_body -> Mod_declarations.module_type_body -> 'a
val error_signature_mismatch : subtyping_trace_elt list -> Names.Label.t -> signature_mismatch_error -> 'a
val error_no_such_label : Names.Label.t -> Names.ModPath.t -> 'a
val error_not_a_module_label : Names.Label.t -> 'a
val error_not_a_constant : Names.Label.t -> 'a
val error_incorrect_with_constraint : Names.Label.t -> 'a
val error_generative_module_expected : Names.Label.t -> 'a
val error_no_such_label_sub : Names.Label.t -> string -> 'a
val error_include_restricted_functor : Names.ModPath.t -> 'a
\ No newline at end of file diff --git a/master/api/rocq-runtime/Nativelibrary/index.html b/master/api/rocq-runtime/Nativelibrary/index.html index b9368f7a36..2bcd59dc63 100644 --- a/master/api/rocq-runtime/Nativelibrary/index.html +++ b/master/api/rocq-runtime/Nativelibrary/index.html @@ -1,2 +1,2 @@ -Nativelibrary (rocq-runtime.Nativelibrary)

Module Nativelibrary

This file implements separate compilation for libraries in the native compiler

\ No newline at end of file +Nativelibrary (rocq-runtime.Nativelibrary)

Module Nativelibrary

This file implements separate compilation for libraries in the native compiler

\ No newline at end of file diff --git a/master/api/rocq-runtime/Printer/index.html b/master/api/rocq-runtime/Printer/index.html index 520b753b84..e54f3c1e62 100644 --- a/master/api/rocq-runtime/Printer/index.html +++ b/master/api/rocq-runtime/Printer/index.html @@ -1,3 +1,3 @@ Printer (rocq-runtime.Printer)

Module Printer

These are the entry points for printing terms, context, tac, ...

val print_goal_tag_opt_name : string list

Terms

Printers for terms.

The "lconstr" variant does not require parentheses to isolate the expression from the surrounding context (for instance 3 + 4 will be written 3 + 4). The "constr" variant (w/o "l") enforces parentheses whenever the term is not an atom (for instance, 3 will be written 3 but 3 + 4 will be written (3 + 4).

~inctx:true indicates that the term is intended to be printed in a context where its type is known so that a head coercion would be skipped, or implicit arguments inferable from the context will not be made explicit. For instance, if foo is declared as a coercion, foo bar will be printed as bar if inctx is true and as foo bar otherwise.

~scope:some_scope_name indicates that the head of the term is intended to be printed in scope some_scope_name. It defaults to None.

~impargs:some_list_of_binding_kind indicates the implicit arguments of the external quatification. Only used for printing types (not terms), and at toplevel (only "l" versions). It defaults to None.

val pr_constr_env : ?inctx:bool -> ?scope:Notation_term.scope_name -> Environ.env -> Evd.evar_map -> Constr.constr -> Pp.t
val pr_lconstr_env : ?inctx:bool -> ?scope:Notation_term.scope_name -> Environ.env -> Evd.evar_map -> Constr.constr -> Pp.t
val pr_constr_n_env : ?inctx:bool -> ?scope:Notation_term.scope_name -> Environ.env -> Evd.evar_map -> Constrexpr.entry_relative_level -> Constr.constr -> Pp.t

Same, but resilient to Nametab errors. Prints fully-qualified names when shortest_qualid_of_global has failed. Prints "??" in case of remaining issues (such as reference not in env).

val safe_pr_constr_env : Environ.env -> Evd.evar_map -> Constr.constr -> Pp.t
val safe_pr_lconstr_env : Environ.env -> Evd.evar_map -> Constr.constr -> Pp.t
val pr_econstr_env : ?inctx:bool -> ?scope:Notation_term.scope_name -> Environ.env -> Evd.evar_map -> EConstr.t -> Pp.t
val pr_leconstr_env : ?inctx:bool -> ?scope:Notation_term.scope_name -> Environ.env -> Evd.evar_map -> EConstr.t -> Pp.t
val pr_econstr_n_env : ?inctx:bool -> ?scope:Notation_term.scope_name -> Environ.env -> Evd.evar_map -> Constrexpr.entry_relative_level -> EConstr.t -> Pp.t
val pr_etype_env : ?goal_concl_style:bool -> Environ.env -> Evd.evar_map -> EConstr.types -> Pp.t
val pr_letype_env : ?goal_concl_style:bool -> Environ.env -> Evd.evar_map -> ?impargs:Glob_term.binding_kind list -> EConstr.types -> Pp.t
val pr_open_constr_env : ?inctx:bool -> ?scope:Notation_term.scope_name -> Environ.env -> Evd.evar_map -> Evd.open_constr -> Pp.t
val pr_open_lconstr_env : ?inctx:bool -> ?scope:Notation_term.scope_name -> Environ.env -> Evd.evar_map -> Evd.open_constr -> Pp.t
val pr_constr_under_binders_env : Environ.env -> Evd.evar_map -> Ltac_pretype.constr_under_binders -> Pp.t
val pr_lconstr_under_binders_env : Environ.env -> Evd.evar_map -> Ltac_pretype.constr_under_binders -> Pp.t

Printers for types. Types are printed in scope "type_scope" and under the constraint of being of type a sort.

The "ltype" variant does not require parentheses to isolate the expression from the surrounding context (for instance nat * bool will be written nat * bool). The "type" variant (w/o "l") enforces parentheses whenever the term is not an atom (for instance, nat will be written nat but nat * bool will be written (nat * bool).

~goal_concl_style:true tells to print the type the same way as command Show would print a goal. Concretely, it means that all names of goal/section variables and all names of variables referred by de Bruijn indices (if any) in the given environment and all short names of global definitions of the current module must be avoided while printing bound variables. Otherwise, short names of global definitions are printed qualified and only names of goal/section variables and rel names that do _not_ occur in the scope of the binder to be printed are avoided.

val pr_ltype_env : ?goal_concl_style:bool -> Environ.env -> Evd.evar_map -> ?impargs:Glob_term.binding_kind list -> Constr.types -> Pp.t
val pr_type_env : ?goal_concl_style:bool -> Environ.env -> Evd.evar_map -> Constr.types -> Pp.t
val pr_closed_glob_n_env : ?goal_concl_style:bool -> ?inctx:bool -> ?scope:Notation_term.scope_name -> -Environ.env -> Evd.evar_map -> Constrexpr.entry_relative_level -> Ltac_pretype.closed_glob_constr -> Pp.t
val pr_closed_glob_env : ?goal_concl_style:bool -> ?inctx:bool -> ?scope:Notation_term.scope_name -> Environ.env -> Evd.evar_map -> Ltac_pretype.closed_glob_constr -> Pp.t
val pr_lglob_constr_env : Environ.env -> Evd.evar_map -> 'a Glob_term.glob_constr_g -> Pp.t
val pr_glob_constr_env : Environ.env -> Evd.evar_map -> 'a Glob_term.glob_constr_g -> Pp.t
val pr_lconstr_pattern_env : Environ.env -> Evd.evar_map -> _ Pattern.constr_pattern_r -> Pp.t
val pr_constr_pattern_env : Environ.env -> Evd.evar_map -> _ Pattern.constr_pattern_r -> Pp.t
val pr_cases_pattern : Glob_term.cases_pattern -> Pp.t
val pr_sort : Evd.evar_map -> Sorts.t -> Pp.t

Universe constraints

val pr_universe_instance : Evd.evar_map -> UVars.Instance.t -> Pp.t
val pr_universe_instance_constraints : Evd.evar_map -> UVars.Instance.t -> Univ.Constraints.t -> Pp.t
val pr_universe_ctx : Evd.evar_map -> ?variance:UVars.Variance.t array -> UVars.UContext.t -> Pp.t
val pr_abstract_universe_ctx : Evd.evar_map -> ?variance:UVars.Variance.t array -> ?priv:Univ.ContextSet.t -> UVars.AbstractContext.t -> Pp.t
val pr_universe_ctx_set : Evd.evar_map -> Univ.ContextSet.t -> Pp.t
val pr_universes : Evd.evar_map -> ?variance:UVars.Variance.t array -> ?priv:Univ.ContextSet.t -> Declarations.universes -> Pp.t

universe_binders_with_opt_names ref l

If l is Some univs return the universe binders naming the bound levels of ref by univs (generating names for Anonymous). May error if the lengths mismatch.

Otherwise return the bound universe names registered for ref.

Inefficient on large contexts due to name generation.

Printing global references using names as short as possible

val pr_global_env : Names.Id.Set.t -> Names.GlobRef.t -> Pp.t
val pr_global : Names.GlobRef.t -> Pp.t
val pr_constant : Environ.env -> Names.Constant.t -> Pp.t
val pr_existential_key : Environ.env -> Evd.evar_map -> Evar.t -> Pp.t
val pr_existential : Environ.env -> Evd.evar_map -> Constr.existential -> Pp.t
val pr_constructor : Environ.env -> Names.constructor -> Pp.t
val pr_inductive : Environ.env -> Names.inductive -> Pp.t
val pr_evaluable_reference : Evaluable.t -> Pp.t
val pr_pconstant : Environ.env -> Evd.evar_map -> Constr.pconstant -> Pp.t
val pr_pinductive : Environ.env -> Evd.evar_map -> Constr.pinductive -> Pp.t
val pr_pconstructor : Environ.env -> Evd.evar_map -> Constr.pconstructor -> Pp.t
val pr_notation_interpretation_env : Environ.env -> Evd.evar_map -> Glob_term.glob_constr -> Pp.t
val pr_notation_interpretation : Glob_term.glob_constr -> Pp.t

Contexts

val set_compact_context : bool -> unit

Display compact contexts of goals (simple hyps on the same line)

val get_compact_context : unit -> bool
val pr_context_unlimited : Environ.env -> Evd.evar_map -> Pp.t
val pr_ne_context_of : Pp.t -> Environ.env -> Evd.evar_map -> Pp.t
val pr_named_context : Environ.env -> Evd.evar_map -> Constr.named_context -> Pp.t
val pr_named_context_of : Environ.env -> Evd.evar_map -> Pp.t
val pr_rel_context : Environ.env -> Evd.evar_map -> Constr.rel_context -> Pp.t
val pr_rel_context_of : Environ.env -> Evd.evar_map -> Pp.t
val pr_context_of : Environ.env -> Evd.evar_map -> Pp.t

Predicates

val pr_predicate : ('a -> Pp.t) -> (bool * 'a list) -> Pp.t
val pr_cpred : Names.Cpred.t -> Pp.t
val pr_idpred : Names.Id.Pred.t -> Pp.t
val pr_prpred : Names.PRpred.t -> Pp.t
val pr_transparent_state : TransparentState.t -> Pp.t

Proofs, these functions obey Hyps Limit and Compact contexts.

val pr_open_subgoals : ?quiet:bool -> ?diffs:Proof.t option -> Proof.t -> Pp.t

pr_open_subgoals ~quiet ?diffs proof shows the context for proof as used by, for example, coqtop. The first active goal is printed with all its antecedents and the conclusion. The other active goals only show their conclusions. If diffs is Some oproof, highlight the differences between the old proof oproof, and proof. quiet disables printing messages as Feedback.

val pr_nth_open_subgoal : proof:Proof.t -> int -> Pp.t
val pr_evars_int : Evd.evar_map -> shelf:Evar.t list -> given_up:Evar.t list -> int -> Evd.undefined Evd.evar_info Evar.Map.t -> Pp.t
val pr_ne_evar_set : Pp.t -> Pp.t -> Evd.evar_map -> Evar.Set.t -> Pp.t
type axiom =
| Constant of Names.Constant.t
| Positive of Names.MutInd.t
| Guarded of Names.GlobRef.t
| TypeInType of Names.GlobRef.t
| UIP of Names.MutInd.t

Declarations for the "Print Assumption" command

type context_object =
| Variable of Names.Id.t
| Axiom of axiom * (Names.Label.t * Constr.rel_context * Constr.types) list
| Opaque of Names.Constant.t
| Transparent of Names.Constant.t
val pr_goal_by_id : proof:Proof.t -> Names.Id.t -> Pp.t
val pr_goal_emacs : proof:Proof.t option -> int -> int -> Pp.t
val pr_typing_flags : Declarations.typing_flags -> Pp.t
val print_goal_names : unit -> bool

Tells if flag "Printing Goal Names" is activated

module Debug : sig ... end

Debug printers

\ No newline at end of file +Environ.env -> Evd.evar_map -> Constrexpr.entry_relative_level -> Ltac_pretype.closed_glob_constr -> Pp.t
val pr_closed_glob_env : ?goal_concl_style:bool -> ?inctx:bool -> ?scope:Notation_term.scope_name -> Environ.env -> Evd.evar_map -> Ltac_pretype.closed_glob_constr -> Pp.t
val pr_ljudge_env : Environ.env -> Evd.evar_map -> EConstr.unsafe_judgment -> Pp.t * Pp.t
val pr_lglob_constr_env : Environ.env -> Evd.evar_map -> 'a Glob_term.glob_constr_g -> Pp.t
val pr_glob_constr_env : Environ.env -> Evd.evar_map -> 'a Glob_term.glob_constr_g -> Pp.t
val pr_lconstr_pattern_env : Environ.env -> Evd.evar_map -> _ Pattern.constr_pattern_r -> Pp.t
val pr_constr_pattern_env : Environ.env -> Evd.evar_map -> _ Pattern.constr_pattern_r -> Pp.t
val pr_cases_pattern : Glob_term.cases_pattern -> Pp.t
val pr_sort : Evd.evar_map -> Sorts.t -> Pp.t

Universe constraints

val pr_universe_instance : Evd.evar_map -> UVars.Instance.t -> Pp.t
val pr_universe_instance_constraints : Evd.evar_map -> UVars.Instance.t -> Univ.Constraints.t -> Pp.t
val pr_universe_ctx : Evd.evar_map -> ?variance:UVars.Variance.t array -> UVars.UContext.t -> Pp.t
val pr_abstract_universe_ctx : Evd.evar_map -> ?variance:UVars.Variance.t array -> ?priv:Univ.ContextSet.t -> UVars.AbstractContext.t -> Pp.t
val pr_universe_ctx_set : Evd.evar_map -> Univ.ContextSet.t -> Pp.t
val pr_universes : Evd.evar_map -> ?variance:UVars.Variance.t array -> ?priv:Univ.ContextSet.t -> Declarations.universes -> Pp.t
val universe_binders_with_opt_names : UVars.AbstractContext.t -> (Names.GlobRef.t * UnivNames.full_name_list) option -> UnivNames.universe_binders * UnivNames.rev_binders

universe_binders_with_opt_names ref l

If l is Some univs return the universe binders naming the bound levels of ref by univs (generating names for Anonymous). May error if the lengths mismatch.

Otherwise return the bound universe names registered for ref.

Inefficient on large contexts due to name generation.

Printing global references using names as short as possible

val pr_global_env : Names.Id.Set.t -> Names.GlobRef.t -> Pp.t
val pr_global : Names.GlobRef.t -> Pp.t
val pr_constant : Environ.env -> Names.Constant.t -> Pp.t
val pr_existential_key : Environ.env -> Evd.evar_map -> Evar.t -> Pp.t
val pr_existential : Environ.env -> Evd.evar_map -> Constr.existential -> Pp.t
val pr_constructor : Environ.env -> Names.constructor -> Pp.t
val pr_inductive : Environ.env -> Names.inductive -> Pp.t
val pr_evaluable_reference : Evaluable.t -> Pp.t
val pr_pconstant : Environ.env -> Evd.evar_map -> Constr.pconstant -> Pp.t
val pr_pinductive : Environ.env -> Evd.evar_map -> Constr.pinductive -> Pp.t
val pr_pconstructor : Environ.env -> Evd.evar_map -> Constr.pconstructor -> Pp.t
val pr_notation_interpretation_env : Environ.env -> Evd.evar_map -> Glob_term.glob_constr -> Pp.t
val pr_notation_interpretation : Glob_term.glob_constr -> Pp.t

Contexts

val set_compact_context : bool -> unit

Display compact contexts of goals (simple hyps on the same line)

val get_compact_context : unit -> bool
val pr_context_unlimited : Environ.env -> Evd.evar_map -> Pp.t
val pr_ne_context_of : Pp.t -> Environ.env -> Evd.evar_map -> Pp.t
val pr_named_decl : Environ.env -> Evd.evar_map -> Constr.named_declaration -> Pp.t
val pr_compacted_decl : Environ.env -> Evd.evar_map -> Constr.compacted_declaration -> Pp.t
val pr_rel_decl : Environ.env -> Evd.evar_map -> Constr.rel_declaration -> Pp.t
val pr_enamed_decl : Environ.env -> Evd.evar_map -> EConstr.named_declaration -> Pp.t
val pr_ecompacted_decl : Environ.env -> Evd.evar_map -> EConstr.compacted_declaration -> Pp.t
val pr_erel_decl : Environ.env -> Evd.evar_map -> EConstr.rel_declaration -> Pp.t
val pr_named_context : Environ.env -> Evd.evar_map -> Constr.named_context -> Pp.t
val pr_named_context_of : Environ.env -> Evd.evar_map -> Pp.t
val pr_rel_context : Environ.env -> Evd.evar_map -> Constr.rel_context -> Pp.t
val pr_rel_context_of : Environ.env -> Evd.evar_map -> Pp.t
val pr_context_of : Environ.env -> Evd.evar_map -> Pp.t

Predicates

val pr_predicate : ('a -> Pp.t) -> (bool * 'a list) -> Pp.t
val pr_cpred : Names.Cpred.t -> Pp.t
val pr_idpred : Names.Id.Pred.t -> Pp.t
val pr_prpred : Names.PRpred.t -> Pp.t
val pr_transparent_state : TransparentState.t -> Pp.t

Proofs, these functions obey Hyps Limit and Compact contexts.

val pr_open_subgoals : ?quiet:bool -> ?diffs:Proof.t option -> Proof.t -> Pp.t

pr_open_subgoals ~quiet ?diffs proof shows the context for proof as used by, for example, coqtop. The first active goal is printed with all its antecedents and the conclusion. The other active goals only show their conclusions. If diffs is Some oproof, highlight the differences between the old proof oproof, and proof. quiet disables printing messages as Feedback.

val pr_nth_open_subgoal : proof:Proof.t -> int -> Pp.t
val pr_evar : Evd.evar_map -> (Evar.t * Evd.undefined Evd.evar_info) -> Pp.t
val pr_evars_int : Evd.evar_map -> shelf:Evar.t list -> given_up:Evar.t list -> int -> Evd.undefined Evd.evar_info Evar.Map.t -> Pp.t
val pr_ne_evar_set : Pp.t -> Pp.t -> Evd.evar_map -> Evar.Set.t -> Pp.t
type axiom =
| Constant of Names.Constant.t
| Positive of Names.MutInd.t
| Guarded of Names.GlobRef.t
| TypeInType of Names.GlobRef.t
| UIP of Names.MutInd.t

Declarations for the "Print Assumption" command

type context_object =
| Variable of Names.Id.t
| Axiom of axiom * (Names.Label.t * Constr.rel_context * Constr.types) list
| Opaque of Names.Constant.t
| Transparent of Names.Constant.t
module ContextObjectSet : CSet.ExtS with type elt = context_object
module ContextObjectMap : CMap.ExtS with type key = context_object and module Set := ContextObjectSet
val pr_assumptionset : Environ.env -> Evd.evar_map -> Constr.types ContextObjectMap.t -> Pp.t
val pr_goal_by_id : proof:Proof.t -> Names.Id.t -> Pp.t
val pr_goal_emacs : proof:Proof.t option -> int -> int -> Pp.t
val pr_typing_flags : Declarations.typing_flags -> Pp.t
val print_goal_names : unit -> bool

Tells if flag "Printing Goal Names" is activated

module Debug : sig ... end

Debug printers

\ No newline at end of file diff --git a/master/api/rocq-runtime/Safe_typing/index.html b/master/api/rocq-runtime/Safe_typing/index.html index 20473cc89d..2dbf88438d 100644 --- a/master/api/rocq-runtime/Safe_typing/index.html +++ b/master/api/rocq-runtime/Safe_typing/index.html @@ -1,2 +1,2 @@ -Safe_typing (rocq-runtime.Safe_typing)

Module Safe_typing

type vodigest =
| Dvo_or_vi of Stdlib.Digest.t
val digest_match : actual:vodigest -> required:vodigest -> bool
Safe environments

Since we are now able to type terms, we can define an abstract type of safe environments, where objects are typed before being added.

We also provide functionality for modules : start_module, end_module, etc.

type safe_environment
type section_data
val empty_environment : safe_environment
val env_of_safe_env : safe_environment -> Environ.env
val sections_of_safe_env : safe_environment -> section_data Section.t option
val structure_body_of_safe_env : safe_environment -> Declarations.structure_body

The safe_environment state monad

type safe_transformer0 = safe_environment -> safe_environment
type 'a safe_transformer = safe_environment -> 'a * safe_environment
Stm machinery
type private_constants
val empty_private_constants : private_constants
val is_empty_private_constants : private_constants -> bool

concat_private e1 e2 adds the constants of e1 to e2, i.e. constants in e1 must be more recent than those of e2.

Abstract the private constants of a proof over the proof output

val push_private_constants : Environ.env -> private_constants -> Environ.env

Push the constants in the environment if not already there.

val universes_of_private : private_constants -> Univ.ContextSet.t
val is_curmod_library : safe_environment -> bool
val is_joined_environment : safe_environment -> bool

Enriching a safe environment

Insertion of global axioms or definitions

type side_effect_declaration =
| DefinitionEff : Entries.definition_entry -> side_effect_declaration
| OpaqueEff : Constr.constr Entries.opaque_entry -> side_effect_declaration
type exported_opaque
type exported_private_constant = Names.Constant.t * exported_opaque option
val export_private_constants : private_constants -> exported_private_constant list safe_transformer

returns the main constant

Similar to add_constant but also returns a certificate

Delayed proofs
type opaque_certificate

Witness that a delayed Qed hole has a proof. This datatype is marshallable but care must be taken to marshal it at the same time as the environment it is referring to, since fill_opaque relies on a shared pointer between the environment and the certificate.

Check that the provided proof is correct for the corresponding handle. This does not modify the environment. Call fill_opaque below for that.

Given an already checked proof for an opaque hole, actually fill it with the proof. This might fail if the current set of global universes is inconsistent with the one at the time of the call to check_opaque. Precondition: the underlying handle must exist and must not have been filled.

val is_filled_opaque : Opaqueproof.opaque_handle -> safe_environment -> bool

Check whether a handle was filled. It assumes that the handle was introduced in the opaque table and throws an anomaly otherwise.

Get the proof term that was checked by the kernel.

Rewrite rules

Add a rewrite rule corresponding to the equality witnessed by the constant.

Inductive blocks

Adding an inductive type

Adding a module or a module type

Adding universe constraints

val push_context_set : strict:bool -> Univ.ContextSet.t -> safe_transformer0
val add_constraints : Univ.Constraints.t -> safe_transformer0
val set_rewrite_rules_allowed : bool -> safe_transformer0

Setting the type theory flavor

val set_impredicative_set : bool -> safe_transformer0
val set_indices_matter : bool -> safe_transformer0
val set_share_reduction : bool -> safe_transformer0
val set_check_guarded : bool -> safe_transformer0
val set_check_positive : bool -> safe_transformer0
val set_check_universes : bool -> safe_transformer0
val set_VM : bool -> safe_transformer0
val set_native_compiler : bool -> safe_transformer0
val set_allow_sprop : bool -> safe_transformer0
Interactive section functions
val open_section : safe_transformer0
val close_section : safe_transformer0
val sections_are_opened : safe_environment -> bool

Insertion of local declarations (Local or Variables)

val push_named_assum : (Names.Id.t * Constr.types) -> safe_transformer0
val push_section_context : UVars.UContext.t -> safe_transformer0

Add local universes to a polymorphic section

Interactive module functions
val module_num_parameters : safe_environment -> int list

returns the number of module (type) parameters following the nested module structure. The inner module (type) comes first in the list.

val module_is_modtype : safe_environment -> bool list

returns true if the module is a module type following the nested module structure. The inner module (type) comes first in the list. true means a module type, false a regular module

val allow_delayed_constants : bool Stdlib.ref

Traditional mode: check at end of module that no future was created.

The optional result type is given without its functorial part

val current_modpath : safe_environment -> Names.ModPath.t
val current_dirpath : safe_environment -> Names.DirPath.t
Libraries : loading and saving compilation units
type compiled_library
val module_of_library : compiled_library -> Declarations.module_body
val univs_of_library : compiled_library -> Univ.ContextSet.t
val check_flags_for_library : compiled_library -> safe_transformer0
Safe typing judgments
type judgment = private {
jdg_env : safe_environment;
jdg_val : Constr.constr;
jdg_type : Constr.types;
}

The safe typing of a term returns a typing judgment.

Queries
val exists_objlabel : Names.Label.t -> safe_environment -> bool
val constant_of_delta_kn_senv : safe_environment -> Names.KerName.t -> Names.Constant.t
val mind_of_delta_kn_senv : safe_environment -> Names.KerName.t -> Names.MutInd.t
Retroknowledge / Native compiler
val register_inline : Names.Constant.t -> safe_transformer0
val register_inductive : Names.inductive -> 'a CPrimitives.prim_ind -> safe_transformer0
\ No newline at end of file +Safe_typing (rocq-runtime.Safe_typing)

Module Safe_typing

type vodigest =
| Dvo_or_vi of Stdlib.Digest.t
val digest_match : actual:vodigest -> required:vodigest -> bool
Safe environments

Since we are now able to type terms, we can define an abstract type of safe environments, where objects are typed before being added.

We also provide functionality for modules : start_module, end_module, etc.

type safe_environment
type section_data
val empty_environment : safe_environment
val env_of_safe_env : safe_environment -> Environ.env
val sections_of_safe_env : safe_environment -> section_data Section.t option
val structure_body_of_safe_env : safe_environment -> Mod_declarations.structure_body

The safe_environment state monad

type safe_transformer0 = safe_environment -> safe_environment
type 'a safe_transformer = safe_environment -> 'a * safe_environment
Stm machinery
type private_constants
val empty_private_constants : private_constants
val is_empty_private_constants : private_constants -> bool

concat_private e1 e2 adds the constants of e1 to e2, i.e. constants in e1 must be more recent than those of e2.

Abstract the private constants of a proof over the proof output

val push_private_constants : Environ.env -> private_constants -> Environ.env

Push the constants in the environment if not already there.

val universes_of_private : private_constants -> Univ.ContextSet.t
val is_curmod_library : safe_environment -> bool
val is_joined_environment : safe_environment -> bool

Enriching a safe environment

Insertion of global axioms or definitions

type side_effect_declaration =
| DefinitionEff : Entries.definition_entry -> side_effect_declaration
| OpaqueEff : Constr.constr Entries.opaque_entry -> side_effect_declaration
type exported_opaque
type exported_private_constant = Names.Constant.t * exported_opaque option
val export_private_constants : private_constants -> exported_private_constant list safe_transformer

returns the main constant

Similar to add_constant but also returns a certificate

Delayed proofs
type opaque_certificate

Witness that a delayed Qed hole has a proof. This datatype is marshallable but care must be taken to marshal it at the same time as the environment it is referring to, since fill_opaque relies on a shared pointer between the environment and the certificate.

Check that the provided proof is correct for the corresponding handle. This does not modify the environment. Call fill_opaque below for that.

Given an already checked proof for an opaque hole, actually fill it with the proof. This might fail if the current set of global universes is inconsistent with the one at the time of the call to check_opaque. Precondition: the underlying handle must exist and must not have been filled.

val is_filled_opaque : Opaqueproof.opaque_handle -> safe_environment -> bool

Check whether a handle was filled. It assumes that the handle was introduced in the opaque table and throws an anomaly otherwise.

Get the proof term that was checked by the kernel.

Rewrite rules

Add a rewrite rule corresponding to the equality witnessed by the constant.

Inductive blocks

Adding an inductive type

Adding a module or a module type

Adding universe constraints

val push_context_set : strict:bool -> Univ.ContextSet.t -> safe_transformer0
val add_constraints : Univ.Constraints.t -> safe_transformer0
val set_rewrite_rules_allowed : bool -> safe_transformer0

Setting the type theory flavor

val set_impredicative_set : bool -> safe_transformer0
val set_indices_matter : bool -> safe_transformer0
val set_share_reduction : bool -> safe_transformer0
val set_check_guarded : bool -> safe_transformer0
val set_check_positive : bool -> safe_transformer0
val set_check_universes : bool -> safe_transformer0
val set_VM : bool -> safe_transformer0
val set_native_compiler : bool -> safe_transformer0
val set_allow_sprop : bool -> safe_transformer0
Interactive section functions
val open_section : safe_transformer0
val close_section : safe_transformer0
val sections_are_opened : safe_environment -> bool

Insertion of local declarations (Local or Variables)

val push_named_assum : (Names.Id.t * Constr.types) -> safe_transformer0
val push_section_context : UVars.UContext.t -> safe_transformer0

Add local universes to a polymorphic section

Interactive module functions
val module_num_parameters : safe_environment -> int list

returns the number of module (type) parameters following the nested module structure. The inner module (type) comes first in the list.

val module_is_modtype : safe_environment -> bool list

returns true if the module is a module type following the nested module structure. The inner module (type) comes first in the list. true means a module type, false a regular module

val allow_delayed_constants : bool Stdlib.ref

Traditional mode: check at end of module that no future was created.

The optional result type is given without its functorial part

val current_modpath : safe_environment -> Names.ModPath.t
val current_dirpath : safe_environment -> Names.DirPath.t
Libraries : loading and saving compilation units
type compiled_library
val univs_of_library : compiled_library -> Univ.ContextSet.t
val check_flags_for_library : compiled_library -> safe_transformer0
Safe typing judgments
type judgment = private {
jdg_env : safe_environment;
jdg_val : Constr.constr;
jdg_type : Constr.types;
}

The safe typing of a term returns a typing judgment.

Queries
val exists_objlabel : Names.Label.t -> safe_environment -> bool
val constant_of_delta_kn_senv : safe_environment -> Names.KerName.t -> Names.Constant.t
val mind_of_delta_kn_senv : safe_environment -> Names.KerName.t -> Names.MutInd.t
Retroknowledge / Native compiler
val register_inline : Names.Constant.t -> safe_transformer0
val register_inductive : Names.inductive -> 'a CPrimitives.prim_ind -> safe_transformer0
\ No newline at end of file diff --git a/master/api/rocq-runtime/Subtyping/index.html b/master/api/rocq-runtime/Subtyping/index.html index 75915b3080..4c28289218 100644 --- a/master/api/rocq-runtime/Subtyping/index.html +++ b/master/api/rocq-runtime/Subtyping/index.html @@ -1,2 +1,2 @@ -Subtyping (rocq-runtime.Subtyping)

Module Subtyping

\ No newline at end of file +Subtyping (rocq-runtime.Subtyping)

Module Subtyping

\ No newline at end of file diff --git a/master/api/rocq-runtime/UnivGen/index.html b/master/api/rocq-runtime/UnivGen/index.html index cbd5eebda2..e275f40701 100644 --- a/master/api/rocq-runtime/UnivGen/index.html +++ b/master/api/rocq-runtime/UnivGen/index.html @@ -1,2 +1,2 @@ -UnivGen (rocq-runtime.UnivGen)

Module UnivGen

type univ_length_mismatch = {
actual : int * int;
expect : int * int;
}
exception UniverseLengthMismatch of univ_length_mismatch

Side-effecting functions creating new universe levels.

val new_univ_global : unit -> Univ.UGlobal.t
val new_sort_global : unit -> Sorts.QVar.t
val fresh_level : unit -> Univ.Level.t
val new_global_univ : unit -> Univ.Universe.t Univ.in_universe_context_set

Build a fresh instance for a given context, its associated substitution and the instantiated constraints.

type 'a in_sort_context_set = 'a * sort_context_set
val sort_context_union : sort_context_set -> sort_context_set -> sort_context_set
val empty_sort_context : sort_context_set
val is_empty_sort_context : sort_context_set -> bool
val diff_sort_context : sort_context_set -> sort_context_set -> sort_context_set
val fresh_sort_in_family : Sorts.family -> Sorts.t in_sort_context_set

NB: InQSort is treated as InType

val fresh_array_instance : Environ.env -> UVars.Instance.t in_sort_context_set
val fresh_global_instance : ?loc:Loc.t -> ?names:UVars.Instance.t -> Environ.env -> Names.GlobRef.t -> Constr.constr in_sort_context_set
val fresh_universe_context_set_instance : Univ.ContextSet.t -> Univ.universe_level_subst * Univ.ContextSet.t

Get fresh variables for the universe context. Useful to make tactics that manipulate constrs in universe contexts polymorphic.

val fresh_sort_context_instance : sort_context_set -> UVars.sort_level_subst * sort_context_set
val constr_of_monomorphic_global : Environ.env -> Names.GlobRef.t -> Constr.constr

Create a fresh global in the environment argument, without side effects. BEWARE: this raises an error on polymorphic constants/inductives: the constraints should be properly added to an evd. See Evd.fresh_global, Evarutil.new_global, and pf_constr_of_global for the proper way to get a fresh copy of a polymorphic global reference.

\ No newline at end of file +UnivGen (rocq-runtime.UnivGen)

Module UnivGen

type univ_length_mismatch = {
gref : Names.GlobRef.t;
actual : int * int;
expect : int * int;
}
exception UniverseLengthMismatch of univ_length_mismatch

Side-effecting functions creating new universe levels.

val new_univ_global : unit -> Univ.UGlobal.t
val new_sort_global : unit -> Sorts.QVar.t
val fresh_level : unit -> Univ.Level.t
val new_global_univ : unit -> Univ.Universe.t Univ.in_universe_context_set

Build a fresh instance for a given context, its associated substitution and the instantiated constraints.

type 'a in_sort_context_set = 'a * sort_context_set
val sort_context_union : sort_context_set -> sort_context_set -> sort_context_set
val empty_sort_context : sort_context_set
val is_empty_sort_context : sort_context_set -> bool
val diff_sort_context : sort_context_set -> sort_context_set -> sort_context_set

The globref is only used for the error message when there is a mismatch.

val fresh_sort_in_family : Sorts.family -> Sorts.t in_sort_context_set

NB: InQSort is treated as InType

val fresh_array_instance : Environ.env -> UVars.Instance.t in_sort_context_set
val fresh_global_instance : ?loc:Loc.t -> ?names:UVars.Instance.t -> Environ.env -> Names.GlobRef.t -> Constr.constr in_sort_context_set
val fresh_universe_context_set_instance : Univ.ContextSet.t -> Univ.universe_level_subst * Univ.ContextSet.t

Get fresh variables for the universe context. Useful to make tactics that manipulate constrs in universe contexts polymorphic.

val fresh_sort_context_instance : sort_context_set -> UVars.sort_level_subst * sort_context_set
val constr_of_monomorphic_global : Environ.env -> Names.GlobRef.t -> Constr.constr

Create a fresh global in the environment argument, without side effects. BEWARE: this raises an error on polymorphic constants/inductives: the constraints should be properly added to an evd. See Evd.fresh_global, Evarutil.new_global, and pf_constr_of_global for the proper way to get a fresh copy of a polymorphic global reference.

\ No newline at end of file diff --git a/master/api/rocq-runtime/index.html b/master/api/rocq-runtime/index.html index 3e65fceeca..e20625a4a0 100644 --- a/master/api/rocq-runtime/index.html +++ b/master/api/rocq-runtime/index.html @@ -1,2 +1,2 @@ -index (rocq-runtime.index)

rocq-runtime index

Library rocq-runtime.boot

The entry point of this library is the module: Boot.

Library rocq-runtime.checklib

The entry point of this library is the module: Coq_checklib.

Library rocq-runtime.clib

This library exposes the following toplevel modules:

Library rocq-runtime.config

The entry point of this library is the module: Coq_config.

Library rocq-runtime.config.byte

The entry point of this library is the module: Coq_byte_config.

Library rocq-runtime.coqargs

The entry point of this library is the module: Coqargs.

Library rocq-runtime.coqdeplib

The entry point of this library is the module: Coqdeplib.

Library rocq-runtime.coqworkmgrapi

The entry point of this library is the module: CoqworkmgrApi.

Library rocq-runtime.debugger_support

The entry point of this library is the module: Debugger_support.

Library rocq-runtime.dev

This library exposes the following toplevel modules:

Library rocq-runtime.engine

This library exposes the following toplevel modules:

Library rocq-runtime.gramlib

The entry point of this library is the module: Gramlib.

Library rocq-runtime.interp

This library exposes the following toplevel modules:

Library rocq-runtime.kernel

This library exposes the following toplevel modules:

Library rocq-runtime.lib

This library exposes the following toplevel modules:

Library rocq-runtime.library

This library exposes the following toplevel modules:

Library rocq-runtime.parsing

This library exposes the following toplevel modules:

Library rocq-runtime.perf

The entry point of this library is the module: Perf.

Library rocq-runtime.plugins.btauto

The entry point of this library is the module: Btauto_plugin.

Library rocq-runtime.plugins.cc

The entry point of this library is the module: Cc_plugin.

Library rocq-runtime.plugins.cc_core

The entry point of this library is the module: Cc_core_plugin.

Library rocq-runtime.plugins.derive

The entry point of this library is the module: Derive_plugin.

Library rocq-runtime.plugins.extraction

The entry point of this library is the module: Extraction_plugin.

Library rocq-runtime.plugins.firstorder

The entry point of this library is the module: Firstorder_plugin.

Library rocq-runtime.plugins.firstorder_core

The entry point of this library is the module: Firstorder_core_plugin.

Library rocq-runtime.plugins.funind

The entry point of this library is the module: Funind_plugin.

Library rocq-runtime.plugins.ltac

The entry point of this library is the module: Ltac_plugin.

Library rocq-runtime.plugins.ltac2

The entry point of this library is the module: Ltac2_plugin.

Library rocq-runtime.plugins.ltac2_ltac1

The entry point of this library is the module: Ltac2_ltac1_plugin.

Library rocq-runtime.plugins.micromega

The entry point of this library is the module: Micromega_plugin.

Library rocq-runtime.plugins.micromega_core

The entry point of this library is the module: Micromega_core_plugin.

Library rocq-runtime.plugins.nsatz

The entry point of this library is the module: Nsatz_plugin.

Library rocq-runtime.plugins.nsatz_core

The entry point of this library is the module: Nsatz_core_plugin.

Library rocq-runtime.plugins.number_string_notation

The entry point of this library is the module: Number_string_notation_plugin.

Library rocq-runtime.plugins.ring

The entry point of this library is the module: Ring_plugin.

Library rocq-runtime.plugins.rtauto

The entry point of this library is the module: Rtauto_plugin.

Library rocq-runtime.plugins.ssreflect

The entry point of this library is the module: Ssreflect_plugin.

Library rocq-runtime.plugins.ssrmatching

The entry point of this library is the module: Ssrmatching_plugin.

Library rocq-runtime.plugins.tauto

The entry point of this library is the module: Tauto_plugin.

Library rocq-runtime.plugins.tutorial.p0

The entry point of this library is the module: Tuto0_plugin.

Library rocq-runtime.plugins.tutorial.p1

The entry point of this library is the module: Tuto1_plugin.

Library rocq-runtime.plugins.tutorial.p2

The entry point of this library is the module: Tuto2_plugin.

Library rocq-runtime.plugins.tutorial.p3

The entry point of this library is the module: Tuto3_plugin.

Library rocq-runtime.plugins.zify

The entry point of this library is the module: Zify_plugin.

Library rocq-runtime.pretyping

This library exposes the following toplevel modules:

Library rocq-runtime.printing

This library exposes the following toplevel modules:

Library rocq-runtime.proofs

This library exposes the following toplevel modules:

Library rocq-runtime.rocqshim

The entry point of this library is the module: Rocqshim.

Library rocq-runtime.stm

This library exposes the following toplevel modules:

Library rocq-runtime.sysinit

This library exposes the following toplevel modules:

Library rocq-runtime.tactics

This library exposes the following toplevel modules:

Library rocq-runtime.toplevel

This library exposes the following toplevel modules:

Library rocq-runtime.vernac

This library exposes the following toplevel modules:

Library rocq-runtime.vm

The entry point of this library is the module: Coqrun.

\ No newline at end of file +index (rocq-runtime.index)

rocq-runtime index

Library rocq-runtime.boot

The entry point of this library is the module: Boot.

Library rocq-runtime.checklib

The entry point of this library is the module: Coq_checklib.

Library rocq-runtime.clib

This library exposes the following toplevel modules:

Library rocq-runtime.config

The entry point of this library is the module: Coq_config.

Library rocq-runtime.config.byte

The entry point of this library is the module: Coq_byte_config.

Library rocq-runtime.coqargs

The entry point of this library is the module: Coqargs.

Library rocq-runtime.coqdeplib

The entry point of this library is the module: Coqdeplib.

Library rocq-runtime.coqworkmgrapi

The entry point of this library is the module: CoqworkmgrApi.

Library rocq-runtime.debugger_support

The entry point of this library is the module: Debugger_support.

Library rocq-runtime.dev

This library exposes the following toplevel modules:

Library rocq-runtime.engine

This library exposes the following toplevel modules:

Library rocq-runtime.gramlib

The entry point of this library is the module: Gramlib.

Library rocq-runtime.interp

This library exposes the following toplevel modules:

Library rocq-runtime.kernel

This library exposes the following toplevel modules:

Library rocq-runtime.lib

This library exposes the following toplevel modules:

Library rocq-runtime.library

This library exposes the following toplevel modules:

Library rocq-runtime.parsing

This library exposes the following toplevel modules:

Library rocq-runtime.perf

The entry point of this library is the module: Perf.

Library rocq-runtime.plugins.btauto

The entry point of this library is the module: Btauto_plugin.

Library rocq-runtime.plugins.cc

The entry point of this library is the module: Cc_plugin.

Library rocq-runtime.plugins.cc_core

The entry point of this library is the module: Cc_core_plugin.

Library rocq-runtime.plugins.derive

The entry point of this library is the module: Derive_plugin.

Library rocq-runtime.plugins.extraction

The entry point of this library is the module: Extraction_plugin.

Library rocq-runtime.plugins.firstorder

The entry point of this library is the module: Firstorder_plugin.

Library rocq-runtime.plugins.firstorder_core

The entry point of this library is the module: Firstorder_core_plugin.

Library rocq-runtime.plugins.funind

The entry point of this library is the module: Funind_plugin.

Library rocq-runtime.plugins.ltac

The entry point of this library is the module: Ltac_plugin.

Library rocq-runtime.plugins.ltac2

The entry point of this library is the module: Ltac2_plugin.

Library rocq-runtime.plugins.ltac2_ltac1

The entry point of this library is the module: Ltac2_ltac1_plugin.

Library rocq-runtime.plugins.micromega

The entry point of this library is the module: Micromega_plugin.

Library rocq-runtime.plugins.micromega_core

The entry point of this library is the module: Micromega_core_plugin.

Library rocq-runtime.plugins.nsatz

The entry point of this library is the module: Nsatz_plugin.

Library rocq-runtime.plugins.nsatz_core

The entry point of this library is the module: Nsatz_core_plugin.

Library rocq-runtime.plugins.number_string_notation

The entry point of this library is the module: Number_string_notation_plugin.

Library rocq-runtime.plugins.ring

The entry point of this library is the module: Ring_plugin.

Library rocq-runtime.plugins.rtauto

The entry point of this library is the module: Rtauto_plugin.

Library rocq-runtime.plugins.ssreflect

The entry point of this library is the module: Ssreflect_plugin.

Library rocq-runtime.plugins.ssrmatching

The entry point of this library is the module: Ssrmatching_plugin.

Library rocq-runtime.plugins.tauto

The entry point of this library is the module: Tauto_plugin.

Library rocq-runtime.plugins.tutorial.p0

The entry point of this library is the module: Tuto0_plugin.

Library rocq-runtime.plugins.tutorial.p1

The entry point of this library is the module: Tuto1_plugin.

Library rocq-runtime.plugins.tutorial.p2

The entry point of this library is the module: Tuto2_plugin.

Library rocq-runtime.plugins.tutorial.p3

The entry point of this library is the module: Tuto3_plugin.

Library rocq-runtime.plugins.zify

The entry point of this library is the module: Zify_plugin.

Library rocq-runtime.pretyping

This library exposes the following toplevel modules:

Library rocq-runtime.printing

This library exposes the following toplevel modules:

Library rocq-runtime.proofs

This library exposes the following toplevel modules:

Library rocq-runtime.rocqshim

The entry point of this library is the module: Rocqshim.

Library rocq-runtime.stm

This library exposes the following toplevel modules:

Library rocq-runtime.sysinit

This library exposes the following toplevel modules:

Library rocq-runtime.tactics

This library exposes the following toplevel modules:

Library rocq-runtime.toplevel

This library exposes the following toplevel modules:

Library rocq-runtime.vernac

This library exposes the following toplevel modules:

Library rocq-runtime.vm

The entry point of this library is the module: Coqrun.

\ No newline at end of file diff --git a/master/corelib/Corelib.Array.ArrayAxioms.html b/master/corelib/Corelib.Array.ArrayAxioms.html new file mode 100644 index 0000000000..201383a55c --- /dev/null +++ b/master/corelib/Corelib.Array.ArrayAxioms.html @@ -0,0 +1,119 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Array.ArrayAxioms

+ +
+From Corelib Require Import PrimArray.
+ +
+Local Notation in_bounds i t := (PrimInt63.ltb i (length t)).
+ +
+Axiom get_out_of_bounds : forall A (t:array A) i,
+  in_bounds i t = false -> t.[i] = default t.
+ +
+Axiom get_set_same : forall A t i (a:A),
+  in_bounds i t = true -> t.[i<-a].[i] = a.
+Axiom get_set_other : forall A t i j (a:A), i <> j -> t.[i<-a].[j] = t.[j].
+Axiom default_set : forall A t i (a:A), default t.[i<-a] = default t.
+ +
+Axiom get_make : forall A (a:A) size i, (make size a).[i] = a.
+ +
+Axiom leb_length : forall A (t:array A),
+  PrimInt63.leb (length t) max_length = true.
+ +
+Axiom length_make : forall A size (a:A),
+  length (make size a) = if PrimInt63.leb size max_length then size else max_length.
+Axiom length_set : forall A t i (a:A),
+  length t.[i<-a] = length t.
+ +
+Axiom get_copy : forall A (t:array A) i, (copy t).[i] = t.[i].
+Axiom length_copy : forall A (t:array A), length (copy t) = length t.
+ +
+Axiom array_ext : forall A (t1 t2:array A),
+  length t1 = length t2 ->
+  (forall i, in_bounds i t1 = true -> t1.[i] = t2.[i]) ->
+  default t1 = default t2 ->
+  t1 = t2.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Array.PrimArray.html b/master/corelib/Corelib.Array.PrimArray.html new file mode 100644 index 0000000000..0fef4490a1 --- /dev/null +++ b/master/corelib/Corelib.Array.PrimArray.html @@ -0,0 +1,128 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Array.PrimArray

+ +
+From Corelib Require Import PrimInt63.
+ +
+ +
+Primitive array := #array_type.
+ +
+Primitive make : forall A, int -> A -> array A := #array_make.
+Arguments make {_} _ _.
+ +
+Primitive get : forall A, array A -> int -> A := #array_get.
+Arguments get {_} _ _.
+ +
+Primitive default : forall A, array A -> A:= #array_default.
+Arguments default {_} _.
+ +
+Primitive set : forall A, array A -> int -> A -> array A := #array_set.
+Arguments set {_} _ _ _.
+ +
+Primitive length : forall A, array A -> int := #array_length.
+Arguments length {_} _.
+ +
+Primitive copy : forall A, array A -> array A := #array_copy.
+Arguments copy {_} _.
+ +
+Module Export PArrayNotations.
+ +
+Declare Scope array_scope.
+Delimit Scope array_scope with array.
+Notation "t .[ i ]" := (get t i)
+  (at level 2, left associativity, format "t .[ i ]").
+Notation "t .[ i <- a ]" := (set t i a)
+  (at level 2, left associativity, format "t .[ i <- a ]").
+ +
+End PArrayNotations.
+ +
+Primitive max_length := #array_max_length.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.BinNums.IntDef.html b/master/corelib/Corelib.BinNums.IntDef.html new file mode 100644 index 0000000000..dcb245d1cf --- /dev/null +++ b/master/corelib/Corelib.BinNums.IntDef.html @@ -0,0 +1,715 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.BinNums.IntDef

+ +
+From Corelib Require Import BinNums PosDef NatDef.
+ +
+Local Open Scope Z_scope.
+ +
+Local Notation "0" := Z0.
+Local Notation "1" := (Zpos 1).
+Local Notation "2" := (Zpos 2).
+ +
+
+ +
+

Binary Integers, Definitions of Operations

+ +
+ + Initial author: Pierre Crégut, CNET, Lannion, France +
+
+ +
+Module Z.
+ +
+
+ +
+

Doubling and variants

+ +
+
+ +
+Definition double x :=
+  match x with
+    | 0 => 0
+    | Zpos p => Zpos p~0
+    | Zneg p => Zneg p~0
+  end.
+ +
+Definition succ_double x :=
+  match x with
+    | 0 => 1
+    | Zpos p => Zpos p~1
+    | Zneg p => Zneg (Pos.pred_double p)
+  end.
+ +
+Definition pred_double x :=
+  match x with
+    | 0 => Zneg 1
+    | Zneg p => Zneg p~1
+    | Zpos p => Zpos (Pos.pred_double p)
+  end.
+ +
+
+ +
+

Subtraction of positive into Z

+ +
+
+ +
+Fixpoint pos_sub (x y:positive) {struct y} : Z :=
+  match x, y with
+    | p~1, q~1 => double (pos_sub p q)
+    | p~1, q~0 => succ_double (pos_sub p q)
+    | p~1, xH => Zpos p~0
+    | p~0, q~1 => pred_double (pos_sub p q)
+    | p~0, q~0 => double (pos_sub p q)
+    | p~0, xH => Zpos (Pos.pred_double p)
+    | xH, q~1 => Zneg q~0
+    | xH, q~0 => Zneg (Pos.pred_double q)
+    | xH, xH => Z0
+  end%positive.
+ +
+
+ +
+

Addition

+ +
+
+ +
+Definition add x y :=
+  match x, y with
+    | 0, y => y
+    | x, 0 => x
+    | Zpos x', Zpos y' => Zpos (Pos.add x' y')
+    | Zpos x', Zneg y' => pos_sub x' y'
+    | Zneg x', Zpos y' => pos_sub y' x'
+    | Zneg x', Zneg y' => Zneg (Pos.add x' y')
+  end.
+ +
+Infix "+" := add : Z_scope.
+ +
+
+ +
+

Opposite

+ +
+
+ +
+Definition opp x :=
+  match x with
+    | 0 => 0
+    | Zpos x => Zneg x
+    | Zneg x => Zpos x
+  end.
+ +
+Notation "- x" := (opp x) : Z_scope.
+ +
+
+ +
+

Subtraction

+ +
+
+ +
+Definition sub m n := m + -n.
+ +
+Infix "-" := sub : Z_scope.
+ +
+
+ +
+

Multiplication

+ +
+
+ +
+Definition mul x y :=
+  match x, y with
+    | 0, _ => 0
+    | _, 0 => 0
+    | Zpos x', Zpos y' => Zpos (Pos.mul x' y')
+    | Zpos x', Zneg y' => Zneg (Pos.mul x' y')
+    | Zneg x', Zpos y' => Zneg (Pos.mul x' y')
+    | Zneg x', Zneg y' => Zpos (Pos.mul x' y')
+  end.
+ +
+Infix "*" := mul : Z_scope.
+ +
+
+ +
+

Power function

+ +
+
+ +
+Definition pow_pos (z:Z) := Pos.iter (mul z) 1.
+ +
+Definition pow x y :=
+  match y with
+    | Zpos p => pow_pos x p
+    | 0 => 1
+    | Zneg _ => 0
+  end.
+ +
+Infix "^" := pow : Z_scope.
+ +
+
+ +
+

Comparison

+ +
+
+ +
+Definition compare x y :=
+  match x, y with
+    | 0, 0 => Eq
+    | 0, Zpos y' => Lt
+    | 0, Zneg y' => Gt
+    | Zpos x', 0 => Gt
+    | Zpos x', Zpos y' => Pos.compare x' y'
+    | Zpos x', Zneg y' => Gt
+    | Zneg x', 0 => Lt
+    | Zneg x', Zpos y' => Lt
+    | Zneg x', Zneg y' => CompOpp (Pos.compare x' y')
+  end.
+ +
+Infix "?=" := compare (at level 70, no associativity) : Z_scope.
+ +
+Definition lt x y := (x ?= y) = Lt.
+Definition gt x y := (x ?= y) = Gt.
+Definition le x y := (x ?= y) <> Gt.
+Definition ge x y := (x ?= y) <> Lt.
+ +
+Infix "<=" := le : Z_scope.
+Infix "<" := lt : Z_scope.
+Infix ">=" := ge : Z_scope.
+Infix ">" := gt : Z_scope.
+ +
+
+ +
+Boolean equality and comparisons +
+
+ +
+Definition leb x y :=
+  match compare x y with
+    | Gt => false
+    | _ => true
+  end.
+ +
+Definition ltb x y :=
+  match compare x y with
+    | Lt => true
+    | _ => false
+  end.
+ +
+Definition eqb x y :=
+  match x, y with
+    | 0, 0 => true
+    | Zpos p, Zpos q => Pos.eqb p q
+    | Zneg p, Zneg q => Pos.eqb p q
+    | _, _ => false
+  end.
+ +
+
+ +
+

Minimum and maximum

+ +
+
+ +
+Definition max n m :=
+  match compare n m with
+    | Eq | Gt => n
+    | Lt => m
+  end.
+ +
+Definition min n m :=
+  match compare n m with
+    | Eq | Lt => n
+    | Gt => m
+  end.
+ +
+
+ +
+

Conversions

+ +
+ + From Z to nat by rounding negative numbers to 0 +
+
+ +
+Definition to_nat (z:Z) : nat :=
+  match z with
+    | Zpos p => Pos.to_nat p
+    | _ => O
+  end.
+ +
+
+ +
+From nat to Z +
+
+ +
+Definition of_nat (n:nat) : Z :=
+  match n with
+   | O => 0
+   | S n => Zpos (Pos.of_succ_nat n)
+  end.
+ +
+
+ +
+From N to Z +
+
+ +
+Definition of_N (n:N) : Z :=
+  match n with
+    | N0 => 0
+    | Npos p => Zpos p
+  end.
+ +
+
+ +
+From Z to positive by rounding nonpositive numbers to 1 +
+
+ +
+Definition to_pos (z:Z) : positive :=
+  match z with
+    | Zpos p => p
+    | _ => 1%positive
+  end.
+ +
+
+ +
+

Euclidean divisions for binary integers

+ +
+ +

Floor division

+ +
+ + div_eucl provides a Truncated-Toward-Bottom (a.k.a Floor) + Euclidean division. Its projections are named div (noted "/") + and modulo (noted with an infix "mod"). + These functions correspond to the `div` and `mod` of Haskell. + This is the historical convention of Rocq. + +
+ + The main properties of this convention are : +
    +
  • we have sgn (a mod b) = sgn (b) + +
    • +
  • div a b is the greatest integer smaller or equal to the exact + fraction a/b. + +
    • +
  • there is no easy sign rule. + +
    • +
+ +
+ + In addition, note that we take a/0 = 0 and a mod 0 = a. + This choice is motivated by the div-mod equation + a = (a / b) * b + (a mod b) for b = 0. + +
+ + First, a division for positive numbers. Even if the second + argument is a Z, the answer is arbitrary if it isn't a Zpos. +
+
+ +
+Fixpoint pos_div_eucl (a:positive) (b:Z) : Z * Z :=
+  match a with
+    | xH => if leb 2 b then (0, 1) else (1, 0)
+    | xO a' =>
+      let (q, r) := pos_div_eucl a' b in
+      let r' := 2 * r in
+      if ltb r' b then (2 * q, r') else (2 * q + 1, r' - b)
+    | xI a' =>
+      let (q, r) := pos_div_eucl a' b in
+      let r' := 2 * r + 1 in
+      if ltb r' b then (2 * q, r') else (2 * q + 1, r' - b)
+  end.
+ +
+
+ +
+Then the general euclidean division +
+
+ +
+Definition div_eucl (a b:Z) : Z * Z :=
+  match a, b with
+    | 0, _ => (0, 0)
+    | _, 0 => (0, a)
+    | Zpos a', Zpos _ => pos_div_eucl a' b
+    | Zneg a', Zpos _ =>
+      let (q, r) := pos_div_eucl a' b in
+        match r with
+          | 0 => (- q, 0)
+          | _ => (- (q + 1), b - r)
+        end
+    | Zneg a', Zneg b' =>
+      let (q, r) := pos_div_eucl a' (Zpos b') in (q, - r)
+    | Zpos a', Zneg b' =>
+      let (q, r) := pos_div_eucl a' (Zpos b') in
+        match r with
+          | 0 => (- q, 0)
+          | _ => (- (q + 1), b + r)
+        end
+  end.
+ +
+Definition div (a b:Z) : Z := let (q, _) := div_eucl a b in q.
+Definition modulo (a b:Z) : Z := let (_, r) := div_eucl a b in r.
+ +
+
+ +
+

Trunc Division

+ +
+ + quotrem provides a Truncated-Toward-Zero Euclidean division. + Its projections are named quot (noted "÷") and rem. + These functions correspond to the `quot` and `rem` of Haskell. + This division convention is used in most programming languages, + e.g. Ocaml. + +
+ + With this convention: +
    +
  • we have sgn(a rem b) = sgn(a) + +
    • +
  • sign rule for division: quot (-a) b = quot a (-b) = -(quot a b) + +
    • +
  • and for modulo: a rem (-b) = a rem b and (-a) rem b = -(a rem b) + +
    • +
+ +
+ + Note that we take here quot a 0 = 0 and a rem 0 = a. + This choice is motivated by the quot-rem equation + a = (quot a b) * b + (a rem b) for b = 0. + +
+
+ +
+Definition quotrem (a b:Z) : Z * Z :=
+  match a, b with
+   | 0, _ => (0, 0)
+   | _, 0 => (0, a)
+   | Zpos a, Zpos b =>
+     let (q, r) := N.pos_div_eucl a (Npos b) in (of_N q, of_N r)
+   | Zneg a, Zpos b =>
+     let (q, r) := N.pos_div_eucl a (Npos b) in (-of_N q, - of_N r)
+   | Zpos a, Zneg b =>
+     let (q, r) := N.pos_div_eucl a (Npos b) in (-of_N q, of_N r)
+   | Zneg a, Zneg b =>
+     let (q, r) := N.pos_div_eucl a (Npos b) in (of_N q, - of_N r)
+  end.
+ +
+Definition quot a b := fst (quotrem a b).
+Definition rem a b := snd (quotrem a b).
+ +
+Infix "÷" := quot (at level 40, left associativity) : Z_scope.
+
+ +
+No infix notation for rem, otherwise it becomes a keyword +
+ +

Parity functions

+ +
+
+ +
+Definition even z :=
+  match z with
+    | 0 => true
+    | Zpos (xO _) => true
+    | Zneg (xO _) => true
+    | _ => false
+  end.
+ +
+
+ +
+

Division by two

+ +
+ + div2 performs rounding toward bottom, it is hence a particular + case of div, and for all relative number n we have: + n = 2 * div2 n + if odd n then 1 else 0. +
+
+ +
+Definition div2 z :=
+ match z with
+   | 0 => 0
+   | Zpos 1 => 0
+   | Zpos p => Zpos (Pos.div2 p)
+   | Zneg p => Zneg (Pos.div2_up p)
+ end.
+ +
+
+ +
+

Square root

+ +
+
+ +
+Definition sqrtrem n :=
+ match n with
+  | 0 => (0, 0)
+  | Zpos p =>
+    match Pos.sqrtrem p with
+     | (s, Pos.IsPos r) => (Zpos s, Zpos r)
+     | (s, _) => (Zpos s, 0)
+    end
+  | Zneg _ => (0,0)
+ end.
+ +
+
+ +
+Shifts + +
+ + Nota: a shift to the right by -n will be a shift to the left + by n, and vice-versa. + +
+ + For fulfilling the two's complement convention, shifting to + the right a negative number should correspond to a division + by 2 with rounding toward bottom, hence the use of div2 + instead of quot2. + +
+
+ +
+Definition shiftl a n :=
+ match n with
+   | 0 => a
+   | Zpos p => Pos.iter (mul 2) a p
+   | Zneg p => Pos.iter div2 a p
+ end.
+ +
+Definition shiftr a n := shiftl a (-n).
+ +
+
+ +
+Bitwise operations lor land ldiff lxor +
+
+ +
+Definition lor a b :=
+ match a, b with
+   | 0, _ => b
+   | _, 0 => a
+   | Zpos a, Zpos b => Zpos (Pos.lor a b)
+   | Zneg a, Zpos b => Zneg (N.succ_pos (N.ldiff (Pos.pred_N a) (Npos b)))
+   | Zpos a, Zneg b => Zneg (N.succ_pos (N.ldiff (Pos.pred_N b) (Npos a)))
+   | Zneg a, Zneg b => Zneg (N.succ_pos (N.land (Pos.pred_N a) (Pos.pred_N b)))
+ end.
+ +
+Definition land a b :=
+ match a, b with
+   | 0, _ => 0
+   | _, 0 => 0
+   | Zpos a, Zpos b => of_N (Pos.land a b)
+   | Zneg a, Zpos b => of_N (N.ldiff (Npos b) (Pos.pred_N a))
+   | Zpos a, Zneg b => of_N (N.ldiff (Npos a) (Pos.pred_N b))
+   | Zneg a, Zneg b => Zneg (N.succ_pos (N.lor (Pos.pred_N a) (Pos.pred_N b)))
+ end.
+ +
+Definition lxor a b :=
+ match a, b with
+   | 0, _ => b
+   | _, 0 => a
+   | Zpos a, Zpos b => of_N (Pos.lxor a b)
+   | Zneg a, Zpos b => Zneg (N.succ_pos (N.lxor (Pos.pred_N a) (Npos b)))
+   | Zpos a, Zneg b => Zneg (N.succ_pos (N.lxor (Npos a) (Pos.pred_N b)))
+   | Zneg a, Zneg b => of_N (N.lxor (Pos.pred_N a) (Pos.pred_N b))
+ end.
+ +
+End Z.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.BinNums.NatDef.html b/master/corelib/Corelib.BinNums.NatDef.html new file mode 100644 index 0000000000..c3c53e35c8 --- /dev/null +++ b/master/corelib/Corelib.BinNums.NatDef.html @@ -0,0 +1,288 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.BinNums.NatDef

+ +
+ +
+From Corelib Require Export BinNums PosDef.
+ +
+
+ +
+

Binary natural numbers, definitions of operations

+ +
+
+ +
+Module N.
+ +
+
+ +
+

Operation x -> 2*x+1

+ +
+
+ +
+Definition succ_double x :=
+  match x with
+  | N0 => Npos 1
+  | Npos p => Npos p~1
+  end.
+ +
+
+ +
+

Operation x -> 2*x

+ +
+
+ +
+Definition double n :=
+  match n with
+  | N0 => N0
+  | Npos p => Npos p~0
+  end.
+ +
+
+ +
+

The successor of a N can be seen as a positive

+ +
+
+ +
+Definition succ_pos (n : N) : positive :=
+ match n with
+   | N0 => xH
+   | Npos p => Pos.succ p
+ end.
+ +
+
+ +
+Subtraction +
+
+ +
+Definition sub n m :=
+match n, m with
+| N0, _ => N0
+| n, N0 => n
+| Npos n', Npos m' =>
+  match Pos.sub_mask n' m' with
+  | Pos.IsPos p => Npos p
+  | _ => N0
+  end
+end.
+ +
+
+ +
+Order +
+
+ +
+Definition compare n m :=
+  match n, m with
+  | N0, N0 => Eq
+  | N0, Npos m' => Lt
+  | Npos n', N0 => Gt
+  | Npos n', Npos m' => Pos.compare n' m'
+  end.
+ +
+
+ +
+Boolean equality and comparison +
+
+ +
+Definition leb x y :=
+ match compare x y with Gt => false | _ => true end.
+ +
+
+ +
+Euclidean division +
+
+ +
+Fixpoint pos_div_eucl (a:positive)(b:N) : N * N :=
+  match a with
+    | xH =>
+       match b with Npos 1 => (Npos 1, N0) | _ => (N0, Npos 1) end
+    | xO a' =>
+       let (q, r) := pos_div_eucl a' b in
+       let r' := double r in
+       if leb b r' then (succ_double q, sub r' b)
+        else (double q, r')
+    | xI a' =>
+       let (q, r) := pos_div_eucl a' b in
+       let r' := succ_double r in
+       if leb b r' then (succ_double q, sub r' b)
+        else (double q, r')
+  end.
+ +
+
+ +
+Operation over bits of a N number. +
+ + Logical or +
+
+ +
+Definition lor n m :=
+ match n, m with
+   | N0, _ => m
+   | _, N0 => n
+   | Npos p, Npos q => Npos (Pos.lor p q)
+ end.
+ +
+
+ +
+Logical and +
+
+ +
+Definition land n m :=
+ match n, m with
+  | N0, _ => N0
+  | _, N0 => N0
+  | Npos p, Npos q => Pos.land p q
+ end.
+ +
+
+ +
+Logical diff +
+
+ +
+Definition ldiff n m :=
+ match n, m with
+  | N0, _ => N0
+  | _, N0 => n
+  | Npos p, Npos q => Pos.ldiff p q
+ end.
+ +
+
+ +
+xor +
+
+ +
+Definition lxor n m :=
+  match n, m with
+    | N0, _ => m
+    | _, N0 => n
+    | Npos p, Npos q => Pos.lxor p q
+  end.
+ +
+End N.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.BinNums.PosDef.html b/master/corelib/Corelib.BinNums.PosDef.html new file mode 100644 index 0000000000..cb0bc6d4e7 --- /dev/null +++ b/master/corelib/Corelib.BinNums.PosDef.html @@ -0,0 +1,641 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.BinNums.PosDef

+ +
+ +
+
+ +
+

Binary positive numbers, operations

+ +
+ + Initial development by Pierre Crégut, CNET, Lannion, France +
+ + The type positive and its constructors xI and xO and xH + are now defined in BinNums.v +
+
+ +
+From Corelib Require Export BinNums.
+ +
+Local Open Scope positive_scope.
+ +
+
+ +
+Postfix notation for positive numbers, which allows mimicking + the position of bits in a big-endian representation. + For instance, we can write 1~1~0 instead of (xO (xI xH)) + for the number 6 (which is 110 in binary notation). + +
+
+ +
+Notation "p ~ 1" := (xI p)
+ (at level 7, left associativity, format "p '~' '1'") : positive_scope.
+Notation "p ~ 0" := (xO p)
+ (at level 7, left associativity, format "p '~' '0'") : positive_scope.
+ +
+Notation "1" := xH : positive_scope.
+Notation "2" := 1~0 : positive_scope.
+Notation "3" := 1~1 : positive_scope.
+ +
+Module Pos.
+ +
+
+ +
+

Operations over positive numbers

+ +
+ +

Successor

+ +
+
+ +
+Fixpoint succ x :=
+  match x with
+    | p~1 => (succ p)~0
+    | p~0 => p~1
+    | 1 => 1~0
+  end.
+ +
+
+ +
+

Addition

+ +
+
+ +
+Fixpoint add x y :=
+  match x, y with
+    | p~1, q~1 => (add_carry p q)~0
+    | p~1, q~0 => (add p q)~1
+    | p~1, 1 => (succ p)~0
+    | p~0, q~1 => (add p q)~1
+    | p~0, q~0 => (add p q)~0
+    | p~0, 1 => p~1
+    | 1, q~1 => (succ q)~0
+    | 1, q~0 => q~1
+    | 1, 1 => 1~0
+  end
+
+with add_carry x y :=
+  match x, y with
+    | p~1, q~1 => (add_carry p q)~1
+    | p~1, q~0 => (add_carry p q)~0
+    | p~1, 1 => (succ p)~1
+    | p~0, q~1 => (add_carry p q)~0
+    | p~0, q~0 => (add p q)~1
+    | p~0, 1 => (succ p)~0
+    | 1, q~1 => (succ q)~1
+    | 1, q~0 => (succ q)~0
+    | 1, 1 => 1~1
+  end.
+ +
+
+ +
+

Operation x -> 2*x-1

+ +
+
+ +
+Fixpoint pred_double x :=
+  match x with
+    | p~1 => p~0~1
+    | p~0 => (pred_double p)~1
+    | 1 => 1
+  end.
+ +
+
+ +
+

The predecessor of a positive number can be seen as a N

+ +
+
+ +
+Definition pred_N x :=
+  match x with
+    | p~1 => Npos (p~0)
+    | p~0 => Npos (pred_double p)
+    | 1 => N0
+  end.
+ +
+
+ +
+

An auxiliary type for subtraction

+ +
+
+ +
+Inductive mask : Set :=
+| IsNul : mask
+| IsPos : positive -> mask
+| IsNeg : mask.
+ +
+
+ +
+

Operation x -> 2*x+1

+ +
+
+ +
+Definition succ_double_mask (x:mask) : mask :=
+  match x with
+    | IsNul => IsPos 1
+    | IsNeg => IsNeg
+    | IsPos p => IsPos p~1
+  end.
+ +
+
+ +
+

Operation x -> 2*x

+ +
+
+ +
+Definition double_mask (x:mask) : mask :=
+  match x with
+    | IsNul => IsNul
+    | IsNeg => IsNeg
+    | IsPos p => IsPos p~0
+  end.
+ +
+
+ +
+

Operation x -> 2*x-2

+ +
+
+ +
+Definition double_pred_mask x : mask :=
+  match x with
+    | p~1 => IsPos p~0~0
+    | p~0 => IsPos (pred_double p)~0
+    | 1 => IsNul
+  end.
+ +
+
+ +
+

Subtraction, result as a mask

+ +
+
+ +
+Fixpoint sub_mask (x y:positive) {struct y} : mask :=
+  match x, y with
+    | p~1, q~1 => double_mask (sub_mask p q)
+    | p~1, q~0 => succ_double_mask (sub_mask p q)
+    | p~1, 1 => IsPos p~0
+    | p~0, q~1 => succ_double_mask (sub_mask_carry p q)
+    | p~0, q~0 => double_mask (sub_mask p q)
+    | p~0, 1 => IsPos (pred_double p)
+    | 1, 1 => IsNul
+    | 1, _ => IsNeg
+  end
+
+with sub_mask_carry (x y:positive) {struct y} : mask :=
+  match x, y with
+    | p~1, q~1 => succ_double_mask (sub_mask_carry p q)
+    | p~1, q~0 => double_mask (sub_mask p q)
+    | p~1, 1 => IsPos (pred_double p)
+    | p~0, q~1 => double_mask (sub_mask_carry p q)
+    | p~0, q~0 => succ_double_mask (sub_mask_carry p q)
+    | p~0, 1 => double_pred_mask p
+    | 1, _ => IsNeg
+  end.
+ +
+
+ +
+

Subtraction, result as a positive, returning 1 if x<=y

+ +
+
+ +
+Definition sub x y :=
+  match sub_mask x y with
+    | IsPos z => z
+    | _ => 1
+  end.
+ +
+
+ +
+

Multiplication

+ +
+
+ +
+Fixpoint mul x y :=
+  match x with
+    | p~1 => add y (mul p y)~0
+    | p~0 => (mul p y)~0
+    | 1 => y
+  end.
+ +
+
+ +
+

Iteration over a positive number

+ +
+
+ +
+Definition iter {A} (f:A -> A) : A -> positive -> A :=
+  fix iter_fix x n := match n with
+    | xH => f x
+    | xO n' => iter_fix (iter_fix x n') n'
+    | xI n' => f (iter_fix (iter_fix x n') n')
+  end.
+ +
+
+ +
+

Division by 2 rounded below but for 1

+ +
+
+ +
+Definition div2 p :=
+  match p with
+    | 1 => 1
+    | p~0 => p
+    | p~1 => p
+  end.
+ +
+
+ +
+Division by 2 rounded up +
+
+ +
+Definition div2_up p :=
+ match p with
+   | 1 => 1
+   | p~0 => p
+   | p~1 => succ p
+ end.
+ +
+
+ +
+

Comparison on binary positive numbers

+ +
+
+ +
+Fixpoint compare_cont (r:comparison) (x y:positive) {struct y} : comparison :=
+  match x, y with
+    | p~1, q~1 => compare_cont r p q
+    | p~1, q~0 => compare_cont Gt p q
+    | p~1, 1 => Gt
+    | p~0, q~1 => compare_cont Lt p q
+    | p~0, q~0 => compare_cont r p q
+    | p~0, 1 => Gt
+    | 1, q~1 => Lt
+    | 1, q~0 => Lt
+    | 1, 1 => r
+  end.
+ +
+Definition compare := compare_cont Eq.
+ +
+
+ +
+

Boolean equality and comparisons

+ +
+
+ +
+Fixpoint eqb p q {struct q} :=
+  match p, q with
+    | p~1, q~1 => eqb p q
+    | p~0, q~0 => eqb p q
+    | 1, 1 => true
+    | _, _ => false
+  end.
+ +
+Definition leb x y :=
+ match compare x y with Gt => false | _ => true end.
+ +
+
+ +
+

A Square Root function for positive numbers

+ +
+ + We proceed by blocks of two digits : if p is written qbb' + then sqrt(p) will be sqrt(q)~0 or sqrt(q)~1. + For deciding easily in which case we are, we store the remainder + (as a mask, since it can be null). + Instead of copy-pasting the following code four times, we + factorize as an auxiliary function, with f and g being either + xO or xI depending of the initial digits. + NB: (sub_mask (g (f 1)) 4) is a hack, morally it's g (f 0). + +
+
+ +
+Definition sqrtrem_step (f g:positive->positive) p :=
+ match p with
+  | (s, IsPos r) =>
+    let s' := s~0~1 in
+    let r' := g (f r) in
+    if leb s' r' then (s~1, sub_mask r' s')
+    else (s~0, IsPos r')
+  | (s,_) => (s~0, sub_mask (g (f 1)) 1~0~0)
+ end.
+ +
+Fixpoint sqrtrem p : positive * mask :=
+ match p with
+  | 1 => (1,IsNul)
+  | 1~0 => (1,IsPos 1)
+  | 1~1 => (1,IsPos 1~0)
+  | p~0~0 => sqrtrem_step xO xO (sqrtrem p)
+  | p~0~1 => sqrtrem_step xO xI (sqrtrem p)
+  | p~1~0 => sqrtrem_step xI xO (sqrtrem p)
+  | p~1~1 => sqrtrem_step xI xI (sqrtrem p)
+ end.
+ +
+Definition sqrt p := fst (sqrtrem p).
+ +
+Definition Nsucc_double x :=
+  match x with
+  | N0 => Npos 1
+  | Npos p => Npos p~1
+  end.
+ +
+Definition Ndouble n :=
+  match n with
+  | N0 => N0
+  | Npos p => Npos p~0
+  end.
+ +
+
+ +
+Operation over bits. +
+ + Logical or +
+
+ +
+Fixpoint lor (p q : positive) : positive :=
+  match p, q with
+    | 1, q~0 => q~1
+    | 1, _ => q
+    | p~0, 1 => p~1
+    | _, 1 => p
+    | p~0, q~0 => (lor p q)~0
+    | p~0, q~1 => (lor p q)~1
+    | p~1, q~0 => (lor p q)~1
+    | p~1, q~1 => (lor p q)~1
+  end.
+ +
+
+ +
+Logical and +
+
+ +
+Fixpoint land (p q : positive) : N :=
+  match p, q with
+    | 1, q~0 => N0
+    | 1, _ => Npos 1
+    | p~0, 1 => N0
+    | _, 1 => Npos 1
+    | p~0, q~0 => Ndouble (land p q)
+    | p~0, q~1 => Ndouble (land p q)
+    | p~1, q~0 => Ndouble (land p q)
+    | p~1, q~1 => Nsucc_double (land p q)
+  end.
+ +
+
+ +
+Logical diff +
+
+ +
+Fixpoint ldiff (p q:positive) : N :=
+  match p, q with
+    | 1, q~0 => Npos 1
+    | 1, _ => N0
+    | _~0, 1 => Npos p
+    | p~1, 1 => Npos (p~0)
+    | p~0, q~0 => Ndouble (ldiff p q)
+    | p~0, q~1 => Ndouble (ldiff p q)
+    | p~1, q~1 => Ndouble (ldiff p q)
+    | p~1, q~0 => Nsucc_double (ldiff p q)
+  end.
+ +
+
+ +
+xor +
+
+ +
+Fixpoint lxor (p q:positive) : N :=
+  match p, q with
+    | 1, 1 => N0
+    | 1, q~0 => Npos (q~1)
+    | 1, q~1 => Npos (q~0)
+    | p~0, 1 => Npos (p~1)
+    | p~0, q~0 => Ndouble (lxor p q)
+    | p~0, q~1 => Nsucc_double (lxor p q)
+    | p~1, 1 => Npos (p~0)
+    | p~1, q~0 => Nsucc_double (lxor p q)
+    | p~1, q~1 => Ndouble (lxor p q)
+  end.
+ +
+
+ +
+

From binary positive numbers to Peano natural numbers

+ +
+
+ +
+Definition iter_op {A}(op:A->A->A) :=
+  fix iter (p:positive)(a:A) : A :=
+  match p with
+    | 1 => a
+    | p~0 => iter p (op a a)
+    | p~1 => op a (iter p (op a a))
+  end.
+ +
+Definition to_nat (x:positive) : nat := iter_op plus x (S O).
+Arguments to_nat x: simpl never.
+ +
+
+ +
+

From Peano natural numbers to binary positive numbers

+ +
+
+ +
+ +
+Fixpoint of_succ_nat (n:nat) : positive :=
+  match n with
+    | O => 1
+    | S x => succ (of_succ_nat x)
+  end.
+ +
+End Pos.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Classes.CMorphisms.html b/master/corelib/Corelib.Classes.CMorphisms.html new file mode 100644 index 0000000000..cc2d3d2c27 --- /dev/null +++ b/master/corelib/Corelib.Classes.CMorphisms.html @@ -0,0 +1,986 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Classes.CMorphisms

+ +
+ +
+
+ +
+

Typeclass-based morphism definition and standard, minimal instances

+ + +
+ + Author: Matthieu Sozeau + Institution: LRI, CNRS UMR 8623 - University Paris Sud + +
+
+ +
+Require Import Corelib.Program.Basics.
+Require Import Corelib.Program.Tactics.
+Require Export Corelib.Classes.CRelationClasses.
+ +
+Generalizable Variables A eqA B C D R RA RB RC m f x y.
+Local Obligation Tactic := try solve [ simpl_crelation ].
+ +
+Local Arguments transitivity {A R Transitive x} y {z}.
+ +
+ +
+
+ +
+

Morphisms.

+ + +
+ + We now turn to the definition of Proper and declare standard instances. + These will be used by the setoid_rewrite tactic later. +
+ + A morphism for a relation R is a proper element of the relation. + The relation R will be instantiated by respectful and A by an arrow + type for usual morphisms. +
+
+Section Proper.
+  Context {A : Type}.
+ +
+  Class Proper (R : crelation A) (m : A) :=
+    proper_prf : R m m.
+ +
+
+ +
+Every element in the carrier of a reflexive relation is a morphism + for this relation. We use a proxy class for this case which is used + internally to discharge reflexivity constraints. The Reflexive + instance will almost always be used, but it won't apply in general to + any kind of Proper (A -> B) _ _ goal, making proof-search much + slower. A cleaner solution would be to be able to set different + priorities in different hint bases and select a particular hint + database for resolution of a type class constraint. +
+
+ +
+  Class ProperProxy (R : crelation A) (m : A) :=
+    proper_proxy : R m m.
+ +
+  Lemma eq_proper_proxy (x : A) : ProperProxy (@eq A) x.
+ +
+  Lemma reflexive_proper_proxy `(Reflexive A R) (x : A) : ProperProxy R x.
+ +
+  Lemma proper_proper_proxy x `(Proper R x) : ProperProxy R x.
+ +
+
+ +
+Respectful morphisms. +
+ + The fully dependent version, not used yet. +
+
+ +
+  Definition respectful_hetero
+  (A B : Type)
+  (C : A -> Type) (D : B -> Type)
+  (R : A -> B -> Type)
+  (R' : forall (x : A) (y : B), C x -> D y -> Type) :
+    (forall x : A, C x) -> (forall x : B, D x) -> Type :=
+    fun f g => forall x y, R x y -> R' x y (f x) (g y).
+ +
+
+ +
+The non-dependent version is an instance where we forget dependencies. +
+
+ +
+  Definition respectful {B} (R : crelation A) (R' : crelation B) : crelation (A -> B) :=
+    Eval compute in @respectful_hetero A A (fun _ => B) (fun _ => B) R (fun _ _ => R').
+End Proper.
+ +
+
+ +
+We favor the use of Leibniz equality or a declared reflexive crelation + when resolving ProperProxy, otherwise, if the crelation is given (not an evar), + we fall back to Proper. +
+
+#[global]
+Hint Extern 1 (ProperProxy _ _) =>
+  class_apply @eq_proper_proxy || class_apply @reflexive_proper_proxy : typeclass_instances.
+ +
+#[global]
+Hint Extern 2 (ProperProxy ?R _) =>
+  not_evar R; class_apply @proper_proper_proxy : typeclass_instances.
+ +
+
+ +
+Notations reminiscent of the old syntax for declaring morphisms. +
+
+Declare Scope signatureT_scope.
+Delimit Scope signatureT_scope with signatureT.
+ +
+Module ProperNotations.
+ +
+  Notation " R ++> R' " := (@respectful _ _ (R%signatureT) (R'%signatureT))
+    (right associativity, at level 55) : signatureT_scope.
+ +
+  Notation " R ==> R' " := (@respectful _ _ (R%signatureT) (R'%signatureT))
+    (right associativity, at level 55) : signatureT_scope.
+ +
+  Notation " R --> R' " := (@respectful _ _ (flip (R%signatureT)) (R'%signatureT))
+    (right associativity, at level 55) : signatureT_scope.
+ +
+End ProperNotations.
+ +
+Arguments Proper {A}%_type R%_signatureT m.
+Arguments respectful {A B}%_type (R R')%_signatureT _ _.
+ +
+Export ProperNotations.
+ +
+Local Open Scope signatureT_scope.
+ +
+
+ +
+solve_proper try to solve the goal Proper (?==> ... ==>?) f + by repeated introductions and setoid rewrites. It should work + fine when f is a combination of already known morphisms and + quantifiers. +
+
+ +
+Ltac solve_respectful t :=
+ match goal with
+   | |- respectful _ _ _ _ =>
+     let H := fresh "H" in
+     intros ? ? H; solve_respectful ltac:(setoid_rewrite H; t)
+   | _ => t; reflexivity
+ end.
+ +
+Ltac solve_proper := unfold Proper; solve_respectful ltac:(idtac).
+ +
+
+ +
+f_equiv is a clone of f_equal that handles setoid equivalences. + For example, if we know that f is a morphism for E1==>E2==>E, + then the goal E (f x y) (f x' y') will be transformed by f_equiv + into the subgoals E1 x x' and E2 y y'. + +
+
+ +
+Ltac f_equiv :=
+ match goal with
+  | |- ?R (?f ?x) (?f' _) =>
+    let T := type of x in
+    let Rx := fresh "R" in
+    evar (Rx : crelation T);
+    let H := fresh in
+    assert (H : (Rx==>R)%signatureT f f');
+    unfold Rx in *; clear Rx; [ f_equiv | apply H; clear H; try reflexivity ]
+  | |- ?R ?f ?f' =>
+    solve [change (Proper R f); eauto with typeclass_instances | reflexivity ]
+  | _ => idtac
+ end.
+ +
+Section Relations.
+  Context {A : Type}.
+ +
+
+ +
+forall_def reifies the dependent product as a definition. +
+
+ +
+  Definition forall_def (P : A -> Type) : Type := forall x : A, P x.
+ +
+
+ +
+Dependent pointwise lifting of a crelation on the range. +
+
+ +
+  Definition forall_relation (P : A -> Type)
+             (sig : forall a, crelation (P a)) : crelation (forall x, P x) :=
+    fun f g => forall a, sig a (f a) (g a).
+ +
+
+ +
+Non-dependent pointwise lifting +
+
+  Definition pointwise_relation {B} (R : crelation B) : crelation (A -> B) :=
+    fun f g => forall a, R (f a) (g a).
+ +
+  Lemma pointwise_pointwise {B} (R : crelation B) :
+    relation_equivalence (pointwise_relation R) (@eq A ==> R).
+ +
+
+ +
+Subcrelations induce a morphism on the identity. +
+
+ +
+  Global Instance subrelation_id_proper `(subrelation A RA RA') : Proper (RA ==> RA') id.
+ +
+
+ +
+The subrelation property goes through products as usual. +
+
+ +
+  Lemma subrelation_respectful `(subl : subrelation A RA' RA, subr : subrelation B RB RB') :
+    subrelation (RA ==> RB) (RA' ==> RB').
+ +
+
+ +
+And of course it is reflexive. +
+
+ +
+  Lemma subrelation_refl R : @subrelation A R R.
+ +
+
+ +
+Proper is itself a covariant morphism for subrelation. + We use an unconvertible premise to avoid looping. + +
+
+ +
+  Lemma subrelation_proper `(mor : Proper A R' m)
+        `(unc : Unconvertible (crelation A) R R')
+        `(sub : subrelation A R' R) : Proper R m.
+ +
+  Global Instance proper_subrelation_proper_arrow :
+    Proper (subrelation ++> eq ==> arrow) (@Proper A).
+ +
+  Global Instance pointwise_subrelation `(sub : subrelation B R R') :
+    subrelation (pointwise_relation R) (pointwise_relation R') | 4.
+ +
+
+ +
+For dependent function types. +
+
+  Lemma forall_subrelation (P : A -> Type) (R S : forall x : A, crelation (P x)) :
+    (forall a, subrelation (R a) (S a)) ->
+    subrelation (forall_relation P R) (forall_relation P S).
+ End Relations.
+Global Typeclasses Opaque respectful pointwise_relation forall_relation.
+Arguments forall_relation {A P}%_type sig%_signatureT _ _.
+Arguments pointwise_relation A%_type {B}%_type R%_signatureT _ _.
+ +
+#[global]
+Hint Unfold Reflexive : core.
+#[global]
+Hint Unfold Symmetric : core.
+#[global]
+Hint Unfold Transitive : core.
+ +
+
+ +
+Resolution with subrelation: favor decomposing products over applying reflexivity + for unconstrained goals. +
+
+Ltac subrelation_tac T U :=
+  (is_ground T ; is_ground U ; class_apply @subrelation_refl) ||
+    class_apply @subrelation_respectful || class_apply @subrelation_refl.
+ +
+#[global]
+Hint Extern 3 (@subrelation _ ?T ?U) => subrelation_tac T U : typeclass_instances.
+ +
+CoInductive apply_subrelation : Prop := do_subrelation.
+ +
+Ltac proper_subrelation :=
+  match goal with
+    [ H : apply_subrelation |- _ ] => clear H ; class_apply @subrelation_proper
+  end.
+ +
+#[global]
+Hint Extern 5 (@Proper _ ?H _) => proper_subrelation : typeclass_instances.
+ +
+
+ +
+Essential subrelation instances for iff, impl and pointwise_relation. +
+
+ +
+#[global]
+Instance iff_impl_subrelation : subrelation iff impl | 2.
+ +
+#[global]
+Instance iff_flip_impl_subrelation : subrelation iff (flip impl) | 2.
+ +
+
+ +
+Essential subrelation instances for iffT and arrow. +
+
+ +
+#[global]
+Instance iffT_arrow_subrelation : subrelation iffT arrow | 2.
+ +
+#[global]
+Instance iffT_flip_arrow_subrelation : subrelation iffT (flip arrow) | 2.
+ +
+
+ +
+We use an extern hint to help unification. +
+
+ +
+#[global]
+Hint Extern 4 (subrelation (@forall_relation ?A ?B ?R) (@forall_relation _ _ ?S)) =>
+  apply (@forall_subrelation A B R S) ; intro : typeclass_instances.
+ +
+Section GenericInstances.
+  Implicit Types A B C : Type.
+ +
+
+ +
+We can build a PER on the Rocq function space if we have PERs on the domain and + codomain. +
+
+ +
+  Program Instance respectful_per `(PER A R, PER B R') : PER (R ==> R').
+ +
+ +
+ +
+
+ +
+The complement of a crelation conserves its proper elements. +
+ + The flip too, actually the flip instance is a bit more general. +
+
+  Program Definition flip_proper
+          `(mor : Proper (A -> B -> C) (RA ==> RB ==> RC) f) :
+    Proper (RB ==> RA ==> RC) (flip f) := _.
+ +
+ +
+
+ +
+Every Transitive crelation gives rise to a binary morphism on impl, + contravariant in the first argument, covariant in the second. +
+
+ +
+ +
+ +
+
+ +
+Proper declarations for partial applications. +
+
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+  Global Program Instance trans_sym_contra_arrow_morphism
+    `(PER A R) {x} : Proper (R --> arrow) (R x) | 3.
+ +
+ +
+  Global Program Instance per_partial_app_type_morphism
+  `(PER A R) {x} : Proper (R ==> iffT) (R x) | 2.
+ +
+ +
+
+ +
+Every Transitive crelation induces a morphism by "pushing" an R x y on the left of an R x z proof to get an R y z goal. +
+
+ +
+ +
+ +
+
+ +
+Every Symmetric and Transitive crelation gives rise to an equivariant morphism. +
+
+ +
+ +
+ +
+  Lemma symmetric_equiv_flip `(Symmetric A R) : relation_equivalence R (flip R).
+ +
+  Global Program Instance compose_proper A B C RA RB RC :
+    Proper ((RB ==> RC) ==> (RA ==> RB) ==> (RA ==> RC)) (@compose A B C).
+ +
+ +
+
+ +
+Rocq functions are morphisms for Leibniz equality, + applied only if really needed. +
+
+ +
+  Global Instance reflexive_eq_dom_reflexive `(Reflexive B R') {A} :
+    Reflexive (@Logic.eq A ==> R').
+ +
+
+ +
+respectful is a morphism for crelation equivalence . +
+
+ +
+  Global Instance respectful_morphism {A B} :
+    Proper (relation_equivalence ++> relation_equivalence ++> relation_equivalence)
+           (@respectful A B).
+ +
+
+ +
+R is Reflexive, hence we can build the needed proof. +
+
+ +
+  Lemma Reflexive_partial_app_morphism `(Proper (A -> B) (R ==> R') m, ProperProxy A R x) :
+    Proper R' (m x).
+ +
+  Class Params {A} (of : A) (arity : nat).
+ +
+  Lemma flip_respectful {A B} (R : crelation A) (R' : crelation B) :
+    relation_equivalence (flip (R ==> R')) (flip R ==> flip R').
+ +
+ +
+
+ +
+Treating flip: can't make them direct instances as we + need at least a flip present in the goal. +
+
+ +
+  Lemma flip1 `(subrelation A R' R) : subrelation (flip (flip R')) R.
+ +
+  Lemma flip2 `(subrelation A R R') : subrelation R (flip (flip R')).
+ +
+
+ +
+That's if and only if +
+
+ +
+  Lemma eq_subrelation `(Reflexive A R) : subrelation (@eq A) R.
+ +
+
+ +
+Once we have normalized, we will apply this instance to simplify the problem. +
+
+ +
+  Definition proper_flip_proper `(mor : Proper A R m) : Proper (flip R) m := mor.
+ +
+
+ +
+Every reflexive crelation gives rise to a morphism, + only for immediately solving goals without variables. +
+
+ +
+  Lemma reflexive_proper `{Reflexive A R} (x : A) : Proper R x.
+ +
+  Lemma proper_eq {A} (x : A) : Proper (@eq A) x.
+ +
+End GenericInstances.
+ +
+Class PartialApplication.
+ +
+CoInductive normalization_done : Prop := did_normalization.
+ +
+Ltac partial_application_tactic :=
+  let rec do_partial_apps H m cont :=
+    match m with
+      | ?m' ?x => class_apply @Reflexive_partial_app_morphism ;
+        [(do_partial_apps H m' ltac:(idtac))|clear H]
+      | _ => cont
+    end
+  in
+  let rec do_partial H ar m :=
+    match ar with
+      | 0%nat => do_partial_apps H m ltac:(fail 1)
+      | S ?n' =>
+        match m with
+          ?m' ?x => do_partial H n' m'
+        end
+    end
+  in
+  let params m sk fk :=
+    (let m' := fresh in head_of_constr m' m ;
+     let n := fresh in evar (n:nat) ;
+     let v := eval compute in n in clear n ;
+      let H := fresh in
+        assert(H:Params m' v) by typeclasses eauto ;
+          let v' := eval compute in v in subst m';
+            (sk H v' || fail 1))
+    || fk
+  in
+  let on_morphism m cont :=
+    params m ltac:(fun H n => do_partial H n m)
+      ltac:(cont)
+  in
+  match goal with
+    | [ _ : normalization_done |- _ ] => fail 1
+    | [ _ : @Params _ _ _ |- _ ] => fail 1
+    | [ |- @Proper ?T _ (?m ?x) ] =>
+      match goal with
+        | [ H : PartialApplication |- _ ] =>
+          class_apply @Reflexive_partial_app_morphism; [|clear H]
+        | _ => on_morphism (m x)
+          ltac:(class_apply @Reflexive_partial_app_morphism)
+      end
+  end.
+ +
+
+ +
+Bootstrap !!! +
+
+ +
+#[global]
+Instance proper_proper {A} : Proper (relation_equivalence ==> eq ==> iffT) (@Proper A).
+ +
+Ltac proper_reflexive :=
+  match goal with
+    | [ _ : normalization_done |- _ ] => fail 1
+    | _ => class_apply proper_eq || class_apply @reflexive_proper
+  end.
+ +
+#[global]
+Hint Extern 1 (subrelation (flip _) _) => class_apply @flip1 : typeclass_instances.
+#[global]
+Hint Extern 1 (subrelation _ (flip _)) => class_apply @flip2 : typeclass_instances.
+ +
+#[global]
+Hint Extern 1 (Proper _ (flip _)) => apply @flip_proper
+  : typeclass_instances.
+#[global]
+Hint Extern 2 (@Proper _ (flip _) _) => class_apply @proper_flip_proper
+  : typeclass_instances.
+#[global]
+Hint Extern 4 (@Proper _ _ _) => partial_application_tactic
+  : typeclass_instances.
+#[global]
+Hint Extern 7 (@Proper _ _ _) => proper_reflexive
+  : typeclass_instances.
+ +
+
+ +
+Special-purpose class to do normalization of signatures w.r.t. flip. +
+
+ +
+Section Normalize.
+  Context (A : Type).
+ +
+  Class Normalizes (m : crelation A) (m' : crelation A) :=
+    normalizes : relation_equivalence m m'.
+ +
+
+ +
+Current strategy: add flip everywhere and reduce using subrelation + afterwards. +
+
+ +
+  Lemma proper_normalizes_proper `(Normalizes R0 R1, Proper A R1 m) : Proper R0 m.
+ +
+  Lemma flip_atom R : Normalizes R (flip (flip R)).
+ +
+End Normalize.
+ +
+Lemma flip_arrow `(NA : Normalizes A R (flip R'''), NB : Normalizes B R' (flip R'')) :
+  Normalizes (A -> B) (R ==> R') (flip (R''' ==> R'')%signatureT).
+ +
+Ltac normalizes :=
+  match goal with
+    | [ |- Normalizes _ (respectful _ _) _ ] => class_apply @flip_arrow
+    | _ => class_apply @flip_atom
+  end.
+ +
+Ltac proper_normalization :=
+  match goal with
+    | [ _ : normalization_done |- _ ] => fail 1
+    | [ _ : apply_subrelation |- @Proper _ ?R _ ] =>
+      let H := fresh "H" in
+      set(H:=did_normalization) ; class_apply @proper_normalizes_proper
+  end.
+ +
+#[global]
+Hint Extern 1 (Normalizes _ _ _) => normalizes : typeclass_instances.
+#[global]
+Hint Extern 6 (@Proper _ _ _) => proper_normalization
+  : typeclass_instances.
+ +
+
+ +
+When the crelation on the domain is symmetric, we can + flip the crelation on the codomain. Same for binary functions. +
+
+ +
+Lemma proper_sym_flip :
+ forall `(Symmetric A R1)`(Proper (A->B) (R1==>R2) f),
+ Proper (R1==>flip R2) f.
+ +
+Lemma proper_sym_flip_2 :
+ forall `(Symmetric A R1)`(Symmetric B R2)`(Proper (A->B->C) (R1==>R2==>R3) f),
+ Proper (R1==>R2==>flip R3) f.
+ +
+
+ +
+When the crelation on the domain is symmetric, a predicate is + compatible with iff as soon as it is compatible with impl. + Same with a binary crelation. +
+
+ +
+Lemma proper_sym_impl_iff : forall `(Symmetric A R)`(Proper _ (R==>impl) f),
+ Proper (R==>iff) f.
+ +
+Lemma proper_sym_arrow_iffT : forall `(Symmetric A R)`(Proper _ (R==>arrow) f),
+ Proper (R==>iffT) f.
+ +
+Lemma proper_sym_impl_iff_2 :
+ forall `(Symmetric A R)`(Symmetric B R')`(Proper _ (R==>R'==>impl) f),
+ Proper (R==>R'==>iff) f.
+ +
+Lemma proper_sym_arrow_iffT_2 :
+ forall `(Symmetric A R)`(Symmetric B R')`(Proper _ (R==>R'==>arrow) f),
+ Proper (R==>R'==>iffT) f.
+ +
+
+ +
+A PartialOrder is compatible with its underlying equivalence. +
+
+Require Import Relation_Definitions.
+ +
+#[global]
+Instance PartialOrder_proper_type `(PartialOrder A eqA R) :
+  Proper (eqA==>eqA==>iffT) R.
+ +
+
+ +
+From a PartialOrder to the corresponding StrictOrder: + lt = le /\ ~eq. + If the order is total, we could also say gt = ~le. +
+
+ +
+Lemma PartialOrder_StrictOrder `(PartialOrder A eqA R) :
+  StrictOrder (relation_conjunction R (complement eqA)).
+ +
+
+ +
+From a StrictOrder to the corresponding PartialOrder: + le = lt \/ eq. + If the order is total, we could also say ge = ~lt. +
+
+ +
+Lemma StrictOrder_PreOrder
+ `(Equivalence A eqA, StrictOrder A R, Proper _ (eqA==>eqA==>iffT) R) :
+ PreOrder (relation_disjunction R eqA).
+ +
+#[global]
+Hint Extern 4 (PreOrder (relation_disjunction _ _)) =>
+  class_apply StrictOrder_PreOrder : typeclass_instances.
+ +
+Lemma StrictOrder_PartialOrder
+  `(Equivalence A eqA, StrictOrder A R, Proper _ (eqA==>eqA==>iffT) R) :
+  PartialOrder eqA (relation_disjunction R eqA).
+ +
+#[global]
+Hint Extern 4 (StrictOrder (relation_conjunction _ _)) =>
+  class_apply PartialOrder_StrictOrder : typeclass_instances.
+ +
+#[global]
+Hint Extern 4 (PartialOrder _ (relation_disjunction _ _)) =>
+  class_apply StrictOrder_PartialOrder : typeclass_instances.
+ +
+ +
+Register forall_relation as rewrite.type.forall_relation.
+Register pointwise_relation as rewrite.type.pointwise_relation.
+Register respectful as rewrite.type.respectful.
+Register forall_def as rewrite.type.forall_def.
+Register do_subrelation as rewrite.type.do_subrelation.
+Register apply_subrelation as rewrite.type.apply_subrelation.
+Register Proper as rewrite.type.Proper.
+Register ProperProxy as rewrite.type.ProperProxy.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Classes.CRelationClasses.html b/master/corelib/Corelib.Classes.CRelationClasses.html new file mode 100644 index 0000000000..c68009f1fb --- /dev/null +++ b/master/corelib/Corelib.Classes.CRelationClasses.html @@ -0,0 +1,706 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Classes.CRelationClasses

+ +
+ +
+
+ +
+

Typeclass-based relations, tactics and standard instances

+ + +
+ + This is the basic theory needed to formalize morphisms and setoids. + +
+ + Author: Matthieu Sozeau + Institution: LRI, CNRS UMR 8623 - University Paris Sud + +
+
+ +
+Require Export Corelib.Classes.Init.
+Require Import Corelib.Program.Basics.
+Require Import Corelib.Program.Tactics.
+ +
+Generalizable Variables A B C D R S T U l eqA eqB eqC eqD.
+ +
+ +
+Definition crelation (A : Type) := A -> A -> Type.
+ +
+Definition arrow (A B : Type) := A -> B.
+ +
+Definition flip {A B C : Type} (f : A -> B -> C) := fun x y => f y x.
+ +
+Definition iffT (A B : Type) := ((A -> B) * (B -> A))%type.
+ +
+Global Typeclasses Opaque flip arrow iffT.
+ +
+
+ +
+We allow to unfold the crelation definition while doing morphism search. +
+
+ +
+Section Defs.
+  Context {A : Type}.
+ +
+
+ +
+We rebind crelational properties in separate classes to be able to overload each proof. +
+
+ +
+  Class Reflexive (R : crelation A) :=
+    reflexivity : forall x : A, R x x.
+ +
+  Definition complement (R : crelation A) : crelation A :=
+    fun x y => R x y -> False.
+ +
+
+ +
+Opaque for proof-search. +
+
+  Typeclasses Opaque complement iffT.
+ +
+
+ +
+These are convertible. +
+
+  Lemma complement_inverse R : complement (flip R) = flip (complement R).
+ +
+  Class Irreflexive (R : crelation A) :=
+    irreflexivity : Reflexive (complement R).
+ +
+  Class Symmetric (R : crelation A) :=
+    symmetry : forall {x y}, R x y -> R y x.
+ +
+  Class Asymmetric (R : crelation A) :=
+    asymmetry : forall {x y}, R x y -> (complement R y x : Type).
+ +
+  Class Transitive (R : crelation A) :=
+    transitivity : forall {x y z}, R x y -> R y z -> R x z.
+ +
+
+ +
+Various combinations of reflexivity, symmetry and transitivity. +
+ + A PreOrder is both Reflexive and Transitive. +
+
+ +
+  Class PreOrder (R : crelation A) := {
+    #[global] PreOrder_Reflexive :: Reflexive R | 2 ;
+    #[global] PreOrder_Transitive :: Transitive R | 2 }.
+ +
+
+ +
+A StrictOrder is both Irreflexive and Transitive. +
+
+ +
+  Class StrictOrder (R : crelation A) := {
+    #[global] StrictOrder_Irreflexive :: Irreflexive R ;
+    #[global] StrictOrder_Transitive :: Transitive R }.
+ +
+
+ +
+By definition, a strict order is also asymmetric +
+
+  Global Instance StrictOrder_Asymmetric `(StrictOrder R) : Asymmetric R.
+ +
+
+ +
+A partial equivalence crelation is Symmetric and Transitive. +
+
+ +
+  Class PER (R : crelation A) := {
+    #[global] PER_Symmetric :: Symmetric R | 3 ;
+    #[global] PER_Transitive :: Transitive R | 3 }.
+ +
+
+ +
+Equivalence crelations. +
+
+ +
+  Class Equivalence (R : crelation A) := {
+    #[global] Equivalence_Reflexive :: Reflexive R ;
+    #[global] Equivalence_Symmetric :: Symmetric R ;
+    #[global] Equivalence_Transitive :: Transitive R }.
+ +
+
+ +
+An Equivalence is a PER plus reflexivity. +
+
+ +
+  Global Instance Equivalence_PER {R} `(Equivalence R) : PER R | 10 :=
+    { PER_Symmetric := Equivalence_Symmetric ;
+      PER_Transitive := Equivalence_Transitive }.
+ +
+
+ +
+We can now define antisymmetry w.r.t. an equivalence crelation on the carrier. +
+
+ +
+  Class Antisymmetric eqA `{equ : Equivalence eqA} (R : crelation A) :=
+    antisymmetry : forall {x y}, R x y -> R y x -> eqA x y.
+ +
+  Class subrelation (R R' : crelation A) :=
+    is_subrelation : forall {x y}, R x y -> R' x y.
+ +
+
+ +
+Any symmetric crelation is equal to its inverse. +
+
+ +
+  Lemma subrelation_symmetric R `(Symmetric R) : subrelation (flip R) R.
+ +
+  Section flip.
+ +
+    Lemma flip_Reflexive `{Reflexive R} : Reflexive (flip R).
+ +
+    Program Definition flip_Irreflexive `(Irreflexive R) : Irreflexive (flip R) :=
+      irreflexivity (R:=R).
+ +
+    Program Definition flip_Symmetric `(Symmetric R) : Symmetric (flip R) :=
+      fun x y H => symmetry (R:=R) H.
+ +
+    Program Definition flip_Asymmetric `(Asymmetric R) : Asymmetric (flip R) :=
+      fun x y H H' => asymmetry (R:=R) H H'.
+ +
+    Program Definition flip_Transitive `(Transitive R) : Transitive (flip R) :=
+      fun x y z H H' => transitivity (R:=R) H' H.
+ +
+    Program Lemma flip_Antisymmetric `(Antisymmetric eqA R) :
+      Antisymmetric eqA (flip R).
+ +
+
+ +
+Inversing the larger structures +
+
+ +
+    Lemma flip_PreOrder `(PreOrder R) : PreOrder (flip R).
+ +
+    Lemma flip_StrictOrder `(StrictOrder R) : StrictOrder (flip R).
+ +
+    Lemma flip_PER `(PER R) : PER (flip R).
+ +
+    Lemma flip_Equivalence `(Equivalence R) : Equivalence (flip R).
+ +
+  End flip.
+ +
+  Section complement.
+ +
+    Lemma complement_Irreflexive `(Reflexive R)
+      : Irreflexive (complement R).
+ +
+    Lemma complement_Symmetric `(Symmetric R) : Symmetric (complement R).
+   End complement.
+ +
+
+ +
+Rewrite crelation on a given support: declares a crelation as a rewrite + crelation for use by the generalized rewriting tactic. + It helps choosing if a rewrite should be handled + by the generalized or the regular rewriting tactic using leibniz equality. + Users can declare an RewriteRelation A RA anywhere to declare default + crelations. This is also done automatically by the Declare Relation A RA + commands. +
+
+ +
+  Class RewriteRelation (RA : crelation A).
+ +
+
+ +
+Any Equivalence declared in the context is automatically considered + a rewrite crelation. +
+
+ +
+  Global Instance equivalence_rewrite_crelation `(Equivalence eqA) : RewriteRelation eqA.
+  Defined.
+ +
+
+ +
+Leibniz equality. +
+
+  Section Leibniz.
+    Global Instance eq_Reflexive : Reflexive (@eq A) := @eq_refl A.
+    Global Instance eq_Symmetric : Symmetric (@eq A) := @eq_sym A.
+    Global Instance eq_Transitive : Transitive (@eq A) := @eq_trans A.
+ +
+
+ +
+Leibinz equality eq is an equivalence crelation. + The instance has low priority as it is always applicable + if only the type is constrained. +
+
+ +
+    Global Program Instance eq_equivalence : Equivalence (@eq A) | 10.
+  End Leibniz.
+ +
+End Defs.
+ +
+
+ +
+Default rewrite crelations handled by setoid_rewrite. +
+
+#[global]
+Instance: RewriteRelation impl.
+Defined.
+ +
+#[global]
+Instance: RewriteRelation iff.
+Defined.
+ +
+
+ +
+Hints to drive the typeclass resolution avoiding loops + due to the use of full unification. +
+
+#[global]
+Hint Extern 1 (Reflexive (complement _)) => class_apply @irreflexivity : typeclass_instances.
+#[global]
+Hint Extern 3 (Symmetric (complement _)) => class_apply complement_Symmetric : typeclass_instances.
+#[global]
+Hint Extern 3 (Irreflexive (complement _)) => class_apply complement_Irreflexive : typeclass_instances.
+ +
+#[global]
+Hint Extern 3 (Reflexive (flip _)) => apply flip_Reflexive : typeclass_instances.
+#[global]
+Hint Extern 3 (Irreflexive (flip _)) => class_apply flip_Irreflexive : typeclass_instances.
+#[global]
+Hint Extern 3 (Symmetric (flip _)) => class_apply flip_Symmetric : typeclass_instances.
+#[global]
+Hint Extern 3 (Asymmetric (flip _)) => class_apply flip_Asymmetric : typeclass_instances.
+#[global]
+Hint Extern 3 (Antisymmetric (flip _)) => class_apply flip_Antisymmetric : typeclass_instances.
+#[global]
+Hint Extern 3 (Transitive (flip _)) => class_apply flip_Transitive : typeclass_instances.
+#[global]
+Hint Extern 3 (StrictOrder (flip _)) => class_apply flip_StrictOrder : typeclass_instances.
+#[global]
+Hint Extern 3 (PreOrder (flip _)) => class_apply flip_PreOrder : typeclass_instances.
+ +
+#[global]
+Hint Extern 4 (subrelation (flip _) _) =>
+  class_apply @subrelation_symmetric : typeclass_instances.
+ +
+#[global]
+Hint Resolve irreflexivity : ord.
+ +
+Unset Implicit Arguments.
+ +
+Ltac solve_crelation :=
+  match goal with
+  | [ |- ?R ?x ?x ] => reflexivity
+  | [ H : ?R ?x ?y |- ?R ?y ?x ] => symmetry ; exact H
+  end.
+ +
+#[global]
+Hint Extern 4 => solve_crelation : crelations.
+ +
+
+ +
+We can already dualize all these properties. +
+ +

Standard instances.

+ +
+
+ +
+Ltac reduce_hyp H :=
+  match type of H with
+    | context [ _ <-> _ ] => fail 1
+    | _ => red in H ; try reduce_hyp H
+  end.
+ +
+Ltac reduce_goal :=
+  match goal with
+    | [ |- _ <-> _ ] => fail 1
+    | _ => red ; intros ; try reduce_goal
+  end.
+ +
+Tactic Notation "reduce" "in" hyp(Hid) := reduce_hyp Hid.
+ +
+Ltac reduce := reduce_goal.
+ +
+Tactic Notation "apply" "*" constr(t) :=
+  first [ refine t | refine (t _) | refine (t _ _) | refine (t _ _ _) | refine (t _ _ _ _) |
+    refine (t _ _ _ _ _) | refine (t _ _ _ _ _ _) | refine (t _ _ _ _ _ _ _) ].
+ +
+Ltac simpl_crelation :=
+  unfold flip, impl, arrow ; try reduce ; program_simpl ;
+    try ( solve [ dintuition auto with crelations ]).
+ +
+Local Obligation Tactic := simpl_crelation.
+ +
+
+ +
+Logical implication. +
+
+ +
+#[global]
+Program Instance impl_Reflexive : Reflexive impl.
+#[global]
+Program Instance impl_Transitive : Transitive impl.
+ +
+
+ +
+Logical equivalence. +
+
+ +
+#[global]
+Instance iff_Reflexive : Reflexive iff := iff_refl.
+#[global]
+Instance iff_Symmetric : Symmetric iff := iff_sym.
+#[global]
+Instance iff_Transitive : Transitive iff := iff_trans.
+ +
+
+ +
+Logical equivalence iff is an equivalence crelation. +
+
+ +
+#[global]
+Program Instance iff_equivalence : Equivalence iff.
+#[global]
+Program Instance arrow_Reflexive : Reflexive arrow.
+#[global]
+Program Instance arrow_Transitive : Transitive arrow.
+ +
+#[global]
+Instance iffT_Reflexive : Reflexive iffT.
+ #[global]
+Instance iffT_Symmetric : Symmetric iffT.
+ #[global]
+Instance iffT_Transitive : Transitive iffT.
+ +
+
+ +
+We now develop a generalization of results on crelations for arbitrary predicates. + The resulting theory can be applied to homogeneous binary crelations but also to + arbitrary n-ary predicates. +
+
+ +
+Local Open Scope list_scope.
+ +
+
+ +
+A compact representation of non-dependent arities, with the codomain singled-out. +
+ + We define the various operations which define the algebra on binary crelations +
+
+Section Binary.
+  Context {A : Type}.
+ +
+  Definition relation_equivalence : crelation (crelation A) :=
+    fun R R' => forall x y, iffT (R x y) (R' x y).
+ +
+  Global Instance: RewriteRelation relation_equivalence.
+  Defined.
+ +
+  Definition relation_conjunction (R : crelation A) (R' : crelation A) : crelation A :=
+    fun x y => prod (R x y) (R' x y).
+ +
+  Definition relation_disjunction (R : crelation A) (R' : crelation A) : crelation A :=
+    fun x y => sum (R x y) (R' x y).
+ +
+
+ +
+Relation equivalence is an equivalence, and subrelation defines a partial order. +
+
+ +
+  Global Instance relation_equivalence_equivalence :
+    Equivalence relation_equivalence.
+ +
+  Global Instance relation_implication_preorder : PreOrder (@subrelation A).
+ +
+
+ +
+

Partial Order.

+ + A partial order is a preorder which is additionally antisymmetric. + We give an equivalent definition, up-to an equivalence crelation + on the carrier. +
+
+ +
+  Class PartialOrder eqA `{equ : Equivalence A eqA} R `{preo : PreOrder A R} :=
+    partial_order_equivalence : relation_equivalence eqA (relation_conjunction R (flip R)).
+ +
+
+ +
+The equivalence proof is sufficient for proving that R must be a + morphism for equivalence (see Morphisms). It is also sufficient to + show that R is antisymmetric w.r.t. eqA +
+
+ +
+  Global Instance partial_order_antisym `(PartialOrder eqA R) : Antisymmetric eqA R.
+ +
+  Lemma PartialOrder_inverse `(PartialOrder eqA R) : PartialOrder eqA (flip R).
+End Binary.
+ +
+#[global]
+Hint Extern 3 (PartialOrder (flip _)) => class_apply PartialOrder_inverse : typeclass_instances.
+ +
+
+ +
+The partial order defined by subrelation and crelation equivalence. +
+
+ +
+ +
+ +
+Global Typeclasses Opaque relation_equivalence.
+ +
+ +
+Register arrow as rewrite.type.arrow.
+Register flip as rewrite.type.flip.
+Register crelation as rewrite.type.relation.
+Register subrelation as rewrite.type.subrelation.
+Register Reflexive as rewrite.type.Reflexive.
+Register reflexivity as rewrite.type.reflexivity.
+Register Symmetric as rewrite.type.Symmetric.
+Register symmetry as rewrite.type.symmetry.
+Register Transitive as rewrite.type.Transitive.
+Register transitivity as rewrite.type.transitivity.
+Register RewriteRelation as rewrite.type.RewriteRelation.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Classes.Equivalence.html b/master/corelib/Corelib.Classes.Equivalence.html new file mode 100644 index 0000000000..914d17c248 --- /dev/null +++ b/master/corelib/Corelib.Classes.Equivalence.html @@ -0,0 +1,311 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Classes.Equivalence

+ +
+ +
+
+ +
+

Typeclass-based setoids. Definitions on Equivalence.

+ + +
+ + Author: Matthieu Sozeau + Institution: LRI, CNRS UMR 8623 - University Paris Sud + +
+
+ +
+Require Import Corelib.Program.Basics.
+Require Import Corelib.Program.Tactics.
+ +
+Require Import Corelib.Classes.Init.
+Require Import Relation_Definitions.
+Require Export Corelib.Classes.RelationClasses.
+Require Import Corelib.Classes.Morphisms.
+ +
+Set Implicit Arguments.
+ +
+Generalizable Variables A R eqA B S eqB.
+Local Obligation Tactic := try solve [simpl_relation].
+ +
+Local Open Scope signature_scope.
+ +
+Definition equiv `{Equivalence A R} : relation A := R.
+ +
+
+ +
+Overloaded notations for setoid equivalence and inequivalence. + Not to be confused with eq and =. +
+
+ +
+Declare Scope equiv_scope.
+ +
+Notation " x === y " := (equiv x y) (at level 70, no associativity) : equiv_scope.
+ +
+Notation " x =/= y " := (complement equiv x y) (at level 70, no associativity) : equiv_scope.
+ +
+Local Open Scope equiv_scope.
+ +
+
+ +
+Overloading for PER. +
+
+ +
+Definition pequiv `{PER A R} : relation A := R.
+ +
+
+ +
+Overloaded notation for partial equivalence. +
+
+ +
+Infix "=~=" := pequiv (at level 70, no associativity) : equiv_scope.
+ +
+
+ +
+Shortcuts to make proof search easier. +
+
+ +
+#[global]
+ Program Instance equiv_reflexive `(sa : Equivalence A) : Reflexive equiv | 1.
+ +
+#[global]
+Program Instance equiv_symmetric `(sa : Equivalence A) : Symmetric equiv | 1.
+ +
+#[global]
+Program Instance equiv_transitive `(sa : Equivalence A) : Transitive equiv | 1.
+ +
+ +
+Arguments equiv_symmetric {A R} sa x y : rename.
+Arguments equiv_transitive {A R} sa x y z : rename.
+ +
+
+ +
+Use the substitute command which substitutes an equivalence in every hypothesis. +
+
+ +
+Ltac setoid_subst H :=
+  match type of H with
+    ?x === ?y => substitute H ; clear H x
+  end.
+ +
+Ltac setoid_subst_nofail :=
+  match goal with
+    | [ H : ?x === ?y |- _ ] => setoid_subst H ; setoid_subst_nofail
+    | _ => idtac
+  end.
+ +
+
+ +
+subst* will try its best at substituting every equality in the goal. +
+
+ +
+Tactic Notation "subst" "*" := subst_no_fail ; setoid_subst_nofail.
+ +
+
+ +
+Simplify the goal w.r.t. equivalence. +
+
+ +
+Ltac equiv_simplify_one :=
+  match goal with
+    | [ H : ?x === ?x |- _ ] => clear H
+    | [ H : ?x === ?y |- _ ] => setoid_subst H
+    | [ |- ?x =/= ?y ] => let name:=fresh "Hneq" in intro name
+    | [ |- ~ ?x === ?y ] => let name:=fresh "Hneq" in intro name
+  end.
+ +
+Ltac equiv_simplify := repeat equiv_simplify_one.
+ +
+
+ +
+"reify" relations which are equivalences to applications of the overloaded equiv method + for easy recognition in tactics. +
+
+ +
+Ltac equivify_tac :=
+  match goal with
+    | [ s : Equivalence ?A ?R, H : ?R ?x ?y |- _ ] => change R with (@equiv A R s) in H
+    | [ s : Equivalence ?A ?R |- context C [ ?R ?x ?y ] ] => change (R x y) with (@equiv A R s x y)
+  end.
+ +
+Ltac equivify := repeat equivify_tac.
+ +
+Section Respecting.
+ +
+
+ +
+Here we build an equivalence instance for functions which relates respectful ones only, + we do not export it. +
+
+ +
+  Definition respecting `(eqa : Equivalence A (R : relation A),
+                          eqb : Equivalence B (R' : relation B)) : Type :=
+    { morph : A -> B | respectful R R' morph morph }.
+ +
+  Program Instance respecting_equiv `(eqa : Equivalence A R, eqb : Equivalence B R') :
+    Equivalence (fun (f g : respecting eqa eqb) =>
+                   forall (x y : A), R x y -> R' (proj1_sig f x) (proj1_sig g y)).
+ +
+  Solve Obligations with unfold respecting in * ; simpl_relation ; program_simpl.
+ +
+ +
+End Respecting.
+ +
+
+ +
+The default equivalence on function spaces, with higher priority than eq. +
+
+ +
+#[global]
+Instance pointwise_reflexive {A} `(reflb : Reflexive B eqB) :
+  Reflexive (pointwise_relation A eqB) | 9.
+ #[global]
+Instance pointwise_symmetric {A} `(symb : Symmetric B eqB) :
+  Symmetric (pointwise_relation A eqB) | 9.
+ #[global]
+Instance pointwise_transitive {A} `(transb : Transitive B eqB) :
+  Transitive (pointwise_relation A eqB) | 9.
+ #[global]
+Instance pointwise_equivalence {A} `(eqb : Equivalence B eqB) :
+  Equivalence (pointwise_relation A eqB) | 9.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Classes.Init.html b/master/corelib/Corelib.Classes.Init.html new file mode 100644 index 0000000000..b934d830fe --- /dev/null +++ b/master/corelib/Corelib.Classes.Init.html @@ -0,0 +1,139 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Classes.Init

+ +
+ +
+
+ +
+

Initialization code for typeclasses, setting up the default tactic

+ + for instance search. + +
+ + Author: Matthieu Sozeau + Institution: LRI, CNRS UMR 8623 - University Paris Sud + +
+ + Hints for the proof search: these combinators should be considered rigid. +
+
+ +
+Require Import Corelib.Program.Basics.
+ +
+Global Typeclasses Opaque id const flip compose arrow impl iff not all.
+ +
+
+ +
+Apply using the same opacity information as typeclass proof search. +
+
+ +
+Ltac class_apply c := autoapply c with typeclass_instances.
+ +
+
+ +
+The unconvertible typeclass, to test that two objects of the same type are + actually different. +
+
+#[universes(polymorphic)]
+Class Unconvertible (A : Type) (a b : A) := unconvertible : unit.
+ +
+Ltac unconvertible :=
+  match goal with
+    | |- @Unconvertible _ ?x ?y => unify x y with typeclass_instances ; fail 1 "Convertible"
+    | |- _ => exact tt
+  end.
+ +
+#[global]
+Hint Extern 0 (@Unconvertible _ _ _) => unconvertible : typeclass_instances.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Classes.Morphisms.html b/master/corelib/Corelib.Classes.Morphisms.html new file mode 100644 index 0000000000..968215951b --- /dev/null +++ b/master/corelib/Corelib.Classes.Morphisms.html @@ -0,0 +1,1056 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Classes.Morphisms

+ +
+ +
+
+ +
+

Typeclass-based morphism definition and standard, minimal instances

+ + +
+ + Author: Matthieu Sozeau + Institution: LRI, CNRS UMR 8623 - University Paris Sud + +
+
+ +
+Require Import Corelib.Program.Basics.
+Require Import Corelib.Program.Tactics.
+Require Import Corelib.Relations.Relation_Definitions.
+Require Export Corelib.Classes.RelationClasses.
+ +
+Generalizable Variables A eqA B C D R RA RB RC m f x y.
+Local Obligation Tactic := try solve [ simpl_relation ].
+ +
+
+ +
+

Morphisms.

+ + +
+ + We now turn to the definition of Proper and declare standard instances. + These will be used by the setoid_rewrite tactic later. +
+ + A morphism for a relation R is a proper element of the relation. + The relation R will be instantiated by respectful and A by an arrow + type for usual morphisms. +
+
+Section Proper.
+  Let U := Type.
+  Context {A B : U}.
+ +
+  Class Proper (R : relation A) (m : A) : Prop :=
+    proper_prf : R m m.
+ +
+
+ +
+Every element in the carrier of a reflexive relation is a morphism + for this relation. We use a proxy class for this case which is used + internally to discharge reflexivity constraints. The Reflexive + instance will almost always be used, but it won't apply in general to + any kind of Proper (A -> B) _ _ goal, making proof-search much + slower. A cleaner solution would be to be able to set different + priorities in different hint bases and select a particular hint + database for resolution of a type class constraint. +
+
+ +
+  Class ProperProxy (R : relation A) (m : A) : Prop :=
+    proper_proxy : R m m.
+ +
+  Class ReflexiveProxy (R : relation A) : Prop :=
+    reflexive_proxy : forall x, R x x.
+ +
+  Lemma eq_proper_proxy (x : A) : ProperProxy (@eq A) x.
+ +
+
+ +
+Every reflexive relation gives rise to a morphism. + If the relation is not determined (is an evar), + then we restrict the solutions to predefined ones (equality, or iff on Prop), + using ground instances. If the relation is determined then + ReflexiveProxy calls back to Reflexive. +
+
+ +
+  Lemma reflexive_proper `{ReflexiveProxy R} (x : A) : Proper R x.
+ +
+  Lemma reflexive_proper_proxy `(ReflexiveProxy R) (x : A) : ProperProxy R x.
+ +
+  Lemma proper_proper_proxy x `(Proper R x) : ProperProxy R x.
+ +
+  Lemma reflexive_reflexive_proxy `(Reflexive A R) : ReflexiveProxy R.
+ +
+
+ +
+Respectful morphisms. +
+ + The fully dependent version, not used yet. +
+
+ +
+  Definition respectful_hetero
+  (A B : Type)
+  (C : A -> Type) (D : B -> Type)
+  (R : A -> B -> Prop)
+  (R' : forall (x : A) (y : B), C x -> D y -> Prop) :
+    (forall x : A, C x) -> (forall x : B, D x) -> Prop :=
+    fun f g => forall x y, R x y -> R' x y (f x) (g y).
+ +
+
+ +
+The non-dependent version is an instance where we forget dependencies. +
+
+ +
+  Definition respectful (R : relation A) (R' : relation B) : relation (A -> B) :=
+    Eval compute in @respectful_hetero A A (fun _ => B) (fun _ => B) R (fun _ _ => R').
+ +
+End Proper.
+ +
+
+ +
+Non-dependent pointwise lifting +
+
+Definition pointwise_relation A {B} (R : relation B) : relation (A -> B) :=
+  fun f g => forall a, R (f a) (g a).
+ +
+
+ +
+We let Rocq infer these relations when a default relation should + be found on the function space. +
+
+Lemma rewrite_relation_pointwise {A B R} `{RewriteRelation B R}:
+  RewriteRelation (@pointwise_relation A B R).
+ +
+Lemma rewrite_relation_eq_dom {A B R} `{RewriteRelation B R}:
+  RewriteRelation (respectful (@Logic.eq A) R).
+ +
+
+ +
+Pointwise reflexive +
+
+ +
+Ltac rewrite_relation_fun :=
+  
+  class_apply @rewrite_relation_pointwise ||
+  
+  class_apply @rewrite_relation_eq_dom.
+ +
+Global Hint Extern 2 (@RewriteRelation (_ -> _) _) =>
+  rewrite_relation_fun : typeclass_instances.
+ +
+Lemma eq_rewrite_relation {A} : RewriteRelation (@eq A).
+ +
+Ltac eq_rewrite_relation A :=
+  solve [unshelve class_apply @eq_rewrite_relation].
+ +
+Global Hint Extern 100 (@RewriteRelation ?A _) => eq_rewrite_relation A : typeclass_instances.
+ +
+
+ +
+We favor the use of Leibniz equality or a declared reflexive relation + when resolving ProperProxy, otherwise, if the relation is given (not an evar), + we fall back to Proper. +
+
+#[global]
+Hint Extern 1 (ProperProxy _ _) =>
+  class_apply @eq_proper_proxy || class_apply @reflexive_proper_proxy : typeclass_instances.
+ +
+#[global]
+Hint Extern 2 (ProperProxy ?R _) =>
+  not_evar R; class_apply @proper_proper_proxy : typeclass_instances.
+ +
+Ltac find_rewrite_relation A R kont :=
+  assert (@RewriteRelation A R); [solve [unshelve typeclasses eauto]|]; kont R.
+ +
+
+ +
+This hint helps infer "generic" reflexive relations, based only on the type of the + carrier, when the relation is only partially defined (contains evars). +
+
+ +
+Ltac reflexive_proxy_tac A R :=
+  tryif has_evar R then
+    
+    find_rewrite_relation A R ltac:(fun RA =>
+      class_apply (@reflexive_reflexive_proxy A RA))
+      
+  else
+    
+    class_apply @reflexive_reflexive_proxy.
+ +
+#[global]
+Hint Extern 1 (@ReflexiveProxy ?A ?R) => reflexive_proxy_tac A R : typeclass_instances.
+ +
+
+ +
+Notations reminiscent of the old syntax for declaring morphisms. +
+
+Declare Scope signature_scope.
+Delimit Scope signature_scope with signature.
+ +
+Module ProperNotations.
+ +
+  Notation " R ++> R' " := (@respectful _ _ (R%signature) (R'%signature))
+    (right associativity, at level 55) : signature_scope.
+ +
+  Notation " R ==> R' " := (@respectful _ _ (R%signature) (R'%signature))
+    (right associativity, at level 55) : signature_scope.
+ +
+  Notation " R --> R' " := (@respectful _ _ (flip (R%signature)) (R'%signature))
+    (right associativity, at level 55) : signature_scope.
+ +
+End ProperNotations.
+ +
+Arguments Proper {A}%_type R%_signature m.
+Arguments respectful {A B}%_type (R R')%_signature _ _.
+ +
+Export ProperNotations.
+ +
+Local Open Scope signature_scope.
+ +
+
+ +
+solve_proper try to solve the goal Proper (?==> ... ==>?) f + by repeated introductions and setoid rewrites. It should work + fine when f is a combination of already known morphisms and + quantifiers. +
+
+ +
+Ltac solve_respectful t :=
+ match goal with
+   | |- respectful _ _ _ _ =>
+     let H := fresh "H" in
+     intros ? ? H; solve_respectful ltac:(setoid_rewrite H; t)
+   | _ => t; reflexivity
+ end.
+ +
+Ltac solve_proper := unfold Proper; solve_respectful ltac:(idtac).
+ +
+
+ +
+f_equiv is a clone of f_equal that handles setoid equivalences. + For example, if we know that f is a morphism for E1==>E2==>E, + then the goal E (f x y) (f x' y') will be transformed by f_equiv + into the subgoals E1 x x' and E2 y y'. + +
+
+ +
+Ltac f_equiv :=
+ match goal with
+  | |- ?R (?f ?x) (?f' _) =>
+    let T := type of x in
+    let Rx := fresh "R" in
+    evar (Rx : relation T);
+    let H := fresh in
+    assert (H : (Rx==>R)%signature f f');
+    unfold Rx in *; clear Rx; [ f_equiv | apply H; clear H; try reflexivity ]
+  | |- ?R ?f ?f' =>
+    solve [change (Proper R f); eauto with typeclass_instances | reflexivity ]
+  | _ => idtac
+ end.
+ +
+Section Relations.
+  Let U := Type.
+  Context {A B : U} (P : A -> U).
+ +
+
+ +
+forall_def reifies the dependent product as a definition. +
+
+ +
+  Definition forall_def : Type := forall x : A, P x.
+ +
+
+ +
+Dependent pointwise lifting of a relation on the range. +
+
+ +
+  Definition forall_relation
+             (sig : forall a, relation (P a)) : relation (forall x, P x) :=
+    fun f g => forall a, sig a (f a) (g a).
+ +
+  Lemma pointwise_pointwise (R : relation B) :
+    relation_equivalence (pointwise_relation A R) (@eq A ==> R).
+ +
+
+ +
+Subrelations induce a morphism on the identity. +
+
+ +
+  Global Instance subrelation_id_proper `(subrelation A RA RA') : Proper (RA ==> RA') id.
+ +
+
+ +
+The subrelation property goes through products as usual. +
+
+ +
+  Lemma subrelation_respectful `(subl : subrelation A RA' RA, subr : subrelation B RB RB') :
+    subrelation (RA ==> RB) (RA' ==> RB').
+ +
+
+ +
+And of course it is reflexive. +
+
+ +
+  Lemma subrelation_refl R : @subrelation A R R.
+ +
+
+ +
+Proper is itself a covariant morphism for subrelation. + We use an unconvertible premise to avoid looping. + +
+
+ +
+  Lemma subrelation_proper `(mor : Proper A R' m)
+        `(unc : Unconvertible (relation A) R R')
+        `(sub : subrelation A R' R) : Proper R m.
+ +
+  Global Instance proper_subrelation_proper :
+    Proper (subrelation ++> eq ==> impl) (@Proper A).
+ +
+  Global Instance pointwise_subrelation `(sub : subrelation B R R') :
+    subrelation (pointwise_relation A R) (pointwise_relation A R') | 4.
+ +
+
+ +
+For dependent function types. +
+
+  Lemma forall_subrelation (R S : forall x : A, relation (P x)) :
+    (forall a, subrelation (R a) (S a)) -> subrelation (forall_relation R) (forall_relation S).
+ End Relations.
+ +
+Global Typeclasses Opaque respectful pointwise_relation forall_relation.
+Arguments forall_relation {A P}%_type sig%_signature _ _.
+Arguments pointwise_relation A%_type {B}%_type R%_signature _ _.
+ +
+#[global]
+Hint Unfold Reflexive : core.
+#[global]
+Hint Unfold Symmetric : core.
+#[global]
+Hint Unfold Transitive : core.
+ +
+
+ +
+Resolution with subrelation: favor decomposing products over applying reflexivity + for unconstrained goals. +
+
+Ltac subrelation_tac T U :=
+  (is_ground T ; is_ground U ; class_apply @subrelation_refl) ||
+    class_apply @subrelation_respectful || class_apply @subrelation_refl.
+ +
+#[global]
+Hint Extern 3 (@subrelation _ ?T ?U) => subrelation_tac T U : typeclass_instances.
+ +
+CoInductive apply_subrelation : Prop := do_subrelation.
+ +
+Ltac proper_subrelation :=
+  match goal with
+    [ H : apply_subrelation |- _ ] => clear H ; class_apply @subrelation_proper
+  end.
+ +
+#[global]
+Hint Extern 5 (@Proper _ ?H _) => proper_subrelation : typeclass_instances.
+ +
+
+ +
+Essential subrelation instances for iff, impl and pointwise_relation. +
+
+ +
+#[global]
+Instance iff_impl_subrelation : subrelation iff impl | 2.
+ +
+#[global]
+Instance iff_flip_impl_subrelation : subrelation iff (flip impl) | 2.
+ +
+
+ +
+We use an extern hint to help unification. +
+
+ +
+#[global]
+Hint Extern 4 (subrelation (@forall_relation ?A ?B ?R) (@forall_relation _ _ ?S)) =>
+  apply (@forall_subrelation A B R S) ; intro : typeclass_instances.
+ +
+Section GenericInstances.
+  Let U := Type.
+  Context {A B C : U}.
+ +
+
+ +
+We can build a PER on the Rocq function space if we have PERs on the domain and + codomain. +
+
+ +
+  Program Instance respectful_per `(PER A R, PER B R') : PER (R ==> R').
+ +
+ +
+
+ +
+The complement of a relation conserves its proper elements. +
+
+ +
+  Program Definition complement_proper
+          `(mR : Proper (A -> A -> Prop) (RA ==> RA ==> iff) R) :
+    Proper (RA ==> RA ==> iff) (complement R) := _.
+ +
+ +
+
+ +
+The flip too, actually the flip instance is a bit more general. +
+
+ +
+  Program Definition flip_proper
+          `(mor : Proper (A -> B -> C) (RA ==> RB ==> RC) f) :
+    Proper (RB ==> RA ==> RC) (flip f) := _.
+ +
+ +
+
+ +
+Every Transitive relation gives rise to a binary morphism on impl, + contravariant in the first argument, covariant in the second. +
+
+ +
+ +
+ +
+
+ +
+Proper declarations for partial applications. +
+
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+  Global Program Instance trans_sym_contra_impl_morphism
+    `(PER A R) {x} : Proper (R --> impl) (R x) | 3.
+ +
+ +
+  Global Program Instance per_partial_app_morphism
+  `(PER A R) {x} : Proper (R ==> iff) (R x) | 2.
+ +
+ +
+
+ +
+Every Transitive relation induces a morphism by "pushing" an R x y on the left of an R x z proof to get an R y z goal. +
+
+ +
+ +
+ +
+
+ +
+Every Symmetric and Transitive relation gives rise to an equivariant morphism. +
+
+ +
+ +
+ +
+  Lemma symmetric_equiv_flip `(Symmetric A R) : relation_equivalence R (flip R).
+ +
+  Global Program Instance compose_proper RA RB RC :
+    Proper ((RB ==> RC) ==> (RA ==> RB) ==> (RA ==> RC)) (@compose A B C).
+ +
+ +
+  Global Instance reflexive_eq_dom_reflexive `{Reflexive B R'}:
+    Reflexive (respectful (@Logic.eq A) R').
+ +
+
+ +
+respectful is a morphism for relation equivalence. +
+
+ +
+  Global Instance respectful_morphism :
+    Proper (relation_equivalence ++> relation_equivalence ++> relation_equivalence)
+           (@respectful A B).
+ +
+
+ +
+R is Reflexive, hence we can build the needed proof. +
+
+ +
+  Lemma Reflexive_partial_app_morphism `(Proper (A -> B) (R ==> R') m, ProperProxy A R x) :
+    Proper R' (m x).
+ +
+  Lemma flip_respectful (R : relation A) (R' : relation B) :
+    relation_equivalence (flip (R ==> R')) (flip R ==> flip R').
+ +
+ +
+
+ +
+Treating flip: can't make them direct instances as we + need at least a flip present in the goal. +
+
+ +
+  Lemma flip1 `(subrelation A R' R) : subrelation (flip (flip R')) R.
+ +
+  Lemma flip2 `(subrelation A R R') : subrelation R (flip (flip R')).
+ +
+
+ +
+That's if and only if +
+
+ +
+  Lemma eq_subrelation `(Reflexive A R) : subrelation (@eq A) R.
+ +
+
+ +
+Once we have normalized, we will apply this instance to simplify the problem. +
+
+ +
+  Definition proper_flip_proper `(mor : Proper A R m) : Proper (flip R) m := mor.
+ +
+  Lemma proper_eq (x : A) : Proper (@eq A) x.
+ +
+End GenericInstances.
+ +
+Class PartialApplication.
+ +
+CoInductive normalization_done : Prop := did_normalization.
+ +
+Class Params {A : Type} (of : A) (arity : nat).
+#[global] Instance eq_pars : Params (@eq) 1 := {}.
+#[global] Instance iff_pars : Params (@iff) 0 := {}.
+#[global] Instance impl_pars : Params (@impl) 0 := {}.
+#[global] Instance flip_pars : Params (@flip) 4 := {}.
+ +
+Ltac partial_application_tactic :=
+  let rec do_partial_apps H m cont :=
+    match m with
+      | ?m' ?x => class_apply @Reflexive_partial_app_morphism ;
+        [(do_partial_apps H m' ltac:(idtac))|clear H]
+      | _ => cont
+    end
+  in
+  let rec do_partial H ar m :=
+    lazymatch ar with
+      | 0%nat => do_partial_apps H m ltac:(fail 1)
+      | S ?n' =>
+        match m with
+          ?m' ?x => do_partial H n' m'
+        end
+    end
+  in
+  let params m sk fk :=
+    (let m' := fresh in head_of_constr m' m ;
+     let n := fresh in evar (n:nat) ;
+     let v := eval compute in n in clear n ;
+      let H := fresh in
+        assert(H:Params m' v) by (subst m'; once typeclasses eauto) ;
+          let v' := eval compute in v in subst m';
+            (sk H v' || fail 1))
+    || fk
+  in
+  let on_morphism m cont :=
+    params m ltac:(fun H n => do_partial H n m)
+      ltac:(cont)
+  in
+  match goal with
+    | [ _ : normalization_done |- _ ] => fail 1
+    | [ _ : @Params _ _ _ |- _ ] => fail 1
+    | [ |- @Proper ?T _ (?m ?x) ] =>
+      match goal with
+        | [ H : PartialApplication |- _ ] =>
+          class_apply @Reflexive_partial_app_morphism; [|clear H]
+        | _ => on_morphism (m x)
+          ltac:(class_apply @Reflexive_partial_app_morphism)
+      end
+  end.
+ +
+
+ +
+Bootstrap !!! +
+
+ +
+#[global]
+Instance proper_proper {A} : Proper (relation_equivalence ==> eq ==> iff) (@Proper A).
+ +
+Ltac proper_reflexive :=
+  match goal with
+    | [ _ : normalization_done |- _ ] => fail 1
+    | _ => class_apply proper_eq || class_apply @reflexive_proper
+  end.
+ +
+#[global]
+Hint Extern 1 (subrelation (flip _) _) => class_apply @flip1 : typeclass_instances.
+#[global]
+Hint Extern 1 (subrelation _ (flip _)) => class_apply @flip2 : typeclass_instances.
+ +
+#[global]
+Hint Extern 1 (Proper _ (complement _)) => apply @complement_proper
+  : typeclass_instances.
+#[global]
+Hint Extern 1 (Proper _ (flip _)) => apply @flip_proper
+  : typeclass_instances.
+#[global]
+Hint Extern 2 (@Proper _ (flip _) _) => class_apply @proper_flip_proper
+  : typeclass_instances.
+#[global]
+Hint Extern 4 (@Proper _ _ _) => partial_application_tactic
+  : typeclass_instances.
+#[global]
+Hint Extern 7 (@Proper _ _ _) => proper_reflexive
+  : typeclass_instances.
+ +
+
+ +
+Special-purpose class to do normalization of signatures w.r.t. flip. +
+
+ +
+Section Normalize.
+  Context (A : Type).
+ +
+  Class Normalizes (m : relation A) (m' : relation A) : Prop :=
+    normalizes : relation_equivalence m m'.
+ +
+
+ +
+Current strategy: add flip everywhere and reduce using subrelation + afterwards. +
+
+ +
+  Lemma proper_normalizes_proper `(Normalizes R0 R1, Proper A R1 m) : Proper R0 m.
+ +
+  Lemma flip_atom R : Normalizes R (flip (flip R)).
+ +
+End Normalize.
+ +
+Lemma flip_arrow {A : Type} {B : Type}
+      `(NA : Normalizes A R (flip R'''), NB : Normalizes B R' (flip R'')) :
+  Normalizes (A -> B) (R ==> R') (flip (R''' ==> R'')%signature).
+ +
+Ltac normalizes :=
+  match goal with
+    | [ |- Normalizes _ (respectful _ _) _ ] => class_apply @flip_arrow
+    | _ => class_apply @flip_atom
+  end.
+ +
+Ltac proper_normalization :=
+  match goal with
+    | [ _ : normalization_done |- _ ] => fail 1
+    | [ _ : apply_subrelation |- @Proper _ ?R _ ] =>
+      let H := fresh "H" in
+      set(H:=did_normalization) ; class_apply @proper_normalizes_proper
+  end.
+ +
+#[global]
+Hint Extern 1 (Normalizes _ _ _) => normalizes : typeclass_instances.
+#[global]
+Hint Extern 6 (@Proper _ _ _) => proper_normalization
+  : typeclass_instances.
+ +
+
+ +
+When the relation on the domain is symmetric, we can + flip the relation on the codomain. Same for binary functions. +
+
+ +
+Lemma proper_sym_flip :
+ forall `(Symmetric A R1)`(Proper (A->B) (R1==>R2) f),
+ Proper (R1==>flip R2) f.
+ +
+Lemma proper_sym_flip_2 :
+ forall `(Symmetric A R1)`(Symmetric B R2)`(Proper (A->B->C) (R1==>R2==>R3) f),
+ Proper (R1==>R2==>flip R3) f.
+ +
+
+ +
+When the relation on the domain is symmetric, a predicate is + compatible with iff as soon as it is compatible with impl. + Same with a binary relation. +
+
+ +
+Lemma proper_sym_impl_iff : forall `(Symmetric A R)`(Proper _ (R==>impl) f),
+ Proper (R==>iff) f.
+ +
+Lemma proper_sym_impl_iff_2 :
+ forall `(Symmetric A R)`(Symmetric B R')`(Proper _ (R==>R'==>impl) f),
+ Proper (R==>R'==>iff) f.
+ +
+
+ +
+A PartialOrder is compatible with its underlying equivalence. +
+
+ +
+#[global]
+Instance PartialOrder_proper `(PartialOrder A eqA R) :
+  Proper (eqA==>eqA==>iff) R.
+ +
+
+ +
+From a PartialOrder to the corresponding StrictOrder: + lt = le /\ ~eq. + If the order is total, we could also say gt = ~le. +
+
+ +
+Lemma PartialOrder_StrictOrder `(PartialOrder A eqA R) :
+  StrictOrder (relation_conjunction R (complement eqA)).
+ +
+
+ +
+From a StrictOrder to the corresponding PartialOrder: + le = lt \/ eq. + If the order is total, we could also say ge = ~lt. +
+
+ +
+Lemma StrictOrder_PreOrder
+ `(Equivalence A eqA, StrictOrder A R, Proper _ (eqA==>eqA==>iff) R) :
+ PreOrder (relation_disjunction R eqA).
+ +
+#[global]
+Hint Extern 4 (PreOrder (relation_disjunction _ _)) =>
+  class_apply StrictOrder_PreOrder : typeclass_instances.
+ +
+Lemma StrictOrder_PartialOrder
+  `(Equivalence A eqA, StrictOrder A R, Proper _ (eqA==>eqA==>iff) R) :
+  PartialOrder eqA (relation_disjunction R eqA).
+ +
+#[global]
+Hint Extern 4 (StrictOrder (relation_conjunction _ _)) =>
+  class_apply PartialOrder_StrictOrder : typeclass_instances.
+ +
+#[global]
+Hint Extern 4 (PartialOrder _ (relation_disjunction _ _)) =>
+  class_apply StrictOrder_PartialOrder : typeclass_instances.
+ +
+ +
+Register forall_relation as rewrite.prop.forall_relation.
+Register pointwise_relation as rewrite.prop.pointwise_relation.
+Register respectful as rewrite.prop.respectful.
+Register forall_def as rewrite.prop.forall_def.
+Register do_subrelation as rewrite.prop.do_subrelation.
+Register apply_subrelation as rewrite.prop.apply_subrelation.
+Register RewriteRelation as rewrite.prop.RewriteRelation.
+Register Proper as rewrite.prop.Proper.
+Register ProperProxy as rewrite.prop.ProperProxy.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Classes.Morphisms_Prop.html b/master/corelib/Corelib.Classes.Morphisms_Prop.html new file mode 100644 index 0000000000..cf9cf6548b --- /dev/null +++ b/master/corelib/Corelib.Classes.Morphisms_Prop.html @@ -0,0 +1,250 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Classes.Morphisms_Prop

+ +
+ +
+
+ +
+

Proper instances for propositional connectives.

+ + +
+ + Author: Matthieu Sozeau + Institution: LRI, CNRS UMR 8623 - University Paris Sud + +
+
+ +
+Require Import Corelib.Classes.Morphisms.
+Require Import Corelib.Program.Basics.
+Require Import Corelib.Program.Tactics.
+ +
+Local Obligation Tactic := try solve [simpl_relation | firstorder auto].
+ +
+
+ +
+Standard instances for not, iff and impl. +
+ + Logical negation. +
+
+ +
+#[global]
+Program Instance not_impl_morphism :
+  Proper (impl --> impl) not | 1.
+ +
+#[global]
+Program Instance not_iff_morphism :
+  Proper (iff ++> iff) not.
+ +
+
+ +
+Logical conjunction. +
+
+ +
+#[global]
+Program Instance and_impl_morphism :
+  Proper (impl ==> impl ==> impl) and | 1.
+ +
+#[global]
+Program Instance and_iff_morphism :
+  Proper (iff ==> iff ==> iff) and.
+ +
+
+ +
+Logical disjunction. +
+
+ +
+#[global]
+Program Instance or_impl_morphism :
+  Proper (impl ==> impl ==> impl) or | 1.
+ +
+#[global]
+Program Instance or_iff_morphism :
+  Proper (iff ==> iff ==> iff) or.
+ +
+
+ +
+Logical implication impl is a morphism for logical equivalence. +
+
+ +
+#[global]
+Program Instance iff_iff_iff_impl_morphism : Proper (iff ==> iff ==> iff) impl.
+ +
+
+ +
+Morphisms for quantifiers +
+
+ +
+#[global]
+Program Instance ex_iff_morphism {A : Type} : Proper (pointwise_relation A iff ==> iff) (@ex A).
+ +
+#[global]
+Program Instance ex_impl_morphism {A : Type} :
+  Proper (pointwise_relation A impl ==> impl) (@ex A) | 1.
+ +
+#[global]
+Program Instance ex_flip_impl_morphism {A : Type} :
+  Proper (pointwise_relation A (flip impl) ==> flip impl) (@ex A) | 1.
+ +
+#[global]
+Program Instance all_iff_morphism {A : Type} :
+  Proper (pointwise_relation A iff ==> iff) (@all A).
+ +
+#[global]
+Program Instance all_impl_morphism {A : Type} :
+  Proper (pointwise_relation A impl ==> impl) (@all A) | 1.
+ +
+#[global]
+Program Instance all_flip_impl_morphism {A : Type} :
+  Proper (pointwise_relation A (flip impl) ==> flip impl) (@all A) | 1.
+ +
+
+ +
+Equivalent points are simultaneously accessible or not +
+
+ +
+#[global]
+Instance Acc_pt_morphism {A:Type}(E R : A->A->Prop)
+ `(Equivalence _ E) `(Proper _ (E==>E==>iff) R) :
+ Proper (E==>iff) (Acc R).
+ +
+
+ +
+Equivalent relations have the same accessible points +
+
+ +
+#[global]
+Instance Acc_rel_morphism {A:Type} :
+ Proper (relation_equivalence ==> Logic.eq ==> iff) (@Acc A).
+ +
+
+ +
+Equivalent relations are simultaneously well-founded or not +
+
+ +
+#[global]
+Instance well_founded_morphism {A : Type} :
+ Proper (relation_equivalence ==> iff) (@well_founded A).
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Classes.RelationClasses.html b/master/corelib/Corelib.Classes.RelationClasses.html new file mode 100644 index 0000000000..49531c8bd8 --- /dev/null +++ b/master/corelib/Corelib.Classes.RelationClasses.html @@ -0,0 +1,947 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Classes.RelationClasses

+ +
+ +
+
+ +
+

Typeclass-based relations, tactics and standard instances

+ + +
+ + This is the basic theory needed to formalize morphisms and setoids. + +
+ + Author: Matthieu Sozeau + Institution: LRI, CNRS UMR 8623 - University Paris Sud + +
+
+ +
+Require Export Corelib.Classes.Init.
+Require Import Corelib.Program.Basics.
+Require Import Corelib.Program.Tactics.
+Require Import Corelib.Relations.Relation_Definitions.
+ +
+Generalizable Variables A B C D R S T U l eqA eqB eqC eqD.
+ +
+
+ +
+We allow to unfold the relation definition while doing morphism search. +
+
+ +
+Section Defs.
+  Context {A : Type}.
+ +
+
+ +
+We rebind relational properties in separate classes to be able to overload each proof. +
+
+ +
+  Class Reflexive (R : relation A) :=
+    reflexivity : forall x : A, R x x.
+ +
+  Definition complement (R : relation A) : relation A := fun x y => R x y -> False.
+ +
+
+ +
+Opaque for proof-search. +
+
+  Typeclasses Opaque complement.
+ +
+
+ +
+These are convertible. +
+
+  Lemma complement_inverse R : complement (flip R) = flip (complement R).
+ +
+  Class Irreflexive (R : relation A) :=
+    irreflexivity : Reflexive (complement R).
+ +
+  Class Symmetric (R : relation A) :=
+    symmetry : forall {x y}, R x y -> R y x.
+ +
+  Class Asymmetric (R : relation A) :=
+    asymmetry : forall {x y}, R x y -> R y x -> False.
+ +
+  Class Transitive (R : relation A) :=
+    transitivity : forall {x y z}, R x y -> R y z -> R x z.
+ +
+
+ +
+Various combinations of reflexivity, symmetry and transitivity. +
+ + A PreOrder is both Reflexive and Transitive. +
+
+ +
+  Class PreOrder (R : relation A) : Prop := {
+    #[global] PreOrder_Reflexive :: Reflexive R | 2 ;
+    #[global] PreOrder_Transitive :: Transitive R | 2 }.
+ +
+
+ +
+A StrictOrder is both Irreflexive and Transitive. +
+
+ +
+  Class StrictOrder (R : relation A) : Prop := {
+    #[global] StrictOrder_Irreflexive :: Irreflexive R ;
+    #[global] StrictOrder_Transitive :: Transitive R }.
+ +
+
+ +
+By definition, a strict order is also asymmetric +
+
+  Global Instance StrictOrder_Asymmetric `(StrictOrder R) : Asymmetric R.
+ +
+
+ +
+A partial equivalence relation is Symmetric and Transitive. +
+
+ +
+  Class PER (R : relation A) : Prop := {
+    #[global] PER_Symmetric :: Symmetric R | 3 ;
+    #[global] PER_Transitive :: Transitive R | 3 }.
+ +
+
+ +
+Equivalence relations. +
+
+ +
+  Class Equivalence (R : relation A) : Prop := {
+    #[global] Equivalence_Reflexive :: Reflexive R ;
+    #[global] Equivalence_Symmetric :: Symmetric R ;
+    #[global] Equivalence_Transitive :: Transitive R }.
+ +
+
+ +
+An Equivalence is a PER plus reflexivity. +
+
+ +
+  Global Instance Equivalence_PER {R} `(E:Equivalence R) : PER R | 10 :=
+    { }.
+ +
+
+ +
+An Equivalence is a PreOrder plus symmetry. +
+
+ +
+  Global Instance Equivalence_PreOrder {R} `(E:Equivalence R) : PreOrder R | 10 :=
+    { }.
+ +
+
+ +
+We can now define antisymmetry w.r.t. an equivalence relation on the carrier. +
+
+ +
+  Class Antisymmetric eqA `{equ : Equivalence eqA} (R : relation A) :=
+    antisymmetry : forall {x y}, R x y -> R y x -> eqA x y.
+ +
+  Class subrelation (R R' : relation A) : Prop :=
+    is_subrelation : forall {x y}, R x y -> R' x y.
+ +
+
+ +
+Any symmetric relation is equal to its inverse. +
+
+ +
+  Lemma subrelation_symmetric R `(Symmetric R) : subrelation (flip R) R.
+ +
+  Section flip.
+ +
+    Lemma flip_Reflexive `{Reflexive R} : Reflexive (flip R).
+ +
+    Program Definition flip_Irreflexive `(Irreflexive R) : Irreflexive (flip R) :=
+      irreflexivity (R:=R).
+ +
+    Program Definition flip_Symmetric `(Symmetric R) : Symmetric (flip R) :=
+      fun x y H => symmetry (R:=R) H.
+ +
+    Program Definition flip_Asymmetric `(Asymmetric R) : Asymmetric (flip R) :=
+      fun x y H H' => asymmetry (R:=R) H H'.
+ +
+    Program Definition flip_Transitive `(Transitive R) : Transitive (flip R) :=
+      fun x y z H H' => transitivity (R:=R) H' H.
+ +
+    Program Lemma flip_Antisymmetric `(Antisymmetric eqA R) :
+      Antisymmetric eqA (flip R).
+ +
+
+ +
+Inversing the larger structures +
+
+ +
+    Lemma flip_PreOrder `(PreOrder R) : PreOrder (flip R).
+ +
+    Lemma flip_StrictOrder `(StrictOrder R) : StrictOrder (flip R).
+ +
+    Lemma flip_PER `(PER R) : PER (flip R).
+ +
+    Lemma flip_Equivalence `(Equivalence R) : Equivalence (flip R).
+ +
+  End flip.
+ +
+  Section complement.
+ +
+    Lemma complement_Irreflexive `(Reflexive R)
+      : Irreflexive (complement R).
+ +
+    Lemma complement_Symmetric `(Symmetric R) : Symmetric (complement R).
+   End complement.
+ +
+
+ +
+Rewrite relation on a given support: declares a relation as a rewrite + relation for use by the generalized rewriting tactic. + It helps choosing if a rewrite should be handled + by the generalized or the regular rewriting tactic using leibniz equality. + Users can declare an RewriteRelation A RA anywhere to declare default + relations on a given type `A`. This is also done automatically by + the Declare Relation A RA commands. It has no mode declaration: + it will assign `?A := Prop, ?R := iff` on an entirely unspecified query + `RewriteRelation ?A ?R`, or any prefered rewrite relation of priority < 2. +
+
+ +
+  Class RewriteRelation (RA : relation A).
+ +
+
+ +
+Leibniz equality. +
+
+  Section Leibniz.
+    Global Instance eq_Reflexive : Reflexive (@eq A) := @eq_refl A.
+    Global Instance eq_Symmetric : Symmetric (@eq A) := @eq_sym A.
+    Global Instance eq_Transitive : Transitive (@eq A) := @eq_trans A.
+ +
+
+ +
+Leibinz equality eq is an equivalence relation. + The instance has low priority as it is always applicable + if only the type is constrained. +
+
+ +
+    Global Program Instance eq_equivalence : Equivalence (@eq A) | 10.
+  End Leibniz.
+ +
+
+ +
+Leibniz disequality. +
+
+  Section LeibnizNot.
+
+ +
+Disequality is symmetric. +
+
+    Global Instance neq_Symmetric : Symmetric (fun x y : A => x <> y) := (@not_eq_sym A).
+  End LeibnizNot.
+End Defs.
+ +
+
+ +
+Default rewrite relations handled by setoid_rewrite on Prop. +
+
+#[global]
+Instance inverse_impl_rewrite_relation : RewriteRelation (flip impl) | 3 := {}.
+#[global]
+Instance impl_rewrite_relation : RewriteRelation impl | 3 := {}.
+#[global]
+Instance iff_rewrite_relation : RewriteRelation iff | 2 := {}.
+ +
+
+ +
+Any Equivalence declared in the context is automatically considered + a rewrite relation. This only applies if the relation is at least partially + defined: setoid_rewrite won't try to infer arbitrary user rewrite relations. +
+
+ +
+Definition equivalence_rewrite_relation `(eqa : Equivalence A eqA) : RewriteRelation eqA :=
+  Build_RewriteRelation _.
+ +
+Ltac equiv_rewrite_relation R :=
+  tryif is_evar R then fail
+  else class_apply equivalence_rewrite_relation.
+ +
+#[global]
+Hint Extern 10 (@RewriteRelation ?A ?R) => equiv_rewrite_relation R : typeclass_instances.
+ +
+
+ +
+Hints to drive the typeclass resolution avoiding loops + due to the use of full unification. +
+
+#[global]
+Hint Extern 1 (Reflexive (complement _)) => class_apply @irreflexivity : typeclass_instances.
+#[global]
+Hint Extern 3 (Symmetric (complement _)) => class_apply complement_Symmetric : typeclass_instances.
+#[global]
+Hint Extern 3 (Irreflexive (complement _)) => class_apply complement_Irreflexive : typeclass_instances.
+ +
+#[global]
+Hint Extern 3 (Reflexive (flip _)) => apply flip_Reflexive : typeclass_instances.
+#[global]
+Hint Extern 3 (Irreflexive (flip _)) => class_apply flip_Irreflexive : typeclass_instances.
+#[global]
+Hint Extern 3 (Symmetric (flip _)) => class_apply flip_Symmetric : typeclass_instances.
+#[global]
+Hint Extern 3 (Asymmetric (flip _)) => class_apply flip_Asymmetric : typeclass_instances.
+#[global]
+Hint Extern 3 (Antisymmetric (flip _)) => class_apply flip_Antisymmetric : typeclass_instances.
+#[global]
+Hint Extern 3 (Transitive (flip _)) => class_apply flip_Transitive : typeclass_instances.
+#[global]
+Hint Extern 3 (StrictOrder (flip _)) => class_apply flip_StrictOrder : typeclass_instances.
+#[global]
+Hint Extern 3 (PreOrder (flip _)) => class_apply flip_PreOrder : typeclass_instances.
+ +
+#[global]
+Hint Extern 4 (subrelation (flip _) _) =>
+  class_apply @subrelation_symmetric : typeclass_instances.
+ +
+Arguments irreflexivity {A R Irreflexive} [x] _ : rename.
+Arguments symmetry {A} {R} {_} [x] [y] _.
+Arguments asymmetry {A} {R} {_} [x] [y] _ _.
+Arguments transitivity {A} {R} {_} [x] [y] [z] _ _.
+Arguments Antisymmetric A eqA {_} _.
+ +
+#[global]
+Hint Resolve irreflexivity : ord.
+ +
+Unset Implicit Arguments.
+ +
+Ltac solve_relation :=
+  match goal with
+  | [ |- ?R ?x ?x ] => reflexivity
+  | [ H : ?R ?x ?y |- ?R ?y ?x ] => symmetry ; exact H
+  end.
+ +
+#[global]
+Hint Extern 4 => solve_relation : relations.
+ +
+
+ +
+We can already dualize all these properties. +
+ +

Standard instances.

+ +
+
+ +
+Ltac reduce_hyp H :=
+  match type of H with
+    | context [ _ <-> _ ] => fail 1
+    | _ => red in H ; try reduce_hyp H
+  end.
+ +
+Ltac reduce_goal :=
+  match goal with
+    | [ |- _ <-> _ ] => fail 1
+    | _ => red ; intros ; try reduce_goal
+  end.
+ +
+Tactic Notation "reduce" "in" hyp(Hid) := reduce_hyp Hid.
+ +
+Ltac reduce := reduce_goal.
+ +
+Tactic Notation "apply" "*" constr(t) :=
+  first [ refine t | refine (t _) | refine (t _ _) | refine (t _ _ _) | refine (t _ _ _ _) |
+    refine (t _ _ _ _ _) | refine (t _ _ _ _ _ _) | refine (t _ _ _ _ _ _ _) ].
+ +
+Ltac simpl_relation :=
+  unfold flip, impl, arrow ; try reduce ; program_simpl ;
+    try ( solve [ dintuition auto with relations ]).
+ +
+Local Obligation Tactic := try solve [ simpl_relation ].
+ +
+
+ +
+Logical implication. +
+
+ +
+#[global]
+Program Instance impl_Reflexive : Reflexive impl.
+#[global]
+Program Instance impl_Transitive : Transitive impl.
+ +
+
+ +
+Logical equivalence. +
+
+ +
+#[global]
+Instance iff_Reflexive : Reflexive iff := iff_refl.
+#[global]
+Instance iff_Symmetric : Symmetric iff := iff_sym.
+#[global]
+Instance iff_Transitive : Transitive iff := iff_trans.
+ +
+
+ +
+Logical equivalence iff is an equivalence relation. +
+
+ +
+#[global]
+Program Instance iff_equivalence : Equivalence iff.
+ +
+
+ +
+We now develop a generalization of results on relations for arbitrary predicates. + The resulting theory can be applied to homogeneous binary relations but also to + arbitrary n-ary predicates. +
+
+ +
+Local Open Scope list_scope.
+ +
+
+ +
+A compact representation of non-dependent arities, with the codomain singled-out. +
+
+ +
+Inductive Tlist : Type := Tnil : Tlist | Tcons : Type -> Tlist -> Tlist.
+Local Infix "::" := Tcons.
+ +
+Fixpoint arrows (l : Tlist) (r : Type) : Type :=
+  match l with
+    | Tnil => r
+    | A :: l' => A -> arrows l' r
+  end.
+ +
+
+ +
+We can define abbreviations for operation and relation types based on arrows. +
+
+ +
+Definition unary_operation A := arrows (A::Tnil) A.
+Definition binary_operation A := arrows (A::A::Tnil) A.
+Definition ternary_operation A := arrows (A::A::A::Tnil) A.
+ +
+
+ +
+We define n-ary predicates as functions into Prop. +
+
+ +
+Notation predicate l := (arrows l Prop).
+ +
+
+ +
+Unary predicates, or sets. +
+
+ +
+Definition unary_predicate A := predicate (A::Tnil).
+ +
+
+ +
+Homogeneous binary relations, equivalent to relation A. +
+
+ +
+Definition binary_relation A := predicate (A::A::Tnil).
+ +
+
+ +
+We can close a predicate by universal or existential quantification. +
+
+ +
+Fixpoint predicate_all (l : Tlist) : predicate l -> Prop :=
+  match l with
+    | Tnil => fun f => f
+    | A :: tl => fun f => forall x : A, predicate_all tl (f x)
+  end.
+ +
+Fixpoint predicate_exists (l : Tlist) : predicate l -> Prop :=
+  match l with
+    | Tnil => fun f => f
+    | A :: tl => fun f => exists x : A, predicate_exists tl (f x)
+  end.
+ +
+
+ +
+Pointwise extension of a binary operation on T to a binary operation + on functions whose codomain is T. + For an operator on Prop this lifts the operator to a binary operation. +
+
+ +
+Fixpoint pointwise_extension {T : Type} (op : binary_operation T)
+  (l : Tlist) : binary_operation (arrows l T) :=
+  match l with
+    | Tnil => fun R R' => op R R'
+    | A :: tl => fun R R' =>
+      fun x => pointwise_extension op tl (R x) (R' x)
+  end.
+ +
+
+ +
+Pointwise lifting, equivalent to doing pointwise_extension and closing using predicate_all. +
+
+ +
+Fixpoint pointwise_lifting (op : binary_relation Prop) (l : Tlist) : binary_relation (predicate l) :=
+  match l with
+    | Tnil => fun R R' => op R R'
+    | A :: tl => fun R R' =>
+      forall x, pointwise_lifting op tl (R x) (R' x)
+  end.
+ +
+
+ +
+The n-ary equivalence relation, defined by lifting the 0-ary iff relation. +
+
+ +
+Definition predicate_equivalence {l : Tlist} : binary_relation (predicate l) :=
+  pointwise_lifting iff l.
+ +
+
+ +
+The n-ary implication relation, defined by lifting the 0-ary impl relation. +
+
+ +
+Definition predicate_implication {l : Tlist} :=
+  pointwise_lifting impl l.
+ +
+
+ +
+Notations for pointwise equivalence and implication of predicates. +
+
+ +
+Declare Scope predicate_scope.
+ +
+Infix "<∙>" := predicate_equivalence (at level 95, no associativity) : predicate_scope.
+Infix "-∙>" := predicate_implication (at level 70, right associativity) : predicate_scope.
+ +
+Local Open Scope predicate_scope.
+ +
+
+ +
+The pointwise liftings of conjunction and disjunctions. + Note that these are binary_operations, building new relations out of old ones. +
+
+ +
+Definition predicate_intersection := pointwise_extension and.
+Definition predicate_union := pointwise_extension or.
+ +
+Infix "/∙\" := predicate_intersection (at level 80, right associativity) : predicate_scope.
+Infix "\∙/" := predicate_union (at level 85, right associativity) : predicate_scope.
+ +
+
+ +
+The always True and always False predicates. +
+
+ +
+Fixpoint true_predicate {l : Tlist} : predicate l :=
+  match l with
+    | Tnil => True
+    | A :: tl => fun _ => @true_predicate tl
+  end.
+ +
+Fixpoint false_predicate {l : Tlist} : predicate l :=
+  match l with
+    | Tnil => False
+    | A :: tl => fun _ => @false_predicate tl
+  end.
+ +
+Notation "∙⊤∙" := true_predicate : predicate_scope.
+Notation "∙⊥∙" := false_predicate : predicate_scope.
+ +
+
+ +
+Predicate equivalence is an equivalence, and predicate implication defines a preorder. +
+
+ +
+#[global]
+Program Instance predicate_equivalence_equivalence {l} :
+  Equivalence (@predicate_equivalence l).
+ +
+ +
+#[global]
+Program Instance predicate_implication_preorder {l} :
+  PreOrder (@predicate_implication l).
+ +
+
+ +
+We define the various operations which define the algebra on binary relations, + from the general ones. +
+
+ +
+Section Binary.
+  Context {A : Type}.
+ +
+  Definition relation_equivalence : relation (relation A) :=
+    @predicate_equivalence (_::_::Tnil).
+ +
+  Global Instance relation_equivalence_rewrite_relation: RewriteRelation relation_equivalence := {}.
+ +
+  Definition relation_conjunction (R : relation A) (R' : relation A) : relation A :=
+    @predicate_intersection (A::A::Tnil) R R'.
+ +
+  Definition relation_disjunction (R : relation A) (R' : relation A) : relation A :=
+    @predicate_union (A::A::Tnil) R R'.
+ +
+
+ +
+Relation equivalence is an equivalence, and subrelation defines a partial order. +
+
+ +
+  Global Instance relation_equivalence_equivalence :
+    Equivalence relation_equivalence.
+ +
+  Global Instance relation_implication_preorder : PreOrder (@subrelation A).
+ +
+
+ +
+

Partial Order.

+ + A partial order is a preorder which is additionally antisymmetric. + We give an equivalent definition, up-to an equivalence relation + on the carrier. +
+
+ +
+  Class PartialOrder eqA `{equ : Equivalence A eqA} R `{preo : PreOrder A R} :=
+    partial_order_equivalence : relation_equivalence eqA (relation_conjunction R (flip R)).
+ +
+
+ +
+The equivalence proof is sufficient for proving that R must be a + morphism for equivalence (see Morphisms). It is also sufficient to + show that R is antisymmetric w.r.t. eqA +
+
+ +
+  Global Instance partial_order_antisym `(PartialOrder eqA R) : Antisymmetric A eqA R.
+ +
+  Lemma PartialOrder_inverse `(PartialOrder eqA R) : PartialOrder eqA (flip R).
+ End Binary.
+ +
+#[global]
+Hint Extern 3 (PartialOrder (flip _)) => class_apply PartialOrder_inverse : typeclass_instances.
+ +
+
+ +
+The partial order defined by subrelation and relation equivalence. +
+
+ +
+#[global]
+Program Instance subrelation_partial_order {A} :
+  PartialOrder (@relation_equivalence A) subrelation.
+ +
+ +
+Global Typeclasses Opaque arrows predicate_implication predicate_equivalence
+            relation_equivalence pointwise_lifting.
+ +
+ +
+Register relation as rewrite.prop.relation.
+Register subrelation as rewrite.prop.subrelation.
+Register Reflexive as rewrite.prop.Reflexive.
+Register reflexivity as rewrite.prop.reflexivity.
+Register Symmetric as rewrite.prop.Symmetric.
+Register symmetry as rewrite.prop.symmetry.
+Register Transitive as rewrite.prop.Transitive.
+Register transitivity as rewrite.prop.transitivity.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Classes.SetoidTactics.html b/master/corelib/Corelib.Classes.SetoidTactics.html new file mode 100644 index 0000000000..25f178b662 --- /dev/null +++ b/master/corelib/Corelib.Classes.SetoidTactics.html @@ -0,0 +1,335 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Classes.SetoidTactics

+ +
+ +
+
+ +
+

Tactics for typeclass-based setoids.

+ + +
+ + Author: Matthieu Sozeau + Institution: LRI, CNRS UMR 8623 - University Paris Sud + +
+
+ +
+Require Corelib.Classes.CRelationClasses Corelib.Classes.CMorphisms.
+Require Import Corelib.Classes.Morphisms Corelib.Classes.Morphisms_Prop.
+Require Export Corelib.Classes.RelationClasses Corelib.Relations.Relation_Definitions.
+Require Import Corelib.Classes.Equivalence Corelib.Program.Basics.
+ +
+Generalizable Variables A R.
+ +
+Export ProperNotations.
+ +
+Set Implicit Arguments.
+ +
+
+ +
+Default relation on a given support. Can be used by tactics + to find a sensible default relation on any carrier. Users can + declare an Instance def : DefaultRelation A RA anywhere to + declare a default relation. This is used by setoid_replace to infer + the relation to use on a given type, in a given context. + +
+
+ +
+Class DefaultRelation A (R : relation A).
+Register DefaultRelation as rewrite.DefaultRelation.
+ +
+
+ +
+To search for the default relation, just call default_relation. +
+
+ +
+Definition default_relation `{DefaultRelation A R} := R.
+ +
+
+ +
+Every Equivalence gives a default relation, if no other is given + (lowest priority). +
+
+ +
+#[global]
+Instance equivalence_default `(Equivalence A R) : DefaultRelation R | 4.
+Defined.
+ +
+
+ +
+The setoid_replace tactics in Ltac, defined in terms of default relations + and the setoid_rewrite tactic. +
+
+ +
+Ltac setoidreplace H t :=
+  let Heq := fresh "Heq" in
+    cut(H) ; unfold default_relation ; [ intro Heq ; setoid_rewrite Heq ; clear Heq | t ].
+ +
+Ltac setoidreplacein H H' t :=
+  let Heq := fresh "Heq" in
+    cut(H) ; unfold default_relation ; [ intro Heq ; setoid_rewrite Heq in H' ; clear Heq | t ].
+ +
+Ltac setoidreplaceinat H H' t occs :=
+  let Heq := fresh "Heq" in
+    cut(H) ; unfold default_relation ; [ intro Heq ; setoid_rewrite Heq in H' at occs ; clear Heq | t ].
+ +
+Ltac setoidreplaceat H t occs :=
+  let Heq := fresh "Heq" in
+    cut(H) ; unfold default_relation ; [ intro Heq ; setoid_rewrite Heq at occs ; clear Heq | t ].
+ +
+Tactic Notation "setoid_replace" constr(x) "with" constr(y) :=
+  setoidreplace (default_relation x y) idtac.
+ +
+Tactic Notation "setoid_replace" constr(x) "with" constr(y)
+  "at" int_or_var_list(o) :=
+  setoidreplaceat (default_relation x y) idtac o.
+ +
+Tactic Notation "setoid_replace" constr(x) "with" constr(y)
+  "in" hyp(id) :=
+  setoidreplacein (default_relation x y) id idtac.
+ +
+Tactic Notation "setoid_replace" constr(x) "with" constr(y)
+  "in" hyp(id)
+  "at" int_or_var_list(o) :=
+  setoidreplaceinat (default_relation x y) id idtac o.
+ +
+Tactic Notation "setoid_replace" constr(x) "with" constr(y)
+  "by" tactic3(t) :=
+  setoidreplace (default_relation x y) ltac:(t).
+ +
+Tactic Notation "setoid_replace" constr(x) "with" constr(y)
+  "at" int_or_var_list(o)
+  "by" tactic3(t) :=
+  setoidreplaceat (default_relation x y) ltac:(t) o.
+ +
+Tactic Notation "setoid_replace" constr(x) "with" constr(y)
+  "in" hyp(id)
+  "by" tactic3(t) :=
+  setoidreplacein (default_relation x y) id ltac:(t).
+ +
+Tactic Notation "setoid_replace" constr(x) "with" constr(y)
+  "in" hyp(id)
+  "at" int_or_var_list(o)
+  "by" tactic3(t) :=
+  setoidreplaceinat (default_relation x y) id ltac:(t) o.
+ +
+Tactic Notation "setoid_replace" constr(x) "with" constr(y)
+  "using" "relation" constr(rel) :=
+  setoidreplace (rel x y) idtac.
+ +
+Tactic Notation "setoid_replace" constr(x) "with" constr(y)
+  "using" "relation" constr(rel)
+  "at" int_or_var_list(o) :=
+  setoidreplaceat (rel x y) idtac o.
+ +
+Tactic Notation "setoid_replace" constr(x) "with" constr(y)
+  "using" "relation" constr(rel)
+  "by" tactic3(t) :=
+  setoidreplace (rel x y) ltac:(t).
+ +
+Tactic Notation "setoid_replace" constr(x) "with" constr(y)
+  "using" "relation" constr(rel)
+  "at" int_or_var_list(o)
+  "by" tactic3(t) :=
+  setoidreplaceat (rel x y) ltac:(t) o.
+ +
+Tactic Notation "setoid_replace" constr(x) "with" constr(y)
+  "using" "relation" constr(rel)
+  "in" hyp(id) :=
+  setoidreplacein (rel x y) id idtac.
+ +
+Tactic Notation "setoid_replace" constr(x) "with" constr(y)
+  "using" "relation" constr(rel)
+  "in" hyp(id)
+  "at" int_or_var_list(o) :=
+  setoidreplaceinat (rel x y) id idtac o.
+ +
+Tactic Notation "setoid_replace" constr(x) "with" constr(y)
+  "using" "relation" constr(rel)
+  "in" hyp(id)
+  "by" tactic3(t) :=
+  setoidreplacein (rel x y) id ltac:(t).
+ +
+Tactic Notation "setoid_replace" constr(x) "with" constr(y)
+  "using" "relation" constr(rel)
+  "in" hyp(id)
+  "at" int_or_var_list(o)
+  "by" tactic3(t) :=
+  setoidreplaceinat (rel x y) id ltac:(t) o.
+ +
+
+ +
+The add_morphism_tactic tactic is run at each Add Morphism + command before giving the hand back to the user to discharge the + proof. It essentially amounts to unfold the right amount of + respectful calls and substitute leibniz equalities. One can + redefine it using Ltac add_morphism_tactic ::= t. +
+
+ +
+Require Import Corelib.Program.Tactics.
+ +
+Local Open Scope signature_scope.
+ +
+Ltac red_subst_eq_morphism concl :=
+  match concl with
+    | @Logic.eq ?A ==> ?R' => red ; intros ; subst ; red_subst_eq_morphism R'
+    | ?R ==> ?R' => red ; intros ; red_subst_eq_morphism R'
+    | _ => idtac
+  end.
+ +
+Ltac destruct_proper :=
+  match goal with
+    | [ |- @Proper ?A ?R ?m ] => red
+  end.
+ +
+Ltac reverse_arrows x :=
+  match x with
+    | @Logic.eq ?A ==> ?R' => revert_last ; reverse_arrows R'
+    | ?R ==> ?R' => do 3 revert_last ; reverse_arrows R'
+    | _ => idtac
+  end.
+ +
+Ltac default_add_morphism_tactic :=
+  unfold flip ; intros ;
+  (try destruct_proper) ;
+  match goal with
+    | [ |- (?x ==> ?y) _ _ ] => red_subst_eq_morphism (x ==> y) ; reverse_arrows (x ==> y)
+  end.
+ +
+Ltac add_morphism_tactic := default_add_morphism_tactic.
+ +
+#[global] Obligation Tactic := program_simpl.
+#[export] Obligation Tactic := program_simpl.
+ +
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Compat.Coq818.html b/master/corelib/Corelib.Compat.Coq818.html new file mode 100644 index 0000000000..614019c9a2 --- /dev/null +++ b/master/corelib/Corelib.Compat.Coq818.html @@ -0,0 +1,95 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Compat.Coq818

+ +
+ +
+
+ +
+Compatibility file for making Rocq act similar to Coq v8.18 +
+
+ +
+Require Export Corelib.Compat.Coq819.
+ +
+#[export] Set Warnings "-deprecated-since-8.19".
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Compat.Coq819.html b/master/corelib/Corelib.Compat.Coq819.html new file mode 100644 index 0000000000..7b44bce3bb --- /dev/null +++ b/master/corelib/Corelib.Compat.Coq819.html @@ -0,0 +1,95 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Compat.Coq819

+ +
+ +
+
+ +
+Compatibility file for making Rocq act similar to Coq v8.19 +
+
+ +
+Require Export Corelib.Compat.Coq820.
+ +
+#[export] Set Warnings "-deprecated-since-8.20".
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Compat.Coq820.html b/master/corelib/Corelib.Compat.Coq820.html new file mode 100644 index 0000000000..c2226e2ef0 --- /dev/null +++ b/master/corelib/Corelib.Compat.Coq820.html @@ -0,0 +1,96 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Compat.Coq820

+ +
+ +
+
+ +
+Compatibility file for making Rocq act similar to Coq v8.20 +
+ + When removing this file, please cleanup the "-compat" option code + in sysinit/coqargs.ml +
+
+ +
+#[export] Set Warnings "-deprecated-since-9.0".
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Floats.FloatAxioms.html b/master/corelib/Corelib.Floats.FloatAxioms.html new file mode 100644 index 0000000000..aa30f78836 --- /dev/null +++ b/master/corelib/Corelib.Floats.FloatAxioms.html @@ -0,0 +1,165 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Floats.FloatAxioms

+ +
+ +
+From Corelib Require Import BinNums IntDef Uint63Axioms.
+From Corelib Require Import SpecFloat PrimFloat FloatOps.
+ +
+
+ +
+

Properties of the primitive operators for the Binary64 format

+ +
+
+ +
+Notation valid_binary := (valid_binary prec emax).
+ +
+Definition SF64classify := SFclassify prec.
+Definition SF64mul := SFmul prec emax.
+Definition SF64add := SFadd prec emax.
+Definition SF64sub := SFsub prec emax.
+Definition SF64div := SFdiv prec emax.
+Definition SF64sqrt := SFsqrt prec emax.
+Definition SF64succ := SFsucc prec emax.
+Definition SF64pred := SFpred prec emax.
+ +
+Axiom Prim2SF_valid : forall x, valid_binary (Prim2SF x) = true.
+Axiom SF2Prim_Prim2SF : forall x, SF2Prim (Prim2SF x) = x.
+Axiom Prim2SF_SF2Prim : forall x, valid_binary x = true -> Prim2SF (SF2Prim x) = x.
+ +
+Theorem Prim2SF_inj : forall x y, Prim2SF x = Prim2SF y -> x = y.
+ +
+Theorem SF2Prim_inj : forall x y, SF2Prim x = SF2Prim y -> valid_binary x = true -> valid_binary y = true -> x = y.
+ +
+Axiom opp_spec : forall x, Prim2SF (-x)%float = SFopp (Prim2SF x).
+Axiom abs_spec : forall x, Prim2SF (abs x) = SFabs (Prim2SF x).
+ +
+Axiom eqb_spec : forall x y, (x =? y)%float = SFeqb (Prim2SF x) (Prim2SF y).
+Axiom ltb_spec : forall x y, (x <? y)%float = SFltb (Prim2SF x) (Prim2SF y).
+Axiom leb_spec : forall x y, (x <=? y)%float = SFleb (Prim2SF x) (Prim2SF y).
+ +
+Definition flatten_cmp_opt c :=
+  match c with
+  | None => FNotComparable
+  | Some Eq => FEq
+  | Some Lt => FLt
+  | Some Gt => FGt
+  end.
+Axiom compare_spec : forall x y, (x ?= y)%float = flatten_cmp_opt (SFcompare (Prim2SF x) (Prim2SF y)).
+ +
+Module Leibniz.
+Axiom eqb_spec : forall x y, Leibniz.eqb x y = true <-> x = y.
+End Leibniz.
+ +
+Axiom classify_spec : forall x, classify x = SF64classify (Prim2SF x).
+Axiom mul_spec : forall x y, Prim2SF (x * y)%float = SF64mul (Prim2SF x) (Prim2SF y).
+Axiom add_spec : forall x y, Prim2SF (x + y)%float = SF64add (Prim2SF x) (Prim2SF y).
+Axiom sub_spec : forall x y, Prim2SF (x - y)%float = SF64sub (Prim2SF x) (Prim2SF y).
+Axiom div_spec : forall x y, Prim2SF (x / y)%float = SF64div (Prim2SF x) (Prim2SF y).
+Axiom sqrt_spec : forall x, Prim2SF (sqrt x) = SF64sqrt (Prim2SF x).
+ +
+Axiom of_uint63_spec : forall n, Prim2SF (of_uint63 n) = binary_normalize prec emax (to_Z n) Z0 false.
+Axiom normfr_mantissa_spec : forall f, to_Z (normfr_mantissa f) = Z.of_N (SFnormfr_mantissa prec (Prim2SF f)).
+ +
+Axiom frshiftexp_spec : forall f,
+  let (m,e) := frshiftexp f in
+  (Prim2SF m, Z.sub (to_Z e) shift) = SFfrexp prec emax (Prim2SF f).
+Axiom ldshiftexp_spec : forall f e,
+  Prim2SF (ldshiftexp f e) = SFldexp prec emax (Prim2SF f) (Z.sub (to_Z e) shift).
+ +
+Axiom next_up_spec : forall x, Prim2SF (next_up x) = SF64succ (Prim2SF x).
+Axiom next_down_spec : forall x, Prim2SF (next_down x) = SF64pred (Prim2SF x).
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Floats.FloatClass.html b/master/corelib/Corelib.Floats.FloatClass.html new file mode 100644 index 0000000000..b971a9798a --- /dev/null +++ b/master/corelib/Corelib.Floats.FloatClass.html @@ -0,0 +1,85 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Floats.FloatClass

+ +
+ +
+Variant float_class : Set :=
+  | PNormal | NNormal | PSubn | NSubn | PZero | NZero | PInf | NInf | NaN.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Floats.FloatOps.html b/master/corelib/Corelib.Floats.FloatOps.html new file mode 100644 index 0000000000..5601caa876 --- /dev/null +++ b/master/corelib/Corelib.Floats.FloatOps.html @@ -0,0 +1,158 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Floats.FloatOps

+ +
+ +
+From Corelib Require Import BinNums PosDef IntDef Uint63Axioms.
+From Corelib Require Import FloatClass SpecFloat PrimFloat.
+ +
+
+ +
+

Derived operations and mapping between primitive floats and spec_floats

+ +
+
+ +
+Definition prec := Eval compute in Z.of_nat 53.
+Definition emax := Eval compute in Z.of_nat 1024.
+Notation emin := (emin prec emax).
+ +
+Definition shift := Eval compute in Z.of_nat 2101.
+ +
+= 2*emax + prec +
+
+ +
+Module Z.
+  Definition frexp f :=
+    let (m, se) := frshiftexp f in
+    (m, (Z.sub (to_Z se) shift)).
+ +
+  Definition ldexp f e :=
+    let e' := Z.max (Z.min e (Z.sub emax emin)) (Z.sub (Z.sub emin emax) (Zpos 1)) in
+    ldshiftexp f (of_Z (Z.add e' shift)).
+End Z.
+ +
+Definition ulp f := Z.ldexp one (fexp prec emax (snd (Z.frexp f))).
+ +
+
+ +
+Prim2SF is an injective function that will be useful to express +the properties of the implemented Binary64 format (see FloatAxioms). + +
+
+Definition Prim2SF f :=
+  if is_nan f then S754_nan
+  else if is_zero f then S754_zero (get_sign f)
+       else if is_infinity f then S754_infinity (get_sign f)
+            else
+              let (r, exp) := Z.frexp f in
+              let e := Z.sub exp prec in
+              let (shr, e') := shr_fexp prec emax (to_Z (normfr_mantissa r))%uint63 e loc_Exact in
+              match shr_m shr with
+              | Zpos p => S754_finite (get_sign f) p e'
+              | Zneg _ | Z0 => S754_zero false
+              end.
+ +
+Definition SF2Prim ef :=
+  match ef with
+  | S754_nan => nan
+  | S754_zero false => zero
+  | S754_zero true => neg_zero
+  | S754_infinity false => infinity
+  | S754_infinity true => neg_infinity
+  | S754_finite s m e =>
+    let pm := of_uint63 (of_Z (Zpos m)) in
+    let f := Z.ldexp pm e in
+    if s then (-f)%float else f
+  end.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Floats.PrimFloat.html b/master/corelib/Corelib.Floats.PrimFloat.html new file mode 100644 index 0000000000..447f857842 --- /dev/null +++ b/master/corelib/Corelib.Floats.PrimFloat.html @@ -0,0 +1,364 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Floats.PrimFloat

+ +
+ +
+Require Import PrimInt63 FloatClass.
+ +
+
+ +
+

Definition of the interface for primitive floating-point arithmetic

+ + +
+ +This interface provides processor operators for the Binary64 format of the +IEEE 754-2008 standard. +
+ +

Type definition for the co-domain of compare

+ +
+
+Variant float_comparison : Set := FEq | FLt | FGt | FNotComparable.
+ +
+Register float_comparison as kernel.ind_f_cmp.
+ +
+Register float_class as kernel.ind_f_class.
+ +
+
+ +
+

The main type

+ float: primitive type for Binary64 floating-point numbers. +
+
+Primitive float := #float64_type.
+Register float as num.float.type.
+ +
+Record float_wrapper := wrap_float { float_wrap : float }.
+Register float_wrapper as num.float.float_wrapper.
+Register wrap_float as num.float.wrap_float.
+Definition printer (x : float_wrapper) : float := float_wrap x.
+Definition parser (x : float) : float := x.
+ +
+
+ +
+

Syntax support

+ +
+
+Module Import PrimFloatNotationsInternalA.
+Declare Scope float_scope.
+Delimit Scope float_scope with float.
+Bind Scope float_scope with float.
+End PrimFloatNotationsInternalA.
+Number Notation float parser printer : float_scope.
+ +
+
+ +
+

Floating-point operators

+ +
+
+Primitive classify := #float64_classify.
+ +
+Primitive abs := #float64_abs.
+ +
+Primitive sqrt := #float64_sqrt.
+ +
+Primitive opp := #float64_opp.
+ +
+
+ +
+For the record: this is the IEEE754 equality + (eqb nan nan = false and eqb +0 -0 = true) +
+
+Primitive eqb := #float64_eq.
+ +
+Primitive ltb := #float64_lt.
+ +
+Primitive leb := #float64_le.
+ +
+Primitive compare := #float64_compare.
+ +
+
+ +
+Boolean Leibniz equality +
+
+Module Leibniz.
+Primitive eqb := #float64_equal.
+Register eqb as num.float.leibniz.eqb.
+End Leibniz.
+ +
+Primitive mul := #float64_mul.
+ +
+Primitive add := #float64_add.
+ +
+Primitive sub := #float64_sub.
+ +
+Primitive div := #float64_div.
+ +
+Module Import PrimFloatNotationsInternalB.
+Notation "- x" := (opp x) : float_scope.
+Notation "x =? y" := (eqb x y) (at level 70, no associativity) : float_scope.
+Notation "x <? y" := (ltb x y) (at level 70, no associativity) : float_scope.
+Notation "x <=? y" := (leb x y) (at level 70, no associativity) : float_scope.
+Notation "x ?= y" := (compare x y) (at level 70, no associativity) : float_scope.
+Notation "x * y" := (mul x y) : float_scope.
+Notation "x + y" := (add x y) : float_scope.
+Notation "x - y" := (sub x y) : float_scope.
+Notation "x / y" := (div x y) : float_scope.
+End PrimFloatNotationsInternalB.
+ +
+
+ +
+

Conversions

+ +
+ + of_uint63: convert a primitive unsigned integer into a float value. + The value is rounded if need be. +
+
+Primitive of_uint63 := #float64_of_uint63.
+ +
+
+ +
+Specification of normfr_mantissa: +
    +
  • If the input is a float value with an absolute value inside [0.5, 1.); + +
    • +
  • Then return its mantissa as a primitive integer. + The mantissa will be a 53-bit integer with its most significant bit set to 1; + +
    • +
  • Else return zero. + +
    • +
+ +
+ +The sign bit is always ignored. +
+
+Primitive normfr_mantissa := #float64_normfr_mantissa.
+ +
+
+ +
+

Exponent manipulation functions

+ frshiftexp: convert a float to fractional part in [0.5, 1.) +and integer part. +
+
+Primitive frshiftexp := #float64_frshiftexp.
+ +
+
+ +
+ldshiftexp: multiply a float by an integral power of 2. +
+
+Primitive ldshiftexp := #float64_ldshiftexp.
+ +
+
+ +
+

Predecesor/Successor functions

+ +
+ + next_up: return the next float towards positive infinity. +
+
+Primitive next_up := #float64_next_up.
+ +
+
+ +
+next_down: return the next float towards negative infinity. +
+
+Primitive next_down := #float64_next_down.
+ +
+
+ +
+

Special values (needed for pretty-printing)

+ +
+
+Definition infinity := Eval compute in div (of_uint63 1) (of_uint63 0).
+Definition neg_infinity := Eval compute in opp infinity.
+Definition nan := Eval compute in div (of_uint63 0) (of_uint63 0).
+ +
+Register infinity as num.float.infinity.
+Register neg_infinity as num.float.neg_infinity.
+Register nan as num.float.nan.
+ +
+
+ +
+

Other special values

+ +
+
+Definition one := Eval compute in (of_uint63 1).
+Definition zero := Eval compute in (of_uint63 0).
+Definition neg_zero := Eval compute in (-zero)%float.
+Definition two := Eval compute in (of_uint63 2).
+ +
+
+ +
+

Predicates and helper functions

+ +
+
+Definition is_nan f := negb (f =? f)%float.
+ +
+Definition is_zero f := (f =? zero)%float. +
+Definition is_infinity f := (abs f =? infinity)%float.
+ +
+Definition is_finite (x : float) := negb (is_nan x || is_infinity x).
+ +
+
+ +
+get_sign: return true for - sign, false for + sign. +
+
+Definition get_sign f :=
+  let f := if is_zero f then (one / f)%float else f in
+  (f <? zero)%float.
+ +
+Module Export PrimFloatNotations.
+  Local Open Scope float_scope.
+  Export PrimFloatNotationsInternalA.
+  Export PrimFloatNotationsInternalB.
+End PrimFloatNotations.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Floats.SpecFloat.html b/master/corelib/Corelib.Floats.SpecFloat.html new file mode 100644 index 0000000000..a2bdf25464 --- /dev/null +++ b/master/corelib/Corelib.Floats.SpecFloat.html @@ -0,0 +1,575 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Floats.SpecFloat

+ +
+ +
+From Corelib Require Import BinNums PosDef IntDef FloatClass.
+ +
+
+ +
+

Specification of floating-point arithmetic

+ + +
+ +This specification is mostly borrowed from the IEEE754.Binary module +of the Flocq library (see http://flocq.gforge.inria.fr/) +
+ +

Inductive specification of floating-point numbers

+ + +
+ +Similar to Flocq.IEEE754.Binary.full_float, but with no NaN payload. +
+
+Variant spec_float :=
+  | S754_zero (s : bool)
+  | S754_infinity (s : bool)
+  | S754_nan
+  | S754_finite (s : bool) (m : positive) (e : Z).
+ +
+
+ +
+

Parameterized definitions

+ + +
+ +prec is the number of bits of the mantissa including the implicit one; +emax is the exponent of the infinities. + +
+ +For instance, Binary64 is defined by prec = 53 and emax = 1024. +
+
+Section FloatOps.
+  Variable prec emax : Z.
+ +
+  Definition emin := Z.sub (Z.sub (Zpos 3) emax) prec.
+  Definition fexp e := Z.max (Z.sub e prec) emin.
+ +
+  Section Zdigits2.
+    Fixpoint digits2_pos (n : positive) : positive :=
+      match n with
+      | xH => xH
+      | xO p => Pos.succ (digits2_pos p)
+      | xI p => Pos.succ (digits2_pos p)
+      end.
+ +
+    Definition Zdigits2 n :=
+      match n with
+      | Z0 => n
+      | Zpos p => Zpos (digits2_pos p)
+      | Zneg p => Zpos (digits2_pos p)
+      end.
+  End Zdigits2.
+ +
+  Section ValidBinary.
+    Definition canonical_mantissa m e :=
+      Z.eqb (fexp (Z.add (Zpos (digits2_pos m)) e)) e.
+ +
+    Definition bounded m e :=
+      andb (canonical_mantissa m e) (Z.leb e (Z.sub emax prec)).
+ +
+    Definition valid_binary x :=
+      match x with
+      | S754_finite _ m e => bounded m e
+      | _ => true
+      end.
+  End ValidBinary.
+ +
+  Section Iter.
+    Context {A : Type}.
+    Variable (f : A -> A).
+ +
+    Fixpoint iter_pos (n : positive) (x : A) {struct n} : A :=
+      match n with
+      | xI n' => iter_pos n' (iter_pos n' (f x))
+      | xO n' => iter_pos n' (iter_pos n' x)
+      | xH => f x
+      end.
+  End Iter.
+ +
+  Section Rounding.
+    Inductive location := loc_Exact | loc_Inexact : comparison -> location.
+ +
+    Record shr_record := { shr_m : Z ; shr_r : bool ; shr_s : bool }.
+ +
+    Definition shr_1 mrs :=
+      let '(Build_shr_record m r s) := mrs in
+      let s := orb r s in
+      match m with
+      | Z0 => Build_shr_record Z0 false s
+      | Zpos xH => Build_shr_record Z0 true s
+      | Zpos (xO p) => Build_shr_record (Zpos p) false s
+      | Zpos (xI p) => Build_shr_record (Zpos p) true s
+      | Zneg xH => Build_shr_record Z0 true s
+      | Zneg (xO p) => Build_shr_record (Zneg p) false s
+      | Zneg (xI p) => Build_shr_record (Zneg p) true s
+      end.
+ +
+    Definition loc_of_shr_record mrs :=
+      match mrs with
+      | Build_shr_record _ false false => loc_Exact
+      | Build_shr_record _ false true => loc_Inexact Lt
+      | Build_shr_record _ true false => loc_Inexact Eq
+      | Build_shr_record _ true true => loc_Inexact Gt
+      end.
+ +
+    Definition shr_record_of_loc m l :=
+      match l with
+      | loc_Exact => Build_shr_record m false false
+      | loc_Inexact Lt => Build_shr_record m false true
+      | loc_Inexact Eq => Build_shr_record m true false
+      | loc_Inexact Gt => Build_shr_record m true true
+      end.
+ +
+    Definition shr mrs e n :=
+      match n with
+      | Zpos p => (iter_pos shr_1 p mrs, Z.add e n)
+      | _ => (mrs, e)
+      end.
+ +
+    Definition shr_fexp m e l :=
+      shr (shr_record_of_loc m l) e (Z.sub (fexp (Z.add (Zdigits2 m) e)) e).
+ +
+    Definition round_nearest_even mx lx :=
+      match lx with
+      | loc_Exact => mx
+      | loc_Inexact Lt => mx
+      | loc_Inexact Eq => if Z.even mx then mx else Z.add mx (Zpos 1)
+      | loc_Inexact Gt => Z.add mx (Zpos 1)
+      end.
+ +
+    Definition binary_round_aux sx mx ex lx :=
+      let '(mrs', e') := shr_fexp mx ex lx in
+      let '(mrs'', e'') := shr_fexp (round_nearest_even (shr_m mrs') (loc_of_shr_record mrs')) e' loc_Exact in
+      match shr_m mrs'' with
+      | Z0 => S754_zero sx
+      | Zpos m => if Z.leb e'' (Z.sub emax prec) then S754_finite sx m e'' else S754_infinity sx
+      | _ => S754_nan
+      end.
+ +
+    Definition shl_align mx ex ex' :=
+      match Z.sub ex' ex with
+      | Zneg d => (Pos.iter xO mx d, ex')
+      | _ => (mx, ex)
+      end.
+ +
+    Definition binary_round sx mx ex :=
+      let '(mz, ez) := shl_align mx ex (fexp (Z.add (Zpos (digits2_pos mx)) ex))in
+      binary_round_aux sx (Zpos mz) ez loc_Exact.
+ +
+    Definition binary_normalize m e szero :=
+      match m with
+      | Z0 => S754_zero szero
+      | Zpos m => binary_round false m e
+      | Zneg m => binary_round true m e
+      end.
+  End Rounding.
+ +
+
+ +
+

Define operations

+ +
+
+ +
+  Definition SFopp x :=
+    match x with
+    | S754_nan => S754_nan
+    | S754_infinity sx => S754_infinity (negb sx)
+    | S754_finite sx mx ex => S754_finite (negb sx) mx ex
+    | S754_zero sx => S754_zero (negb sx)
+    end.
+ +
+  Definition SFabs x :=
+    match x with
+    | S754_nan => S754_nan
+    | S754_infinity sx => S754_infinity false
+    | S754_finite sx mx ex => S754_finite false mx ex
+    | S754_zero sx => S754_zero false
+    end.
+ +
+  Definition SFcompare f1 f2 :=
+    match f1, f2 with
+    | S754_nan , _ | _, S754_nan => None
+    | S754_infinity s1, S754_infinity s2 =>
+      Some match s1, s2 with
+      | true, true => Eq
+      | false, false => Eq
+      | true, false => Lt
+      | false, true => Gt
+      end
+    | S754_infinity s, _ => Some (if s then Lt else Gt)
+    | _, S754_infinity s => Some (if s then Gt else Lt)
+    | S754_finite s _ _, S754_zero _ => Some (if s then Lt else Gt)
+    | S754_zero _, S754_finite s _ _ => Some (if s then Gt else Lt)
+    | S754_zero _, S754_zero _ => Some Eq
+    | S754_finite s1 m1 e1, S754_finite s2 m2 e2 =>
+      Some match s1, s2 with
+      | true, false => Lt
+      | false, true => Gt
+      | false, false =>
+        match Z.compare e1 e2 with
+        | Lt => Lt
+        | Gt => Gt
+        | Eq => Pos.compare_cont Eq m1 m2
+        end
+      | true, true =>
+        match Z.compare e1 e2 with
+        | Lt => Gt
+        | Gt => Lt
+        | Eq => CompOpp (Pos.compare_cont Eq m1 m2)
+        end
+      end
+    end.
+ +
+  Definition SFeqb f1 f2 :=
+    match SFcompare f1 f2 with
+    | Some Eq => true
+    | _ => false
+    end.
+ +
+  Definition SFltb f1 f2 :=
+    match SFcompare f1 f2 with
+    | Some Lt => true
+    | _ => false
+    end.
+ +
+  Definition SFleb f1 f2 :=
+    match SFcompare f1 f2 with
+    | Some (Lt | Eq) => true
+    | _ => false
+    end.
+ +
+  Definition SFclassify f :=
+    match f with
+    | S754_nan => NaN
+    | S754_infinity false => PInf
+    | S754_infinity true => NInf
+    | S754_zero false => PZero
+    | S754_zero true => NZero
+    | S754_finite false m _ =>
+      if Z.eqb (Zpos (digits2_pos m)) prec then PNormal
+      else PSubn
+    | S754_finite true m _ =>
+      if Z.eqb (Zpos (digits2_pos m)) prec then NNormal
+      else NSubn
+    end.
+ +
+  Definition SFmul x y :=
+    match x, y with
+    | S754_nan, _ | _, S754_nan => S754_nan
+    | S754_infinity sx, S754_infinity sy => S754_infinity (xorb sx sy)
+    | S754_infinity sx, S754_finite sy _ _ => S754_infinity (xorb sx sy)
+    | S754_finite sx _ _, S754_infinity sy => S754_infinity (xorb sx sy)
+    | S754_infinity _, S754_zero _ => S754_nan
+    | S754_zero _, S754_infinity _ => S754_nan
+    | S754_finite sx _ _, S754_zero sy => S754_zero (xorb sx sy)
+    | S754_zero sx, S754_finite sy _ _ => S754_zero (xorb sx sy)
+    | S754_zero sx, S754_zero sy => S754_zero (xorb sx sy)
+    | S754_finite sx mx ex, S754_finite sy my ey =>
+      binary_round_aux (xorb sx sy) (Zpos (Pos.mul mx my)) (Z.add ex ey) loc_Exact
+    end.
+ +
+  Definition cond_Zopp (b : bool) m := if b then Z.opp m else m.
+ +
+  Definition SFadd x y :=
+    match x, y with
+    | S754_nan, _ | _, S754_nan => S754_nan
+    | S754_infinity sx, S754_infinity sy =>
+      match sx, sy with true, true | false, false => x | _, _ => S754_nan end
+    | S754_infinity _, _ => x
+    | _, S754_infinity _ => y
+    | S754_zero sx, S754_zero sy =>
+      match sx, sy with true, true | false, false => x | _, _ => S754_zero false end
+    | S754_zero _, _ => y
+    | _, S754_zero _ => x
+    | S754_finite sx mx ex, S754_finite sy my ey =>
+      let ez := Z.min ex ey in
+      binary_normalize (Z.add (cond_Zopp sx (Zpos (fst (shl_align mx ex ez)))) (cond_Zopp sy (Zpos (fst (shl_align my ey ez)))))
+        ez false
+    end.
+ +
+  Definition SFsub x y :=
+    match x, y with
+    | S754_nan, _ | _, S754_nan => S754_nan
+    | S754_infinity sx, S754_infinity sy =>
+      match sx, sy with true, false | false, true => x | _, _ => S754_nan end
+    | S754_infinity _, _ => x
+    | _, S754_infinity sy => S754_infinity (negb sy)
+    | S754_zero sx, S754_zero sy =>
+      match sx, sy with true, false | false, true => x | _, _ => S754_zero false end
+    | S754_zero _, S754_finite sy my ey => S754_finite (negb sy) my ey
+    | _, S754_zero _ => x
+    | S754_finite sx mx ex, S754_finite sy my ey =>
+      let ez := Z.min ex ey in
+      binary_normalize (Z.sub (cond_Zopp sx (Zpos (fst (shl_align mx ex ez)))) (cond_Zopp sy (Zpos (fst (shl_align my ey ez)))))
+        ez false
+    end.
+ +
+  Definition new_location_even nb_steps k :=
+    if Z.eqb k Z0 then loc_Exact
+    else loc_Inexact (Z.compare (Z.mul (Zpos 2) k) nb_steps).
+ +
+  Definition new_location_odd nb_steps k :=
+    if Z.eqb k Z0 then loc_Exact
+    else
+      loc_Inexact
+      match Z.compare (Z.add (Z.mul (Zpos 2) k) (Zpos 1)) nb_steps with
+      | Lt => Lt
+      | Eq => Lt
+      | Gt => Gt
+      end.
+ +
+  Definition new_location nb_steps :=
+    if Z.even nb_steps then new_location_even nb_steps else new_location_odd nb_steps.
+ +
+  Definition SFdiv_core_binary m1 e1 m2 e2 :=
+    let d1 := Zdigits2 m1 in
+    let d2 := Zdigits2 m2 in
+    let e' := Z.min (fexp (Z.sub (Z.add d1 e1) (Z.add d2 e2))) (Z.sub e1 e2) in
+    let s := Z.sub (Z.sub e1 e2) e' in
+    let m' :=
+      match s with
+      | Zpos _ => Z.shiftl m1 s
+      | Z0 => m1
+      | Zneg _ => Z0
+      end in
+    let '(q, r) := Z.div_eucl m' m2 in
+    (q, e', new_location m2 r).
+ +
+  Definition SFdiv x y :=
+    match x, y with
+    | S754_nan, _ | _, S754_nan => S754_nan
+    | S754_infinity sx, S754_infinity sy => S754_nan
+    | S754_infinity sx, S754_finite sy _ _ => S754_infinity (xorb sx sy)
+    | S754_finite sx _ _, S754_infinity sy => S754_zero (xorb sx sy)
+    | S754_infinity sx, S754_zero sy => S754_infinity (xorb sx sy)
+    | S754_zero sx, S754_infinity sy => S754_zero (xorb sx sy)
+    | S754_finite sx _ _, S754_zero sy => S754_infinity (xorb sx sy)
+    | S754_zero sx, S754_finite sy _ _ => S754_zero (xorb sx sy)
+    | S754_zero sx, S754_zero sy => S754_nan
+    | S754_finite sx mx ex, S754_finite sy my ey =>
+      let '(mz, ez, lz) := SFdiv_core_binary (Zpos mx) ex (Zpos my) ey in
+      binary_round_aux (xorb sx sy) mz ez lz
+    end.
+ +
+  Definition SFsqrt_core_binary m e :=
+    let d := Zdigits2 m in
+    let e' := Z.min (fexp (Z.div2 (Z.add (Z.add d e) (Zpos 1)))) (Z.div2 e) in
+    let s := Z.sub e (Z.mul (Zpos 2) e') in
+    let m' :=
+      match s with
+      | Zpos p => Z.shiftl m s
+      | Z0 => m
+      | Zneg _ => Z0
+      end in
+    let (q, r) := Z.sqrtrem m' in
+    let l :=
+      if Z.eqb r Z0 then loc_Exact
+      else loc_Inexact (if Z.leb r q then Lt else Gt) in
+    (q, e', l).
+ +
+  Definition SFsqrt x :=
+    match x with
+    | S754_nan => S754_nan
+    | S754_infinity false => x
+    | S754_infinity true => S754_nan
+    | S754_finite true _ _ => S754_nan
+    | S754_zero _ => x
+    | S754_finite false mx ex =>
+      let '(mz, ez, lz) := SFsqrt_core_binary (Zpos mx) ex in
+      binary_round_aux false mz ez lz
+    end.
+ +
+  Definition SFnormfr_mantissa f :=
+    match f with
+    | S754_finite _ mx ex =>
+      if Z.eqb ex (Z.opp prec) then Npos mx else N0
+    | _ => N0
+    end.
+ +
+  Definition SFldexp f e :=
+    match f with
+    | S754_finite sx mx ex => binary_round sx mx (Z.add ex e)
+    | _ => f
+    end.
+ +
+  Definition SFfrexp f :=
+    match f with
+    | S754_finite sx mx ex =>
+      if Z.leb prec (Zpos (digits2_pos mx)) then
+        (S754_finite sx mx (Z.opp prec), Z.add ex prec)
+      else
+        let d := Z.sub prec (Zpos (digits2_pos mx)) in
+        (S754_finite sx (Pos.iter xO mx (Z.to_pos d)) (Z.opp prec), Z.sub (Z.add ex prec) d)
+    | _ => (f, Z.sub (Z.mul (Zneg 2) emax) prec)
+    end.
+ +
+  Definition SFone := binary_round false 1 Z0.
+ +
+  Definition SFulp x := SFldexp SFone (fexp (snd (SFfrexp x))).
+ +
+  Definition SFpred_pos x :=
+    match x with
+    | S754_finite _ mx _ =>
+      let d :=
+        if Pos.eqb mx~0 (Pos.iter xO xH (Z.to_pos prec)) then
+          SFldexp SFone (fexp (Z.sub (snd (SFfrexp x)) (Zpos 1)))
+        else
+          SFulp x in
+      SFsub x d
+    | _ => x
+    end.
+ +
+  Definition SFmax_float :=
+    S754_finite false (Pos.sub (Pos.iter xO xH (Z.to_pos prec)) 1) (Z.sub emax prec).
+ +
+  Definition SFsucc x :=
+    match x with
+    | S754_zero _ => SFldexp SFone emin
+    | S754_infinity false => x
+    | S754_infinity true => SFopp SFmax_float
+    | S754_nan => x
+    | S754_finite false _ _ => SFadd x (SFulp x)
+    | S754_finite true _ _ => SFopp (SFpred_pos (SFopp x))
+    end.
+ +
+  Definition SFpred f := SFopp (SFsucc (SFopp f)).
+End FloatOps.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Init.Byte.html b/master/corelib/Corelib.Init.Byte.html new file mode 100644 index 0000000000..8578d35e77 --- /dev/null +++ b/master/corelib/Corelib.Init.Byte.html @@ -0,0 +1,925 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Init.Byte

+ +
+ +
+
+ +
+

Bytes

+ +
+
+ +
+Require Import Corelib.Init.Ltac.
+Require Import Corelib.Init.Datatypes.
+Require Import Corelib.Init.Logic.
+Require Import Corelib.Init.Specif.
+Require Corelib.Init.Nat.
+ +
+ +
+
+ +
+We define an inductive for use with the String Notation command + which contains all ascii characters. We use 256 constructors for + efficiency and ease of conversion. +
+
+ +
+Declare Scope byte_scope.
+Delimit Scope byte_scope with byte.
+ +
+Inductive byte :=
+| x00
+| x01
+| x02
+| x03
+| x04
+| x05
+| x06
+| x07
+| x08
+| x09
+| x0a
+| x0b
+| x0c
+| x0d
+| x0e
+| x0f
+| x10
+| x11
+| x12
+| x13
+| x14
+| x15
+| x16
+| x17
+| x18
+| x19
+| x1a
+| x1b
+| x1c
+| x1d
+| x1e
+| x1f
+| x20
+| x21
+| x22
+| x23
+| x24
+| x25
+| x26
+| x27
+| x28
+| x29
+| x2a
+| x2b
+| x2c
+| x2d
+| x2e
+| x2f
+| x30
+| x31
+| x32
+| x33
+| x34
+| x35
+| x36
+| x37
+| x38
+| x39
+| x3a
+| x3b
+| x3c
+| x3d
+| x3e
+| x3f
+| x40
+| x41
+| x42
+| x43
+| x44
+| x45
+| x46
+| x47
+| x48
+| x49
+| x4a
+| x4b
+| x4c
+| x4d
+| x4e
+| x4f
+| x50
+| x51
+| x52
+| x53
+| x54
+| x55
+| x56
+| x57
+| x58
+| x59
+| x5a
+| x5b
+| x5c
+| x5d
+| x5e
+| x5f
+| x60
+| x61
+| x62
+| x63
+| x64
+| x65
+| x66
+| x67
+| x68
+| x69
+| x6a
+| x6b
+| x6c
+| x6d
+| x6e
+| x6f
+| x70
+| x71
+| x72
+| x73
+| x74
+| x75
+| x76
+| x77
+| x78
+| x79
+| x7a
+| x7b
+| x7c
+| x7d
+| x7e
+| x7f
+| x80
+| x81
+| x82
+| x83
+| x84
+| x85
+| x86
+| x87
+| x88
+| x89
+| x8a
+| x8b
+| x8c
+| x8d
+| x8e
+| x8f
+| x90
+| x91
+| x92
+| x93
+| x94
+| x95
+| x96
+| x97
+| x98
+| x99
+| x9a
+| x9b
+| x9c
+| x9d
+| x9e
+| x9f
+| xa0
+| xa1
+| xa2
+| xa3
+| xa4
+| xa5
+| xa6
+| xa7
+| xa8
+| xa9
+| xaa
+| xab
+| xac
+| xad
+| xae
+| xaf
+| xb0
+| xb1
+| xb2
+| xb3
+| xb4
+| xb5
+| xb6
+| xb7
+| xb8
+| xb9
+| xba
+| xbb
+| xbc
+| xbd
+| xbe
+| xbf
+| xc0
+| xc1
+| xc2
+| xc3
+| xc4
+| xc5
+| xc6
+| xc7
+| xc8
+| xc9
+| xca
+| xcb
+| xcc
+| xcd
+| xce
+| xcf
+| xd0
+| xd1
+| xd2
+| xd3
+| xd4
+| xd5
+| xd6
+| xd7
+| xd8
+| xd9
+| xda
+| xdb
+| xdc
+| xdd
+| xde
+| xdf
+| xe0
+| xe1
+| xe2
+| xe3
+| xe4
+| xe5
+| xe6
+| xe7
+| xe8
+| xe9
+| xea
+| xeb
+| xec
+| xed
+| xee
+| xef
+| xf0
+| xf1
+| xf2
+| xf3
+| xf4
+| xf5
+| xf6
+| xf7
+| xf8
+| xf9
+| xfa
+| xfb
+| xfc
+| xfd
+| xfe
+| xff
+.
+ +
+Bind Scope byte_scope with byte.
+ +
+Register byte as core.byte.type.
+ +
+Local Notation "0" := false.
+Local Notation "1" := true.
+ +
+
+ +
+We pick a definition that matches with Ascii.ascii +
+
+Definition of_bits (b : bool * (bool * (bool * (bool * (bool * (bool * (bool * bool))))))) : byte
+  := match b with
+     | (0,(0,(0,(0,(0,(0,(0,0))))))) => x00
+     | (1,(0,(0,(0,(0,(0,(0,0))))))) => x01
+     | (0,(1,(0,(0,(0,(0,(0,0))))))) => x02
+     | (1,(1,(0,(0,(0,(0,(0,0))))))) => x03
+     | (0,(0,(1,(0,(0,(0,(0,0))))))) => x04
+     | (1,(0,(1,(0,(0,(0,(0,0))))))) => x05
+     | (0,(1,(1,(0,(0,(0,(0,0))))))) => x06
+     | (1,(1,(1,(0,(0,(0,(0,0))))))) => x07
+     | (0,(0,(0,(1,(0,(0,(0,0))))))) => x08
+     | (1,(0,(0,(1,(0,(0,(0,0))))))) => x09
+     | (0,(1,(0,(1,(0,(0,(0,0))))))) => x0a
+     | (1,(1,(0,(1,(0,(0,(0,0))))))) => x0b
+     | (0,(0,(1,(1,(0,(0,(0,0))))))) => x0c
+     | (1,(0,(1,(1,(0,(0,(0,0))))))) => x0d
+     | (0,(1,(1,(1,(0,(0,(0,0))))))) => x0e
+     | (1,(1,(1,(1,(0,(0,(0,0))))))) => x0f
+     | (0,(0,(0,(0,(1,(0,(0,0))))))) => x10
+     | (1,(0,(0,(0,(1,(0,(0,0))))))) => x11
+     | (0,(1,(0,(0,(1,(0,(0,0))))))) => x12
+     | (1,(1,(0,(0,(1,(0,(0,0))))))) => x13
+     | (0,(0,(1,(0,(1,(0,(0,0))))))) => x14
+     | (1,(0,(1,(0,(1,(0,(0,0))))))) => x15
+     | (0,(1,(1,(0,(1,(0,(0,0))))))) => x16
+     | (1,(1,(1,(0,(1,(0,(0,0))))))) => x17
+     | (0,(0,(0,(1,(1,(0,(0,0))))))) => x18
+     | (1,(0,(0,(1,(1,(0,(0,0))))))) => x19
+     | (0,(1,(0,(1,(1,(0,(0,0))))))) => x1a
+     | (1,(1,(0,(1,(1,(0,(0,0))))))) => x1b
+     | (0,(0,(1,(1,(1,(0,(0,0))))))) => x1c
+     | (1,(0,(1,(1,(1,(0,(0,0))))))) => x1d
+     | (0,(1,(1,(1,(1,(0,(0,0))))))) => x1e
+     | (1,(1,(1,(1,(1,(0,(0,0))))))) => x1f
+     | (0,(0,(0,(0,(0,(1,(0,0))))))) => x20
+     | (1,(0,(0,(0,(0,(1,(0,0))))))) => x21
+     | (0,(1,(0,(0,(0,(1,(0,0))))))) => x22
+     | (1,(1,(0,(0,(0,(1,(0,0))))))) => x23
+     | (0,(0,(1,(0,(0,(1,(0,0))))))) => x24
+     | (1,(0,(1,(0,(0,(1,(0,0))))))) => x25
+     | (0,(1,(1,(0,(0,(1,(0,0))))))) => x26
+     | (1,(1,(1,(0,(0,(1,(0,0))))))) => x27
+     | (0,(0,(0,(1,(0,(1,(0,0))))))) => x28
+     | (1,(0,(0,(1,(0,(1,(0,0))))))) => x29
+     | (0,(1,(0,(1,(0,(1,(0,0))))))) => x2a
+     | (1,(1,(0,(1,(0,(1,(0,0))))))) => x2b
+     | (0,(0,(1,(1,(0,(1,(0,0))))))) => x2c
+     | (1,(0,(1,(1,(0,(1,(0,0))))))) => x2d
+     | (0,(1,(1,(1,(0,(1,(0,0))))))) => x2e
+     | (1,(1,(1,(1,(0,(1,(0,0))))))) => x2f
+     | (0,(0,(0,(0,(1,(1,(0,0))))))) => x30
+     | (1,(0,(0,(0,(1,(1,(0,0))))))) => x31
+     | (0,(1,(0,(0,(1,(1,(0,0))))))) => x32
+     | (1,(1,(0,(0,(1,(1,(0,0))))))) => x33
+     | (0,(0,(1,(0,(1,(1,(0,0))))))) => x34
+     | (1,(0,(1,(0,(1,(1,(0,0))))))) => x35
+     | (0,(1,(1,(0,(1,(1,(0,0))))))) => x36
+     | (1,(1,(1,(0,(1,(1,(0,0))))))) => x37
+     | (0,(0,(0,(1,(1,(1,(0,0))))))) => x38
+     | (1,(0,(0,(1,(1,(1,(0,0))))))) => x39
+     | (0,(1,(0,(1,(1,(1,(0,0))))))) => x3a
+     | (1,(1,(0,(1,(1,(1,(0,0))))))) => x3b
+     | (0,(0,(1,(1,(1,(1,(0,0))))))) => x3c
+     | (1,(0,(1,(1,(1,(1,(0,0))))))) => x3d
+     | (0,(1,(1,(1,(1,(1,(0,0))))))) => x3e
+     | (1,(1,(1,(1,(1,(1,(0,0))))))) => x3f
+     | (0,(0,(0,(0,(0,(0,(1,0))))))) => x40
+     | (1,(0,(0,(0,(0,(0,(1,0))))))) => x41
+     | (0,(1,(0,(0,(0,(0,(1,0))))))) => x42
+     | (1,(1,(0,(0,(0,(0,(1,0))))))) => x43
+     | (0,(0,(1,(0,(0,(0,(1,0))))))) => x44
+     | (1,(0,(1,(0,(0,(0,(1,0))))))) => x45
+     | (0,(1,(1,(0,(0,(0,(1,0))))))) => x46
+     | (1,(1,(1,(0,(0,(0,(1,0))))))) => x47
+     | (0,(0,(0,(1,(0,(0,(1,0))))))) => x48
+     | (1,(0,(0,(1,(0,(0,(1,0))))))) => x49
+     | (0,(1,(0,(1,(0,(0,(1,0))))))) => x4a
+     | (1,(1,(0,(1,(0,(0,(1,0))))))) => x4b
+     | (0,(0,(1,(1,(0,(0,(1,0))))))) => x4c
+     | (1,(0,(1,(1,(0,(0,(1,0))))))) => x4d
+     | (0,(1,(1,(1,(0,(0,(1,0))))))) => x4e
+     | (1,(1,(1,(1,(0,(0,(1,0))))))) => x4f
+     | (0,(0,(0,(0,(1,(0,(1,0))))))) => x50
+     | (1,(0,(0,(0,(1,(0,(1,0))))))) => x51
+     | (0,(1,(0,(0,(1,(0,(1,0))))))) => x52
+     | (1,(1,(0,(0,(1,(0,(1,0))))))) => x53
+     | (0,(0,(1,(0,(1,(0,(1,0))))))) => x54
+     | (1,(0,(1,(0,(1,(0,(1,0))))))) => x55
+     | (0,(1,(1,(0,(1,(0,(1,0))))))) => x56
+     | (1,(1,(1,(0,(1,(0,(1,0))))))) => x57
+     | (0,(0,(0,(1,(1,(0,(1,0))))))) => x58
+     | (1,(0,(0,(1,(1,(0,(1,0))))))) => x59
+     | (0,(1,(0,(1,(1,(0,(1,0))))))) => x5a
+     | (1,(1,(0,(1,(1,(0,(1,0))))))) => x5b
+     | (0,(0,(1,(1,(1,(0,(1,0))))))) => x5c
+     | (1,(0,(1,(1,(1,(0,(1,0))))))) => x5d
+     | (0,(1,(1,(1,(1,(0,(1,0))))))) => x5e
+     | (1,(1,(1,(1,(1,(0,(1,0))))))) => x5f
+     | (0,(0,(0,(0,(0,(1,(1,0))))))) => x60
+     | (1,(0,(0,(0,(0,(1,(1,0))))))) => x61
+     | (0,(1,(0,(0,(0,(1,(1,0))))))) => x62
+     | (1,(1,(0,(0,(0,(1,(1,0))))))) => x63
+     | (0,(0,(1,(0,(0,(1,(1,0))))))) => x64
+     | (1,(0,(1,(0,(0,(1,(1,0))))))) => x65
+     | (0,(1,(1,(0,(0,(1,(1,0))))))) => x66
+     | (1,(1,(1,(0,(0,(1,(1,0))))))) => x67
+     | (0,(0,(0,(1,(0,(1,(1,0))))))) => x68
+     | (1,(0,(0,(1,(0,(1,(1,0))))))) => x69
+     | (0,(1,(0,(1,(0,(1,(1,0))))))) => x6a
+     | (1,(1,(0,(1,(0,(1,(1,0))))))) => x6b
+     | (0,(0,(1,(1,(0,(1,(1,0))))))) => x6c
+     | (1,(0,(1,(1,(0,(1,(1,0))))))) => x6d
+     | (0,(1,(1,(1,(0,(1,(1,0))))))) => x6e
+     | (1,(1,(1,(1,(0,(1,(1,0))))))) => x6f
+     | (0,(0,(0,(0,(1,(1,(1,0))))))) => x70
+     | (1,(0,(0,(0,(1,(1,(1,0))))))) => x71
+     | (0,(1,(0,(0,(1,(1,(1,0))))))) => x72
+     | (1,(1,(0,(0,(1,(1,(1,0))))))) => x73
+     | (0,(0,(1,(0,(1,(1,(1,0))))))) => x74
+     | (1,(0,(1,(0,(1,(1,(1,0))))))) => x75
+     | (0,(1,(1,(0,(1,(1,(1,0))))))) => x76
+     | (1,(1,(1,(0,(1,(1,(1,0))))))) => x77
+     | (0,(0,(0,(1,(1,(1,(1,0))))))) => x78
+     | (1,(0,(0,(1,(1,(1,(1,0))))))) => x79
+     | (0,(1,(0,(1,(1,(1,(1,0))))))) => x7a
+     | (1,(1,(0,(1,(1,(1,(1,0))))))) => x7b
+     | (0,(0,(1,(1,(1,(1,(1,0))))))) => x7c
+     | (1,(0,(1,(1,(1,(1,(1,0))))))) => x7d
+     | (0,(1,(1,(1,(1,(1,(1,0))))))) => x7e
+     | (1,(1,(1,(1,(1,(1,(1,0))))))) => x7f
+     | (0,(0,(0,(0,(0,(0,(0,1))))))) => x80
+     | (1,(0,(0,(0,(0,(0,(0,1))))))) => x81
+     | (0,(1,(0,(0,(0,(0,(0,1))))))) => x82
+     | (1,(1,(0,(0,(0,(0,(0,1))))))) => x83
+     | (0,(0,(1,(0,(0,(0,(0,1))))))) => x84
+     | (1,(0,(1,(0,(0,(0,(0,1))))))) => x85
+     | (0,(1,(1,(0,(0,(0,(0,1))))))) => x86
+     | (1,(1,(1,(0,(0,(0,(0,1))))))) => x87
+     | (0,(0,(0,(1,(0,(0,(0,1))))))) => x88
+     | (1,(0,(0,(1,(0,(0,(0,1))))))) => x89
+     | (0,(1,(0,(1,(0,(0,(0,1))))))) => x8a
+     | (1,(1,(0,(1,(0,(0,(0,1))))))) => x8b
+     | (0,(0,(1,(1,(0,(0,(0,1))))))) => x8c
+     | (1,(0,(1,(1,(0,(0,(0,1))))))) => x8d
+     | (0,(1,(1,(1,(0,(0,(0,1))))))) => x8e
+     | (1,(1,(1,(1,(0,(0,(0,1))))))) => x8f
+     | (0,(0,(0,(0,(1,(0,(0,1))))))) => x90
+     | (1,(0,(0,(0,(1,(0,(0,1))))))) => x91
+     | (0,(1,(0,(0,(1,(0,(0,1))))))) => x92
+     | (1,(1,(0,(0,(1,(0,(0,1))))))) => x93
+     | (0,(0,(1,(0,(1,(0,(0,1))))))) => x94
+     | (1,(0,(1,(0,(1,(0,(0,1))))))) => x95
+     | (0,(1,(1,(0,(1,(0,(0,1))))))) => x96
+     | (1,(1,(1,(0,(1,(0,(0,1))))))) => x97
+     | (0,(0,(0,(1,(1,(0,(0,1))))))) => x98
+     | (1,(0,(0,(1,(1,(0,(0,1))))))) => x99
+     | (0,(1,(0,(1,(1,(0,(0,1))))))) => x9a
+     | (1,(1,(0,(1,(1,(0,(0,1))))))) => x9b
+     | (0,(0,(1,(1,(1,(0,(0,1))))))) => x9c
+     | (1,(0,(1,(1,(1,(0,(0,1))))))) => x9d
+     | (0,(1,(1,(1,(1,(0,(0,1))))))) => x9e
+     | (1,(1,(1,(1,(1,(0,(0,1))))))) => x9f
+     | (0,(0,(0,(0,(0,(1,(0,1))))))) => xa0
+     | (1,(0,(0,(0,(0,(1,(0,1))))))) => xa1
+     | (0,(1,(0,(0,(0,(1,(0,1))))))) => xa2
+     | (1,(1,(0,(0,(0,(1,(0,1))))))) => xa3
+     | (0,(0,(1,(0,(0,(1,(0,1))))))) => xa4
+     | (1,(0,(1,(0,(0,(1,(0,1))))))) => xa5
+     | (0,(1,(1,(0,(0,(1,(0,1))))))) => xa6
+     | (1,(1,(1,(0,(0,(1,(0,1))))))) => xa7
+     | (0,(0,(0,(1,(0,(1,(0,1))))))) => xa8
+     | (1,(0,(0,(1,(0,(1,(0,1))))))) => xa9
+     | (0,(1,(0,(1,(0,(1,(0,1))))))) => xaa
+     | (1,(1,(0,(1,(0,(1,(0,1))))))) => xab
+     | (0,(0,(1,(1,(0,(1,(0,1))))))) => xac
+     | (1,(0,(1,(1,(0,(1,(0,1))))))) => xad
+     | (0,(1,(1,(1,(0,(1,(0,1))))))) => xae
+     | (1,(1,(1,(1,(0,(1,(0,1))))))) => xaf
+     | (0,(0,(0,(0,(1,(1,(0,1))))))) => xb0
+     | (1,(0,(0,(0,(1,(1,(0,1))))))) => xb1
+     | (0,(1,(0,(0,(1,(1,(0,1))))))) => xb2
+     | (1,(1,(0,(0,(1,(1,(0,1))))))) => xb3
+     | (0,(0,(1,(0,(1,(1,(0,1))))))) => xb4
+     | (1,(0,(1,(0,(1,(1,(0,1))))))) => xb5
+     | (0,(1,(1,(0,(1,(1,(0,1))))))) => xb6
+     | (1,(1,(1,(0,(1,(1,(0,1))))))) => xb7
+     | (0,(0,(0,(1,(1,(1,(0,1))))))) => xb8
+     | (1,(0,(0,(1,(1,(1,(0,1))))))) => xb9
+     | (0,(1,(0,(1,(1,(1,(0,1))))))) => xba
+     | (1,(1,(0,(1,(1,(1,(0,1))))))) => xbb
+     | (0,(0,(1,(1,(1,(1,(0,1))))))) => xbc
+     | (1,(0,(1,(1,(1,(1,(0,1))))))) => xbd
+     | (0,(1,(1,(1,(1,(1,(0,1))))))) => xbe
+     | (1,(1,(1,(1,(1,(1,(0,1))))))) => xbf
+     | (0,(0,(0,(0,(0,(0,(1,1))))))) => xc0
+     | (1,(0,(0,(0,(0,(0,(1,1))))))) => xc1
+     | (0,(1,(0,(0,(0,(0,(1,1))))))) => xc2
+     | (1,(1,(0,(0,(0,(0,(1,1))))))) => xc3
+     | (0,(0,(1,(0,(0,(0,(1,1))))))) => xc4
+     | (1,(0,(1,(0,(0,(0,(1,1))))))) => xc5
+     | (0,(1,(1,(0,(0,(0,(1,1))))))) => xc6
+     | (1,(1,(1,(0,(0,(0,(1,1))))))) => xc7
+     | (0,(0,(0,(1,(0,(0,(1,1))))))) => xc8
+     | (1,(0,(0,(1,(0,(0,(1,1))))))) => xc9
+     | (0,(1,(0,(1,(0,(0,(1,1))))))) => xca
+     | (1,(1,(0,(1,(0,(0,(1,1))))))) => xcb
+     | (0,(0,(1,(1,(0,(0,(1,1))))))) => xcc
+     | (1,(0,(1,(1,(0,(0,(1,1))))))) => xcd
+     | (0,(1,(1,(1,(0,(0,(1,1))))))) => xce
+     | (1,(1,(1,(1,(0,(0,(1,1))))))) => xcf
+     | (0,(0,(0,(0,(1,(0,(1,1))))))) => xd0
+     | (1,(0,(0,(0,(1,(0,(1,1))))))) => xd1
+     | (0,(1,(0,(0,(1,(0,(1,1))))))) => xd2
+     | (1,(1,(0,(0,(1,(0,(1,1))))))) => xd3
+     | (0,(0,(1,(0,(1,(0,(1,1))))))) => xd4
+     | (1,(0,(1,(0,(1,(0,(1,1))))))) => xd5
+     | (0,(1,(1,(0,(1,(0,(1,1))))))) => xd6
+     | (1,(1,(1,(0,(1,(0,(1,1))))))) => xd7
+     | (0,(0,(0,(1,(1,(0,(1,1))))))) => xd8
+     | (1,(0,(0,(1,(1,(0,(1,1))))))) => xd9
+     | (0,(1,(0,(1,(1,(0,(1,1))))))) => xda
+     | (1,(1,(0,(1,(1,(0,(1,1))))))) => xdb
+     | (0,(0,(1,(1,(1,(0,(1,1))))))) => xdc
+     | (1,(0,(1,(1,(1,(0,(1,1))))))) => xdd
+     | (0,(1,(1,(1,(1,(0,(1,1))))))) => xde
+     | (1,(1,(1,(1,(1,(0,(1,1))))))) => xdf
+     | (0,(0,(0,(0,(0,(1,(1,1))))))) => xe0
+     | (1,(0,(0,(0,(0,(1,(1,1))))))) => xe1
+     | (0,(1,(0,(0,(0,(1,(1,1))))))) => xe2
+     | (1,(1,(0,(0,(0,(1,(1,1))))))) => xe3
+     | (0,(0,(1,(0,(0,(1,(1,1))))))) => xe4
+     | (1,(0,(1,(0,(0,(1,(1,1))))))) => xe5
+     | (0,(1,(1,(0,(0,(1,(1,1))))))) => xe6
+     | (1,(1,(1,(0,(0,(1,(1,1))))))) => xe7
+     | (0,(0,(0,(1,(0,(1,(1,1))))))) => xe8
+     | (1,(0,(0,(1,(0,(1,(1,1))))))) => xe9
+     | (0,(1,(0,(1,(0,(1,(1,1))))))) => xea
+     | (1,(1,(0,(1,(0,(1,(1,1))))))) => xeb
+     | (0,(0,(1,(1,(0,(1,(1,1))))))) => xec
+     | (1,(0,(1,(1,(0,(1,(1,1))))))) => xed
+     | (0,(1,(1,(1,(0,(1,(1,1))))))) => xee
+     | (1,(1,(1,(1,(0,(1,(1,1))))))) => xef
+     | (0,(0,(0,(0,(1,(1,(1,1))))))) => xf0
+     | (1,(0,(0,(0,(1,(1,(1,1))))))) => xf1
+     | (0,(1,(0,(0,(1,(1,(1,1))))))) => xf2
+     | (1,(1,(0,(0,(1,(1,(1,1))))))) => xf3
+     | (0,(0,(1,(0,(1,(1,(1,1))))))) => xf4
+     | (1,(0,(1,(0,(1,(1,(1,1))))))) => xf5
+     | (0,(1,(1,(0,(1,(1,(1,1))))))) => xf6
+     | (1,(1,(1,(0,(1,(1,(1,1))))))) => xf7
+     | (0,(0,(0,(1,(1,(1,(1,1))))))) => xf8
+     | (1,(0,(0,(1,(1,(1,(1,1))))))) => xf9
+     | (0,(1,(0,(1,(1,(1,(1,1))))))) => xfa
+     | (1,(1,(0,(1,(1,(1,(1,1))))))) => xfb
+     | (0,(0,(1,(1,(1,(1,(1,1))))))) => xfc
+     | (1,(0,(1,(1,(1,(1,(1,1))))))) => xfd
+     | (0,(1,(1,(1,(1,(1,(1,1))))))) => xfe
+     | (1,(1,(1,(1,(1,(1,(1,1))))))) => xff
+     end.
+ +
+Definition to_bits (b : byte) : bool * (bool * (bool * (bool * (bool * (bool * (bool * bool))))))
+  := match b with
+     | x00 => (0,(0,(0,(0,(0,(0,(0,0)))))))
+     | x01 => (1,(0,(0,(0,(0,(0,(0,0)))))))
+     | x02 => (0,(1,(0,(0,(0,(0,(0,0)))))))
+     | x03 => (1,(1,(0,(0,(0,(0,(0,0)))))))
+     | x04 => (0,(0,(1,(0,(0,(0,(0,0)))))))
+     | x05 => (1,(0,(1,(0,(0,(0,(0,0)))))))
+     | x06 => (0,(1,(1,(0,(0,(0,(0,0)))))))
+     | x07 => (1,(1,(1,(0,(0,(0,(0,0)))))))
+     | x08 => (0,(0,(0,(1,(0,(0,(0,0)))))))
+     | x09 => (1,(0,(0,(1,(0,(0,(0,0)))))))
+     | x0a => (0,(1,(0,(1,(0,(0,(0,0)))))))
+     | x0b => (1,(1,(0,(1,(0,(0,(0,0)))))))
+     | x0c => (0,(0,(1,(1,(0,(0,(0,0)))))))
+     | x0d => (1,(0,(1,(1,(0,(0,(0,0)))))))
+     | x0e => (0,(1,(1,(1,(0,(0,(0,0)))))))
+     | x0f => (1,(1,(1,(1,(0,(0,(0,0)))))))
+     | x10 => (0,(0,(0,(0,(1,(0,(0,0)))))))
+     | x11 => (1,(0,(0,(0,(1,(0,(0,0)))))))
+     | x12 => (0,(1,(0,(0,(1,(0,(0,0)))))))
+     | x13 => (1,(1,(0,(0,(1,(0,(0,0)))))))
+     | x14 => (0,(0,(1,(0,(1,(0,(0,0)))))))
+     | x15 => (1,(0,(1,(0,(1,(0,(0,0)))))))
+     | x16 => (0,(1,(1,(0,(1,(0,(0,0)))))))
+     | x17 => (1,(1,(1,(0,(1,(0,(0,0)))))))
+     | x18 => (0,(0,(0,(1,(1,(0,(0,0)))))))
+     | x19 => (1,(0,(0,(1,(1,(0,(0,0)))))))
+     | x1a => (0,(1,(0,(1,(1,(0,(0,0)))))))
+     | x1b => (1,(1,(0,(1,(1,(0,(0,0)))))))
+     | x1c => (0,(0,(1,(1,(1,(0,(0,0)))))))
+     | x1d => (1,(0,(1,(1,(1,(0,(0,0)))))))
+     | x1e => (0,(1,(1,(1,(1,(0,(0,0)))))))
+     | x1f => (1,(1,(1,(1,(1,(0,(0,0)))))))
+     | x20 => (0,(0,(0,(0,(0,(1,(0,0)))))))
+     | x21 => (1,(0,(0,(0,(0,(1,(0,0)))))))
+     | x22 => (0,(1,(0,(0,(0,(1,(0,0)))))))
+     | x23 => (1,(1,(0,(0,(0,(1,(0,0)))))))
+     | x24 => (0,(0,(1,(0,(0,(1,(0,0)))))))
+     | x25 => (1,(0,(1,(0,(0,(1,(0,0)))))))
+     | x26 => (0,(1,(1,(0,(0,(1,(0,0)))))))
+     | x27 => (1,(1,(1,(0,(0,(1,(0,0)))))))
+     | x28 => (0,(0,(0,(1,(0,(1,(0,0)))))))
+     | x29 => (1,(0,(0,(1,(0,(1,(0,0)))))))
+     | x2a => (0,(1,(0,(1,(0,(1,(0,0)))))))
+     | x2b => (1,(1,(0,(1,(0,(1,(0,0)))))))
+     | x2c => (0,(0,(1,(1,(0,(1,(0,0)))))))
+     | x2d => (1,(0,(1,(1,(0,(1,(0,0)))))))
+     | x2e => (0,(1,(1,(1,(0,(1,(0,0)))))))
+     | x2f => (1,(1,(1,(1,(0,(1,(0,0)))))))
+     | x30 => (0,(0,(0,(0,(1,(1,(0,0)))))))
+     | x31 => (1,(0,(0,(0,(1,(1,(0,0)))))))
+     | x32 => (0,(1,(0,(0,(1,(1,(0,0)))))))
+     | x33 => (1,(1,(0,(0,(1,(1,(0,0)))))))
+     | x34 => (0,(0,(1,(0,(1,(1,(0,0)))))))
+     | x35 => (1,(0,(1,(0,(1,(1,(0,0)))))))
+     | x36 => (0,(1,(1,(0,(1,(1,(0,0)))))))
+     | x37 => (1,(1,(1,(0,(1,(1,(0,0)))))))
+     | x38 => (0,(0,(0,(1,(1,(1,(0,0)))))))
+     | x39 => (1,(0,(0,(1,(1,(1,(0,0)))))))
+     | x3a => (0,(1,(0,(1,(1,(1,(0,0)))))))
+     | x3b => (1,(1,(0,(1,(1,(1,(0,0)))))))
+     | x3c => (0,(0,(1,(1,(1,(1,(0,0)))))))
+     | x3d => (1,(0,(1,(1,(1,(1,(0,0)))))))
+     | x3e => (0,(1,(1,(1,(1,(1,(0,0)))))))
+     | x3f => (1,(1,(1,(1,(1,(1,(0,0)))))))
+     | x40 => (0,(0,(0,(0,(0,(0,(1,0)))))))
+     | x41 => (1,(0,(0,(0,(0,(0,(1,0)))))))
+     | x42 => (0,(1,(0,(0,(0,(0,(1,0)))))))
+     | x43 => (1,(1,(0,(0,(0,(0,(1,0)))))))
+     | x44 => (0,(0,(1,(0,(0,(0,(1,0)))))))
+     | x45 => (1,(0,(1,(0,(0,(0,(1,0)))))))
+     | x46 => (0,(1,(1,(0,(0,(0,(1,0)))))))
+     | x47 => (1,(1,(1,(0,(0,(0,(1,0)))))))
+     | x48 => (0,(0,(0,(1,(0,(0,(1,0)))))))
+     | x49 => (1,(0,(0,(1,(0,(0,(1,0)))))))
+     | x4a => (0,(1,(0,(1,(0,(0,(1,0)))))))
+     | x4b => (1,(1,(0,(1,(0,(0,(1,0)))))))
+     | x4c => (0,(0,(1,(1,(0,(0,(1,0)))))))
+     | x4d => (1,(0,(1,(1,(0,(0,(1,0)))))))
+     | x4e => (0,(1,(1,(1,(0,(0,(1,0)))))))
+     | x4f => (1,(1,(1,(1,(0,(0,(1,0)))))))
+     | x50 => (0,(0,(0,(0,(1,(0,(1,0)))))))
+     | x51 => (1,(0,(0,(0,(1,(0,(1,0)))))))
+     | x52 => (0,(1,(0,(0,(1,(0,(1,0)))))))
+     | x53 => (1,(1,(0,(0,(1,(0,(1,0)))))))
+     | x54 => (0,(0,(1,(0,(1,(0,(1,0)))))))
+     | x55 => (1,(0,(1,(0,(1,(0,(1,0)))))))
+     | x56 => (0,(1,(1,(0,(1,(0,(1,0)))))))
+     | x57 => (1,(1,(1,(0,(1,(0,(1,0)))))))
+     | x58 => (0,(0,(0,(1,(1,(0,(1,0)))))))
+     | x59 => (1,(0,(0,(1,(1,(0,(1,0)))))))
+     | x5a => (0,(1,(0,(1,(1,(0,(1,0)))))))
+     | x5b => (1,(1,(0,(1,(1,(0,(1,0)))))))
+     | x5c => (0,(0,(1,(1,(1,(0,(1,0)))))))
+     | x5d => (1,(0,(1,(1,(1,(0,(1,0)))))))
+     | x5e => (0,(1,(1,(1,(1,(0,(1,0)))))))
+     | x5f => (1,(1,(1,(1,(1,(0,(1,0)))))))
+     | x60 => (0,(0,(0,(0,(0,(1,(1,0)))))))
+     | x61 => (1,(0,(0,(0,(0,(1,(1,0)))))))
+     | x62 => (0,(1,(0,(0,(0,(1,(1,0)))))))
+     | x63 => (1,(1,(0,(0,(0,(1,(1,0)))))))
+     | x64 => (0,(0,(1,(0,(0,(1,(1,0)))))))
+     | x65 => (1,(0,(1,(0,(0,(1,(1,0)))))))
+     | x66 => (0,(1,(1,(0,(0,(1,(1,0)))))))
+     | x67 => (1,(1,(1,(0,(0,(1,(1,0)))))))
+     | x68 => (0,(0,(0,(1,(0,(1,(1,0)))))))
+     | x69 => (1,(0,(0,(1,(0,(1,(1,0)))))))
+     | x6a => (0,(1,(0,(1,(0,(1,(1,0)))))))
+     | x6b => (1,(1,(0,(1,(0,(1,(1,0)))))))
+     | x6c => (0,(0,(1,(1,(0,(1,(1,0)))))))
+     | x6d => (1,(0,(1,(1,(0,(1,(1,0)))))))
+     | x6e => (0,(1,(1,(1,(0,(1,(1,0)))))))
+     | x6f => (1,(1,(1,(1,(0,(1,(1,0)))))))
+     | x70 => (0,(0,(0,(0,(1,(1,(1,0)))))))
+     | x71 => (1,(0,(0,(0,(1,(1,(1,0)))))))
+     | x72 => (0,(1,(0,(0,(1,(1,(1,0)))))))
+     | x73 => (1,(1,(0,(0,(1,(1,(1,0)))))))
+     | x74 => (0,(0,(1,(0,(1,(1,(1,0)))))))
+     | x75 => (1,(0,(1,(0,(1,(1,(1,0)))))))
+     | x76 => (0,(1,(1,(0,(1,(1,(1,0)))))))
+     | x77 => (1,(1,(1,(0,(1,(1,(1,0)))))))
+     | x78 => (0,(0,(0,(1,(1,(1,(1,0)))))))
+     | x79 => (1,(0,(0,(1,(1,(1,(1,0)))))))
+     | x7a => (0,(1,(0,(1,(1,(1,(1,0)))))))
+     | x7b => (1,(1,(0,(1,(1,(1,(1,0)))))))
+     | x7c => (0,(0,(1,(1,(1,(1,(1,0)))))))
+     | x7d => (1,(0,(1,(1,(1,(1,(1,0)))))))
+     | x7e => (0,(1,(1,(1,(1,(1,(1,0)))))))
+     | x7f => (1,(1,(1,(1,(1,(1,(1,0)))))))
+     | x80 => (0,(0,(0,(0,(0,(0,(0,1)))))))
+     | x81 => (1,(0,(0,(0,(0,(0,(0,1)))))))
+     | x82 => (0,(1,(0,(0,(0,(0,(0,1)))))))
+     | x83 => (1,(1,(0,(0,(0,(0,(0,1)))))))
+     | x84 => (0,(0,(1,(0,(0,(0,(0,1)))))))
+     | x85 => (1,(0,(1,(0,(0,(0,(0,1)))))))
+     | x86 => (0,(1,(1,(0,(0,(0,(0,1)))))))
+     | x87 => (1,(1,(1,(0,(0,(0,(0,1)))))))
+     | x88 => (0,(0,(0,(1,(0,(0,(0,1)))))))
+     | x89 => (1,(0,(0,(1,(0,(0,(0,1)))))))
+     | x8a => (0,(1,(0,(1,(0,(0,(0,1)))))))
+     | x8b => (1,(1,(0,(1,(0,(0,(0,1)))))))
+     | x8c => (0,(0,(1,(1,(0,(0,(0,1)))))))
+     | x8d => (1,(0,(1,(1,(0,(0,(0,1)))))))
+     | x8e => (0,(1,(1,(1,(0,(0,(0,1)))))))
+     | x8f => (1,(1,(1,(1,(0,(0,(0,1)))))))
+     | x90 => (0,(0,(0,(0,(1,(0,(0,1)))))))
+     | x91 => (1,(0,(0,(0,(1,(0,(0,1)))))))
+     | x92 => (0,(1,(0,(0,(1,(0,(0,1)))))))
+     | x93 => (1,(1,(0,(0,(1,(0,(0,1)))))))
+     | x94 => (0,(0,(1,(0,(1,(0,(0,1)))))))
+     | x95 => (1,(0,(1,(0,(1,(0,(0,1)))))))
+     | x96 => (0,(1,(1,(0,(1,(0,(0,1)))))))
+     | x97 => (1,(1,(1,(0,(1,(0,(0,1)))))))
+     | x98 => (0,(0,(0,(1,(1,(0,(0,1)))))))
+     | x99 => (1,(0,(0,(1,(1,(0,(0,1)))))))
+     | x9a => (0,(1,(0,(1,(1,(0,(0,1)))))))
+     | x9b => (1,(1,(0,(1,(1,(0,(0,1)))))))
+     | x9c => (0,(0,(1,(1,(1,(0,(0,1)))))))
+     | x9d => (1,(0,(1,(1,(1,(0,(0,1)))))))
+     | x9e => (0,(1,(1,(1,(1,(0,(0,1)))))))
+     | x9f => (1,(1,(1,(1,(1,(0,(0,1)))))))
+     | xa0 => (0,(0,(0,(0,(0,(1,(0,1)))))))
+     | xa1 => (1,(0,(0,(0,(0,(1,(0,1)))))))
+     | xa2 => (0,(1,(0,(0,(0,(1,(0,1)))))))
+     | xa3 => (1,(1,(0,(0,(0,(1,(0,1)))))))
+     | xa4 => (0,(0,(1,(0,(0,(1,(0,1)))))))
+     | xa5 => (1,(0,(1,(0,(0,(1,(0,1)))))))
+     | xa6 => (0,(1,(1,(0,(0,(1,(0,1)))))))
+     | xa7 => (1,(1,(1,(0,(0,(1,(0,1)))))))
+     | xa8 => (0,(0,(0,(1,(0,(1,(0,1)))))))
+     | xa9 => (1,(0,(0,(1,(0,(1,(0,1)))))))
+     | xaa => (0,(1,(0,(1,(0,(1,(0,1)))))))
+     | xab => (1,(1,(0,(1,(0,(1,(0,1)))))))
+     | xac => (0,(0,(1,(1,(0,(1,(0,1)))))))
+     | xad => (1,(0,(1,(1,(0,(1,(0,1)))))))
+     | xae => (0,(1,(1,(1,(0,(1,(0,1)))))))
+     | xaf => (1,(1,(1,(1,(0,(1,(0,1)))))))
+     | xb0 => (0,(0,(0,(0,(1,(1,(0,1)))))))
+     | xb1 => (1,(0,(0,(0,(1,(1,(0,1)))))))
+     | xb2 => (0,(1,(0,(0,(1,(1,(0,1)))))))
+     | xb3 => (1,(1,(0,(0,(1,(1,(0,1)))))))
+     | xb4 => (0,(0,(1,(0,(1,(1,(0,1)))))))
+     | xb5 => (1,(0,(1,(0,(1,(1,(0,1)))))))
+     | xb6 => (0,(1,(1,(0,(1,(1,(0,1)))))))
+     | xb7 => (1,(1,(1,(0,(1,(1,(0,1)))))))
+     | xb8 => (0,(0,(0,(1,(1,(1,(0,1)))))))
+     | xb9 => (1,(0,(0,(1,(1,(1,(0,1)))))))
+     | xba => (0,(1,(0,(1,(1,(1,(0,1)))))))
+     | xbb => (1,(1,(0,(1,(1,(1,(0,1)))))))
+     | xbc => (0,(0,(1,(1,(1,(1,(0,1)))))))
+     | xbd => (1,(0,(1,(1,(1,(1,(0,1)))))))
+     | xbe => (0,(1,(1,(1,(1,(1,(0,1)))))))
+     | xbf => (1,(1,(1,(1,(1,(1,(0,1)))))))
+     | xc0 => (0,(0,(0,(0,(0,(0,(1,1)))))))
+     | xc1 => (1,(0,(0,(0,(0,(0,(1,1)))))))
+     | xc2 => (0,(1,(0,(0,(0,(0,(1,1)))))))
+     | xc3 => (1,(1,(0,(0,(0,(0,(1,1)))))))
+     | xc4 => (0,(0,(1,(0,(0,(0,(1,1)))))))
+     | xc5 => (1,(0,(1,(0,(0,(0,(1,1)))))))
+     | xc6 => (0,(1,(1,(0,(0,(0,(1,1)))))))
+     | xc7 => (1,(1,(1,(0,(0,(0,(1,1)))))))
+     | xc8 => (0,(0,(0,(1,(0,(0,(1,1)))))))
+     | xc9 => (1,(0,(0,(1,(0,(0,(1,1)))))))
+     | xca => (0,(1,(0,(1,(0,(0,(1,1)))))))
+     | xcb => (1,(1,(0,(1,(0,(0,(1,1)))))))
+     | xcc => (0,(0,(1,(1,(0,(0,(1,1)))))))
+     | xcd => (1,(0,(1,(1,(0,(0,(1,1)))))))
+     | xce => (0,(1,(1,(1,(0,(0,(1,1)))))))
+     | xcf => (1,(1,(1,(1,(0,(0,(1,1)))))))
+     | xd0 => (0,(0,(0,(0,(1,(0,(1,1)))))))
+     | xd1 => (1,(0,(0,(0,(1,(0,(1,1)))))))
+     | xd2 => (0,(1,(0,(0,(1,(0,(1,1)))))))
+     | xd3 => (1,(1,(0,(0,(1,(0,(1,1)))))))
+     | xd4 => (0,(0,(1,(0,(1,(0,(1,1)))))))
+     | xd5 => (1,(0,(1,(0,(1,(0,(1,1)))))))
+     | xd6 => (0,(1,(1,(0,(1,(0,(1,1)))))))
+     | xd7 => (1,(1,(1,(0,(1,(0,(1,1)))))))
+     | xd8 => (0,(0,(0,(1,(1,(0,(1,1)))))))
+     | xd9 => (1,(0,(0,(1,(1,(0,(1,1)))))))
+     | xda => (0,(1,(0,(1,(1,(0,(1,1)))))))
+     | xdb => (1,(1,(0,(1,(1,(0,(1,1)))))))
+     | xdc => (0,(0,(1,(1,(1,(0,(1,1)))))))
+     | xdd => (1,(0,(1,(1,(1,(0,(1,1)))))))
+     | xde => (0,(1,(1,(1,(1,(0,(1,1)))))))
+     | xdf => (1,(1,(1,(1,(1,(0,(1,1)))))))
+     | xe0 => (0,(0,(0,(0,(0,(1,(1,1)))))))
+     | xe1 => (1,(0,(0,(0,(0,(1,(1,1)))))))
+     | xe2 => (0,(1,(0,(0,(0,(1,(1,1)))))))
+     | xe3 => (1,(1,(0,(0,(0,(1,(1,1)))))))
+     | xe4 => (0,(0,(1,(0,(0,(1,(1,1)))))))
+     | xe5 => (1,(0,(1,(0,(0,(1,(1,1)))))))
+     | xe6 => (0,(1,(1,(0,(0,(1,(1,1)))))))
+     | xe7 => (1,(1,(1,(0,(0,(1,(1,1)))))))
+     | xe8 => (0,(0,(0,(1,(0,(1,(1,1)))))))
+     | xe9 => (1,(0,(0,(1,(0,(1,(1,1)))))))
+     | xea => (0,(1,(0,(1,(0,(1,(1,1)))))))
+     | xeb => (1,(1,(0,(1,(0,(1,(1,1)))))))
+     | xec => (0,(0,(1,(1,(0,(1,(1,1)))))))
+     | xed => (1,(0,(1,(1,(0,(1,(1,1)))))))
+     | xee => (0,(1,(1,(1,(0,(1,(1,1)))))))
+     | xef => (1,(1,(1,(1,(0,(1,(1,1)))))))
+     | xf0 => (0,(0,(0,(0,(1,(1,(1,1)))))))
+     | xf1 => (1,(0,(0,(0,(1,(1,(1,1)))))))
+     | xf2 => (0,(1,(0,(0,(1,(1,(1,1)))))))
+     | xf3 => (1,(1,(0,(0,(1,(1,(1,1)))))))
+     | xf4 => (0,(0,(1,(0,(1,(1,(1,1)))))))
+     | xf5 => (1,(0,(1,(0,(1,(1,(1,1)))))))
+     | xf6 => (0,(1,(1,(0,(1,(1,(1,1)))))))
+     | xf7 => (1,(1,(1,(0,(1,(1,(1,1)))))))
+     | xf8 => (0,(0,(0,(1,(1,(1,(1,1)))))))
+     | xf9 => (1,(0,(0,(1,(1,(1,(1,1)))))))
+     | xfa => (0,(1,(0,(1,(1,(1,(1,1)))))))
+     | xfb => (1,(1,(0,(1,(1,(1,(1,1)))))))
+     | xfc => (0,(0,(1,(1,(1,(1,(1,1)))))))
+     | xfd => (1,(0,(1,(1,(1,(1,(1,1)))))))
+     | xfe => (0,(1,(1,(1,(1,(1,(1,1)))))))
+     | xff => (1,(1,(1,(1,(1,(1,(1,1)))))))
+     end.
+ +
+Lemma of_bits_to_bits (b : byte) : of_bits (to_bits b) = b.
+ +
+Lemma to_bits_of_bits (b : _) : to_bits (of_bits b) = b.
+ +
+Definition byte_of_byte (b : byte) : byte := b.
+ +
+Module Export ByteSyntaxNotations.
+  String Notation byte byte_of_byte byte_of_byte : byte_scope.
+End ByteSyntaxNotations.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Init.Datatypes.html b/master/corelib/Corelib.Init.Datatypes.html new file mode 100644 index 0000000000..46d15c4f4f --- /dev/null +++ b/master/corelib/Corelib.Init.Datatypes.html @@ -0,0 +1,756 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Init.Datatypes

+ +
+ +
+Set Implicit Arguments.
+ +
+Require Import Notations.
+Require Import Ltac.
+Require Import Logic.
+ +
+
+ +
+

Datatypes with zero and one element

+ +
+ + Empty_set is a datatype with no inhabitant +
+
+ +
+Inductive Empty_set : Set :=.
+ +
+Register Empty_set as core.Empty_set.type.
+ +
+
+ +
+unit is a singleton datatype with sole inhabitant tt +
+
+ +
+Inductive unit : Set :=
+    tt : unit.
+ +
+Register unit as core.unit.type.
+Register tt as core.unit.tt.
+ +
+
+ +
+

The boolean datatype

+ +
+ + bool is the datatype of the boolean values true and false +
+
+ +
+Inductive bool : Set :=
+  | true : bool
+  | false : bool.
+ +
+Add Printing If bool.
+ +
+Declare Scope bool_scope.
+Delimit Scope bool_scope with bool.
+Bind Scope bool_scope with bool.
+ +
+Register bool as core.bool.type.
+Register true as core.bool.true.
+Register false as core.bool.false.
+ +
+
+ +
+

Reflect: a specialized inductive type for

+ + relating propositions and booleans, + as popularized by the Ssreflect library. +
+
+ +
+Inductive reflect (P : Prop) : bool -> Set :=
+  | ReflectT : P -> reflect P true
+  | ReflectF : ~ P -> reflect P false.
+#[global]
+Hint Constructors reflect : bool.
+Arguments ReflectT : clear implicits.
+Arguments ReflectF : clear implicits.
+ +
+
+ +
+Interest: a case on a reflect lemma or hyp performs clever + unification, and leave the goal in a convenient shape + (a bit like case_eq). +
+ + Basic boolean operators +
+
+ +
+Definition andb (b1 b2:bool) : bool := if b1 then b2 else false.
+ +
+Definition orb (b1 b2:bool) : bool := if b1 then true else b2.
+ +
+Definition implb (b1 b2:bool) : bool := if b1 then b2 else true.
+ +
+Definition xorb (b1 b2:bool) : bool :=
+  if b1 then
+    if b2 then false else true
+  else b2.
+ +
+Definition negb (b:bool) := if b then false else true.
+ +
+Infix "||" := orb : bool_scope.
+Infix "&&" := andb : bool_scope.
+ +
+Register andb as core.bool.andb.
+Register orb as core.bool.orb.
+Register implb as core.bool.implb.
+Register xorb as core.bool.xorb.
+Register negb as core.bool.negb.
+ +
+
+ +
+Basic properties of andb +
+
+ +
+Lemma andb_prop (a b:bool) : andb a b = true -> a = true /\ b = true.
+#[global]
+Hint Resolve andb_prop: bool.
+ +
+Register andb_prop as core.bool.andb_prop.
+ +
+Lemma andb_true_intro (b1 b2:bool) :
+  b1 = true /\ b2 = true -> andb b1 b2 = true.
+#[global]
+Hint Resolve andb_true_intro: bool.
+ +
+Register andb_true_intro as core.bool.andb_true_intro.
+ +
+
+ +
+Interpretation of booleans as propositions +
+
+ +
+Inductive eq_true : bool -> Prop := is_eq_true : eq_true true.
+ +
+#[global]
+Hint Constructors eq_true : eq_true.
+ +
+Register eq_true as core.eq_true.type.
+ +
+
+ +
+Another way of interpreting booleans as propositions +
+
+ +
+Definition is_true b := b = true.
+ +
+
+ +
+is_true can be activated as a coercion by + (Local) Coercion is_true : bool >-> Sortclass. + +
+ + Additional rewriting lemmas about eq_true +
+
+ +
+Lemma eq_true_ind_r :
+  forall (P : bool -> Prop) (b : bool), P b -> eq_true b -> P true.
+ +
+Lemma eq_true_rec_r :
+  forall (P : bool -> Set) (b : bool), P b -> eq_true b -> P true.
+ +
+Lemma eq_true_rect_r :
+  forall (P : bool -> Type) (b : bool), P b -> eq_true b -> P true.
+ +
+
+ +
+The BoolSpec inductive will be used to relate a boolean value + and two propositions corresponding respectively to the true + case and the false case. + Interest: BoolSpec behave nicely with case and destruct. + See also Bool.reflect when Q = ~P. + +
+
+ +
+Inductive BoolSpec (P Q : Prop) : bool -> Prop :=
+  | BoolSpecT : P -> BoolSpec P Q true
+  | BoolSpecF : Q -> BoolSpec P Q false.
+#[global]
+Hint Constructors BoolSpec : core.
+ +
+Register BoolSpec as core.BoolSpec.type.
+Register BoolSpecT as core.BoolSpec.BoolSpecT.
+Register BoolSpecF as core.BoolSpec.BoolSpecF.
+ +
+
+ +
+

Peano natural numbers

+ +
+ + nat is the datatype of natural numbers built from O and successor S; + note that the constructor name is the letter O. + Numbers in nat can be denoted using a decimal notation; + e.g. 3%nat abbreviates S (S (S O)) +
+
+ +
+Inductive nat : Set :=
+  | O : nat
+  | S : nat -> nat.
+ +
+Declare Scope hex_nat_scope.
+Delimit Scope hex_nat_scope with xnat.
+ +
+Declare Scope nat_scope.
+Delimit Scope nat_scope with nat.
+Bind Scope nat_scope with nat.
+Arguments S _%_nat.
+ +
+Register nat as num.nat.type.
+Register O as num.nat.O.
+Register S as num.nat.S.
+ +
+
+ +
+

Container datatypes

+ +
+
+ +
+ +
+
+ +
+option A is the extension of A with an extra element None +
+
+ +
+#[universes(template)]
+Inductive option (A:Type) : Type :=
+  | Some : A -> option A
+  | None : option A.
+ +
+Arguments Some {A} a.
+Arguments None {A}.
+ +
+Register option as core.option.type.
+Register Some as core.option.Some.
+Register None as core.option.None.
+ +
+Definition option_map (A B:Type) (f:A->B) (o : option A) : option B :=
+  match o with
+    | Some a => @Some B (f a)
+    | None => @None B
+  end.
+ +
+
+ +
+sum A B, written A + B, is the disjoint sum of A and B +
+
+ +
+#[universes(template)]
+Inductive sum (A B:Type) : Type :=
+  | inl : A -> sum A B
+  | inr : B -> sum A B.
+ +
+Notation "x + y" := (sum x y) : type_scope.
+ +
+Arguments inl {A B} _ , [A] B _.
+Arguments inr {A B} _ , A [B] _.
+ +
+Register sum as core.sum.type.
+Register inl as core.sum.inl.
+Register inr as core.sum.inr.
+ +
+
+ +
+prod A B, written A * B, is the product of A and B; + the pair pair A B a b of a and b is abbreviated (a,b) +
+
+ +
+#[universes(template)]
+Inductive prod (A B:Type) : Type :=
+  pair : A -> B -> A * B
+
+where "x * y" := (prod x y) : type_scope.
+ +
+Add Printing Let prod.
+ +
+Notation "( x , y , .. , z )" := (pair .. (pair x y) .. z) : core_scope.
+ +
+Arguments pair {A B} _ _.
+ +
+Register prod as core.prod.type.
+Register pair as core.prod.intro.
+Register prod_rect as core.prod.rect.
+ +
+Section projections.
+  Context {A : Type} {B : Type}.
+ +
+  Definition fst (p:A * B) := match p with (x, y) => x end.
+  Definition snd (p:A * B) := match p with (x, y) => y end.
+ +
+  Register fst as core.prod.proj1.
+  Register snd as core.prod.proj2.
+ +
+End projections.
+ +
+#[global]
+Hint Resolve pair inl inr: core.
+ +
+Lemma surjective_pairing (A B:Type) (p:A * B) : p = (fst p, snd p).
+ +
+Lemma injective_projections (A B:Type) (p1 p2:A * B) :
+    fst p1 = fst p2 -> snd p1 = snd p2 -> p1 = p2.
+ +
+Lemma pair_equal_spec (A B : Type) (a1 a2 : A) (b1 b2 : B) :
+    (a1, b1) = (a2, b2) <-> a1 = a2 /\ b1 = b2.
+ +
+Definition curry {A B C:Type} (f:A * B -> C)
+  (x:A) (y:B) : C := f (x,y).
+ +
+Definition uncurry {A B C:Type} (f:A -> B -> C)
+  (p:A * B) : C := match p with (x, y) => f x y end.
+ +
+Import EqNotations.
+ +
+Lemma rew_pair A (P Q : A->Type) x1 x2 (y1:P x1) (y2:Q x1) (H:x1=x2) :
+  (rew H in y1, rew H in y2) = rew [fun x => (P x * Q x)%type] H in (y1,y2).
+ +
+
+ +
+Polymorphic lists and some operations +
+
+ +
+#[universes(template)]
+Inductive list (A : Type) : Type :=
+ | nil : list A
+ | cons : A -> list A -> list A.
+ +
+Arguments nil {A}.
+Arguments cons {A} a l.
+ +
+Declare Scope list_scope.
+Delimit Scope list_scope with list.
+Bind Scope list_scope with list.
+ +
+Infix "::" := cons (at level 60, right associativity) : list_scope.
+ +
+Register list as core.list.type.
+Register nil as core.list.nil.
+Register cons as core.list.cons.
+ +
+Local Open Scope list_scope.
+ +
+Definition length (A : Type) : list A -> nat :=
+  fix length l :=
+  match l with
+   | nil => O
+   | _ :: l' => S (length l')
+  end.
+ +
+
+ +
+Concatenation of two lists +
+
+ +
+Definition app (A : Type) : list A -> list A -> list A :=
+  fix app l m :=
+  match l with
+   | nil => m
+   | a :: l1 => a :: app l1 m
+  end.
+ +
+Infix "++" := app (right associativity, at level 60) : list_scope.
+ +
+ +
+
+ +
+

The comparison datatype

+ +
+
+ +
+Inductive comparison : Set :=
+  | Eq : comparison
+  | Lt : comparison
+  | Gt : comparison.
+ +
+Register comparison as core.comparison.type.
+Register Eq as core.comparison.Eq.
+Register Lt as core.comparison.Lt.
+Register Gt as core.comparison.Gt.
+ +
+Lemma comparison_eq_stable (c c' : comparison) : ~~ c = c' -> c = c'.
+ +
+Definition CompOpp (r:comparison) :=
+  match r with
+    | Eq => Eq
+    | Lt => Gt
+    | Gt => Lt
+  end.
+ +
+Lemma CompOpp_involutive c : CompOpp (CompOpp c) = c.
+ +
+Lemma CompOpp_inj c c' : CompOpp c = CompOpp c' -> c = c'.
+ +
+Lemma CompOpp_iff : forall c c', CompOpp c = c' <-> c = CompOpp c'.
+ +
+
+ +
+The CompareSpec inductive relates a comparison value with three + propositions, one for each possible case. Typically, it can be used to + specify a comparison function via some equality and order predicates. + Interest: CompareSpec behave nicely with case and destruct. +
+
+ +
+Inductive CompareSpec (Peq Plt Pgt : Prop) : comparison -> Prop :=
+ | CompEq : Peq -> CompareSpec Peq Plt Pgt Eq
+ | CompLt : Plt -> CompareSpec Peq Plt Pgt Lt
+ | CompGt : Pgt -> CompareSpec Peq Plt Pgt Gt.
+#[global]
+Hint Constructors CompareSpec : core.
+ +
+Register CompareSpec as core.CompareSpec.type.
+Register CompEq as core.CompareSpec.CompEq.
+Register CompLt as core.CompareSpec.CompLt.
+Register CompGt as core.CompareSpec.CompGt.
+ +
+
+ +
+For having clean interfaces after extraction, CompareSpec is declared + in Prop. For some situations, it is nonetheless useful to have a + version in Type. Interestingly, these two versions are equivalent. +
+
+ +
+Inductive CompareSpecT (Peq Plt Pgt : Prop) : comparison -> Type :=
+ | CompEqT : Peq -> CompareSpecT Peq Plt Pgt Eq
+ | CompLtT : Plt -> CompareSpecT Peq Plt Pgt Lt
+ | CompGtT : Pgt -> CompareSpecT Peq Plt Pgt Gt.
+#[global]
+Hint Constructors CompareSpecT : core.
+ +
+Register CompareSpecT as core.CompareSpecT.type.
+Register CompEqT as core.CompareSpecT.CompEqT.
+Register CompLtT as core.CompareSpecT.CompLtT.
+Register CompGtT as core.CompareSpecT.CompGtT.
+ +
+Lemma CompareSpec2Type Peq Plt Pgt c :
+ CompareSpec Peq Plt Pgt c -> CompareSpecT Peq Plt Pgt c.
+ +
+
+ +
+As an alternate formulation, one may also directly refer to predicates + eq and lt for specifying a comparison, rather that fully-applied + propositions. This CompSpec is now a particular case of CompareSpec. +
+
+ +
+Definition CompSpec {A} (eq lt : A->A->Prop)(x y:A) : comparison -> Prop :=
+ CompareSpec (eq x y) (lt x y) (lt y x).
+ +
+Definition CompSpecT {A} (eq lt : A->A->Prop)(x y:A) : comparison -> Type :=
+ CompareSpecT (eq x y) (lt x y) (lt y x).
+#[global]
+Hint Unfold CompSpec CompSpecT : core.
+ +
+Lemma CompSpec2Type : forall A (eq lt:A->A->Prop) x y c,
+ CompSpec eq lt x y c -> CompSpecT eq lt x y c.
+ +
+
+ +
+

Misc Other Datatypes

+ +
+ + identity A a is the family of datatypes on A whose sole non-empty + member is the singleton datatype identity A a a whose + sole inhabitant is denoted identity_refl A a +
+
+ +
+#[deprecated(since="8.16",note="Use eq instead")]
+Notation identity := eq (only parsing).
+#[deprecated(since="8.16",note="Use eq_refl instead")]
+Notation identity_refl := eq_refl (only parsing).
+#[deprecated(since="8.16",note="Use eq_ind instead")]
+Notation identity_ind := eq_ind (only parsing).
+#[deprecated(since="8.16",note="Use eq_rec instead")]
+Notation identity_rec := eq_rec (only parsing).
+#[deprecated(since="8.16",note="Use eq_rect instead")]
+Notation identity_rect := eq_rect (only parsing).
+#[deprecated(since="8.16",note="Use eq_sym instead")]
+Notation identity_sym := eq_sym (only parsing).
+#[deprecated(since="8.16",note="Use eq_trans instead")]
+Notation identity_trans := eq_trans (only parsing).
+#[deprecated(since="8.16",note="Use f_equal instead")]
+Notation identity_congr := f_equal (only parsing).
+#[deprecated(since="8.16",note="Use not_eq_sym instead")]
+Notation not_identity_sym := not_eq_sym (only parsing).
+#[deprecated(since="8.16",note="Use eq_ind_r instead")]
+Notation identity_ind_r := eq_ind_r (only parsing).
+#[deprecated(since="8.16",note="Use eq_rec_r instead")]
+Notation identity_rec_r := eq_rec_r (only parsing).
+#[deprecated(since="8.16",note="Use eq_rect_r instead")]
+Notation identity_rect_r := eq_rect_r (only parsing).
+ +
+Register eq as core.identity.type.
+Register eq_refl as core.identity.refl.
+Register eq_ind as core.identity.ind.
+Register eq_sym as core.identity.sym.
+Register eq_trans as core.identity.trans.
+Register f_equal as core.identity.congr.
+ +
+#[deprecated(since="8.16",note="Use eq_refl instead")]
+Notation refl_id := eq_refl (only parsing).
+#[deprecated(since="8.16",note="Use eq_sym instead")]
+Notation sym_id := eq_sym (only parsing).
+#[deprecated(since="8.16",note="Use eq_trans instead")]
+Notation trans_id := eq_trans (only parsing).
+#[deprecated(since="8.16",note="Use not_eq_sym instead")]
+Notation sym_not_id := not_eq_sym (only parsing).
+ +
+
+ +
+Identity type +
+
+ +
+Definition ID := forall A:Type, A -> A.
+Definition id : ID := fun A x => x.
+ +
+Definition IDProp := forall A:Prop, A -> A.
+Definition idProp : IDProp := fun A x => x.
+ +
+Register idProp as core.IDProp.idProp.
+ +
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Init.Decimal.html b/master/corelib/Corelib.Init.Decimal.html new file mode 100644 index 0000000000..ef895fa308 --- /dev/null +++ b/master/corelib/Corelib.Init.Decimal.html @@ -0,0 +1,463 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Init.Decimal

+ +
+ +
+
+ +
+

Decimal numbers

+ +
+ + These numbers coded in base 10 will be used for parsing and printing + other Rocq numeral datatypes in an human-readable way. + See the Number Notation command. + We represent numbers in base 10 as lists of decimal digits, + in big-endian order (most significant digit comes first). +
+
+ +
+Require Import Datatypes Specif.
+ +
+
+ +
+Unsigned integers are just lists of digits. + For instance, ten is (D1 (D0 Nil)) +
+
+ +
+Inductive uint :=
+ | Nil
+ | D0 (_:uint)
+ | D1 (_:uint)
+ | D2 (_:uint)
+ | D3 (_:uint)
+ | D4 (_:uint)
+ | D5 (_:uint)
+ | D6 (_:uint)
+ | D7 (_:uint)
+ | D8 (_:uint)
+ | D9 (_:uint).
+ +
+
+ +
+Nil is the number terminator. Taken alone, it behaves as zero, + but rather use D0 Nil instead, since this form will be denoted + as 0, while Nil will be printed as Nil. +
+
+ +
+Notation zero := (D0 Nil).
+ +
+
+ +
+For signed integers, we use two constructors Pos and Neg. +
+
+ +
+Variant signed_int := Pos (d:uint) | Neg (d:uint).
+Notation int := signed_int.
+ +
+
+ +
+For decimal numbers, we use two constructors Decimal and + DecimalExp, depending on whether or not they are given with an + exponent (e.g., 1.02e+01). i is the integral part while f is + the fractional part (beware that leading zeroes do matter). +
+
+ +
+Variant decimal :=
+ | Decimal (i:int) (f:uint)
+ | DecimalExp (i:int) (f:uint) (e:int).
+ +
+Scheme Equality for uint.
+Scheme Equality for int.
+Scheme Equality for decimal.
+Notation int_eq_dec := signed_int_eq_dec.
+Notation int_beq := signed_int_beq.
+Notation internal_int_dec_lb := internal_signed_int_dec_lb.
+Notation internal_int_dec_bl := internal_signed_int_dec_bl.
+ +
+Declare Scope dec_uint_scope.
+Delimit Scope dec_uint_scope with uint.
+Bind Scope dec_uint_scope with uint.
+ +
+Declare Scope dec_int_scope.
+Delimit Scope dec_int_scope with int.
+Bind Scope dec_int_scope with int.
+ +
+Register uint as num.uint.type.
+Register int as num.int.type.
+Register decimal as num.decimal.type.
+ +
+Fixpoint nb_digits d :=
+  match d with
+  | Nil => O
+  | D0 d | D1 d | D2 d | D3 d | D4 d | D5 d | D6 d | D7 d | D8 d | D9 d =>
+    S (nb_digits d)
+  end.
+ +
+
+ +
+This representation favors simplicity over canonicity. + For normalizing numbers, we need to remove head zero digits, + and choose our canonical representation of 0 (here D0 Nil + for unsigned numbers and Pos (D0 Nil) for signed numbers). +
+ + nzhead removes all head zero digits +
+
+ +
+Fixpoint nzhead d :=
+  match d with
+  | D0 d => nzhead d
+  | _ => d
+  end.
+ +
+
+ +
+unorm : normalization of unsigned integers +
+
+ +
+Definition unorm d :=
+  match nzhead d with
+  | Nil => zero
+  | d => d
+  end.
+ +
+
+ +
+norm : normalization of signed integers +
+
+ +
+Definition norm d :=
+  match d with
+  | Pos d => Pos (unorm d)
+  | Neg d =>
+    match nzhead d with
+    | Nil => Pos zero
+    | d => Neg d
+    end
+  end.
+ +
+
+ +
+A few easy operations. For more advanced computations, use the conversions + with other Rocq numeral datatypes (e.g. Z) and the operations on them. +
+
+ +
+Definition opp (d:int) :=
+  match d with
+  | Pos d => Neg d
+  | Neg d => Pos d
+  end.
+ +
+Definition abs (d:int) : uint :=
+  match d with
+  | Pos d => d
+  | Neg d => d
+  end.
+ +
+
+ +
+For conversions with binary numbers, it is easier to operate + on little-endian numbers. +
+
+ +
+Fixpoint revapp (d d' : uint) :=
+  match d with
+  | Nil => d'
+  | D0 d => revapp d (D0 d')
+  | D1 d => revapp d (D1 d')
+  | D2 d => revapp d (D2 d')
+  | D3 d => revapp d (D3 d')
+  | D4 d => revapp d (D4 d')
+  | D5 d => revapp d (D5 d')
+  | D6 d => revapp d (D6 d')
+  | D7 d => revapp d (D7 d')
+  | D8 d => revapp d (D8 d')
+  | D9 d => revapp d (D9 d')
+  end.
+ +
+Definition rev d := revapp d Nil.
+ +
+Definition app d d' := revapp (rev d) d'.
+ +
+Definition app_int d1 d2 :=
+  match d1 with Pos d1 => Pos (app d1 d2) | Neg d1 => Neg (app d1 d2) end.
+ +
+
+ +
+nztail removes all trailing zero digits and return both the + result and the number of removed digits. +
+
+ +
+Definition nztail d :=
+  let fix aux d_rev :=
+    match d_rev with
+    | D0 d_rev => let (r, n) := aux d_rev in pair r (S n)
+    | _ => pair d_rev O
+    end in
+  let (r, n) := aux (rev d) in pair (rev r) n.
+ +
+Definition nztail_int d :=
+  match d with
+  | Pos d => let (r, n) := nztail d in pair (Pos r) n
+  | Neg d => let (r, n) := nztail d in pair (Neg r) n
+  end.
+ +
+
+ +
+del_head n d removes n digits at beginning of d + or returns zero if d has less than n digits. +
+
+ +
+Fixpoint del_head n d :=
+  match n with
+  | O => d
+  | S n =>
+    match d with
+    | Nil => zero
+    | D0 d | D1 d | D2 d | D3 d | D4 d | D5 d | D6 d | D7 d | D8 d | D9 d =>
+      del_head n d
+    end
+  end.
+ +
+Definition del_head_int n d :=
+  match d with
+  | Pos d => del_head n d
+  | Neg d => del_head n d
+  end.
+ +
+
+ +
+del_tail n d removes n digits at end of d + or returns zero if d has less than n digits. +
+
+ +
+Definition del_tail n d := rev (del_head n (rev d)).
+ +
+Definition del_tail_int n d :=
+  match d with
+  | Pos d => Pos (del_tail n d)
+  | Neg d => Neg (del_tail n d)
+  end.
+ +
+Module Little.
+ +
+
+ +
+Successor of little-endian numbers +
+
+ +
+Fixpoint succ d :=
+  match d with
+  | Nil => D1 Nil
+  | D0 d => D1 d
+  | D1 d => D2 d
+  | D2 d => D3 d
+  | D3 d => D4 d
+  | D4 d => D5 d
+  | D5 d => D6 d
+  | D6 d => D7 d
+  | D7 d => D8 d
+  | D8 d => D9 d
+  | D9 d => D0 (succ d)
+  end.
+ +
+
+ +
+Doubling little-endian numbers +
+
+ +
+Fixpoint double d :=
+  match d with
+  | Nil => Nil
+  | D0 d => D0 (double d)
+  | D1 d => D2 (double d)
+  | D2 d => D4 (double d)
+  | D3 d => D6 (double d)
+  | D4 d => D8 (double d)
+  | D5 d => D0 (succ_double d)
+  | D6 d => D2 (succ_double d)
+  | D7 d => D4 (succ_double d)
+  | D8 d => D6 (succ_double d)
+  | D9 d => D8 (succ_double d)
+  end
+
+with succ_double d :=
+  match d with
+  | Nil => D1 Nil
+  | D0 d => D1 (double d)
+  | D1 d => D3 (double d)
+  | D2 d => D5 (double d)
+  | D3 d => D7 (double d)
+  | D4 d => D9 (double d)
+  | D5 d => D1 (succ_double d)
+  | D6 d => D3 (succ_double d)
+  | D7 d => D5 (succ_double d)
+  | D8 d => D7 (succ_double d)
+  | D9 d => D9 (succ_double d)
+  end.
+ +
+End Little.
+ +
+
+ +
+Pseudo-conversion functions used when declaring + Number Notations on uint and int. +
+
+ +
+Definition uint_of_uint (i:uint) := i.
+Definition int_of_int (i:int) := i.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Init.Hexadecimal.html b/master/corelib/Corelib.Init.Hexadecimal.html new file mode 100644 index 0000000000..2b017525c9 --- /dev/null +++ b/master/corelib/Corelib.Init.Hexadecimal.html @@ -0,0 +1,482 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Init.Hexadecimal

+ +
+ +
+
+ +
+

Hexadecimal numbers

+ +
+ + These numbers coded in base 16 will be used for parsing and printing + other Rocq numeral datatypes in an human-readable way. + See the Number Notation command. + We represent numbers in base 16 as lists of hexadecimal digits, + in big-endian order (most significant digit comes first). +
+
+ +
+Require Import Datatypes Specif Decimal.
+ +
+
+ +
+Unsigned integers are just lists of digits. + For instance, sixteen is (D1 (D0 Nil)) +
+
+ +
+Inductive uint :=
+ | Nil
+ | D0 (_:uint)
+ | D1 (_:uint)
+ | D2 (_:uint)
+ | D3 (_:uint)
+ | D4 (_:uint)
+ | D5 (_:uint)
+ | D6 (_:uint)
+ | D7 (_:uint)
+ | D8 (_:uint)
+ | D9 (_:uint)
+ | Da (_:uint)
+ | Db (_:uint)
+ | Dc (_:uint)
+ | Dd (_:uint)
+ | De (_:uint)
+ | Df (_:uint).
+ +
+
+ +
+Nil is the number terminator. Taken alone, it behaves as zero, + but rather use D0 Nil instead, since this form will be denoted + as 0, while Nil will be printed as Nil. +
+
+ +
+Notation zero := (D0 Nil).
+ +
+
+ +
+For signed integers, we use two constructors Pos and Neg. +
+
+ +
+Variant signed_int := Pos (d:uint) | Neg (d:uint).
+Notation int := signed_int.
+ +
+
+ +
+For decimal numbers, we use two constructors Hexadecimal and + HexadecimalExp, depending on whether or not they are given with an + exponent (e.g., 0x1.a2p+01). i is the integral part while f is + the fractional part (beware that leading zeroes do matter). +
+
+ +
+Variant hexadecimal :=
+ | Hexadecimal (i:int) (f:uint)
+ | HexadecimalExp (i:int) (f:uint) (e:Decimal.int).
+ +
+Scheme Equality for uint.
+Scheme Equality for int.
+Scheme Equality for hexadecimal.
+Notation int_eq_dec := signed_int_eq_dec.
+Notation int_beq := signed_int_beq.
+Notation internal_int_dec_lb := internal_signed_int_dec_lb.
+Notation internal_int_dec_bl := internal_signed_int_dec_bl.
+ +
+Declare Scope hex_uint_scope.
+Delimit Scope hex_uint_scope with huint.
+Bind Scope hex_uint_scope with uint.
+ +
+Declare Scope hex_int_scope.
+Delimit Scope hex_int_scope with hint.
+Bind Scope hex_int_scope with int.
+ +
+Register uint as num.hexadecimal_uint.type.
+Register int as num.hexadecimal_int.type.
+Register hexadecimal as num.hexadecimal.type.
+ +
+Fixpoint nb_digits d :=
+  match d with
+  | Nil => O
+  | D0 d | D1 d | D2 d | D3 d | D4 d | D5 d | D6 d | D7 d | D8 d | D9 d
+  | Da d | Db d | Dc d | Dd d | De d | Df d =>
+    S (nb_digits d)
+  end.
+ +
+
+ +
+This representation favors simplicity over canonicity. + For normalizing numbers, we need to remove head zero digits, + and choose our canonical representation of 0 (here D0 Nil + for unsigned numbers and Pos (D0 Nil) for signed numbers). +
+ + nzhead removes all head zero digits +
+
+ +
+Fixpoint nzhead d :=
+  match d with
+  | D0 d => nzhead d
+  | _ => d
+  end.
+ +
+
+ +
+unorm : normalization of unsigned integers +
+
+ +
+Definition unorm d :=
+  match nzhead d with
+  | Nil => zero
+  | d => d
+  end.
+ +
+
+ +
+norm : normalization of signed integers +
+
+ +
+Definition norm d :=
+  match d with
+  | Pos d => Pos (unorm d)
+  | Neg d =>
+    match nzhead d with
+    | Nil => Pos zero
+    | d => Neg d
+    end
+  end.
+ +
+
+ +
+A few easy operations. For more advanced computations, use the conversions + with other Rocq numeral datatypes (e.g. Z) and the operations on them. +
+
+ +
+Definition opp (d:int) :=
+  match d with
+  | Pos d => Neg d
+  | Neg d => Pos d
+  end.
+ +
+Definition abs (d:int) : uint :=
+  match d with
+  | Pos d => d
+  | Neg d => d
+  end.
+ +
+
+ +
+For conversions with binary numbers, it is easier to operate + on little-endian numbers. +
+
+ +
+Fixpoint revapp (d d' : uint) :=
+  match d with
+  | Nil => d'
+  | D0 d => revapp d (D0 d')
+  | D1 d => revapp d (D1 d')
+  | D2 d => revapp d (D2 d')
+  | D3 d => revapp d (D3 d')
+  | D4 d => revapp d (D4 d')
+  | D5 d => revapp d (D5 d')
+  | D6 d => revapp d (D6 d')
+  | D7 d => revapp d (D7 d')
+  | D8 d => revapp d (D8 d')
+  | D9 d => revapp d (D9 d')
+  | Da d => revapp d (Da d')
+  | Db d => revapp d (Db d')
+  | Dc d => revapp d (Dc d')
+  | Dd d => revapp d (Dd d')
+  | De d => revapp d (De d')
+  | Df d => revapp d (Df d')
+  end.
+ +
+Definition rev d := revapp d Nil.
+ +
+Definition app d d' := revapp (rev d) d'.
+ +
+Definition app_int d1 d2 :=
+  match d1 with Pos d1 => Pos (app d1 d2) | Neg d1 => Neg (app d1 d2) end.
+ +
+
+ +
+nztail removes all trailing zero digits and return both the + result and the number of removed digits. +
+
+ +
+Definition nztail d :=
+  let fix aux d_rev :=
+    match d_rev with
+    | D0 d_rev => let (r, n) := aux d_rev in pair r (S n)
+    | _ => pair d_rev O
+    end in
+  let (r, n) := aux (rev d) in pair (rev r) n.
+ +
+Definition nztail_int d :=
+  match d with
+  | Pos d => let (r, n) := nztail d in pair (Pos r) n
+  | Neg d => let (r, n) := nztail d in pair (Neg r) n
+  end.
+ +
+
+ +
+del_head n d removes n digits at beginning of d + or returns zero if d has less than n digits. +
+
+ +
+Fixpoint del_head n d :=
+  match n with
+  | O => d
+  | S n =>
+    match d with
+    | Nil => zero
+    | D0 d | D1 d | D2 d | D3 d | D4 d | D5 d | D6 d | D7 d | D8 d | D9 d
+    | Da d | Db d | Dc d | Dd d | De d | Df d =>
+      del_head n d
+    end
+  end.
+ +
+Definition del_head_int n d :=
+  match d with
+  | Pos d => del_head n d
+  | Neg d => del_head n d
+  end.
+ +
+
+ +
+del_tail n d removes n digits at end of d + or returns zero if d has less than n digits. +
+
+ +
+Definition del_tail n d := rev (del_head n (rev d)).
+ +
+Definition del_tail_int n d :=
+  match d with
+  | Pos d => Pos (del_tail n d)
+  | Neg d => Neg (del_tail n d)
+  end.
+ +
+Module Little.
+ +
+
+ +
+Successor of little-endian numbers +
+
+ +
+Fixpoint succ d :=
+  match d with
+  | Nil => D1 Nil
+  | D0 d => D1 d
+  | D1 d => D2 d
+  | D2 d => D3 d
+  | D3 d => D4 d
+  | D4 d => D5 d
+  | D5 d => D6 d
+  | D6 d => D7 d
+  | D7 d => D8 d
+  | D8 d => D9 d
+  | D9 d => Da d
+  | Da d => Db d
+  | Db d => Dc d
+  | Dc d => Dd d
+  | Dd d => De d
+  | De d => Df d
+  | Df d => D0 (succ d)
+  end.
+ +
+
+ +
+Doubling little-endian numbers +
+
+ +
+Fixpoint double d :=
+  match d with
+  | Nil => Nil
+  | D0 d => D0 (double d)
+  | D1 d => D2 (double d)
+  | D2 d => D4 (double d)
+  | D3 d => D6 (double d)
+  | D4 d => D8 (double d)
+  | D5 d => Da (double d)
+  | D6 d => Dc (double d)
+  | D7 d => De (double d)
+  | D8 d => D0 (succ_double d)
+  | D9 d => D2 (succ_double d)
+  | Da d => D4 (succ_double d)
+  | Db d => D6 (succ_double d)
+  | Dc d => D8 (succ_double d)
+  | Dd d => Da (succ_double d)
+  | De d => Dc (succ_double d)
+  | Df d => De (succ_double d)
+  end
+
+with succ_double d :=
+  match d with
+  | Nil => D1 Nil
+  | D0 d => D1 (double d)
+  | D1 d => D3 (double d)
+  | D2 d => D5 (double d)
+  | D3 d => D7 (double d)
+  | D4 d => D9 (double d)
+  | D5 d => Db (double d)
+  | D6 d => Dd (double d)
+  | D7 d => Df (double d)
+  | D8 d => D1 (succ_double d)
+  | D9 d => D3 (succ_double d)
+  | Da d => D5 (succ_double d)
+  | Db d => D7 (succ_double d)
+  | Dc d => D9 (succ_double d)
+  | Dd d => Db (succ_double d)
+  | De d => Dd (succ_double d)
+  | Df d => Df (succ_double d)
+  end.
+ +
+End Little.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Init.Logic.html b/master/corelib/Corelib.Init.Logic.html new file mode 100644 index 0000000000..5543090c85 --- /dev/null +++ b/master/corelib/Corelib.Init.Logic.html @@ -0,0 +1,1438 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Init.Logic

+ +
+ +
+Set Implicit Arguments.
+ +
+Require Export Notations.
+Require Import Ltac.
+ +
+Notation "A -> B" := (forall (_ : A), B) : type_scope.
+ +
+
+ +
+

Propositional connectives

+ +
+ + True is the always true proposition +
+
+ +
+Inductive True : Prop :=
+  I : True.
+ +
+Register True as core.True.type.
+Register I as core.True.I.
+ +
+
+ +
+False is the always false proposition +
+
+Inductive False : Prop :=.
+ +
+Register False as core.False.type.
+ +
+
+ +
+not A, written ~A, is the negation of A +
+
+Definition not (A:Prop) := A -> False.
+ +
+Notation "~ x" := (not x) : type_scope.
+ +
+Register not as core.not.type.
+ +
+
+ +
+Negation of a type in Type +
+
+ +
+Definition notT (A:Type) := A -> False.
+ +
+
+ +
+Create the "core" hint database, and set its transparent state for + variables and constants explicitly. +
+
+ +
+Create HintDb core.
+#[global]
+Hint Variables Opaque : core.
+#[global]
+Hint Constants Opaque : core.
+ +
+#[global]
+Hint Unfold not: core.
+ +
+
+ +
+and A B, written A /\ B, is the conjunction of A and B + +
+ + conj p q is a proof of A /\ B as soon as + p is a proof of A and q a proof of B + +
+ + proj1 and proj2 are first and second projections of a conjunction +
+
+ +
+Inductive and (A B:Prop) : Prop :=
+  conj : A -> B -> A /\ B
+
+where "A /\ B" := (and A B) : type_scope.
+ +
+Register and as core.and.type.
+Register conj as core.and.conj.
+ +
+Section Conjunction.
+ +
+  Variables A B : Prop.
+ +
+  Theorem proj1 : A /\ B -> A.
+ +
+  Theorem proj2 : A /\ B -> B.
+ +
+End Conjunction.
+ +
+
+ +
+or A B, written A \/ B, is the disjunction of A and B +
+
+ +
+Inductive or (A B:Prop) : Prop :=
+  | or_introl : A -> A \/ B
+  | or_intror : B -> A \/ B
+
+where "A \/ B" := (or A B) : type_scope.
+ +
+Arguments or_introl [A B] _, [A] B _.
+Arguments or_intror [A B] _, A [B] _.
+ +
+Register or as core.or.type.
+ +
+
+ +
+iff A B, written A <-> B, expresses the equivalence of A and B +
+
+ +
+Definition iff (A B:Prop) := (A -> B) /\ (B -> A).
+ +
+Notation "A <-> B" := (iff A B) : type_scope.
+ +
+Register iff as core.iff.type.
+Register proj1 as core.iff.proj1.
+Register proj2 as core.iff.proj2.
+ +
+Section Equivalence.
+ +
+Theorem iff_refl : forall A:Prop, A <-> A.
+ +
+Theorem iff_trans : forall A B C:Prop, (A <-> B) -> (B <-> C) -> (A <-> C).
+ +
+Theorem iff_sym : forall A B:Prop, (A <-> B) -> (B <-> A).
+ +
+End Equivalence.
+ +
+#[global]
+Hint Unfold iff: extcore.
+ +
+
+ +
+Backward direction of the equivalences above does not need assumptions +
+
+ +
+Theorem and_iff_compat_l : forall A B C : Prop,
+  (B <-> C) -> (A /\ B <-> A /\ C).
+ +
+Theorem and_iff_compat_r : forall A B C : Prop,
+  (B <-> C) -> (B /\ A <-> C /\ A).
+ +
+Theorem or_iff_compat_l : forall A B C : Prop,
+  (B <-> C) -> (A \/ B <-> A \/ C).
+ +
+Theorem or_iff_compat_r : forall A B C : Prop,
+  (B <-> C) -> (B \/ A <-> C \/ A).
+ +
+Theorem imp_iff_compat_l : forall A B C : Prop,
+  (B <-> C) -> ((A -> B) <-> (A -> C)).
+ +
+Theorem imp_iff_compat_r : forall A B C : Prop,
+  (B <-> C) -> ((B -> A) <-> (C -> A)).
+ +
+Theorem not_iff_compat : forall A B : Prop,
+  (A <-> B) -> (~ A <-> ~B).
+ +
+
+ +
+Some equivalences +
+
+ +
+Theorem neg_false : forall A : Prop, ~ A <-> (A <-> False).
+ +
+Theorem and_cancel_l : forall A B C : Prop,
+  (B -> A) -> (C -> A) -> ((A /\ B <-> A /\ C) <-> (B <-> C)).
+ +
+Theorem and_cancel_r : forall A B C : Prop,
+  (B -> A) -> (C -> A) -> ((B /\ A <-> C /\ A) <-> (B <-> C)).
+ +
+Theorem and_comm : forall A B : Prop, A /\ B <-> B /\ A.
+ +
+Theorem and_assoc : forall A B C : Prop, (A /\ B) /\ C <-> A /\ B /\ C.
+ +
+Theorem or_cancel_l : forall A B C : Prop,
+  (B -> ~ A) -> (C -> ~ A) -> ((A \/ B <-> A \/ C) <-> (B <-> C)).
+Theorem or_cancel_r : forall A B C : Prop,
+  (B -> ~ A) -> (C -> ~ A) -> ((B \/ A <-> C \/ A) <-> (B <-> C)).
+Theorem or_comm : forall A B : Prop, (A \/ B) <-> (B \/ A).
+ +
+Theorem or_assoc : forall A B C : Prop, (A \/ B) \/ C <-> A \/ B \/ C.
+Lemma iff_and : forall A B : Prop, (A <-> B) -> (A -> B) /\ (B -> A).
+ +
+Lemma iff_to_and : forall A B : Prop, (A <-> B) <-> (A -> B) /\ (B -> A).
+ +
+
+ +
+

First-order quantifiers

+ +
+ + ex P, or simply exists x, P x, or also exists x:A, P x, + expresses the existence of an x of some type A in Set which + satisfies the predicate P. This is existential quantification. + +
+ + ex2 P Q, or simply exists2 x, P x & Q x, or also + exists2 x:A, P x & Q x, expresses the existence of an x of + type A which satisfies both predicates P and Q. + +
+ + Universal quantification is primitively written forall x:A, Q. By + symmetry with existential quantification, the construction all P + is provided too. + +
+
+ +
+Inductive ex (A:Type) (P:A -> Prop) : Prop :=
+  ex_intro : forall x:A, P x -> ex (A:=A) P.
+ +
+Register ex as core.ex.type.
+Register ex_intro as core.ex.intro.
+ +
+Section Projections.
+ +
+  Variables (A:Prop) (P:A->Prop).
+ +
+  Definition ex_proj1 (x:ex P) : A :=
+    match x with ex_intro _ a _ => a end.
+ +
+  Definition ex_proj2 (x:ex P) : P (ex_proj1 x) :=
+    match x with ex_intro _ _ b => b end.
+ +
+  Register ex_proj1 as core.ex.proj1.
+  Register ex_proj2 as core.ex.proj2.
+ +
+End Projections.
+ +
+Inductive ex2 (A:Type) (P Q:A -> Prop) : Prop :=
+  ex_intro2 : forall x:A, P x -> Q x -> ex2 (A:=A) P Q.
+ +
+
+ +
+ex2 of a predicate can be projected to an ex. + +
+ + This allows ex_proj1 and ex_proj2 to be usable with ex2. + +
+ + We have two choices here: either we can set up the definition so + that ex_proj1 of a coerced X : ex2 P Q will unify with let + (a, _, _) := X in a by restricting the first argument of ex2 to + be a Prop, or we can define a more general ex_of_ex2 which + does not satisfy this conversion rule. We choose the former, + under the assumption that there is no reason to turn an ex2 into + an ex unless it is to project out the components. +
+
+ +
+Definition ex_of_ex2 (A : Prop) (P Q : A -> Prop) (X : ex2 P Q) : ex P
+  := ex_intro P
+              (let (a, _, _) := X in a)
+              (let (x, p, _) as s return (P (let (a, _, _) := s in a)) := X in p).
+ +
+Section ex2_Projections.
+ +
+  Variables (A:Prop) (P Q:A->Prop).
+ +
+  Definition ex_proj3 (x:ex2 P Q) : Q (ex_proj1 (ex_of_ex2 x)) :=
+    match x with ex_intro2 _ _ _ _ b => b end.
+ +
+End ex2_Projections.
+ +
+Definition all (A:Type) (P:A -> Prop) := forall x:A, P x.
+Register all as core.all.
+ +
+ +
+Notation "'exists' x .. y , p" := (ex (fun x => .. (ex (fun y => p)) ..))
+  (at level 200, x binder, right associativity,
+   format "'[' 'exists' '/ ' x .. y , '/ ' p ']'")
+  : type_scope.
+ +
+Notation "'exists2' x , p & q" := (ex2 (fun x => p) (fun x => q))
+  (at level 200, x name, p at level 200, right associativity) : type_scope.
+Notation "'exists2' x : A , p & q" := (ex2 (A:=A) (fun x => p) (fun x => q))
+  (at level 200, x name, A at level 200, p at level 200, right associativity,
+    format "'[' 'exists2' '/ ' x : A , '/ ' '[' p & '/' q ']' ']'")
+  : type_scope.
+ +
+Notation "'exists2' ' x , p & q" := (ex2 (fun x => p) (fun x => q))
+  (at level 200, x strict pattern, p at level 200, right associativity) : type_scope.
+Notation "'exists2' ' x : A , p & q" := (ex2 (A:=A) (fun x => p) (fun x => q))
+  (at level 200, x strict pattern, A at level 200, p at level 200, right associativity,
+    format "'[' 'exists2' '/ ' ' x : A , '/ ' '[' p & '/' q ']' ']'")
+  : type_scope.
+ +
+
+ +
+Derived rules for universal quantification +
+
+ +
+Section universal_quantification.
+ +
+  Variable A : Type.
+  Variable P : A -> Prop.
+ +
+  Theorem inst : forall x:A, all (fun x => P x) -> P x.
+ +
+  Theorem gen : forall (B:Prop) (f:forall y:A, B -> P y), B -> all P.
+ +
+End universal_quantification.
+ +
+
+ +
+

Equality

+ +
+ + eq x y, or simply x=y expresses the equality of x and + y. Both x and y must belong to the same type A. + The definition is inductive and states the reflexivity of the equality. + The others properties (symmetry, transitivity, replacement of + equals by equals) are proved below. The type of x and y can be + made explicit using the notation x = y :> A. This is Leibniz equality + as it expresses that x and y are equal iff every property on + A which is true of x is also true of y +
+
+ +
+Inductive eq (A:Type) (x:A) : A -> Prop :=
+    eq_refl : x = x :>A
+
+where "x = y :> A" := (@eq A x y) : type_scope.
+ +
+Arguments eq {A} x _.
+Arguments eq_refl {A x} , [A] x.
+ +
+Arguments eq_ind [A] x P _ y _ : rename.
+Arguments eq_rec [A] x P _ y _ : rename.
+Arguments eq_rect [A] x P _ y _ : rename.
+ +
+Notation "x = y" := (eq x y) : type_scope.
+Notation "x <> y :> T" := (~ x = y :>T) : type_scope.
+Notation "x <> y" := (~ (x = y)) : type_scope.
+ +
+#[global]
+Hint Resolve I conj or_introl or_intror : core.
+#[global]
+Hint Resolve eq_refl: core.
+#[global]
+Hint Resolve ex_intro ex_intro2: core.
+ +
+Register eq as core.eq.type.
+Register eq_refl as core.eq.refl.
+Register eq_ind as core.eq.ind.
+Register eq_rect as core.eq.rect.
+ +
+Section Logic_lemmas.
+ +
+  Theorem absurd : forall A C:Prop, A -> ~ A -> C.
+ +
+  Section equality.
+    Variables A B : Type.
+    Variable f : A -> B.
+    Variables x y z : A.
+ +
+    Theorem eq_sym : x = y -> y = x.
+ +
+    Register eq_sym as core.eq.sym.
+ +
+    Theorem eq_trans : x = y -> y = z -> x = z.
+ +
+    Register eq_trans as core.eq.trans.
+ +
+    Theorem eq_trans_r : x = y -> z = y -> x = z.
+ +
+    Theorem f_equal : x = y -> f x = f y.
+ +
+    Register f_equal as core.eq.congr.
+ +
+    Theorem not_eq_sym : x <> y -> y <> x.
+ +
+  End equality.
+ +
+  Definition eq_sind_r :
+    forall (A:Type) (x:A) (P:A -> SProp), P x -> forall y:A, y = x -> P y.
+ +
+  Definition eq_ind_r :
+    forall (A:Type) (x:A) (P:A -> Prop), P x -> forall y:A, y = x -> P y.
+  Defined.
+ +
+  Register eq_ind_r as core.eq.ind_r.
+ +
+  Definition eq_rec_r :
+    forall (A:Type) (x:A) (P:A -> Set), P x -> forall y:A, y = x -> P y.
+  Defined.
+ +
+  Definition eq_rect_r :
+    forall (A:Type) (x:A) (P:A -> Type), P x -> forall y:A, y = x -> P y.
+  Defined.
+End Logic_lemmas.
+ +
+Module EqNotations.
+  Notation "'rew' H 'in' H'" := (eq_rect _ _ H' _ H)
+    (at level 10, H' at level 10,
+     format "'[' 'rew' H in '/' H' ']'").
+  Notation "'rew' [ P ] H 'in' H'" := (eq_rect _ P H' _ H)
+    (at level 10, H' at level 10,
+     format "'[' 'rew' [ P ] '/ ' H in '/' H' ']'").
+  Notation "'rew' <- H 'in' H'" := (eq_rect_r _ H' H)
+    (at level 10, H' at level 10,
+     format "'[' 'rew' <- H in '/' H' ']'").
+  Notation "'rew' <- [ P ] H 'in' H'" := (eq_rect_r P H' H)
+    (at level 10, H' at level 10,
+     format "'[' 'rew' <- [ P ] '/ ' H in '/' H' ']'").
+  Notation "'rew' -> H 'in' H'" := (eq_rect _ _ H' _ H)
+    (at level 10, H' at level 10, only parsing).
+  Notation "'rew' -> [ P ] H 'in' H'" := (eq_rect _ P H' _ H)
+    (at level 10, H' at level 10, only parsing).
+ +
+  Notation "'rew' 'dependent' H 'in' H'"
+    := (match H with
+        | eq_refl => H'
+        end)
+         (at level 10, H' at level 10,
+          format "'[' 'rew' 'dependent' '/ ' H in '/' H' ']'").
+  Notation "'rew' 'dependent' -> H 'in' H'"
+    := (match H with
+        | eq_refl => H'
+        end)
+         (at level 10, H' at level 10, only parsing).
+  Notation "'rew' 'dependent' <- H 'in' H'"
+    := (match eq_sym H with
+        | eq_refl => H'
+        end)
+         (at level 10, H' at level 10,
+          format "'[' 'rew' 'dependent' <- '/ ' H in '/' H' ']'").
+  Notation "'rew' 'dependent' [ 'fun' y p => P ] H 'in' H'"
+    := (match H as p in (_ = y) return P with
+        | eq_refl => H'
+        end)
+         (at level 10, H' at level 10, y name, p name,
+          format "'[' 'rew' 'dependent' [ 'fun' y p => P ] '/ ' H in '/' H' ']'").
+  Notation "'rew' 'dependent' -> [ 'fun' y p => P ] H 'in' H'"
+    := (match H as p in (_ = y) return P with
+        | eq_refl => H'
+        end)
+         (at level 10, H' at level 10, y name, p name, only parsing).
+  Notation "'rew' 'dependent' <- [ 'fun' y p => P ] H 'in' H'"
+    := (match eq_sym H as p in (_ = y) return P with
+        | eq_refl => H'
+        end)
+         (at level 10, H' at level 10, y name, p name,
+          format "'[' 'rew' 'dependent' <- [ 'fun' y p => P ] '/ ' H in '/' H' ']'").
+  Notation "'rew' 'dependent' [ P ] H 'in' H'"
+    := (match H as p in (_ = y) return P y p with
+        | eq_refl => H'
+        end)
+         (at level 10, H' at level 10,
+          format "'[' 'rew' 'dependent' [ P ] '/ ' H in '/' H' ']'").
+  Notation "'rew' 'dependent' -> [ P ] H 'in' H'"
+    := (match H as p in (_ = y) return P y p with
+        | eq_refl => H'
+        end)
+         (at level 10, H' at level 10,
+          only parsing).
+  Notation "'rew' 'dependent' <- [ P ] H 'in' H'"
+    := (match eq_sym H as p in (_ = y) return P y p with
+        | eq_refl => H'
+        end)
+         (at level 10, H' at level 10,
+          format "'[' 'rew' 'dependent' <- [ P ] '/ ' H in '/' H' ']'").
+End EqNotations.
+ +
+Import EqNotations.
+ +
+Section equality_dep.
+  Variable A : Type.
+  Variable B : A -> Type.
+  Variable f : forall x, B x.
+  Variables x y : A.
+ +
+  Theorem f_equal_dep (H: x = y) : rew H in f x = f y.
+ +
+End equality_dep.
+ +
+Lemma f_equal_dep2 {A A' B B'} (f : A -> A') (g : forall a:A, B a -> B' (f a))
+  {x1 x2 : A} {y1 : B x1} {y2 : B x2} (H : x1 = x2) :
+  rew H in y1 = y2 -> rew f_equal f H in g x1 y1 = g x2 y2.
+ +
+Lemma rew_opp_r A (P:A->Type) (x y:A) (H:x=y) (a:P y) : rew H in rew <- H in a = a.
+ +
+Lemma rew_opp_l A (P:A->Type) (x y:A) (H:x=y) (a:P x) : rew <- H in rew H in a = a.
+ +
+Theorem f_equal2 :
+  forall (A1 A2 B:Type) (f:A1 -> A2 -> B) (x1 y1:A1)
+    (x2 y2:A2), x1 = y1 -> x2 = y2 -> f x1 x2 = f y1 y2.
+ +
+Register f_equal2 as core.eq.congr2.
+ +
+Theorem f_equal3 :
+  forall (A1 A2 A3 B:Type) (f:A1 -> A2 -> A3 -> B) (x1 y1:A1)
+    (x2 y2:A2) (x3 y3:A3),
+    x1 = y1 -> x2 = y2 -> x3 = y3 -> f x1 x2 x3 = f y1 y2 y3.
+ +
+Theorem f_equal4 :
+  forall (A1 A2 A3 A4 B:Type) (f:A1 -> A2 -> A3 -> A4 -> B)
+    (x1 y1:A1) (x2 y2:A2) (x3 y3:A3) (x4 y4:A4),
+    x1 = y1 -> x2 = y2 -> x3 = y3 -> x4 = y4 -> f x1 x2 x3 x4 = f y1 y2 y3 y4.
+ +
+Theorem f_equal5 :
+  forall (A1 A2 A3 A4 A5 B:Type) (f:A1 -> A2 -> A3 -> A4 -> A5 -> B)
+    (x1 y1:A1) (x2 y2:A2) (x3 y3:A3) (x4 y4:A4) (x5 y5:A5),
+    x1 = y1 ->
+    x2 = y2 ->
+    x3 = y3 -> x4 = y4 -> x5 = y5 -> f x1 x2 x3 x4 x5 = f y1 y2 y3 y4 y5.
+ +
+Theorem f_equal_compose A B C (a b:A) (f:A->B) (g:B->C) (e:a=b) :
+  f_equal g (f_equal f e) = f_equal (fun a => g (f a)) e.
+ +
+
+ +
+The groupoid structure of equality +
+
+ +
+Theorem eq_trans_refl_l A (x y:A) (e:x=y) : eq_trans eq_refl e = e.
+ +
+Theorem eq_trans_refl_r A (x y:A) (e:x=y) : eq_trans e eq_refl = e.
+ +
+Theorem eq_sym_involutive A (x y:A) (e:x=y) : eq_sym (eq_sym e) = e.
+ +
+Theorem eq_trans_sym_inv_l A (x y:A) (e:x=y) : eq_trans (eq_sym e) e = eq_refl.
+ +
+Theorem eq_trans_sym_inv_r A (x y:A) (e:x=y) : eq_trans e (eq_sym e) = eq_refl.
+ +
+Theorem eq_trans_assoc A (x y z t:A) (e:x=y) (e':y=z) (e'':z=t) :
+  eq_trans e (eq_trans e' e'') = eq_trans (eq_trans e e') e''.
+ +
+Theorem rew_map A B (P:B->Type) (f:A->B) x1 x2 (H:x1=x2) (y:P (f x1)) :
+  rew [fun x => P (f x)] H in y = rew f_equal f H in y.
+ +
+Theorem eq_trans_map {A B} {x1 x2 x3:A} {y1:B x1} {y2:B x2} {y3:B x3}
+  (H1:x1=x2) (H2:x2=x3) (H1': rew H1 in y1 = y2) (H2': rew H2 in y2 = y3) :
+  rew eq_trans H1 H2 in y1 = y3.
+ +
+Lemma map_subst {A} {P Q:A->Type} (f : forall x, P x -> Q x) {x y} (H:x=y) (z:P x) :
+  rew H in f x z = f y (rew H in z).
+ +
+Lemma map_subst_map {A B} {P:A->Type} {Q:B->Type} (f:A->B) (g : forall x, P x -> Q (f x))
+  {x y} (H:x=y) (z:P x) :
+  rew f_equal f H in g x z = g y (rew H in z).
+ +
+Lemma rew_swap A (P:A->Type) x1 x2 (H:x1=x2) (y1:P x1) (y2:P x2) : rew H in y1 = y2 -> y1 = rew <- H in y2.
+ +
+Lemma rew_compose A (P:A->Type) x1 x2 x3 (H1:x1=x2) (H2:x2=x3) (y:P x1) :
+  rew H2 in rew H1 in y = rew (eq_trans H1 H2) in y.
+ +
+
+ +
+Extra properties of equality +
+
+ +
+Theorem eq_id_comm_l A (f:A->A) (Hf:forall a, a = f a) a : f_equal f (Hf a) = Hf (f a).
+ +
+Theorem eq_id_comm_r A (f:A->A) (Hf:forall a, f a = a) a : f_equal f (Hf a) = Hf (f a).
+ +
+Lemma eq_refl_map_distr A B x (f:A->B) : f_equal f (eq_refl x) = eq_refl (f x).
+ +
+Lemma eq_trans_map_distr A B x y z (f:A->B) (e:x=y) (e':y=z) : f_equal f (eq_trans e e') = eq_trans (f_equal f e) (f_equal f e').
+ +
+Lemma eq_sym_map_distr A B (x y:A) (f:A->B) (e:x=y) : eq_sym (f_equal f e) = f_equal f (eq_sym e).
+ +
+Lemma eq_trans_sym_distr A (x y z:A) (e:x=y) (e':y=z) : eq_sym (eq_trans e e') = eq_trans (eq_sym e') (eq_sym e).
+ +
+Lemma eq_trans_rew_distr A (P:A -> Type) (x y z:A) (e:x=y) (e':y=z) (k:P x) :
+    rew (eq_trans e e') in k = rew e' in rew e in k.
+ +
+Lemma rew_const A P (x y:A) (e:x=y) (k:P) :
+    rew [fun _ => P] e in k = k.
+ +
+ +
+Notation sym_eq := eq_sym (only parsing).
+Notation trans_eq := eq_trans (only parsing).
+Notation sym_not_eq := not_eq_sym (only parsing).
+ +
+Notation refl_equal := eq_refl (only parsing).
+Notation sym_equal := eq_sym (only parsing).
+Notation trans_equal := eq_trans (only parsing).
+Notation sym_not_equal := not_eq_sym (only parsing).
+ +
+#[global]
+Hint Immediate eq_sym not_eq_sym: core.
+ +
+
+ +
+Basic definitions about relations and properties +
+
+ +
+Definition subrelation (A B : Type) (R R' : A->B->Prop) :=
+  forall x y, R x y -> R' x y.
+ +
+Definition unique (A : Type) (P : A->Prop) (x:A) :=
+  P x /\ forall (x':A), P x' -> x=x'.
+ +
+Definition uniqueness (A:Type) (P:A->Prop) := forall x y, P x -> P y -> x = y.
+ +
+
+ +
+Unique existence +
+
+ +
+Notation "'exists' ! x .. y , p" :=
+  (ex (unique (fun x => .. (ex (unique (fun y => p))) ..)))
+  (at level 200, x binder, right associativity,
+   format "'[' 'exists' ! '/ ' x .. y , '/ ' p ']'")
+  : type_scope.
+ +
+Lemma unique_existence : forall (A:Type) (P:A->Prop),
+  ((exists x, P x) /\ uniqueness P) <-> (exists! x, P x).
+ +
+Lemma forall_exists_unique_domain_coincide :
+  forall A (P:A->Prop), (exists! x, P x) ->
+  forall Q:A->Prop, (forall x, P x -> Q x) <-> (exists x, P x /\ Q x).
+ +
+Lemma forall_exists_coincide_unique_domain :
+  forall A (P:A->Prop),
+  (forall Q:A->Prop, (forall x, P x -> Q x) <-> (exists x, P x /\ Q x))
+  -> (exists! x, P x).
+ +
+
+ +
+

Being inhabited

+ +
+ + The predicate inhabited can be used in different contexts. If A is + thought as a type, inhabited A states that A is inhabited. If A is + thought as a computationally relevant proposition, then + inhabited A weakens A so as to hide its computational meaning. + The so-weakened proof remains computationally relevant but only in + a propositional context. + +
+
+ +
+Inductive inhabited (A:Type) : Prop := inhabits : A -> inhabited A.
+ +
+#[global]
+Hint Resolve inhabits: core.
+ +
+Lemma exists_inhabited : forall (A:Type) (P:A->Prop),
+  (exists x, P x) -> inhabited A.
+ +
+Lemma inhabited_covariant (A B : Type) : (A -> B) -> inhabited A -> inhabited B.
+ +
+
+ +
+Declaration of stepl and stepr for eq and iff +
+
+ +
+Lemma eq_stepl : forall (A : Type) (x y z : A), x = y -> x = z -> z = y.
+ +
+Declare Left Step eq_stepl.
+Declare Right Step eq_trans.
+ +
+Lemma iff_stepl : forall A B C : Prop, (A <-> B) -> (A <-> C) -> (C <-> B).
+ +
+Declare Left Step iff_stepl.
+Declare Right Step iff_trans.
+ +
+
+ +
+More properties of ex and ex2 that rely on equality being present +
+ + We define restricted versions of ex_rect and ex_rec which + allow elimination into non-Prop sorts when the inductive is not + informative +
+ + η Principles +
+
+Definition ex_eta {A : Prop} {P} (p : exists a : A, P a)
+  : p = ex_intro _ (ex_proj1 p) (ex_proj2 p).
+ +
+Definition ex2_eta {A : Prop} {P Q} (p : exists2 a : A, P a & Q a)
+  : p = ex_intro2 _ _ (ex_proj1 (ex_of_ex2 p)) (ex_proj2 (ex_of_ex2 p)) (ex_proj3 p).
+ +
+Section ex_Prop.
+  Variables (A:Prop) (P:A->Prop).
+ +
+  Definition ex_rect (P0 : ex P -> Type) (f : forall x p, P0 (ex_intro P x p))
+    : forall e, P0 e
+    := fun e => rew <- ex_eta e in f _ _.
+  Definition ex_rec : forall (P0 : ex P -> Set) (f : forall x p, P0 (ex_intro P x p)),
+      forall e, P0 e
+    := ex_rect.
+ +
+End ex_Prop.
+ +
+
+ +
+Equality for ex +
+
+Section ex.
+  Local Unset Implicit Arguments.
+
+ +
+Projecting an equality of a pair to equality of the first components +
+
+  Definition ex_proj1_eq {A : Prop} {P : A -> Prop} {u v : exists a : A, P a} (p : u = v)
+    : ex_proj1 u = ex_proj1 v
+    := f_equal (@ex_proj1 _ _) p.
+ +
+
+ +
+Projecting an equality of a pair to equality of the second components +
+
+  Definition ex_proj2_eq {A : Prop} {P : A -> Prop} {u v : exists a : A, P a} (p : u = v)
+    : rew ex_proj1_eq p in ex_proj2 u = ex_proj2 v
+    := rew dependent p in eq_refl.
+ +
+
+ +
+Equality of ex is itself a ex (forwards-reasoning version) +
+
+  Definition eq_ex_intro_uncurried {A : Type} {P : A -> Prop} {u1 v1 : A} {u2 : P u1} {v2 : P v1}
+             (pq : exists p : u1 = v1, rew p in u2 = v2)
+    : ex_intro _ u1 u2 = ex_intro _ v1 v2.
+ +
+
+ +
+Equality of ex is itself a ex (backwards-reasoning version) +
+
+  Definition eq_ex_uncurried {A : Prop} {P : A -> Prop} (u v : exists a : A, P a)
+             (pq : exists p : ex_proj1 u = ex_proj1 v, rew p in ex_proj2 u = ex_proj2 v)
+    : u = v.
+ +
+
+ +
+Curried version of proving equality of ex types +
+
+  Definition eq_ex_intro {A : Type} {P : A -> Prop} {u1 v1 : A} {u2 : P u1} {v2 : P v1}
+             (p : u1 = v1) (q : rew p in u2 = v2)
+    : ex_intro _ u1 u2 = ex_intro _ v1 v2
+    := eq_ex_intro_uncurried (ex_intro _ p q).
+ +
+
+ +
+Curried version of proving equality of ex types +
+
+  Definition eq_ex {A : Prop} {P : A -> Prop} (u v : exists a : A, P a)
+             (p : ex_proj1 u = ex_proj1 v) (q : rew p in ex_proj2 u = ex_proj2 v)
+    : u = v
+    := eq_ex_uncurried u v (ex_intro _ p q).
+ +
+
+ +
+In order to have a performant inversion_sigma, we define + specialized versions for when we have constructors on one or + both sides of the equality +
+
+  Definition eq_ex_intro_l {A : Prop} {P : A -> Prop} u1 u2 (v : exists a : A, P a)
+             (p : u1 = ex_proj1 v) (q : rew p in u2 = ex_proj2 v)
+    : ex_intro P u1 u2 = v
+    := eq_ex (ex_intro P u1 u2) v p q.
+  Definition eq_ex_intro_r {A : Prop} {P : A -> Prop} (u : exists a : A, P a) v1 v2
+             (p : ex_proj1 u = v1) (q : rew p in ex_proj2 u = v2)
+    : u = ex_intro P v1 v2
+    := eq_ex u (ex_intro P v1 v2) p q.
+ +
+
+ +
+Induction principle for @eq (ex _) +
+
+  Definition eq_ex_eta {A : Prop} {P : A -> Prop} {u v : exists a : A, P a} (p : u = v) : p = eq_ex u v (ex_proj1_eq p) (ex_proj2_eq p).
+   Definition eq_ex_rect {A : Prop} {P : A -> Prop} {u v : exists a : A, P a} (Q : u = v -> Type)
+             (f : forall p q, Q (eq_ex u v p q))
+    : forall p, Q p
+    := fun p => rew <- eq_ex_eta p in f _ _.
+  Definition eq_ex_rec {A : Prop} {P : A -> Prop} {u v} (Q : u = v :> (exists a : A, P a) -> Set) := eq_ex_rect Q.
+  Definition eq_ex_ind {A : Prop} {P : A -> Prop} {u v} (Q : u = v :> (exists a : A, P a) -> Prop) := eq_ex_rec Q.
+ +
+
+ +
+In order to have a performant inversion_sigma, we define + specialized versions for when we have constructors on one or + both sides of the equality +
+
+  Definition eq_ex_rect_ex_intro_l {A : Prop} {P : A -> Prop} {u1 u2 v} (Q : _ -> Type)
+             (f : forall p q, Q (eq_ex_intro_l (P:=P) u1 u2 v p q))
+    : forall p, Q p
+    := eq_ex_rect Q f.
+  Definition eq_ex_rect_ex_intro_r {A : Prop} {P : A -> Prop} {u v1 v2} (Q : _ -> Type)
+             (f : forall p q, Q (eq_ex_intro_r (P:=P) u v1 v2 p q))
+    : forall p, Q p
+    := eq_ex_rect Q f.
+  Definition eq_ex_rect_ex_intro {A : Prop} {P : A -> Prop} {u1 u2 v1 v2} (Q : _ -> Type)
+             (f : forall p q, Q (@eq_ex_intro A P u1 v1 u2 v2 p q))
+    : forall p, Q p
+    := eq_ex_rect Q f.
+ +
+  Definition eq_ex_rect_uncurried {A : Prop} {P : A -> Prop} {u v : exists a : A, P a} (Q : u = v -> Type)
+             (f : forall pq, Q (eq_ex u v (ex_proj1 pq) (ex_proj2 pq)))
+    : forall p, Q p
+    := eq_ex_rect Q (fun p q => f (ex_intro _ p q)).
+  Definition eq_ex_rec_uncurried {A : Prop} {P : A -> Prop} {u v} (Q : u = v :> (exists a : A, P a) -> Set) := eq_ex_rect_uncurried Q.
+  Definition eq_ex_ind_uncurried {A : Prop} {P : A -> Prop} {u v} (Q : u = v :> (exists a : A, P a) -> Prop) := eq_ex_rec_uncurried Q.
+ +
+
+ +
+Equality of ex when the property is an hProp +
+
+  Definition eq_ex_hprop {A : Prop} {P : A -> Prop} (P_hprop : forall (x : A) (p q : P x), p = q)
+             (u v : exists a : A, P a)
+             (p : ex_proj1 u = ex_proj1 v)
+    : u = v
+    := eq_ex u v p (P_hprop _ _ _).
+ +
+  Definition eq_ex_intro_hprop {A : Type} {P : A -> Prop} (P_hprop : forall (x : A) (p q : P x), p = q)
+             {u1 v1 : A} {u2 : P u1} {v2 : P v1}
+             (p : u1 = v1)
+    : ex_intro P u1 u2 = ex_intro P v1 v2
+    := eq_ex_intro p (P_hprop _ _ _).
+ +
+
+ +
+Equivalence of equality of ex with a ex of equality We could actually prove an isomorphism here, and not just <->, + but for simplicity, we don't. +
+
+  Definition eq_ex_uncurried_iff {A : Prop} {P : A -> Prop} (u v : exists a : A, P a)
+    : u = v <-> exists p : ex_proj1 u = ex_proj1 v, rew p in ex_proj2 u = ex_proj2 v.
+ +
+
+ +
+Equivalence of equality of ex involving hProps with equality of the first components +
+
+  Definition eq_ex_hprop_iff {A : Prop} {P : A -> Prop} (P_hprop : forall (x : A) (p q : P x), p = q)
+             (u v : exists a : A, P a)
+    : u = v <-> (ex_proj1 u = ex_proj1 v)
+    := conj (fun p => f_equal (@ex_proj1 _ _) p) (eq_ex_hprop P_hprop u v).
+ +
+  Lemma rew_ex {A' : Type} {x} {P : A' -> Prop} (Q : forall a, P a -> Prop) (u : exists p : P x, Q x p) {y} (H : x = y)
+    : rew [fun a => exists p : P a, Q a p] H in u
+      = ex_intro
+          (Q y)
+          (rew H in ex_proj1 u)
+          (rew dependent H in ex_proj2 u).
+End ex.
+Global Arguments eq_ex_intro A P _ _ _ _ !p !q / .
+ +
+Section ex2_Prop.
+  Variables (A:Prop) (P Q:A->Prop).
+ +
+  Definition ex2_rect (P0 : ex2 P Q -> Type) (f : forall x p q, P0 (ex_intro2 P Q x p q))
+    : forall e, P0 e
+    := fun e => rew <- ex2_eta e in f _ _ _.
+  Definition ex2_rec : forall (P0 : ex2 P Q -> Set) (f : forall x p q, P0 (ex_intro2 P Q x p q)),
+      forall e, P0 e
+    := ex2_rect.
+ +
+End ex2_Prop.
+ +
+
+ +
+Equality for ex2 +
+
+Section ex2.
+  Local Coercion ex_of_ex2 : ex2 >-> ex.
+  Local Unset Implicit Arguments.
+
+ +
+Projecting an equality of a pair to equality of the first components +
+
+  Definition ex_of_ex2_eq {A : Prop} {P Q : A -> Prop} {u v : exists2 a : A, P a & Q a} (p : u = v)
+    : u = v :> exists a : A, P a
+    := f_equal _ p.
+  Definition ex_proj1_of_ex2_eq {A : Prop} {P Q : A -> Prop} {u v : exists2 a : A, P a & Q a} (p : u = v)
+    : ex_proj1 u = ex_proj1 v
+    := ex_proj1_eq (ex_of_ex2_eq p).
+ +
+
+ +
+Projecting an equality of a pair to equality of the second components +
+
+  Definition ex_proj2_of_ex2_eq {A : Prop} {P Q : A -> Prop} {u v : exists2 a : A, P a & Q a} (p : u = v)
+    : rew ex_proj1_of_ex2_eq p in ex_proj2 u = ex_proj2 v
+    := rew dependent p in eq_refl.
+ +
+
+ +
+Projecting an equality of a pair to equality of the third components +
+
+  Definition ex_proj3_eq {A : Prop} {P Q : A -> Prop} {u v : exists2 a : A, P a & Q a} (p : u = v)
+    : rew ex_proj1_of_ex2_eq p in ex_proj3 u = ex_proj3 v
+    := rew dependent p in eq_refl.
+ +
+
+ +
+Equality of ex2 is itself a ex2 (fowards-reasoning version) +
+
+  Definition eq_ex_intro2_uncurried {A : Type} {P Q : A -> Prop} {u1 v1 : A} {u2 : P u1} {v2 : P v1} {u3 : Q u1} {v3 : Q v1}
+             (pqr : exists2 p : u1 = v1, rew p in u2 = v2 & rew p in u3 = v3)
+    : ex_intro2 _ _ u1 u2 u3 = ex_intro2 _ _ v1 v2 v3.
+ +
+
+ +
+Equality of ex2 is itself a ex2 (backwards-reasoning version) +
+
+  Definition eq_ex2_uncurried {A : Prop} {P Q : A -> Prop} (u v : exists2 a : A, P a & Q a)
+             (pqr : exists2 p : ex_proj1 u = ex_proj1 v,
+                                rew p in ex_proj2 u = ex_proj2 v & rew p in ex_proj3 u = ex_proj3 v)
+    : u = v.
+ +
+
+ +
+Curried version of proving equality of ex types +
+
+  Definition eq_ex2 {A : Prop} {P Q : A -> Prop} (u v : exists2 a : A, P a & Q a)
+             (p : ex_proj1 u = ex_proj1 v)
+             (q : rew p in ex_proj2 u = ex_proj2 v)
+             (r : rew p in ex_proj3 u = ex_proj3 v)
+    : u = v
+    := eq_ex2_uncurried u v (ex_intro2 _ _ p q r).
+ +
+  Definition eq_ex_intro2 {A : Type} {P Q : A -> Prop} {u1 v1 : A} {u2 : P u1} {v2 : P v1} {u3 : Q u1} {v3 : Q v1}
+             (p : u1 = v1)
+             (q : rew p in u2 = v2)
+             (r : rew p in u3 = v3)
+    : ex_intro2 P Q u1 u2 u3 = ex_intro2 P Q v1 v2 v3
+    := eq_ex_intro2_uncurried (ex_intro2 _ _ p q r).
+ +
+
+ +
+In order to have a performant inversion_sigma, we define + specialized versions for when we have constructors on one or + both sides of the equality +
+
+  Definition eq_ex_intro2_l {A : Prop} {P Q : A -> Prop} u1 u2 u3 (v : exists2 a : A, P a & Q a)
+             (p : u1 = ex_proj1 v) (q : rew p in u2 = ex_proj2 v) (r : rew p in u3 = ex_proj3 v)
+    : ex_intro2 P Q u1 u2 u3 = v
+    := eq_ex2 (ex_intro2 P Q u1 u2 u3) v p q r.
+  Definition eq_ex_intro2_r {A : Prop} {P Q : A -> Prop} (u : exists2 a : A, P a & Q a) v1 v2 v3
+             (p : ex_proj1 u = v1) (q : rew p in ex_proj2 u = v2) (r : rew p in ex_proj3 u = v3)
+    : u = ex_intro2 P Q v1 v2 v3
+    := eq_ex2 u (ex_intro2 P Q v1 v2 v3) p q r.
+ +
+
+ +
+Equality of ex2 when the second property is an hProp +
+
+  Definition eq_ex2_hprop {A : Prop} {P Q : A -> Prop} (Q_hprop : forall (x : A) (p q : Q x), p = q)
+             (u v : exists2 a : A, P a & Q a)
+             (p : u = v :> exists a : A, P a)
+    : u = v
+    := eq_ex2 u v (ex_proj1_eq p) (ex_proj2_eq p) (Q_hprop _ _ _).
+ +
+  Definition eq_ex_intro2_hprop_nondep {A : Type} {P : A -> Prop} {Q : Prop} (Q_hprop : forall (p q : Q), p = q)
+             {u1 v1 : A} {u2 : P u1} {v2 : P v1} {u3 v3 : Q}
+             (p : ex_intro _ u1 u2 = ex_intro _ v1 v2)
+    : ex_intro2 _ _ u1 u2 u3 = ex_intro2 _ _ v1 v2 v3
+    := rew [fun v3 => _ = ex_intro2 _ _ _ _ v3] (Q_hprop u3 v3) in
+        f_equal (fun u => match u with ex_intro _ u1 u2 => ex_intro2 _ _ u1 u2 u3 end) p.
+ +
+  Definition eq_ex_intro2_hprop {A : Type} {P Q : A -> Prop}
+             (P_hprop : forall x (p q : P x), p = q)
+             (Q_hprop : forall x (p q : Q x), p = q)
+             {u1 v1 : A} {u2 : P u1} {v2 : P v1} {u3 : Q u1} {v3 : Q v1}
+             (p : u1 = v1)
+    : ex_intro2 P Q u1 u2 u3 = ex_intro2 P Q v1 v2 v3
+    := eq_ex_intro2 p (P_hprop _ _ _) (Q_hprop _ _ _).
+ +
+
+ +
+Equivalence of equality of ex2 with a ex2 of equality We could actually prove an isomorphism here, and not just <->, + but for simplicity, we don't. +
+
+  Definition eq_ex2_uncurried_iff {A : Prop} {P Q : A -> Prop} (u v : exists2 a : A, P a & Q a)
+    : u = v
+      <-> exists2 p : ex_proj1 u = ex_proj1 v,
+                      rew p in ex_proj2 u = ex_proj2 v & rew p in ex_proj3 u = ex_proj3 v.
+ +
+
+ +
+Induction principle for @eq (ex2 _ _) +
+
+  Definition eq_ex2_eta {A : Prop} {P Q : A -> Prop} {u v : exists2 a : A, P a & Q a} (p : u = v)
+    : p = eq_ex2 u v (ex_proj1_of_ex2_eq p) (ex_proj2_of_ex2_eq p) (ex_proj3_eq p).
+   Definition eq_ex2_rect {A : Prop} {P Q : A -> Prop} {u v : exists2 a : A, P a & Q a} (R : u = v -> Type)
+             (f : forall p q r, R (eq_ex2 u v p q r))
+    : forall p, R p
+    := fun p => rew <- eq_ex2_eta p in f _ _ _.
+  Definition eq_ex2_rec {A : Prop} {P Q : A -> Prop} {u v} (R : u = v :> (exists2 a : A, P a & Q a) -> Set) := eq_ex2_rect R.
+  Definition eq_ex2_ind {A : Prop} {P Q : A -> Prop} {u v} (R : u = v :> (exists2 a : A, P a & Q a) -> Prop) := eq_ex2_rec R.
+ +
+
+ +
+In order to have a performant inversion_sigma, we define + specialized versions for when we have constructors on one or + both sides of the equality +
+
+  Definition eq_ex2_rect_ex_intro2_l {A : Prop} {P Q : A -> Prop} {u1 u2 u3 v} (R : _ -> Type)
+             (f : forall p q r, R (eq_ex_intro2_l (P:=P) (Q:=Q) u1 u2 u3 v p q r))
+    : forall p, R p
+    := eq_ex2_rect R f.
+  Definition eq_ex2_rect_ex_intro2_r {A : Prop} {P Q : A -> Prop} {u v1 v2 v3} (R : _ -> Type)
+             (f : forall p q r, R (eq_ex_intro2_r (P:=P) (Q:=Q) u v1 v2 v3 p q r))
+    : forall p, R p
+    := eq_ex2_rect R f.
+  Definition eq_ex2_rect_ex_intro2 {A : Prop} {P Q : A -> Prop} {u1 u2 u3 v1 v2 v3} (R : _ -> Type)
+             (f : forall p q r, R (@eq_ex_intro2 A P Q u1 v1 u2 v2 u3 v3 p q r))
+    : forall p, R p
+    := eq_ex2_rect R f.
+ +
+  Definition eq_ex2_rect_uncurried {A : Prop} {P Q : A -> Prop} {u v : exists2 a : A, P a & Q a} (R : u = v -> Type)
+             (f : forall pqr : exists2 p : _ = _, _ & _, R (eq_ex2 u v (ex_proj1 pqr) (ex_proj2 pqr) (ex_proj3 pqr)))
+    : forall p, R p
+    := eq_ex2_rect R (fun p q r => f (ex_intro2 _ _ p q r)).
+  Definition eq_ex2_rec_uncurried {A : Prop} {P Q : A -> Prop} {u v} (R : u = v :> (exists2 a : A, P a & Q a) -> Set) := eq_ex2_rect_uncurried R.
+  Definition eq_ex2_ind_uncurried {A : Prop} {P Q : A -> Prop} {u v} (R : u = v :> (exists2 a : A, P a & Q a) -> Prop) := eq_ex2_rec_uncurried R.
+ +
+
+ +
+Equivalence of equality of ex2 involving hProps with equality of the first components +
+
+  Definition eq_ex2_hprop_iff {A : Prop} {P Q : A -> Prop} (Q_hprop : forall (x : A) (p q : Q x), p = q)
+             (u v : exists2 a : A, P a & Q a)
+    : u = v <-> (u = v :> exists a : A, P a)
+    := conj (fun p => f_equal (@ex_of_ex2 _ _ _) p) (eq_ex2_hprop Q_hprop u v).
+ +
+
+ +
+Non-dependent classification of equality of ex +
+
+  Definition eq_ex2_nondep {A : Prop} {B C : Prop} (u v : @ex2 A (fun _ => B) (fun _ => C))
+             (p : ex_proj1 u = ex_proj1 v) (q : ex_proj2 u = ex_proj2 v) (r : ex_proj3 u = ex_proj3 v)
+    : u = v
+    := @eq_ex2 _ _ _ u v p (eq_trans (rew_const _ _) q) (eq_trans (rew_const _ _) r).
+ +
+
+ +
+Classification of transporting across an equality of ex2s +
+
+  Lemma rew_ex2 {A' : Type} {x} {P : A' -> Prop} (Q R : forall a, P a -> Prop)
+        (u : exists2 p : P x, Q x p & R x p)
+        {y} (H : x = y)
+    : rew [fun a => exists2 p : P a, Q a p & R a p] H in u
+      = ex_intro2
+          (Q y)
+          (R y)
+          (rew H in ex_proj1 u)
+          (rew dependent H in ex_proj2 u)
+          (rew dependent H in ex_proj3 u).
+End ex2.
+Global Arguments eq_ex_intro2 A P Q _ _ _ _ _ _ !p !q !r / .
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Init.Ltac.html b/master/corelib/Corelib.Init.Ltac.html new file mode 100644 index 0000000000..deb0db1a87 --- /dev/null +++ b/master/corelib/Corelib.Init.Ltac.html @@ -0,0 +1,86 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Init.Ltac

+ +
+ +
+ +
+#[export] Set Default Proof Mode "Classic".
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Init.Nat.html b/master/corelib/Corelib.Init.Nat.html new file mode 100644 index 0000000000..57169025c2 --- /dev/null +++ b/master/corelib/Corelib.Init.Nat.html @@ -0,0 +1,697 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Init.Nat

+ +
+ +
+Require Import Notations Logic Datatypes.
+Require Decimal Hexadecimal Number.
+Local Open Scope nat_scope.
+ +
+
+ +
+

Peano natural numbers, definitions of operations

+ +
+ + This file is meant to be used as a whole module, + without importing it, leading to qualified definitions + (e.g. Nat.pred) +
+
+ +
+Definition t := nat.
+ +
+
+ +
+

Constants

+ +
+
+ +
+Local Notation "0" := O.
+Local Notation "1" := (S O).
+Local Notation "2" := (S (S O)).
+ +
+Definition zero := 0.
+Definition one := 1.
+Definition two := 2.
+ +
+
+ +
+

Basic operations

+ +
+
+ +
+Definition succ := S.
+ +
+Definition pred n :=
+  match n with
+    | 0 => n
+    | S u => u
+  end.
+ +
+Register pred as num.nat.pred.
+ +
+Fixpoint add n m :=
+  match n with
+  | 0 => m
+  | S p => S (p + m)
+  end
+
+where "n + m" := (add n m) : nat_scope.
+ +
+Register add as num.nat.add.
+ +
+Definition double n := n + n.
+ +
+Fixpoint mul n m :=
+  match n with
+  | 0 => 0
+  | S p => m + p * m
+  end
+
+where "n * m" := (mul n m) : nat_scope.
+ +
+Register mul as num.nat.mul.
+ +
+
+ +
+Truncated subtraction: n-m is 0 if n<=m +
+
+ +
+Fixpoint sub n m :=
+  match n, m with
+  | S k, S l => k - l
+  | _, _ => n
+  end
+
+where "n - m" := (sub n m) : nat_scope.
+ +
+Register sub as num.nat.sub.
+ +
+
+ +
+

Comparisons

+ +
+
+ +
+Fixpoint eqb n m : bool :=
+  match n, m with
+    | 0, 0 => true
+    | 0, S _ => false
+    | S _, 0 => false
+    | S n', S m' => eqb n' m'
+  end.
+ +
+Fixpoint leb n m : bool :=
+  match n, m with
+    | 0, _ => true
+    | _, 0 => false
+    | S n', S m' => leb n' m'
+  end.
+ +
+Definition ltb n m := leb (S n) m.
+ +
+Infix "=?" := eqb (at level 70) : nat_scope.
+Infix "<=?" := leb (at level 70) : nat_scope.
+Infix "<?" := ltb (at level 70) : nat_scope.
+ +
+Fixpoint compare n m : comparison :=
+  match n, m with
+   | 0, 0 => Eq
+   | 0, S _ => Lt
+   | S _, 0 => Gt
+   | S n', S m' => compare n' m'
+  end.
+ +
+Infix "?=" := compare (at level 70) : nat_scope.
+ +
+
+ +
+

Minimum, maximum

+ +
+
+ +
+Fixpoint max n m :=
+  match n, m with
+    | 0, _ => m
+    | S n', 0 => n
+    | S n', S m' => S (max n' m')
+  end.
+ +
+Fixpoint min n m :=
+  match n, m with
+    | 0, _ => 0
+    | S n', 0 => 0
+    | S n', S m' => S (min n' m')
+  end.
+ +
+
+ +
+

Parity tests

+ +
+
+ +
+Fixpoint even n : bool :=
+  match n with
+    | 0 => true
+    | 1 => false
+    | S (S n') => even n'
+  end.
+ +
+Definition odd n := negb (even n).
+ +
+
+ +
+

Power

+ +
+
+ +
+Fixpoint pow n m :=
+  match m with
+    | 0 => 1
+    | S m => n * (n^m)
+  end
+
+where "n ^ m" := (pow n m) : nat_scope.
+ +
+
+ +
+

Tail-recursive versions of add and mul

+ +
+
+ +
+Fixpoint tail_add n m :=
+  match n with
+    | O => m
+    | S n => tail_add n (S m)
+  end.
+ +
+
+ +
+tail_addmul r n m is r + n * m. +
+
+ +
+Fixpoint tail_addmul r n m :=
+  match n with
+    | O => r
+    | S n => tail_addmul (tail_add m r) n m
+  end.
+ +
+Definition tail_mul n m := tail_addmul 0 n m.
+ +
+
+ +
+

Conversion with a decimal representation for printing/parsing

+ +
+
+ +
+Local Notation ten := (S (S (S (S (S (S (S (S (S (S O)))))))))).
+ +
+Fixpoint of_uint_acc (d:Decimal.uint)(acc:nat) :=
+  match d with
+  | Decimal.Nil => acc
+  | Decimal.D0 d => of_uint_acc d (tail_mul ten acc)
+  | Decimal.D1 d => of_uint_acc d (S (tail_mul ten acc))
+  | Decimal.D2 d => of_uint_acc d (S (S (tail_mul ten acc)))
+  | Decimal.D3 d => of_uint_acc d (S (S (S (tail_mul ten acc))))
+  | Decimal.D4 d => of_uint_acc d (S (S (S (S (tail_mul ten acc)))))
+  | Decimal.D5 d => of_uint_acc d (S (S (S (S (S (tail_mul ten acc))))))
+  | Decimal.D6 d => of_uint_acc d (S (S (S (S (S (S (tail_mul ten acc)))))))
+  | Decimal.D7 d => of_uint_acc d (S (S (S (S (S (S (S (tail_mul ten acc))))))))
+  | Decimal.D8 d => of_uint_acc d (S (S (S (S (S (S (S (S (tail_mul ten acc)))))))))
+  | Decimal.D9 d => of_uint_acc d (S (S (S (S (S (S (S (S (S (tail_mul ten acc))))))))))
+  end.
+ +
+Definition of_uint (d:Decimal.uint) := of_uint_acc d O.
+ +
+Local Notation sixteen := (S (S (S (S (S (S (S (S (S (S (S (S (S (S (S (S O)))))))))))))))).
+ +
+Fixpoint of_hex_uint_acc (d:Hexadecimal.uint)(acc:nat) :=
+  match d with
+  | Hexadecimal.Nil => acc
+  | Hexadecimal.D0 d => of_hex_uint_acc d (tail_mul sixteen acc)
+  | Hexadecimal.D1 d => of_hex_uint_acc d (S (tail_mul sixteen acc))
+  | Hexadecimal.D2 d => of_hex_uint_acc d (S (S (tail_mul sixteen acc)))
+  | Hexadecimal.D3 d => of_hex_uint_acc d (S (S (S (tail_mul sixteen acc))))
+  | Hexadecimal.D4 d => of_hex_uint_acc d (S (S (S (S (tail_mul sixteen acc)))))
+  | Hexadecimal.D5 d => of_hex_uint_acc d (S (S (S (S (S (tail_mul sixteen acc))))))
+  | Hexadecimal.D6 d => of_hex_uint_acc d (S (S (S (S (S (S (tail_mul sixteen acc)))))))
+  | Hexadecimal.D7 d => of_hex_uint_acc d (S (S (S (S (S (S (S (tail_mul sixteen acc))))))))
+  | Hexadecimal.D8 d => of_hex_uint_acc d (S (S (S (S (S (S (S (S (tail_mul sixteen acc)))))))))
+  | Hexadecimal.D9 d => of_hex_uint_acc d (S (S (S (S (S (S (S (S (S (tail_mul sixteen acc))))))))))
+  | Hexadecimal.Da d => of_hex_uint_acc d (S (S (S (S (S (S (S (S (S (S (tail_mul sixteen acc)))))))))))
+  | Hexadecimal.Db d => of_hex_uint_acc d (S (S (S (S (S (S (S (S (S (S (S (tail_mul sixteen acc))))))))))))
+  | Hexadecimal.Dc d => of_hex_uint_acc d (S (S (S (S (S (S (S (S (S (S (S (S (tail_mul sixteen acc)))))))))))))
+  | Hexadecimal.Dd d => of_hex_uint_acc d (S (S (S (S (S (S (S (S (S (S (S (S (S (tail_mul sixteen acc))))))))))))))
+  | Hexadecimal.De d => of_hex_uint_acc d (S (S (S (S (S (S (S (S (S (S (S (S (S (S (tail_mul sixteen acc)))))))))))))))
+  | Hexadecimal.Df d => of_hex_uint_acc d (S (S (S (S (S (S (S (S (S (S (S (S (S (S (S (tail_mul sixteen acc))))))))))))))))
+  end.
+ +
+Definition of_hex_uint (d:Hexadecimal.uint) := of_hex_uint_acc d O.
+ +
+Definition of_num_uint (d:Number.uint) :=
+  match d with
+  | Number.UIntDecimal d => of_uint d
+  | Number.UIntHexadecimal d => of_hex_uint d
+  end.
+ +
+Fixpoint to_little_uint n acc :=
+  match n with
+  | O => acc
+  | S n => to_little_uint n (Decimal.Little.succ acc)
+  end.
+ +
+Definition to_uint n :=
+  Decimal.rev (to_little_uint n Decimal.zero).
+ +
+Fixpoint to_little_hex_uint n acc :=
+  match n with
+  | O => acc
+  | S n => to_little_hex_uint n (Hexadecimal.Little.succ acc)
+  end.
+ +
+Definition to_hex_uint n :=
+  Hexadecimal.rev (to_little_hex_uint n Hexadecimal.zero).
+ +
+Definition to_num_uint n := Number.UIntDecimal (to_uint n).
+ +
+Definition to_num_hex_uint n := Number.UIntHexadecimal (to_hex_uint n).
+ +
+Definition of_int (d:Decimal.int) : option nat :=
+  match Decimal.norm d with
+    | Decimal.Pos u => Some (of_uint u)
+    | _ => None
+  end.
+ +
+Definition of_hex_int (d:Hexadecimal.int) : option nat :=
+  match Hexadecimal.norm d with
+    | Hexadecimal.Pos u => Some (of_hex_uint u)
+    | _ => None
+  end.
+ +
+Definition of_num_int (d:Number.int) : option nat :=
+  match d with
+  | Number.IntDecimal d => of_int d
+  | Number.IntHexadecimal d => of_hex_int d
+  end.
+ +
+Definition to_int n := Decimal.Pos (to_uint n).
+ +
+Definition to_hex_int n := Hexadecimal.Pos (to_hex_uint n).
+ +
+Definition to_num_int n := Number.IntDecimal (to_int n).
+ +
+
+ +
+

Euclidean division

+ +
+ + This division is linear and tail-recursive. + In divmod, y is the predecessor of the actual divisor, + and u is y minus the real remainder + +
+
+ +
+Fixpoint divmod x y q u :=
+  match x with
+    | 0 => (q,u)
+    | S x' => match u with
+                | 0 => divmod x' y (S q) y
+                | S u' => divmod x' y q u'
+              end
+  end.
+ +
+Definition div x y :=
+  match y with
+    | 0 => y
+    | S y' => fst (divmod x y' 0 y')
+  end.
+ +
+Definition modulo x y :=
+  match y with
+    | 0 => x
+    | S y' => y' - snd (divmod x y' 0 y')
+  end.
+ +
+Infix "/" := div : nat_scope.
+Infix "mod" := modulo (at level 40, no associativity) : nat_scope.
+ +
+
+ +
+

Greatest common divisor

+ +
+ + We use Euclid algorithm, which is normally not structural, + but Rocq is now clever enough to accept this (behind modulo + there is a subtraction, which now preserves being a subterm) + +
+
+ +
+Fixpoint gcd a b :=
+  match a with
+   | O => b
+   | S a' => gcd (b mod (S a')) (S a')
+  end.
+ +
+
+ +
+

Square

+ +
+
+ +
+Definition square n := n * n.
+ +
+
+ +
+

Square root

+ +
+ + The following square root function is linear (and tail-recursive). + With Peano representation, we can't do better. For faster algorithm, + see Psqrt/Zsqrt/Nsqrt... + +
+ + We search the square root of n = k + p^2 + (q - r) + with q = 2p and 0<=r<=q. We start with p=q=r=0, hence + looking for the square root of n = k. Then we progressively + decrease k and r. When k = S k' and r=0, it means we can use (S p) + as new sqrt candidate, since (S k')+p^2+2p = k'+(S p)^2. + When k reaches 0, we have found the biggest p^2 square contained + in n, hence the square root of n is p. + +
+
+ +
+Fixpoint sqrt_iter k p q r :=
+  match k with
+    | O => p
+    | S k' => match r with
+                | O => sqrt_iter k' (S p) (S (S q)) (S (S q))
+                | S r' => sqrt_iter k' p q r'
+              end
+  end.
+ +
+Definition sqrt n := sqrt_iter n 0 0 0.
+ +
+
+ +
+

Log2

+ +
+ + This base-2 logarithm is linear and tail-recursive. + +
+ + In log2_iter, we maintain the logarithm p of the counter q, + while r is the distance between q and the next power of 2, + more precisely q + S r = 2^(S p) and r<2^p. At each + recursive call, q goes up while r goes down. When r + is 0, we know that q has almost reached a power of 2, + and we increase p at the next call, while resetting r + to q. + +
+ + Graphically (numbers are q, stars are r) : + +
+ +
+                    10
+                  9
+                8
+              7   *
+            6       *
+          5           ...
+        4
+      3   *
+    2       *
+  1   *       *
+0   *   *       *
+
+ +
+ + We stop when k, the global downward counter reaches 0. + At that moment, q is the number we're considering (since + k+q is invariant), and p its logarithm. + +
+
+ +
+Fixpoint log2_iter k p q r :=
+  match k with
+    | O => p
+    | S k' => match r with
+                | O => log2_iter k' (S p) (S q) q
+                | S r' => log2_iter k' p (S q) r'
+              end
+  end.
+ +
+Definition log2 n := log2_iter (pred n) 0 1 0.
+ +
+
+ +
+Iterator on natural numbers +
+
+ +
+Definition iter (n:nat) {A} (f:A->A) (x:A) : A :=
+ nat_rect (fun _ => A) x (fun _ => f) n.
+ +
+
+ +
+Bitwise operations +
+ + We provide here some bitwise operations for unary numbers. + Some might be really naive, they are just there for fulfilling + the same interface as other for natural representations. As + soon as binary representations such as NArith are available, + it is clearly better to convert to/from them and use their ops. + +
+
+ +
+Fixpoint div2 n :=
+  match n with
+  | 0 => 0
+  | S 0 => 0
+  | S (S n') => S (div2 n')
+  end.
+ +
+Fixpoint testbit a n : bool :=
+ match n with
+   | 0 => odd a
+   | S n => testbit (div2 a) n
+ end.
+ +
+Definition shiftl a := nat_rect _ a (fun _ => double).
+Definition shiftr a := nat_rect _ a (fun _ => div2).
+ +
+Fixpoint bitwise (op:bool->bool->bool) n a b :=
+ match n with
+  | 0 => 0
+  | S n' =>
+    (if op (odd a) (odd b) then 1 else 0) +
+    2*(bitwise op n' (div2 a) (div2 b))
+ end.
+ +
+Definition land a b := bitwise andb a a b.
+Definition lor a b := bitwise orb (max a b) a b.
+Definition ldiff a b := bitwise (fun b b' => andb b (negb b')) a a b.
+Definition lxor a b := bitwise xorb (max a b) a b.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Init.Notations.html b/master/corelib/Corelib.Init.Notations.html new file mode 100644 index 0000000000..2f04e2f94e --- /dev/null +++ b/master/corelib/Corelib.Init.Notations.html @@ -0,0 +1,298 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Init.Notations

+ +
+ +
+
+ +
+These are the notations whose level and associativity are imposed by Rocq +
+ + Notations for propositional connectives +
+
+ +
+Reserved Notation "x -> y" (at level 99, right associativity, y at level 200).
+Reserved Notation "x <-> y" (at level 95, no associativity).
+Reserved Notation "x /\ y" (at level 80, right associativity).
+Reserved Notation "x \/ y" (at level 85, right associativity).
+Reserved Notation "~ x" (at level 75, right associativity).
+ +
+
+ +
+Notations for equality and inequalities +
+
+ +
+Reserved Notation "x = y :> T"
+(at level 70, y at next level, no associativity).
+Reserved Notation "x = y" (at level 70, no associativity).
+Reserved Notation "x = y = z"
+(at level 70, no associativity, y at next level).
+ +
+Reserved Notation "x <> y :> T"
+(at level 70, y at next level, no associativity).
+Reserved Notation "x <> y" (at level 70, no associativity).
+ +
+Reserved Notation "x <= y" (at level 70, no associativity).
+Reserved Notation "x < y" (at level 70, no associativity).
+Reserved Notation "x >= y" (at level 70, no associativity).
+Reserved Notation "x > y" (at level 70, no associativity).
+ +
+Reserved Notation "x <= y <= z" (at level 70, y at next level).
+Reserved Notation "x <= y < z" (at level 70, y at next level).
+Reserved Notation "x < y < z" (at level 70, y at next level).
+Reserved Notation "x < y <= z" (at level 70, y at next level).
+ +
+
+ +
+Arithmetical notations (also used for type constructors) +
+
+ +
+Reserved Notation "x + y" (at level 50, left associativity).
+Reserved Notation "x - y" (at level 50, left associativity).
+Reserved Notation "x * y" (at level 40, left associativity).
+Reserved Notation "x / y" (at level 40, left associativity).
+Reserved Notation "- x" (at level 35, right associativity).
+Reserved Notation "/ x" (at level 35, right associativity).
+Reserved Notation "x ^ y" (at level 30, right associativity).
+ +
+
+ +
+Notations for booleans +
+
+ +
+Reserved Notation "x || y" (at level 50, left associativity).
+Reserved Notation "x && y" (at level 40, left associativity).
+ +
+
+ +
+Notations for pairs +
+
+ +
+Reserved Notation "( x , y , .. , z )"
+  (at level 0, format "( '[' x , '/' y , '/' .. , '/' z ']' )").
+ +
+
+ +
+Notation "{ x }" is reserved and has a special status as component + of other notations such as "{ A } + { B }" and "A + { B }" (which + are at the same level as "x + y"); + "{ x }" is at level 0 to factor with "{ x : A | P }" +
+
+ +
+Reserved Notation "{ x }" (at level 0, x at level 99).
+ +
+
+ +
+Notations for sigma-types or subsets +
+
+ +
+#[warning="-closed-notation-not-level-0"]
+Reserved Notation "{ A } + { B }" (at level 50, left associativity).
+#[warning="-postfix-notation-not-level-1"]
+Reserved Notation "A + { B }" (at level 50, left associativity).
+ +
+Reserved Notation "{ x | P }" (at level 0, x at level 99).
+Reserved Notation "{ x | P & Q }" (at level 0, x at level 99).
+ +
+Reserved Notation "{ x : A | P }" (at level 0, x at level 99).
+Reserved Notation "{ x : A | P & Q }" (at level 0, x at level 99).
+ +
+Reserved Notation "{ x & P }" (at level 0, x at level 99).
+Reserved Notation "{ x & P & Q }" (at level 0, x at level 99).
+ +
+Reserved Notation "{ x : A & P }" (at level 0, x at level 99).
+Reserved Notation "{ x : A & P & Q }" (at level 0, x at level 99).
+ +
+Reserved Notation "{ ' pat | P }"
+  (at level 0, pat strict pattern, format "{ ' pat | P }").
+Reserved Notation "{ ' pat | P & Q }"
+  (at level 0, pat strict pattern, format "{ ' pat | P & Q }").
+ +
+Reserved Notation "{ ' pat : A | P }"
+  (at level 0, pat strict pattern, format "{ ' pat : A | P }").
+Reserved Notation "{ ' pat : A | P & Q }"
+  (at level 0, pat strict pattern, format "{ ' pat : A | P & Q }").
+ +
+Reserved Notation "{ ' pat & P }"
+  (at level 0, pat strict pattern, format "{ ' pat & P }").
+Reserved Notation "{ ' pat & P & Q }"
+  (at level 0, pat strict pattern, format "{ ' pat & P & Q }").
+ +
+Reserved Notation "{ ' pat : A & P }"
+  (at level 0, pat strict pattern, format "{ ' pat : A & P }").
+Reserved Notation "{ ' pat : A & P & Q }"
+  (at level 0, pat strict pattern, format "{ ' pat : A & P & Q }").
+ +
+
+ +
+Support for Gonthier-Ssreflect's "if c is pat then u else v" +
+
+ +
+Module IfNotations.
+ +
+Notation "'if' c 'is' p 'then' u 'else' v" :=
+  (match c with p => u | _ => v end)
+  (at level 200, p pattern at level 100).
+ +
+End IfNotations.
+ +
+
+ +
+Notations for first and second projections +
+
+ +
+Reserved Notation "p .1" (at level 1, left associativity, format "p .1").
+Reserved Notation "p .2" (at level 1, left associativity, format "p .2").
+ +
+
+ +
+Scopes +
+
+ +
+Declare Scope core_scope.
+Delimit Scope core_scope with core.
+ +
+Declare Scope function_scope.
+Delimit Scope function_scope with function.
+Bind Scope function_scope with Funclass.
+ +
+Declare Scope type_scope.
+Delimit Scope type_scope with type.
+Bind Scope type_scope with Sortclass.
+ +
+Open Scope core_scope.
+Open Scope function_scope.
+Open Scope type_scope.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Init.Number.html b/master/corelib/Corelib.Init.Number.html new file mode 100644 index 0000000000..ac801ba181 --- /dev/null +++ b/master/corelib/Corelib.Init.Number.html @@ -0,0 +1,130 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Init.Number

+ +
+ +
+
+ +
+

Decimal or Hexadecimal numbers

+ +
+
+ +
+Require Import Decimal Hexadecimal.
+ +
+Variant uint := UIntDecimal (u:Decimal.uint) | UIntHexadecimal (u:Hexadecimal.uint).
+ +
+Variant signed_int := IntDecimal (i:Decimal.int) | IntHexadecimal (i:Hexadecimal.int).
+Notation int := signed_int.
+ +
+Variant number := Decimal (d:Decimal.decimal) | Hexadecimal (h:Hexadecimal.hexadecimal).
+ +
+Scheme Equality for uint.
+Scheme Equality for int.
+Scheme Equality for number.
+Notation int_eq_dec := signed_int_eq_dec.
+Notation int_beq := signed_int_beq.
+Notation internal_int_dec_lb := internal_signed_int_dec_lb.
+Notation internal_int_dec_bl := internal_signed_int_dec_bl.
+ +
+Register uint as num.num_uint.type.
+Register int as num.num_int.type.
+Register number as num.number.type.
+ +
+
+ +
+Pseudo-conversion functions used when declaring + Number Notations on uint and int. +
+
+ +
+Definition uint_of_uint (i:uint) := i.
+Definition int_of_int (i:int) := i.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Init.Peano.html b/master/corelib/Corelib.Init.Peano.html new file mode 100644 index 0000000000..f25959e3c5 --- /dev/null +++ b/master/corelib/Corelib.Init.Peano.html @@ -0,0 +1,434 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Init.Peano

+ +
+ +
+
+ +
+The type nat of Peano natural numbers (built from O and S) + is defined in Datatypes.v +
+ + This module defines the following operations on natural numbers : +
    +
  • predecessor pred + +
    • +
  • addition plus + +
    • +
  • multiplication mult + +
    • +
  • less or equal order le + +
    • +
  • less lt + +
    • +
  • greater or equal ge + +
    • +
  • greater gt + +
    • +
+ +
+ + It states various lemmas and theorems about natural numbers, + including Peano's axioms of arithmetic (in Rocq, these are provable). + Case analysis on nat and induction on nat * nat are provided too + +
+
+ +
+Require Import Notations.
+Require Import Ltac.
+Require Import Datatypes.
+Require Import Logic.
+Require Corelib.Init.Nat.
+ +
+Open Scope nat_scope.
+Local Notation "0" := O.
+ +
+Definition eq_S := f_equal S.
+Definition f_equal_nat := f_equal (A:=nat).
+ +
+#[global]
+Hint Resolve f_equal_nat: core.
+ +
+
+ +
+The predecessor function +
+
+ +
+Notation pred := Nat.pred (only parsing).
+ +
+Definition f_equal_pred := f_equal pred.
+ +
+Theorem pred_Sn : forall n:nat, n = pred (S n).
+ +
+
+ +
+Injectivity of successor +
+
+ +
+Definition eq_add_S n m (H: S n = S m): n = m := f_equal pred H.
+#[global]
+Hint Immediate eq_add_S: core.
+ +
+Theorem not_eq_S : forall n m:nat, n <> m -> S n <> S m.
+#[global]
+Hint Resolve not_eq_S: core.
+ +
+Definition IsSucc (n:nat) : Prop :=
+  match n with
+  | O => False
+  | S p => True
+  end.
+ +
+
+ +
+Zero is not the successor of a number +
+
+ +
+Theorem O_S : forall n:nat, 0 <> S n.
+#[global]
+Hint Resolve O_S: core.
+ +
+Theorem n_Sn : forall n:nat, n <> S n.
+#[global]
+Hint Resolve n_Sn: core.
+ +
+
+ +
+Addition +
+
+ +
+Notation plus := Nat.add (only parsing).
+Infix "+" := Nat.add : nat_scope.
+ +
+Definition f_equal2_plus := f_equal2 plus.
+Definition f_equal2_nat := f_equal2 (A1:=nat) (A2:=nat).
+#[global]
+Hint Resolve f_equal2_nat: core.
+ +
+Lemma plus_n_O : forall n:nat, n = n + 0.
+ +
+#[global]
+Remove Hints eq_refl : core.
+#[global]
+Hint Resolve plus_n_O eq_refl: core. +
+Lemma plus_O_n : forall n:nat, 0 + n = n.
+ +
+Lemma plus_n_Sm : forall n m:nat, S (n + m) = n + S m.
+#[global]
+Hint Resolve plus_n_Sm: core.
+ +
+Lemma plus_Sn_m : forall n m:nat, S n + m = S (n + m).
+ +
+
+ +
+Standard associated names +
+
+ +
+Notation plus_0_r_reverse := plus_n_O (only parsing).
+Notation plus_succ_r_reverse := plus_n_Sm (only parsing).
+ +
+
+ +
+Multiplication +
+
+ +
+Notation mult := Nat.mul (only parsing).
+Infix "*" := Nat.mul : nat_scope.
+ +
+Definition f_equal2_mult := f_equal2 mult.
+#[global]
+Hint Resolve f_equal2_mult: core.
+ +
+Lemma mult_n_O : forall n:nat, 0 = n * 0.
+#[global]
+Hint Resolve mult_n_O: core.
+ +
+Lemma mult_n_Sm : forall n m:nat, n * m + n = n * S m.
+#[global]
+Hint Resolve mult_n_Sm: core.
+ +
+
+ +
+Standard associated names +
+
+ +
+Notation mult_0_r_reverse := mult_n_O (only parsing).
+Notation mult_succ_r_reverse := mult_n_Sm (only parsing).
+ +
+
+ +
+Truncated subtraction: m-n is 0 if n>=m +
+
+ +
+Notation minus := Nat.sub (only parsing).
+Infix "-" := Nat.sub : nat_scope.
+ +
+
+ +
+Definition of the usual orders, the basic properties of le and lt + can be found in files Le and Lt +
+
+ +
+Inductive le (n:nat) : nat -> Prop :=
+  | le_n : n <= n
+  | le_S : forall m:nat, n <= m -> n <= S m
+
+where "n <= m" := (le n m) : nat_scope.
+ +
+Register le_n as num.nat.le_n.
+ +
+#[global]
+Hint Constructors le: core.
+ +
+Definition lt (n m:nat) := S n <= m.
+#[global]
+Hint Unfold lt: core.
+ +
+Infix "<" := lt : nat_scope.
+ +
+Definition ge (n m:nat) := m <= n.
+#[global]
+Hint Unfold ge: core.
+ +
+Infix ">=" := ge : nat_scope.
+ +
+Definition gt (n m:nat) := m < n.
+#[global]
+Hint Unfold gt: core.
+ +
+Infix ">" := gt : nat_scope.
+ +
+Notation "x <= y <= z" := (x <= y /\ y <= z) : nat_scope.
+Notation "x <= y < z" := (x <= y /\ y < z) : nat_scope.
+Notation "x < y < z" := (x < y /\ y < z) : nat_scope.
+Notation "x < y <= z" := (x < y /\ y <= z) : nat_scope.
+ +
+Register le as num.nat.le.
+Register lt as num.nat.lt.
+Register ge as num.nat.ge.
+Register gt as num.nat.gt.
+ +
+Theorem le_pred : forall n m, n <= m -> pred n <= pred m.
+ +
+Theorem le_S_n : forall n m, S n <= S m -> n <= m.
+ +
+Theorem le_0_n : forall n, 0 <= n.
+ +
+Theorem le_n_S : forall n m, n <= m -> S n <= S m.
+ +
+
+ +
+Case analysis +
+
+ +
+Theorem nat_case :
+ forall (n:nat) (P:nat -> Prop), P 0 -> (forall m:nat, P (S m)) -> P n.
+ +
+
+ +
+Principle of double induction +
+
+ +
+Theorem nat_double_ind :
+ forall R:nat -> nat -> Prop,
+   (forall n:nat, R 0 n) ->
+   (forall n:nat, R (S n) 0) ->
+   (forall n m:nat, R n m -> R (S n) (S m)) -> forall n m:nat, R n m.
+ +
+
+ +
+Maximum and minimum : definitions and specifications +
+
+ +
+Notation max := Nat.max (only parsing).
+Notation min := Nat.min (only parsing).
+ +
+Lemma max_l n m : m <= n -> Nat.max n m = n.
+ +
+Lemma max_r n m : n <= m -> Nat.max n m = m.
+ +
+Lemma min_l n m : n <= m -> Nat.min n m = n.
+ +
+Lemma min_r n m : m <= n -> Nat.min n m = m.
+ +
+Lemma nat_rect_succ_r {A} (f: A -> A) (x:A) n :
+  nat_rect (fun _ => A) x (fun _ => f) (S n) = nat_rect (fun _ => A) (f x) (fun _ => f) n.
+ +
+Theorem nat_rect_plus :
+  forall (n m:nat) {A} (f:A -> A) (x:A),
+    nat_rect (fun _ => A) x (fun _ => f) (n + m) =
+      nat_rect (fun _ => A) (nat_rect (fun _ => A) x (fun _ => f) m) (fun _ => f) n.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Init.Prelude.html b/master/corelib/Corelib.Init.Prelude.html new file mode 100644 index 0000000000..76b14a6ba2 --- /dev/null +++ b/master/corelib/Corelib.Init.Prelude.html @@ -0,0 +1,132 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Init.Prelude

+ +
+ +
+Require Export Notations.
+Require Export Logic.
+Require Export Datatypes.
+Require Export Specif.
+Require Corelib.Init.Byte.
+Require Corelib.Init.Decimal.
+Require Corelib.Init.Hexadecimal.
+Require Corelib.Init.Number.
+Require Corelib.Init.Nat.
+Require Export Peano.
+Require Export Corelib.Init.Wf.
+Require Export Corelib.Init.Ltac.
+Require Export Corelib.Init.Tactics.
+Require Export Corelib.Init.Tauto.
+Require Export Corelib.Init.Sumbool.
+ +
+Arguments Nat.of_hex_uint d%_hex_uint_scope.
+Arguments Nat.of_hex_int d%_hex_int_scope.
+Number Notation Number.uint Number.uint_of_uint Number.uint_of_uint
+  : hex_uint_scope.
+Number Notation Number.int Number.int_of_int Number.int_of_int
+  : hex_int_scope.
+ +
+Arguments Nat.of_uint d%_dec_uint_scope.
+Arguments Nat.of_int d%_dec_int_scope.
+Number Notation Number.uint Number.uint_of_uint Number.uint_of_uint
+  : dec_uint_scope.
+Number Notation Number.int Number.int_of_int Number.int_of_int
+  : dec_int_scope.
+ +
+Number Notation nat Nat.of_num_uint Nat.to_num_hex_uint (abstract after 5000) : hex_nat_scope.
+Number Notation nat Nat.of_num_uint Nat.to_num_uint (abstract after 5000) : nat_scope.
+ +
+Export Byte.ByteSyntaxNotations.
+ +
+Add Search Blacklist "_subproof" "_subterm" "Private_".
+ +
+#[universes(polymorphic=yes)] Definition ReverseCoercionSource (T : Type) := T.
+#[universes(polymorphic=yes)] Definition ReverseCoercionTarget (T : Type) := T.
+#[warning="-uniform-inheritance", reversible=no, universes(polymorphic=yes)]
+Coercion reverse_coercion {T' T} (x' : T') (x : ReverseCoercionSource T)
+  : ReverseCoercionTarget T' := x'.
+Register reverse_coercion as core.coercion.reverse_coercion.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Init.Specif.html b/master/corelib/Corelib.Init.Specif.html new file mode 100644 index 0000000000..317267e789 --- /dev/null +++ b/master/corelib/Corelib.Init.Specif.html @@ -0,0 +1,1551 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Init.Specif

+ +
+ +
+
+ +
+Basic specifications : sets that may contain logical information +
+
+ +
+Set Implicit Arguments.
+ +
+Require Import Notations.
+Require Import Ltac.
+Require Import Datatypes.
+Require Import Logic.
+ +
+
+ +
+Subsets and Sigma-types +
+ + (sig A P), or more suggestively {x:A | P x}, denotes the subset + of elements of the type A which satisfy the predicate P. + Similarly (sig2 A P Q), or {x:A | P x & Q x}, denotes the subset + of elements of the type A which satisfy both P and Q. +
+
+ +
+#[universes(template)]
+Inductive sig (A:Type) (P:A -> Prop) : Type :=
+    exist : forall x:A, P x -> sig P.
+ +
+Register sig as core.sig.type.
+Register exist as core.sig.intro.
+Register sig_rect as core.sig.rect.
+ +
+#[universes(template)]
+Inductive sig2 (A:Type) (P Q:A -> Prop) : Type :=
+    exist2 : forall x:A, P x -> Q x -> sig2 P Q.
+ +
+
+ +
+(sigT A P), or more suggestively {x:A & (P x)} is a Sigma-type. + Similarly for (sigT2 A P Q), also written {x:A & (P x) & (Q x)}. +
+
+ +
+#[universes(template)]
+Inductive sigT (A:Type) (P:A -> Type) : Type :=
+    existT : forall x:A, P x -> sigT P.
+ +
+Register sigT as core.sigT.type.
+Register existT as core.sigT.intro.
+Register sigT_rect as core.sigT.rect.
+ +
+#[universes(template)]
+Inductive sigT2 (A:Type) (P Q:A -> Type) : Type :=
+    existT2 : forall x:A, P x -> Q x -> sigT2 P Q.
+ +
+ +
+Arguments sig (A P)%_type.
+Arguments sig2 (A P Q)%_type.
+Arguments sigT (A P)%_type.
+Arguments sigT2 (A P Q)%_type.
+ +
+Notation "{ x | P }" := (sig (fun x => P)) : type_scope.
+Notation "{ x | P & Q }" := (sig2 (fun x => P) (fun x => Q)) : type_scope.
+Notation "{ x : A | P }" := (sig (A:=A) (fun x => P)) : type_scope.
+Notation "{ x : A | P & Q }" := (sig2 (A:=A) (fun x => P) (fun x => Q)) :
+  type_scope.
+Notation "{ x & P }" := (sigT (fun x => P)) : type_scope.
+Notation "{ x & P & Q }" := (sigT2 (fun x => P) (fun x => Q)) : type_scope.
+Notation "{ x : A & P }" := (sigT (A:=A) (fun x => P)) : type_scope.
+Notation "{ x : A & P & Q }" := (sigT2 (A:=A) (fun x => P) (fun x => Q)) :
+  type_scope.
+ +
+Notation "{ ' pat | P }" := (sig (fun pat => P)) : type_scope.
+Notation "{ ' pat | P & Q }" := (sig2 (fun pat => P) (fun pat => Q)) : type_scope.
+Notation "{ ' pat : A | P }" := (sig (A:=A) (fun pat => P)) : type_scope.
+Notation "{ ' pat : A | P & Q }" := (sig2 (A:=A) (fun pat => P) (fun pat => Q)) :
+  type_scope.
+Notation "{ ' pat & P }" := (sigT (fun pat => P)) : type_scope.
+Notation "{ ' pat & P & Q }" := (sigT2 (fun pat => P) (fun pat => Q)) : type_scope.
+Notation "{ ' pat : A & P }" := (sigT (A:=A) (fun pat => P)) : type_scope.
+Notation "{ ' pat : A & P & Q }" := (sigT2 (A:=A) (fun pat => P) (fun pat => Q)) :
+  type_scope.
+ +
+Add Printing Let sig.
+Add Printing Let sig2.
+Add Printing Let sigT.
+Add Printing Let sigT2.
+ +
+
+ +
+Projections of sig + +
+ + An element y of a subset {x:A | (P x)} is the pair of an a + of type A and of a proof h that a satisfies P. Then + (proj1_sig y) is the witness a and (proj2_sig y) is the + proof of (P a) +
+
+ +
+Section Subset_projections.
+ +
+  Variable A : Type.
+  Variable P : A -> Prop.
+ +
+  Definition proj1_sig (e:sig P) := match e with
+                                    | exist _ a b => a
+                                    end.
+ +
+  Definition proj2_sig (e:sig P) :=
+    match e return P (proj1_sig e) with
+    | exist _ a b => b
+    end.
+ +
+  Register proj1_sig as core.sig.proj1.
+  Register proj2_sig as core.sig.proj2.
+ +
+End Subset_projections.
+ +
+
+ +
+sig2 of a predicate can be projected to a sig. + +
+ + This allows proj1_sig and proj2_sig to be usable with sig2. + +
+ + The let statements occur in the body of the exist so that + proj1_sig of a coerced X : sig2 P Q will unify with let (a, + _, _) := X in a +
+
+ +
+Definition sig_of_sig2 (A : Type) (P Q : A -> Prop) (X : sig2 P Q) : sig P
+  := exist P
+           (let (a, _, _) := X in a)
+           (let (x, p, _) as s return (P (let (a, _, _) := s in a)) := X in p).
+ +
+
+ +
+Projections of sig2 + +
+ + An element y of a subset {x:A | (P x) & (Q x)} is the triple + of an a of type A, a of a proof h that a satisfies P, + and a proof h' that a satisfies Q. Then + (proj1_sig (sig_of_sig2 y)) is the witness a, + (proj2_sig (sig_of_sig2 y)) is the proof of (P a), and + (proj3_sig y) is the proof of (Q a). +
+
+ +
+Section Subset_projections2.
+ +
+  Variable A : Type.
+  Variables P Q : A -> Prop.
+ +
+  Definition proj3_sig (e : sig2 P Q) :=
+    let (a, b, c) return Q (proj1_sig (sig_of_sig2 e)) := e in c.
+ +
+End Subset_projections2.
+ +
+
+ +
+Projections of sigT + +
+ + An element x of a sigma-type {y:A & P y} is a dependent pair + made of an a of type A and an h of type P a. Then, + (projT1 x) is the first projection and (projT2 x) is the + second projection, the type of which depends on the projT1. +
+
+ +
+Section Projections.
+ +
+  Variable A : Type.
+  Variable P : A -> Type.
+ +
+  Definition projT1 (x:sigT P) : A := match x with
+                                      | existT _ a _ => a
+                                      end.
+ +
+  Definition projT2 (x:sigT P) : P (projT1 x) :=
+    match x return P (projT1 x) with
+    | existT _ _ h => h
+    end.
+ +
+  Register projT1 as core.sigT.proj1.
+  Register projT2 as core.sigT.proj2.
+ +
+End Projections.
+ +
+Module SigTNotations.
+  Notation "( x ; y )" := (existT _ x y) (at level 0, format "( x ; '/ ' y )").
+  Notation "x .1" := (projT1 x) (at level 1, left associativity, format "x .1").
+  Notation "x .2" := (projT2 x) (at level 1, left associativity, format "x .2").
+End SigTNotations.
+ +
+Import SigTNotations.
+ +
+
+ +
+sigT2 of a predicate can be projected to a sigT. + +
+ + This allows projT1 and projT2 to be usable with sigT2. + +
+ + The let statements occur in the body of the existT so that + projT1 of a coerced X : sigT2 P Q will unify with let (a, + _, _) := X in a +
+
+ +
+Definition sigT_of_sigT2 (A : Type) (P Q : A -> Type) (X : sigT2 P Q) : sigT P
+  := existT P
+            (let (a, _, _) := X in a)
+            (let (x, p, _) as s return (P (let (a, _, _) := s in a)) := X in p).
+ +
+
+ +
+Projections of sigT2 + +
+ + An element x of a sigma-type {y:A & P y & Q y} is a dependent + pair made of an a of type A, an h of type P a, and an h' + of type Q a. Then, (projT1 (sigT_of_sigT2 x)) is the first + projection, (projT2 (sigT_of_sigT2 x)) is the second projection, + and (projT3 x) is the third projection, the types of which + depends on the projT1. +
+
+ +
+Section Projections2.
+ +
+  Variable A : Type.
+  Variables P Q : A -> Type.
+ +
+  Definition projT3 (e : sigT2 P Q) :=
+    let (a, b, c) return Q (projT1 (sigT_of_sigT2 e)) := e in c.
+ +
+End Projections2.
+ +
+Local Notation "x .3" := (projT3 x) (at level 1, left associativity, format "x .3").
+ +
+
+ +
+sigT of a predicate is equivalent to sig +
+
+ +
+Definition sig_of_sigT (A : Type) (P : A -> Prop) (X : sigT P) : sig P
+  := exist P (projT1 X) (projT2 X).
+ +
+Definition sigT_of_sig (A : Type) (P : A -> Prop) (X : sig P) : sigT P
+  := existT P (proj1_sig X) (proj2_sig X).
+ +
+
+ +
+sigT2 of a predicate is equivalent to sig2 +
+
+ +
+Definition sig2_of_sigT2 (A : Type) (P Q : A -> Prop) (X : sigT2 P Q) : sig2 P Q
+  := exist2 P Q (projT1 (sigT_of_sigT2 X)) (projT2 (sigT_of_sigT2 X)) (projT3 X).
+ +
+Definition sigT2_of_sig2 (A : Type) (P Q : A -> Prop) (X : sig2 P Q) : sigT2 P Q
+  := existT2 P Q (proj1_sig (sig_of_sig2 X)) (proj2_sig (sig_of_sig2 X)) (proj3_sig X).
+ +
+
+ +
+sig of a predicate on Props can be turned into ex +
+
+ +
+Definition ex_of_sig (A : Type) (P : A -> Prop) (X : sig P) : ex P
+  := ex_intro P (proj1_sig X) (proj2_sig X).
+ +
+
+ +
+sigT of a predicate on Props can be turned into ex +
+
+ +
+Definition ex_of_sigT (A : Type) (P : A -> Prop) (X : sigT P) : ex P
+  := ex_of_sig (sig_of_sigT X).
+ +
+
+ +
+sig2 of a predicate on Props can be turned into ex2 +
+
+ +
+Definition ex2_of_sig2 (A : Type) (P Q : A -> Prop) (X : sig2 P Q) : ex2 P Q
+  := ex_intro2 P Q (proj1_sig (sig_of_sig2 X)) (proj2_sig (sig_of_sig2 X)) (proj3_sig X).
+ +
+
+ +
+sigT2 of a predicate on Props can be turned into ex2 +
+
+ +
+Definition ex2_of_sigT2 (A : Type) (P Q : A -> Prop) (X : sigT2 P Q) : ex2 P Q
+  := ex2_of_sig2 (sig2_of_sigT2 X).
+ +
+
+ +
+η Principles +
+
+Definition sigT_eta {A P} (p : { a : A & P a })
+  : p = existT _ (projT1 p) (projT2 p).
+ +
+Definition sig_eta {A P} (p : { a : A | P a })
+  : p = exist _ (proj1_sig p) (proj2_sig p).
+ +
+Definition sigT2_eta {A P Q} (p : { a : A & P a & Q a })
+  : p = existT2 _ _ (projT1 (sigT_of_sigT2 p)) (projT2 (sigT_of_sigT2 p)) (projT3 p).
+ +
+Definition sig2_eta {A P Q} (p : { a : A | P a & Q a })
+  : p = exist2 _ _ (proj1_sig (sig_of_sig2 p)) (proj2_sig (sig_of_sig2 p)) (proj3_sig p).
+ +
+
+ +
+exists x : A, B is equivalent to inhabited {x : A | B} +
+
+Lemma exists_to_inhabited_sig {A P} : (exists x : A, P x) -> inhabited {x : A | P x}.
+ +
+Lemma inhabited_sig_to_exists {A P} : inhabited {x : A | P x} -> exists x : A, P x.
+ +
+
+ +
+Subtyping for prod +
+
+ +
+Section ProdSigT.
+ +
+  Variable A B : Type.
+ +
+  Definition sigT_of_prod (p : A * B) := (fst p; snd p).
+  Definition prod_of_sigT (s : { _ : A & B }) := (s.1, s.2).
+ +
+  Lemma sigT_prod_sigT p : sigT_of_prod (prod_of_sigT p) = p.
+ +
+  Lemma prod_sigT_prod s : prod_of_sigT (sigT_of_prod s) = s.
+ +
+End ProdSigT.
+ +
+
+ +
+Equality of sigma types +
+
+ +
+Import EqNotations.
+ +
+
+ +
+Equality for sigT +
+
+Section sigT.
+  Local Unset Implicit Arguments.
+
+ +
+Projecting an equality of a pair to equality of the first components +
+
+  Definition projT1_eq {A} {P : A -> Type} {u v : { a : A & P a }} (p : u = v)
+    : u.1 = v.1
+    := f_equal (fun x => x.1) p.
+ +
+
+ +
+Projecting an equality of a pair to equality of the second components +
+
+  Definition projT2_eq {A} {P : A -> Type} {u v : { a : A & P a }} (p : u = v)
+    : rew projT1_eq p in u.2 = v.2
+    := rew dependent p in eq_refl.
+ +
+
+ +
+Equality of sigT is itself a sigT (forwards-reasoning version) +
+
+  Definition eq_existT_uncurried {A : Type} {P : A -> Type} {u1 v1 : A} {u2 : P u1} {v2 : P v1}
+             (pq : { p : u1 = v1 & rew p in u2 = v2 })
+    : (u1; u2) = (v1; v2).
+ +
+
+ +
+Equality of sigT is itself a sigT (backwards-reasoning version) +
+
+  Definition eq_sigT_uncurried {A : Type} {P : A -> Type} (u v : { a : A & P a })
+             (pq : { p : u.1 = v.1 & rew p in u.2 = v.2 })
+    : u = v.
+ +
+  Lemma eq_existT_curried {A : Type} {P : A -> Type} {u1 v1 : A} {u2 : P u1} {v2 : P v1}
+             (p : u1 = v1) (q : rew p in u2 = v2) : (u1; u2) = (v1; v2).
+ +
+  Local Notation "(= u ; v )" := (eq_existT_curried u v) (at level 0, format "(= u ; '/ ' v )").
+ +
+  Lemma eq_existT_curried_map {A A' P P'} (f:A -> A') (g:forall u:A, P u -> P' (f u))
+    {u1 v1 : A} {u2 : P u1} {v2 : P v1} (p : u1 = v1) (q : rew p in u2 = v2) :
+    f_equal (fun x => (f x.1; g x.1 x.2)) (= p; q) =
+    (= f_equal f p; f_equal_dep2 f g p q).
+ +
+  Lemma eq_existT_curried_trans {A P} {u1 v1 w1 : A} {u2 : P u1} {v2 : P v1} {w2 : P w1}
+    (p : u1 = v1) (q : rew p in u2 = v2)
+    (p' : v1 = w1) (q': rew p' in v2 = w2) :
+    eq_trans (= p; q) (= p'; q') =
+      (= eq_trans p p'; eq_trans_map p p' q q').
+ +
+  Theorem eq_existT_curried_congr {A P} {u1 v1 : A} {u2 : P u1} {v2 : P v1}
+    {p p' : u1 = v1} {q : rew p in u2 = v2} {q': rew p' in u2 = v2}
+    (r : p = p') : rew [fun H => rew H in u2 = v2] r in q = q' -> (= p; q) = (= p'; q').
+ +
+
+ +
+Curried version of proving equality of sigma types +
+
+  Definition eq_sigT {A : Type} {P : A -> Type} (u v : { a : A & P a })
+             (p : u.1 = v.1) (q : rew p in u.2 = v.2)
+    : u = v
+    := eq_sigT_uncurried u v (existT _ p q).
+ +
+
+ +
+In order to have a performant inversion_sigma, we define + specialized versions for when we have constructors on one or + both sides of the equality +
+
+  Definition eq_existT_l {A : Type} {P : A -> Type} {u1 : A} {u2 : P u1} {v : { a : A & P a }}
+             (p : u1 = v.1) (q : rew p in u2 = v.2) : (u1; u2) = v
+    := eq_sigT (u1; u2) v p q.
+  Definition eq_existT_r {A : Type} {P : A -> Type} {u : { a : A & P a }} {v1 : A} {v2 : P v1}
+             (p : u.1 = v1) (q : rew p in u.2 = v2) : u = (v1; v2)
+    := eq_sigT u (v1; v2) p q.
+ +
+
+ +
+Equality of sigT when the property is an hProp +
+
+  Definition eq_sigT_hprop {A P} (P_hprop : forall (x : A) (p q : P x), p = q)
+             (u v : { a : A & P a })
+             (p : u.1 = v.1)
+    : u = v
+    := eq_sigT u v p (P_hprop _ _ _).
+ +
+
+ +
+Equivalence of equality of sigT with a sigT of equality We could actually prove an isomorphism here, and not just <->, + but for simplicity, we don't. +
+
+  Definition eq_sigT_uncurried_iff {A P}
+             (u v : { a : A & P a })
+    : u = v <-> { p : u.1 = v.1 & rew p in u.2 = v.2 }.
+ +
+
+ +
+Induction principle for @eq (sigT _) +
+
+  Definition eq_sigT_rect {A P} {u v : { a : A & P a }} (Q : u = v -> Type)
+             (f : forall p q, Q (eq_sigT u v p q))
+    : forall p, Q p.
+   Definition eq_sigT_rec {A P u v} (Q : u = v :> { a : A & P a } -> Set) := eq_sigT_rect Q.
+  Definition eq_sigT_ind {A P u v} (Q : u = v :> { a : A & P a } -> Prop) := eq_sigT_rec Q.
+ +
+
+ +
+In order to have a performant inversion_sigma, we define + specialized versions for when we have constructors on one or + both sides of the equality +
+
+  Definition eq_sigT_rect_existT_l {A P} {u1 u2 v} (Q : _ -> Type)
+             (f : forall p q, Q (@eq_existT_l A P u1 u2 v p q))
+    : forall p, Q p
+    := eq_sigT_rect Q f.
+  Definition eq_sigT_rect_existT_r {A P} {u v1 v2} (Q : _ -> Type)
+             (f : forall p q, Q (@eq_existT_r A P u v1 v2 p q))
+    : forall p, Q p
+    := eq_sigT_rect Q f.
+  Definition eq_sigT_rect_existT {A P} {u1 u2 v1 v2} (Q : _ -> Type)
+             (f : forall p q, Q (@eq_existT_curried A P u1 v1 u2 v2 p q))
+    : forall p, Q p
+    := eq_sigT_rect Q f.
+ +
+
+ +
+We want uncurried versions so inversion_sigma can accept + intropatterns, but we use ex types for the induction + hypothesis to avoid extraction errors about informative + inductive types having Prop instances +
+
+  Definition eq_sigT_rect_uncurried {A P} {u v : { a : A & P a }} (Q : u = v -> Type)
+             (f : forall pq : exists p : u.1 = v.1, _, Q (eq_sigT u v (ex_proj1 pq) (ex_proj2 pq)))
+    : forall p, Q p
+    := eq_sigT_rect Q (fun p q => f (ex_intro _ p q)).
+  Definition eq_sigT_rec_uncurried {A P u v} (Q : u = v :> { a : A & P a } -> Set) := eq_sigT_rect_uncurried Q.
+  Definition eq_sigT_ind_uncurried {A P u v} (Q : u = v :> { a : A & P a } -> Prop) := eq_sigT_rec_uncurried Q.
+ +
+
+ +
+Equivalence of equality of sigT involving hProps with equality of the first components +
+
+  Definition eq_sigT_hprop_iff {A P} (P_hprop : forall (x : A) (p q : P x), p = q)
+             (u v : { a : A & P a })
+    : u = v <-> (u.1 = v.1)
+    := conj (fun p => f_equal (@projT1 _ _) p) (eq_sigT_hprop P_hprop u v).
+ +
+
+ +
+Non-dependent classification of equality of sigT +
+
+  Definition eq_sigT_nondep {A B : Type} (u v : { a : A & B })
+             (p : u.1 = v.1) (q : u.2 = v.2)
+    : u = v
+    := @eq_sigT _ _ u v p (eq_trans (rew_const _ _) q).
+ +
+
+ +
+Classification of transporting across an equality of sigTs +
+
+  Lemma rew_sigT {A x} {P : A -> Type} (Q : forall a, P a -> Prop) (u : { p : P x & Q x p }) {y} (H : x = y)
+    : rew [fun a => { p : P a & Q a p }] H in u
+      = existT
+          (Q y)
+          (rew H in u.1)
+          (rew dependent H in (u.2)).
+End sigT.
+Global Arguments eq_existT_curried A P _ _ _ _ !p !q / .
+ +
+
+ +
+Equality for sig +
+
+Section sig.
+
+ +
+We define this as a Let rather than a Definition to avoid + extraction errors about informative inductive types having Prop + instances +
+
+  Local Unset Implicit Arguments.
+
+ +
+Projecting an equality of a pair to equality of the first components +
+
+  Definition proj1_sig_eq {A} {P : A -> Prop} {u v : { a : A | P a }} (p : u = v)
+    : proj1_sig u = proj1_sig v
+    := f_equal (@proj1_sig _ _) p.
+ +
+
+ +
+Projecting an equality of a pair to equality of the second components +
+
+  Definition proj2_sig_eq {A} {P : A -> Prop} {u v : { a : A | P a }} (p : u = v)
+    : rew proj1_sig_eq p in proj2_sig u = proj2_sig v
+    := rew dependent p in eq_refl.
+ +
+
+ +
+Equality of sig is itself a sig (forwards-reasoning version) +
+
+  Definition eq_exist_uncurried {A : Type} {P : A -> Prop} {u1 v1 : A} {u2 : P u1} {v2 : P v1}
+             (pq : { p : u1 = v1 | rew p in u2 = v2 })
+    : exist _ u1 u2 = exist _ v1 v2.
+ +
+
+ +
+Equality of sig is itself a sig (backwards-reasoning version) +
+
+  Definition eq_sig_uncurried {A : Type} {P : A -> Prop} (u v : { a : A | P a })
+             (pq : { p : proj1_sig u = proj1_sig v | rew p in proj2_sig u = proj2_sig v })
+    : u = v.
+ +
+  Lemma eq_exist_curried {A : Type} {P : A -> Prop} {u1 v1 : A} {u2 : P u1} {v2 : P v1}
+             (p : u1 = v1) (q : rew p in u2 = v2) : exist P u1 u2 = exist P v1 v2.
+ +
+
+ +
+Curried version of proving equality of sigma types +
+
+  Definition eq_sig {A : Type} {P : A -> Prop} (u v : { a : A | P a })
+             (p : proj1_sig u = proj1_sig v) (q : rew p in proj2_sig u = proj2_sig v)
+    : u = v
+    := eq_sig_uncurried u v (exist _ p q).
+ +
+
+ +
+In order to have a performant inversion_sigma, we define + specialized versions for when we have constructors on one or + both sides of the equality +
+
+  Definition eq_exist_l {A : Type} {P : A -> Prop} {u1 : A} {u2 : P u1} {v : { a : A | P a }}
+             (p : u1 = proj1_sig v) (q : rew p in u2 = proj2_sig v) : exist _ u1 u2 = v
+    := eq_sig (exist _ u1 u2) v p q.
+  Definition eq_exist_r {A : Type} {P : A -> Prop} {u : { a : A | P a }} {v1 : A} {v2 : P v1}
+             (p : proj1_sig u = v1) (q : rew p in proj2_sig u = v2) : u = exist _ v1 v2
+    := eq_sig u (exist _ v1 v2) p q.
+ +
+
+ +
+Induction principle for @eq (sig _) +
+
+  Definition eq_sig_rect {A P} {u v : { a : A | P a }} (Q : u = v -> Type)
+             (f : forall p q, Q (eq_sig u v p q))
+    : forall p, Q p.
+   Definition eq_sig_rec {A P u v} (Q : u = v :> { a : A | P a } -> Set) := eq_sig_rect Q.
+  Definition eq_sig_ind {A P u v} (Q : u = v :> { a : A | P a } -> Prop) := eq_sig_rec Q.
+ +
+
+ +
+In order to have a performant inversion_sigma, we define + specialized versions for when we have constructors on one or + both sides of the equality +
+
+  Definition eq_sig_rect_exist_l {A P} {u1 u2 v} (Q : _ -> Type)
+             (f : forall p q, Q (@eq_exist_l A P u1 u2 v p q))
+    : forall p, Q p
+    := eq_sig_rect Q f.
+  Definition eq_sig_rect_exist_r {A P} {u v1 v2} (Q : _ -> Type)
+             (f : forall p q, Q (@eq_exist_r A P u v1 v2 p q))
+    : forall p, Q p
+    := eq_sig_rect Q f.
+  Definition eq_sig_rect_exist {A P} {u1 u2 v1 v2} (Q : _ -> Type)
+             (f : forall p q, Q (@eq_exist_curried A P u1 v1 u2 v2 p q))
+    : forall p, Q p
+    := eq_sig_rect Q f.
+ +
+
+ +
+We want uncurried versions so inversion_sigma can accept + intropatterns, but we use ex types for the induction + hypothesis to avoid extraction errors about informative + inductive types having Prop instances +
+
+  Definition eq_sig_rect_uncurried {A P} {u v : { a : A | P a }} (Q : u = v -> Type)
+             (f : forall pq : exists p : proj1_sig u = proj1_sig v, _, Q (eq_sig u v (ex_proj1 pq) (ex_proj2 pq)))
+    : forall p, Q p
+    := eq_sig_rect Q (fun p q => f (ex_intro _ p q)).
+  Definition eq_sig_rec_uncurried {A P u v} (Q : u = v :> { a : A | P a } -> Set) := eq_sig_rect_uncurried Q.
+  Definition eq_sig_ind_uncurried {A P u v} (Q : u = v :> { a : A | P a } -> Prop) := eq_sig_rec_uncurried Q.
+ +
+
+ +
+Equality of sig when the property is an hProp +
+
+  Definition eq_sig_hprop {A} {P : A -> Prop} (P_hprop : forall (x : A) (p q : P x), p = q)
+             (u v : { a : A | P a })
+             (p : proj1_sig u = proj1_sig v)
+    : u = v
+    := eq_sig u v p (P_hprop _ _ _).
+ +
+
+ +
+Equivalence of equality of sig with a sig of equality We could actually prove an isomorphism here, and not just <->, + but for simplicity, we don't. +
+
+  Definition eq_sig_uncurried_iff {A} {P : A -> Prop}
+             (u v : { a : A | P a })
+    : u = v <-> { p : proj1_sig u = proj1_sig v | rew p in proj2_sig u = proj2_sig v }.
+ +
+
+ +
+Equivalence of equality of sig involving hProps with equality of the first components +
+
+  Definition eq_sig_hprop_iff {A} {P : A -> Prop} (P_hprop : forall (x : A) (p q : P x), p = q)
+             (u v : { a : A | P a })
+    : u = v <-> (proj1_sig u = proj1_sig v)
+    := conj (fun p => f_equal (@proj1_sig _ _) p) (eq_sig_hprop P_hprop u v).
+ +
+  Lemma rew_sig {A x} {P : A -> Type} (Q : forall a, P a -> Prop) (u : { p : P x | Q x p }) {y} (H : x = y)
+    : rew [fun a => { p : P a | Q a p }] H in u
+      = exist
+          (Q y)
+          (rew H in proj1_sig u)
+          (rew dependent H in proj2_sig u).
+End sig.
+Global Arguments eq_exist_curried A P _ _ _ _ !p !q / .
+ +
+
+ +
+Equality for sigT2 +
+
+Section sigT2.
+  Local Coercion sigT_of_sigT2 : sigT2 >-> sigT.
+  Local Coercion ex_of_ex2 : ex2 >-> ex.
+  Local Unset Implicit Arguments.
+
+ +
+Projecting an equality of a pair to equality of the first components +
+
+  Definition sigT_of_sigT2_eq {A} {P Q : A -> Type} {u v : { a : A & P a & Q a }} (p : u = v)
+    : u = v :> { a : A & P a }
+    := f_equal _ p.
+  Definition projT1_of_sigT2_eq {A} {P Q : A -> Type} {u v : { a : A & P a & Q a }} (p : u = v)
+    : u.1 = v.1
+    := projT1_eq (sigT_of_sigT2_eq p).
+ +
+
+ +
+Projecting an equality of a pair to equality of the second components +
+
+  Definition projT2_of_sigT2_eq {A} {P Q : A -> Type} {u v : { a : A & P a & Q a }} (p : u = v)
+    : rew projT1_of_sigT2_eq p in u.2 = v.2
+    := rew dependent p in eq_refl.
+ +
+
+ +
+Projecting an equality of a pair to equality of the third components +
+
+  Definition projT3_eq {A} {P Q : A -> Type} {u v : { a : A & P a & Q a }} (p : u = v)
+    : rew projT1_of_sigT2_eq p in u.3 = v.3
+    := rew dependent p in eq_refl.
+ +
+
+ +
+Equality of sigT2 is itself a sigT2 (forwards-reasoning version) +
+
+  Definition eq_existT2_uncurried {A : Type} {P Q : A -> Type}
+             {u1 v1 : A} {u2 : P u1} {v2 : P v1} {u3 : Q u1} {v3 : Q v1}
+             (pqr : { p : u1 = v1
+                    & rew p in u2 = v2 & rew p in u3 = v3 })
+    : existT2 _ _ u1 u2 u3 = existT2 _ _ v1 v2 v3.
+ +
+
+ +
+Equality of sigT2 is itself a sigT2 (backwards-reasoning version) +
+
+  Definition eq_sigT2_uncurried {A : Type} {P Q : A -> Type} (u v : { a : A & P a & Q a })
+             (pqr : { p : u.1 = v.1
+                    & rew p in u.2 = v.2 & rew p in u.3 = v.3 })
+    : u = v.
+ +
+  Lemma eq_existT2_curried {A : Type} {P Q : A -> Type} {u1 v1 : A} {u2 : P u1} {v2 : P v1} {u3 : Q u1} {v3 : Q v1}
+             (p : u1 = v1) (q : rew p in u2 = v2) (r : rew p in u3 = v3) : existT2 P Q u1 u2 u3 = existT2 P Q v1 v2 v3.
+ +
+
+ +
+Curried version of proving equality of sigma types +
+
+  Definition eq_sigT2 {A : Type} {P Q : A -> Type} (u v : { a : A & P a & Q a })
+             (p : u.1 = v.1)
+             (q : rew p in u.2 = v.2)
+             (r : rew p in u.3 = v.3)
+    : u = v
+    := eq_sigT2_uncurried u v (existT2 _ _ p q r).
+ +
+
+ +
+In order to have a performant inversion_sigma, we define + specialized versions for when we have constructors on one or + both sides of the equality +
+
+  Definition eq_existT2_l {A : Type} {P Q : A -> Type} {u1 : A} {u2 : P u1} {u3 : Q u1} {v : { a : A & P a & Q a }}
+             (p : u1 = v.1) (q : rew p in u2 = v.2) (r : rew p in u3 = v.3) : existT2 P Q u1 u2 u3 = v
+    := eq_sigT2 (existT2 P Q u1 u2 u3) v p q r.
+  Definition eq_existT2_r {A : Type} {P Q : A -> Type} {u : { a : A & P a & Q a }} {v1 : A} {v2 : P v1} {v3 : Q v1}
+             (p : u.1 = v1) (q : rew p in u.2 = v2) (r : rew p in u.3 = v3) : u = existT2 P Q v1 v2 v3
+    := eq_sigT2 u (existT2 P Q v1 v2 v3) p q r.
+ +
+
+ +
+Equality of sigT2 when the second property is an hProp +
+
+  Definition eq_sigT2_hprop {A P Q} (Q_hprop : forall (x : A) (p q : Q x), p = q)
+             (u v : { a : A & P a & Q a })
+             (p : u = v :> { a : A & P a })
+    : u = v
+    := eq_sigT2 u v (projT1_eq p) (projT2_eq p) (Q_hprop _ _ _).
+ +
+
+ +
+Equivalence of equality of sigT2 with a sigT2 of equality We could actually prove an isomorphism here, and not just <->, + but for simplicity, we don't. +
+
+  Definition eq_sigT2_uncurried_iff {A P Q}
+             (u v : { a : A & P a & Q a })
+    : u = v
+      <-> { p : u.1 = v.1
+          & rew p in u.2 = v.2 & rew p in u.3 = v.3 }.
+ +
+
+ +
+Induction principle for @eq (sigT2 _ _) +
+
+  Definition eq_sigT2_rect {A P Q} {u v : { a : A & P a & Q a }} (R : u = v -> Type)
+             (f : forall p q r, R (eq_sigT2 u v p q r))
+    : forall p, R p.
+  Definition eq_sigT2_rec {A P Q u v} (R : u = v :> { a : A & P a & Q a } -> Set) := eq_sigT2_rect R.
+  Definition eq_sigT2_ind {A P Q u v} (R : u = v :> { a : A & P a & Q a } -> Prop) := eq_sigT2_rec R.
+ +
+
+ +
+In order to have a performant inversion_sigma, we define + specialized versions for when we have constructors on one or + both sides of the equality +
+
+  Definition eq_sigT2_rect_existT2_l {A P Q} {u1 u2 u3 v} (R : _ -> Type)
+             (f : forall p q r, R (@eq_existT2_l A P Q u1 u2 u3 v p q r))
+    : forall p, R p
+    := eq_sigT2_rect R f.
+  Definition eq_sigT2_rect_existT2_r {A P Q} {u v1 v2 v3} (R : _ -> Type)
+             (f : forall p q r, R (@eq_existT2_r A P Q u v1 v2 v3 p q r))
+    : forall p, R p
+    := eq_sigT2_rect R f.
+  Definition eq_sigT2_rect_existT2 {A P Q} {u1 u2 u3 v1 v2 v3} (R : _ -> Type)
+             (f : forall p q r, R (@eq_existT2_curried A P Q u1 v1 u2 v2 u3 v3 p q r))
+    : forall p, R p
+    := eq_sigT2_rect R f.
+ +
+
+ +
+We want uncurried versions so inversion_sigma can accept + intropatterns, but we use ex2 types for the induction + hypothesis to avoid extraction errors about informative + inductive types having Prop instances +
+
+  Definition eq_sigT2_rect_uncurried {A P Q} {u v : { a : A & P a & Q a }} (R : u = v -> Type)
+             (f : forall pqr : exists2 p : u.1 = v.1, _ & _, R (eq_sigT2 u v (ex_proj1 pqr) (ex_proj2 pqr) (ex_proj3 pqr)))
+    : forall p, R p
+    := eq_sigT2_rect R (fun p q r => f (ex_intro2 _ _ p q r)).
+  Definition eq_sigT2_rec_uncurried {A P Q u v} (R : u = v :> { a : A & P a & Q a } -> Set) := eq_sigT2_rect_uncurried R.
+  Definition eq_sigT2_ind_uncurried {A P Q u v} (R : u = v :> { a : A & P a & Q a } -> Prop) := eq_sigT2_rec_uncurried R.
+ +
+
+ +
+Equivalence of equality of sigT2 involving hProps with equality of the first components +
+
+  Definition eq_sigT2_hprop_iff {A P Q} (Q_hprop : forall (x : A) (p q : Q x), p = q)
+             (u v : { a : A & P a & Q a })
+    : u = v <-> (u = v :> { a : A & P a })
+    := conj (fun p => f_equal (@sigT_of_sigT2 _ _ _) p) (eq_sigT2_hprop Q_hprop u v).
+ +
+
+ +
+Non-dependent classification of equality of sigT +
+
+  Definition eq_sigT2_nondep {A B C : Type} (u v : { a : A & B & C })
+             (p : u.1 = v.1) (q : u.2 = v.2) (r : u.3 = v.3)
+    : u = v
+    := @eq_sigT2 _ _ _ u v p (eq_trans (rew_const _ _) q) (eq_trans (rew_const _ _) r).
+ +
+
+ +
+Classification of transporting across an equality of sigT2s +
+
+  Lemma rew_sigT2 {A x} {P : A -> Type} (Q R : forall a, P a -> Prop)
+        (u : { p : P x & Q x p & R x p })
+        {y} (H : x = y)
+    : rew [fun a => { p : P a & Q a p & R a p }] H in u
+      = existT2
+          (Q y)
+          (R y)
+          (rew H in u.1)
+          (rew dependent H in u.2)
+          (rew dependent H in u.3).
+End sigT2.
+Global Arguments eq_existT2_curried A P Q _ _ _ _ _ _ !p !q !r / .
+ +
+
+ +
+Equality for sig2 +
+
+Section sig2.
+  Local Coercion sig_of_sig2 : sig2 >-> sig.
+  Local Coercion ex_of_ex2 : ex2 >-> ex.
+  Local Unset Implicit Arguments.
+
+ +
+Projecting an equality of a pair to equality of the first components +
+
+  Definition sig_of_sig2_eq {A} {P Q : A -> Prop} {u v : { a : A | P a & Q a }} (p : u = v)
+    : u = v :> { a : A | P a }
+    := f_equal _ p.
+  Definition proj1_sig_of_sig2_eq {A} {P Q : A -> Prop} {u v : { a : A | P a & Q a }} (p : u = v)
+    : proj1_sig u = proj1_sig v
+    := proj1_sig_eq (sig_of_sig2_eq p).
+ +
+
+ +
+Projecting an equality of a pair to equality of the second components +
+
+  Definition proj2_sig_of_sig2_eq {A} {P Q : A -> Prop} {u v : { a : A | P a & Q a }} (p : u = v)
+    : rew proj1_sig_of_sig2_eq p in proj2_sig u = proj2_sig v
+    := rew dependent p in eq_refl.
+ +
+
+ +
+Projecting an equality of a pair to equality of the third components +
+
+  Definition proj3_sig_eq {A} {P Q : A -> Prop} {u v : { a : A | P a & Q a }} (p : u = v)
+    : rew proj1_sig_of_sig2_eq p in proj3_sig u = proj3_sig v
+    := rew dependent p in eq_refl.
+ +
+
+ +
+Equality of sig2 is itself a sig2 (fowards-reasoning version) +
+
+  Definition eq_exist2_uncurried {A} {P Q : A -> Prop}
+             {u1 v1 : A} {u2 : P u1} {v2 : P v1} {u3 : Q u1} {v3 : Q v1}
+             (pqr : { p : u1 = v1
+                    | rew p in u2 = v2 & rew p in u3 = v3 })
+    : exist2 _ _ u1 u2 u3 = exist2 _ _ v1 v2 v3.
+ +
+
+ +
+Equality of sig2 is itself a sig2 (backwards-reasoning version) +
+
+  Definition eq_sig2_uncurried {A} {P Q : A -> Prop} (u v : { a : A | P a & Q a })
+             (pqr : { p : proj1_sig u = proj1_sig v
+                    | rew p in proj2_sig u = proj2_sig v & rew p in proj3_sig u = proj3_sig v })
+    : u = v.
+ +
+  Lemma eq_exist2_curried {A : Type} {P Q : A -> Prop} {u1 v1 : A} {u2 : P u1} {v2 : P v1} {u3 : Q u1} {v3 : Q v1}
+             (p : u1 = v1) (q : rew p in u2 = v2) (r : rew p in u3 = v3) : exist2 P Q u1 u2 u3 = exist2 P Q v1 v2 v3.
+ +
+
+ +
+Curried version of proving equality of sigma types +
+
+  Definition eq_sig2 {A} {P Q : A -> Prop} (u v : { a : A | P a & Q a })
+             (p : proj1_sig u = proj1_sig v)
+             (q : rew p in proj2_sig u = proj2_sig v)
+             (r : rew p in proj3_sig u = proj3_sig v)
+    : u = v
+    := eq_sig2_uncurried u v (exist2 _ _ p q r).
+ +
+
+ +
+In order to have a performant inversion_sigma, we define + specialized versions for when we have constructors on one or + both sides of the equality +
+
+  Definition eq_exist2_l {A : Type} {P Q : A -> Prop} {u1 : A} {u2 : P u1} {u3 : Q u1} {v : { a : A | P a & Q a }}
+             (p : u1 = proj1_sig v) (q : rew p in u2 = proj2_sig v) (r : rew p in u3 = proj3_sig v) : exist2 P Q u1 u2 u3 = v
+    := eq_sig2 (exist2 P Q u1 u2 u3) v p q r.
+  Definition eq_exist2_r {A : Type} {P Q : A -> Prop} {u : { a : A | P a & Q a }} {v1 : A} {v2 : P v1} {v3 : Q v1}
+             (p : proj1_sig u = v1) (q : rew p in proj2_sig u = v2) (r : rew p in proj3_sig u = v3) : u = exist2 P Q v1 v2 v3
+    := eq_sig2 u (exist2 P Q v1 v2 v3) p q r.
+ +
+
+ +
+Equality of sig2 when the second property is an hProp +
+
+  Definition eq_sig2_hprop {A} {P Q : A -> Prop} (Q_hprop : forall (x : A) (p q : Q x), p = q)
+             (u v : { a : A | P a & Q a })
+             (p : u = v :> { a : A | P a })
+    : u = v
+    := eq_sig2 u v (proj1_sig_eq p) (proj2_sig_eq p) (Q_hprop _ _ _).
+ +
+
+ +
+Equivalence of equality of sig2 with a sig2 of equality We could actually prove an isomorphism here, and not just <->, + but for simplicity, we don't. +
+
+  Definition eq_sig2_uncurried_iff {A P Q}
+             (u v : { a : A | P a & Q a })
+    : u = v
+      <-> { p : proj1_sig u = proj1_sig v
+          | rew p in proj2_sig u = proj2_sig v & rew p in proj3_sig u = proj3_sig v }.
+ +
+
+ +
+Induction principle for @eq (sig2 _ _) +
+
+  Definition eq_sig2_rect {A P Q} {u v : { a : A | P a & Q a }} (R : u = v -> Type)
+             (f : forall p q r, R (eq_sig2 u v p q r))
+    : forall p, R p.
+  Definition eq_sig2_rec {A P Q u v} (R : u = v :> { a : A | P a & Q a } -> Set) := eq_sig2_rect R.
+  Definition eq_sig2_ind {A P Q u v} (R : u = v :> { a : A | P a & Q a } -> Prop) := eq_sig2_rec R.
+ +
+
+ +
+In order to have a performant inversion_sigma, we define + specialized versions for when we have constructors on one or + both sides of the equality +
+
+  Definition eq_sig2_rect_exist2_l {A P Q} {u1 u2 u3 v} (R : _ -> Type)
+             (f : forall p q r, R (@eq_exist2_l A P Q u1 u2 u3 v p q r))
+    : forall p, R p
+    := eq_sig2_rect R f.
+  Definition eq_sig2_rect_exist2_r {A P Q} {u v1 v2 v3} (R : _ -> Type)
+             (f : forall p q r, R (@eq_exist2_r A P Q u v1 v2 v3 p q r))
+    : forall p, R p
+    := eq_sig2_rect R f.
+  Definition eq_sig2_rect_exist2 {A P Q} {u1 u2 u3 v1 v2 v3} (R : _ -> Type)
+             (f : forall p q r, R (@eq_exist2_curried A P Q u1 v1 u2 v2 u3 v3 p q r))
+    : forall p, R p
+    := eq_sig2_rect R f.
+ +
+
+ +
+We want uncurried versions so inversion_sigma can accept + intropatterns, but we use ex2 types for the induction + hypothesis to avoid extraction errors about informative + inductive types having Prop instances +
+
+  Definition eq_sig2_rect_uncurried {A P Q} {u v : { a : A | P a & Q a }} (R : u = v -> Type)
+             (f : forall pqr : exists2 p : proj1_sig u = proj1_sig v, _ & _, R (eq_sig2 u v (ex_proj1 pqr) (ex_proj2 pqr) (ex_proj3 pqr)))
+    : forall p, R p
+    := eq_sig2_rect R (fun p q r => f (ex_intro2 _ _ p q r)).
+  Definition eq_sig2_rec_uncurried {A P Q u v} (R : u = v :> { a : A | P a & Q a } -> Set) := eq_sig2_rect_uncurried R.
+  Definition eq_sig2_ind_uncurried {A P Q u v} (R : u = v :> { a : A | P a & Q a } -> Prop) := eq_sig2_rec_uncurried R.
+ +
+
+ +
+Equivalence of equality of sig2 involving hProps with equality of the first components +
+
+  Definition eq_sig2_hprop_iff {A} {P Q : A -> Prop} (Q_hprop : forall (x : A) (p q : Q x), p = q)
+             (u v : { a : A | P a & Q a })
+    : u = v <-> (u = v :> { a : A | P a })
+    := conj (fun p => f_equal (@sig_of_sig2 _ _ _) p) (eq_sig2_hprop Q_hprop u v).
+ +
+
+ +
+Non-dependent classification of equality of sig +
+
+  Definition eq_sig2_nondep {A} {B C : Prop} (u v : @sig2 A (fun _ => B) (fun _ => C))
+             (p : proj1_sig u = proj1_sig v) (q : proj2_sig u = proj2_sig v) (r : proj3_sig u = proj3_sig v)
+    : u = v
+    := @eq_sig2 _ _ _ u v p (eq_trans (rew_const _ _) q) (eq_trans (rew_const _ _) r).
+ +
+
+ +
+Classification of transporting across an equality of sig2s +
+
+  Lemma rew_sig2 {A x} {P : A -> Type} (Q R : forall a, P a -> Prop)
+        (u : { p : P x | Q x p & R x p })
+        {y} (H : x = y)
+    : rew [fun a => { p : P a | Q a p & R a p }] H in u
+      = exist2
+          (Q y)
+          (R y)
+          (rew H in proj1_sig u)
+          (rew dependent H in proj2_sig u)
+          (rew dependent H in proj3_sig u).
+End sig2.
+Global Arguments eq_exist2_curried A P Q _ _ _ _ _ _ !p !q !r / .
+ +
+
+ +
+sumbool is a boolean type equipped with the justification of + their value +
+
+ +
+Inductive sumbool (A B:Prop) : Set :=
+  | left : A -> {A} + {B}
+  | right : B -> {A} + {B}
+ where "{ A } + { B }" := (sumbool A B) : type_scope.
+ +
+Add Printing If sumbool.
+ +
+Arguments left {A B} _, [A] B _.
+Arguments right {A B} _ , A [B] _.
+ +
+Register sumbool as core.sumbool.type.
+ +
+
+ +
+sumor is an option type equipped with the justification of why + it may not be a regular value +
+
+ +
+#[universes(template)]
+Inductive sumor (A:Type) (B:Prop) : Type :=
+  | inleft : A -> A + {B}
+  | inright : B -> A + {B}
+ where "A + { B }" := (sumor A B) : type_scope.
+ +
+Add Printing If sumor.
+ +
+Arguments inleft {A B} _ , [A] B _.
+Arguments inright {A B} _ , A [B] _.
+ +
+ +
+
+ +
+Various forms of the axiom of choice for specifications +
+
+ +
+Section Choice_lemmas.
+ +
+  Variables S S' : Set.
+  Variable R : S -> S' -> Prop.
+  Variable R' : S -> S' -> Set.
+  Variables R1 R2 : S -> Prop.
+ +
+  Lemma Choice :
+   (forall x:S, {y:S' | R x y}) -> {f:S -> S' | forall z:S, R z (f z)}.
+ +
+  Lemma Choice2 :
+   (forall x:S, {y:S' & R' x y}) -> {f:S -> S' & forall z:S, R' z (f z)}.
+ +
+  Lemma bool_choice :
+   (forall x:S, {R1 x} + {R2 x}) ->
+     {f:S -> bool | forall x:S, f x = true /\ R1 x \/ f x = false /\ R2 x}.
+ +
+End Choice_lemmas.
+ +
+Section Dependent_choice_lemmas.
+ +
+  Variable X : Type.
+  Variable R : X -> X -> Prop.
+ +
+  Lemma dependent_choice :
+    (forall x:X, {y | R x y}) ->
+    forall x0, {f : nat -> X | f O = x0 /\ forall n, R (f n) (f (S n))}.
+ +
+End Dependent_choice_lemmas.
+ +
+
+ +
+A result of type (Exc A) is either a normal value of type A or + an error : + +
+ + Inductive Exc [A:Type] : Type := value : A->(Exc A) | error : (Exc A). + +
+ + It is implemented using the option type. +
+
+Section Exc.
+  Variable A : Type.
+ +
+  Definition Exc := option A.
+  Definition value := @Some A.
+  Definition error := @None A.
+End Exc.
+Arguments error {A}.
+ +
+Definition except := False_rec. +
+Arguments except [P] _.
+ +
+Theorem absurd_set : forall (A:Prop) (C:Set), A -> ~ A -> C.
+ +
+#[global]
+Hint Resolve left right inleft inright: core.
+#[global]
+Hint Resolve exist exist2 existT existT2: core.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Init.Sumbool.html b/master/corelib/Corelib.Init.Sumbool.html new file mode 100644 index 0000000000..916fdf0057 --- /dev/null +++ b/master/corelib/Corelib.Init.Sumbool.html @@ -0,0 +1,189 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Init.Sumbool

+ +
+ +
+
+ +
+Here are collected some results about the type sumbool (see INIT/Specif.v) + sumbool A B, which is written {A}+{B}, is the informative + disjunction "A or B", where A and B are logical propositions. + Its extraction is isomorphic to the type of booleans. +
+ + A boolean is either true or false, and this is decidable +
+
+ +
+Require Import Logic Datatypes Specif.
+ +
+Definition sumbool_of_bool (b : bool) : {b = true} + {b = false} :=
+  if b return {b = true} + {b = false} then left eq_refl else right eq_refl.
+ +
+#[global]
+Hint Resolve sumbool_of_bool: bool.
+ +
+Definition bool_eq_rec :
+  forall (b:bool) (P:bool -> Set),
+    (b = true -> P true) -> (b = false -> P false) -> P b :=
+  fun b =>
+    if b return forall P, (b = true -> P true) -> (b = false -> P false) -> P b
+    then fun _ H _ => H eq_refl else fun _ _ H => H eq_refl.
+ +
+Definition bool_eq_ind :
+  forall (b:bool) (P:bool -> Prop),
+    (b = true -> P true) -> (b = false -> P false) -> P b :=
+  fun b =>
+    if b return forall P, (b = true -> P true) -> (b = false -> P false) -> P b
+    then fun _ H _ => H eq_refl else fun _ _ H => H eq_refl.
+ +
+
+ +
+Logic connectives on type sumbool +
+
+ +
+Section connectives.
+ +
+  Variables A B C D : Prop.
+ +
+  Hypothesis H1 : {A} + {B}.
+  Hypothesis H2 : {C} + {D}.
+ +
+  Definition sumbool_and : {A /\ C} + {B \/ D} :=
+    match H1, H2 with
+    | left a, left c => left (conj a c)
+    | left a, right d => right (or_intror d)
+    | right b, left c => right (or_introl b)
+    | right b, right d => right (or_intror d)
+    end.
+ +
+  Definition sumbool_or : {A \/ C} + {B /\ D} :=
+    match H1, H2 with
+    | left a, left c => left (or_intror c)
+    | left a, right d => left (or_introl a)
+    | right b, left c => left (or_intror c)
+    | right b, right d => right (conj b d)
+    end.
+ +
+  Definition sumbool_not : {B} + {A} :=
+    match H1 with
+    | left a => right a
+    | right b => left b
+    end.
+ +
+End connectives.
+ +
+#[global]
+Hint Resolve sumbool_and sumbool_or: core.
+#[global]
+Hint Immediate sumbool_not : core.
+ +
+
+ +
+Any decidability function in type sumbool can be turned into a function + returning a boolean with the corresponding specification: +
+
+ +
+Definition bool_of_sumbool (A B : Prop) :
+    {A} + {B} -> {b : bool | if b then A else B} :=
+  sumbool_rec _ (exist _ true) (exist _ false).
+Arguments bool_of_sumbool : default implicits.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Init.Tactics.html b/master/corelib/Corelib.Init.Tactics.html new file mode 100644 index 0000000000..eb3302d86b --- /dev/null +++ b/master/corelib/Corelib.Init.Tactics.html @@ -0,0 +1,544 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Init.Tactics

+ +
+ +
+Require Import Notations.
+Require Import Ltac.
+Require Import Logic.
+Require Import Specif.
+ +
+
+ +
+

Useful tactics

+ +
+ + Ex falso quodlibet : a tactic for proving False instead of the current goal. + This is just a nicer name for tactics such as cut False. +
+
+ +
+Ltac exfalso := Corelib.Init.Ltac.exfalso.
+ +
+
+ +
+A tactic for proof by contradiction. With contradict H, +
    +
  • H:~A |- B gives |- A + +
    • +
  • H:~A |- ~B gives H: B |- A + +
    • +
  • H: A |- B gives |- ~A + +
    • +
  • H: A |- ~B gives H: B |- ~A + +
    • +
  • H:False leads to a resolved subgoal. + +
    • +
+ Moreover, negations may be in unfolded forms, + and A or B may live in Type +
+
+ +
+Ltac contradict H :=
+  let save tac H := let x:=fresh in intro x; tac H; rename x into H
+  in
+  let negpos H := case H; clear H
+  in
+  let negneg H := save negpos H
+  in
+  let pospos H :=
+    let A := type of H in (exfalso; revert H; try fold (~A))
+  in
+  let posneg H := save pospos H
+  in
+  let neg H := match goal with
+   | |- (~_) => negneg H
+   | |- (_->False) => negneg H
+   | |- _ => negpos H
+  end in
+  let pos H := match goal with
+   | |- (~_) => posneg H
+   | |- (_->False) => posneg H
+   | |- _ => pospos H
+  end in
+  match type of H with
+   | (~_) => neg H
+   | (_->False) => neg H
+   | _ => (elim H;fail) || pos H
+  end.
+ +
+ +
+Ltac false_hyp H G :=
+  let T := type of H in absurd T; [ apply G | assumption ].
+ +
+ +
+Ltac case_eq x := generalize (eq_refl x); pattern x at -1; case x.
+ +
+ +
+Ltac destr_eq H := discriminate H || (try (injection H as [= H])).
+ +
+ +
+Tactic Notation "destruct_with_eqn" constr(x) :=
+  destruct x eqn:?.
+Tactic Notation "destruct_with_eqn" ident(n) :=
+  try intros until n; destruct n eqn:?.
+Tactic Notation "destruct_with_eqn" ":" ident(H) constr(x) :=
+  destruct x eqn:H.
+Tactic Notation "destruct_with_eqn" ":" ident(H) ident(n) :=
+  try intros until n; destruct n eqn:H.
+ +
+
+ +
+Break every hypothesis of a certain type +
+
+ +
+Ltac destruct_all t :=
+ match goal with
+  | x : t |- _ => destruct x; destruct_all t
+  | _ => idtac
+ end.
+ +
+ +
+Tactic Notation "rewrite_all" constr(eq) := repeat rewrite eq in *.
+Tactic Notation "rewrite_all" "<-" constr(eq) := repeat rewrite <- eq in *.
+ +
+
+ +
+Tactics for applying equivalences. + +
+ +The following code provides tactics "apply -> t", "apply <- t", +"apply -> t in H" and "apply <- t in H". Here t is a term whose type +consists of nested dependent and nondependent products with an +equivalence A <-> B as the conclusion. The tactics with "->" in their +names apply A -> B while those with "<-" in the name apply B -> A. +
+
+ +
+ +
+Ltac find_equiv H :=
+let T := type of H in
+lazymatch T with
+| ?A -> ?B =>
+  let H1 := fresh in
+  let H2 := fresh in
+  cut A;
+  [intro H1; pose proof (H H1) as H2; clear H H1;
+   rename H2 into H; find_equiv H |
+   clear H]
+| forall x : ?t, _ =>
+  let a := fresh "a" in
+  let H1 := fresh "H" in
+    evar (a : t); pose proof (H a) as H1; unfold a in H1;
+    clear a; clear H; rename H1 into H; find_equiv H
+| ?A <-> ?B => idtac
+| _ => fail "The given statement does not seem to end with an equivalence."
+end.
+ +
+Ltac bapply lemma todo :=
+let H := fresh in
+  pose proof lemma as H;
+  find_equiv H; [todo H; clear H | .. ].
+ +
+Tactic Notation "apply" "->" constr(lemma) :=
+bapply lemma ltac:(fun H => destruct H as [H _]; apply H).
+ +
+Tactic Notation "apply" "<-" constr(lemma) :=
+bapply lemma ltac:(fun H => destruct H as [_ H]; apply H).
+ +
+Tactic Notation "apply" "->" constr(lemma) "in" hyp(J) :=
+bapply lemma ltac:(fun H => destruct H as [H _]; apply H in J).
+ +
+Tactic Notation "apply" "<-" constr(lemma) "in" hyp(J) :=
+bapply lemma ltac:(fun H => destruct H as [_ H]; apply H in J).
+ +
+
+ +
+An experimental tactic simpler than auto that is useful for ending + proofs "in one step" +
+
+ +
+Ltac easy :=
+  let rec use_hyp H :=
+    match type of H with
+    | _ /\ _ => exact H || destruct_hyp H
+    | _ => try solve [inversion H]
+    end
+  with do_intro := let H := fresh in intro H; use_hyp H
+  with destruct_hyp H := case H; clear H; do_intro; do_intro in
+  let rec use_hyps :=
+    match goal with
+    | H : _ /\ _ |- _ => exact H || (destruct_hyp H; use_hyps)
+    | H : _ |- _ => solve [inversion H]
+    | _ => idtac
+    end in
+  let do_atom :=
+    solve [ trivial with eq_true | reflexivity | symmetry; trivial | contradiction ] in
+  let rec do_ccl :=
+    try do_atom;
+    repeat (do_intro; try do_atom);
+    solve [ split; do_ccl ] in
+  solve [ do_atom | use_hyps; do_ccl ] ||
+  fail "Cannot solve this goal".
+ +
+Tactic Notation "now" tactic(t) := t; easy.
+ +
+
+ +
+Slightly more than easy +
+
+ +
+Ltac easy' := repeat split; simpl; easy || now destruct 1.
+ +
+
+ +
+A tactic to document or check what is proved at some point of a script +
+
+ +
+Ltac now_show c := change c.
+ +
+
+ +
+Support for rewriting decidability statements +
+
+ +
+Set Implicit Arguments.
+ +
+Lemma decide_left : forall (C:Prop) (decide:{C}+{~C}),
+  C -> forall P:{C}+{~C}->Prop, (forall H:C, P (left _ H)) -> P decide.
+ +
+Lemma decide_right : forall (C:Prop) (decide:{C}+{~C}),
+  ~C -> forall P:{C}+{~C}->Prop, (forall H:~C, P (right _ H)) -> P decide.
+ +
+Tactic Notation "decide" constr(lemma) "with" constr(H) :=
+  let try_to_merge_hyps H :=
+     try (clear H; intro H) ||
+     (let H' := fresh H "bis" in intro H'; try clear H') ||
+     (let H' := fresh in intro H'; try clear H') in
+  match type of H with
+  | ~ ?C => apply (decide_right lemma H); try_to_merge_hyps H
+  | ?C -> False => apply (decide_right lemma H); try_to_merge_hyps H
+  | _ => apply (decide_left lemma H); try_to_merge_hyps H
+  end.
+ +
+
+ +
+Clear an hypothesis and its dependencies +
+
+ +
+Tactic Notation "clear" "dependent" hyp(h) :=
+ let rec depclear h :=
+  clear h ||
+  lazymatch goal with
+   | H : context [ h ] |- _ => depclear H; depclear h
+   | H := context [ h ] |- _ => depclear H; depclear h
+  end ||
+  fail "hypothesis to clear is used in the conclusion (maybe indirectly)"
+ in depclear h.
+ +
+
+ +
+Revert an hypothesis and its dependencies : + this is actually generalize dependent... +
+
+ +
+#[deprecated(note="Use ""generalize dependent"" instead (""revert dependent"" is currently an alias)", since="8.18")]
+Tactic Notation "revert" "dependent" hyp(h) :=
+ generalize dependent h.
+ +
+
+ +
+Provide an error message for dependent induction/dependent destruction that + reports an import is required to use it. Importing Stdlib.Program.Equality will + shadow this notation with the actual tactics. +
+
+ +
+Tactic Notation "dependent" "induction" ident(H) :=
+  fail "To use dependent induction, first [Require Import Stdlib.Program.Equality.]".
+ +
+Tactic Notation "dependent" "destruction" ident(H) :=
+  fail "To use dependent destruction, first [Require Import Stdlib.Program.Equality.]".
+ +
+
+ +
+

inversion_sigma

+ The built-in inversion will frequently leave equalities of + dependent pairs. When the first type in the pair is an hProp or + otherwise simplifies, inversion_sigma is useful; it will replace + the equality of pairs with a pair of equalities, one involving a + term casted along the other. This might also prove useful for + writing a version of inversion / dependent destruction which + does not lose information, i.e., does not turn a goal which is + provable into one which requires axiom K / UIP. +
+
+ +
+Ltac lookup_inversion_sigma_rect H :=
+  lazymatch type of H with
+  | ex_intro _ _ _ = ex_intro _ _ _
+    => uconstr:(eq_ex_rect_ex_intro)
+  | exist _ _ _ = exist _ _ _
+    => uconstr:(eq_sig_rect_exist)
+  | existT _ _ _ = existT _ _ _
+    => uconstr:(eq_sigT_rect_existT)
+  | _ = ex_intro _ _ _
+    => uconstr:(eq_ex_rect_ex_intro_r)
+  | _ = exist _ _ _
+    => uconstr:(eq_sig_rect_exist_r)
+  | _ = existT _ _ _
+    => uconstr:(eq_sigT_rect_existT_r)
+  | ex_intro _ _ _ = _
+    => uconstr:(eq_ex_rect_ex_intro_l)
+  | exist _ _ _ = _
+    => uconstr:(eq_sig_rect_exist_l)
+  | existT _ _ _ = _
+    => uconstr:(eq_sigT_rect_existT_l)
+  | ex_intro2 _ _ _ _ _ = ex_intro2 _ _ _ _ _
+    => uconstr:(eq_ex2_rect_ex_intro2)
+  | exist2 _ _ _ _ _ = exist2 _ _ _ _ _
+    => uconstr:(eq_sig2_rect_exist2)
+  | existT2 _ _ _ _ _ = existT2 _ _ _ _ _
+    => uconstr:(eq_sigT2_rect_existT2)
+  | _ = ex_intro2 _ _ _ _ _
+    => uconstr:(eq_ex2_rect_ex_intro2_r)
+  | _ = exist2 _ _ _ _ _
+    => uconstr:(eq_sig2_rect_exist2_r)
+  | _ = existT2 _ _ _ _ _
+    => uconstr:(eq_sigT2_rect_existT2_r)
+  | ex_intro2 _ _ _ _ _ = _
+    => uconstr:(eq_ex2_rect_ex_intro2_l)
+  | exist2 _ _ _ _ _ = _
+    => uconstr:(eq_sig2_rect_exist2_l)
+  | existT2 _ _ _ _ _ = _
+    => uconstr:(eq_sigT2_rect_existT2_l)
+  | _ = _ :> ?T
+    => let sig := uconstr:(@sig) in
+       let sig2 := uconstr:(@sig2) in
+       let sigT := uconstr:(@sigT) in
+       let sigT2 := uconstr:(@sigT2) in
+       let ex := uconstr:(@ex) in
+       let ex2 := uconstr:(@ex2) in
+       fail 0 "Type" "of" H "is" "not" "an" "equality" "of" "recognized" "Σ" "types:" "expected" "one" "of" sig sig2 sigT sigT2 ex "or" ex2 "but" "got" T
+  | _
+    => fail 0 H "is" "not" "an" "equality" "of" "Σ" "types"
+  end.
+Ltac inversion_sigma_on_as H ip :=
+  let rect := lookup_inversion_sigma_rect H in
+  induction H as ip using rect.
+Ltac inversion_sigma_on H := inversion_sigma_on_as H ipattern:([]).
+Ltac inversion_sigma_step :=
+  match goal with
+  | [ H : _ |- _ ] => inversion_sigma_on H
+  end.
+Ltac inversion_sigma := repeat inversion_sigma_step.
+ +
+Tactic Notation "inversion_sigma" := inversion_sigma.
+Tactic Notation "inversion_sigma" hyp(H) := inversion_sigma_on H.
+Tactic Notation "inversion_sigma" hyp(H) "as" simple_intropattern(ip) := inversion_sigma_on_as H ip.
+ +
+
+ +
+A version of time that works for constrs +
+
+ +
+Ltac time_constr tac :=
+  let eval_early := match goal with _ => restart_timer end in
+  let ret := tac () in
+  let eval_early := match goal with _ => finish_timing ( "Tactic evaluation" ) end in
+  ret.
+ +
+
+ +
+Useful combinators +
+
+ +
+Ltac assert_fails tac :=
+  tryif (once tac) then gfail 0 tac "succeeds" else idtac.
+Tactic Notation "assert_fails" tactic3(tac) :=
+  assert_fails tac.
+ +
+Create HintDb rewrite discriminated.
+#[global]
+Hint Variables Opaque : rewrite.
+Create HintDb typeclass_instances discriminated.
+ +
+
+ +
+A variant of apply using refine, doing as much conversion as necessary. +
+
+ +
+Ltac rapply p :=
+  
+ +
+before we try to add more underscores, first ensure that adding such underscores is valid +
+
+  (assert_succeeds (idtac; let __ := open_constr:(p _) in idtac);
+   rapply uconstr:(p _))
+  || refine p.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Init.Tauto.html b/master/corelib/Corelib.Init.Tauto.html new file mode 100644 index 0000000000..25ee4b6e04 --- /dev/null +++ b/master/corelib/Corelib.Init.Tauto.html @@ -0,0 +1,210 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Init.Tauto

+ +
+ +
+
+ +
+

The tauto and intuition tactics

+ +
+
+ +
+Require Import Notations.
+Require Import Ltac.
+Require Import Datatypes.
+Require Import Logic.
+ +
+ +
+Local Ltac not_dep_intros :=
+  repeat match goal with
+  | |- (forall (_: ?X1), ?X2) => intro
+  | |- (Corelib.Init.Logic.not _) => unfold Corelib.Init.Logic.not at 1; intro
+  end.
+ +
+Local Ltac axioms flags :=
+  match reverse goal with
+    | |- ?X1 => is_unit_or_eq flags X1; constructor 1
+    | H:?X1 |- _ => is_empty flags X1; elim H
+    | _ => assumption
+  end.
+ +
+Local Ltac simplif flags :=
+  not_dep_intros;
+  repeat
+     (match reverse goal with
+      | id: ?X1 |- _ => is_conj flags X1; elim id; do 2 intro; clear id
+      | id: (Corelib.Init.Logic.iff _ _) |- _ => elim id; do 2 intro; clear id
+      | id: (Corelib.Init.Logic.not _) |- _ => red in id
+      | id: ?X1 |- _ => is_disj flags X1; elim id; intro; clear id
+      | _ =>
+        
+        find_cut ltac:(fun id0 id1 X2 =>
+          
+          assert X2; [exact (id0 id1) | clear id0]
+          )
+      | id: forall (_ : ?X1), ?X2|- _ =>
+        is_unit_or_eq flags X1; cut X2;
+    [ intro; clear id
+    |
+      cut X1; [exact id| constructor 1; fail]
+    ]
+      | id: forall (_ : ?X1), ?X2|- _ =>
+        flatten_contravariant_conj flags X1 X2 id
+  
+      | id: forall (_: Corelib.Init.Logic.iff ?X1 ?X2), ?X3|- _ =>
+        assert (forall (_: forall _:X1, X2), forall (_: forall _: X2, X1), X3)
+    by (do 2 intro; apply id; split; assumption);
+          clear id
+      | id: forall (_:?X1), ?X2|- _ =>
+        flatten_contravariant_disj flags X1 X2 id
+  
+      | |- ?X1 => is_conj flags X1; split
+      | |- (Corelib.Init.Logic.iff _ _) => split
+      | |- (Corelib.Init.Logic.not _) => red
+      end;
+      not_dep_intros).
+ +
+Local Ltac tauto_intuit flags t_reduce t_solver :=
+ let rec t_tauto_intuit :=
+ (simplif flags; axioms flags
+ || match reverse goal with
+    | id:forall(_: forall (_: ?X1), ?X2), ?X3|- _ =>
+  cut X3;
+    [ intro; clear id; t_tauto_intuit
+    | cut (forall (_: X1), X2);
+        [ exact id
+        | generalize (fun y:X2 => id (fun x:X1 => y)); intro; clear id;
+          solve [ t_tauto_intuit ]]]
+ | id:forall (_:not ?X1), ?X3|- _ =>
+  cut X3;
+    [ intro; clear id; t_tauto_intuit
+    | cut (not X1); [ exact id | clear id; intro; solve [t_tauto_intuit ]]]
+ | |- ?X1 =>
+        is_disj flags X1; solve [left;t_tauto_intuit | right;t_tauto_intuit]
+    end
+  ||
+  
+  match goal with | |- forall (_ : _), _ => intro; t_tauto_intuit
+  | |- _ => t_reduce;t_solver
+  end
+  ||
+  t_solver
+ ) in t_tauto_intuit.
+ +
+Local Ltac intuition_gen flags solver := tauto_intuit flags reduction_not_iff solver.
+Local Ltac tauto_intuitionistic flags := intuition_gen flags fail || fail "tauto failed".
+Local Ltac tauto_classical flags :=
+  (apply_nnpp || fail "tauto failed"); (tauto_intuitionistic flags || fail "Classical tauto failed").
+Local Ltac tauto_gen flags := tauto_intuitionistic flags || tauto_classical flags.
+ +
+Ltac tauto := with_uniform_flags ltac:(fun flags => tauto_gen flags).
+Ltac dtauto := with_power_flags ltac:(fun flags => tauto_gen flags).
+ +
+Ltac intuition_solver :=
+  first [solve [auto]
+        | tryif solve [auto with *] then warn_auto_with_star else idtac].
+ +
+Local Ltac intuition_then tac := with_uniform_flags ltac:(fun flags => intuition_gen flags tac).
+Ltac intuition := intuition_then ltac:(idtac;intuition_solver).
+ +
+Local Ltac dintuition_then tac := with_power_flags ltac:(fun flags => intuition_gen flags tac).
+Ltac dintuition := dintuition_then ltac:(idtac;intuition_solver).
+ +
+Tactic Notation "intuition" := intuition.
+Tactic Notation "intuition" tactic(t) := intuition_then t.
+ +
+Tactic Notation "dintuition" := dintuition.
+Tactic Notation "dintuition" tactic(t) := dintuition_then t.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Init.Wf.html b/master/corelib/Corelib.Init.Wf.html new file mode 100644 index 0000000000..c66cb62cf9 --- /dev/null +++ b/master/corelib/Corelib.Init.Wf.html @@ -0,0 +1,308 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Init.Wf

+ +
+ +
+
+ +
+

This module proves the validity of

+ +
    +
  • well-founded recursion (also known as course of values) + +
    • +
  • well-founded induction + +
    • +
+ from a well-founded ordering on a given set +
+
+ +
+Set Implicit Arguments.
+ +
+Require Import Notations.
+Require Import Ltac.
+Require Import Logic.
+Require Import Datatypes.
+ +
+
+ +
+Well-founded induction principle on Prop +
+
+ +
+Section Well_founded.
+ +
+ Variable A : Type.
+ Variable R : A -> A -> Prop.
+ +
+
+ +
+The accessibility predicate is defined to be non-informative (Acc_rect is automatically defined because Acc is a singleton type) +
+
+ +
+ Inductive Acc (x: A) : Prop :=
+     Acc_intro : (forall y:A, R y x -> Acc y) -> Acc x.
+ +
+ Register Acc as core.wf.acc.
+ +
+ Lemma Acc_inv : forall x:A, Acc x -> forall y:A, R y x -> Acc y.
+ +
+ Global Arguments Acc_inv [x] _ [y] _, [x] _ y _.
+ Register Acc_inv as core.wf.acc_inv.
+ +
+
+ +
+A relation is well-founded if every element is accessible +
+
+ +
+ Definition well_founded := forall a:A, Acc a.
+ +
+ Register well_founded as core.wf.well_founded.
+ +
+
+ +
+Well-founded induction on Set and Prop +
+
+ +
+ Hypothesis Rwf : well_founded.
+ +
+ Theorem well_founded_induction_type :
+  forall P:A -> Type,
+    (forall x:A, (forall y:A, R y x -> P y) -> P x) -> forall a:A, P a.
+ +
+ Theorem well_founded_induction :
+  forall P:A -> Set,
+    (forall x:A, (forall y:A, R y x -> P y) -> P x) -> forall a:A, P a.
+ +
+ Theorem well_founded_ind :
+  forall P:A -> Prop,
+    (forall x:A, (forall y:A, R y x -> P y) -> P x) -> forall a:A, P a.
+ +
+
+ +
+Well-founded fixpoints +
+
+ +
+ Section FixPoint.
+ +
+  Variable P : A -> Type.
+  Variable F : forall x:A, (forall y:A, R y x -> P y) -> P x.
+ +
+  Fixpoint Fix_F (x:A) (a:Acc x) : P x :=
+    F (fun (y:A) (h:R y x) => Fix_F (Acc_inv a h)).
+ +
+  Scheme Acc_inv_dep := Induction for Acc Sort Prop.
+ +
+  Lemma Fix_F_eq (x:A) (r:Acc x) :
+     F (fun (y:A) (p:R y x) => Fix_F (x:=y) (Acc_inv r p)) = Fix_F (x:=x) r.
+ +
+  Definition Fix (x:A) := Fix_F (Rwf x).
+ +
+
+ +
+Proof that well_founded_induction satisfies the fixpoint equation. + It requires an extra property of the functional +
+
+ +
+  Hypothesis
+    F_ext :
+      forall (x:A) (f g:forall y:A, R y x -> P y),
+        (forall (y:A) (p:R y x), f y p = g y p) -> F f = F g.
+ +
+  Lemma Fix_F_inv : forall (x:A) (r s:Acc x), Fix_F r = Fix_F s.
+ +
+  Lemma Fix_eq : forall x:A, Fix x = F (fun (y:A) (p:R y x) => Fix y).
+ +
+ End FixPoint.
+ +
+End Well_founded.
+ +
+
+ +
+Well-founded fixpoints over pairs +
+
+ +
+Section Well_founded_2.
+ +
+  Variables A B : Type.
+  Variable R : A * B -> A * B -> Prop.
+ +
+  Variable P : A -> B -> Type.
+ +
+  Section FixPoint_2.
+ +
+  Variable
+    F :
+      forall (x:A) (x':B),
+        (forall (y:A) (y':B), R (y, y') (x, x') -> P y y') -> P x x'.
+ +
+  Fixpoint Fix_F_2 (x:A) (x':B) (a:Acc R (x, x')) : P x x' :=
+    F
+      (fun (y:A) (y':B) (h:R (y, y') (x, x')) =>
+         Fix_F_2 (x:=y) (x':=y') (Acc_inv a (y,y') h)).
+ +
+  End FixPoint_2.
+ +
+  Hypothesis Rwf : well_founded R.
+ +
+  Theorem well_founded_induction_type_2 :
+   (forall (x:A) (x':B),
+      (forall (y:A) (y':B), R (y, y') (x, x') -> P y y') -> P x x') ->
+   forall (a:A) (b:B), P a b.
+ +
+End Well_founded_2.
+ +
+Notation Acc_iter := Fix_F (only parsing). Notation Acc_iter_2 := Fix_F_2 (only parsing). +
+ +
+Section Acc_generator.
+  Variable A : Type.
+  Variable R : A -> A -> Prop.
+ +
+  Fixpoint Acc_intro_generator n (wf : well_founded R) :=
+    match n with
+        | O => wf
+        | S n => fun x => Acc_intro x (fun y _ => Acc_intro_generator n (Acc_intro_generator n wf) y)
+    end.
+ +
+End Acc_generator.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Lists.ListDef.html b/master/corelib/Corelib.Lists.ListDef.html new file mode 100644 index 0000000000..4894e1b83b --- /dev/null +++ b/master/corelib/Corelib.Lists.ListDef.html @@ -0,0 +1,281 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Lists.ListDef

+ +
+ +
+Set Implicit Arguments.
+ +
+
+ +
+

Basics: definition of polymorphic lists and some operations

+ +
+
+ +
+#[local] Open Scope bool_scope.
+Open Scope list_scope.
+ +
+
+ +
+

Map

+ +
+
+ +
+Section Map.
+ +
+  Variables (A : Type) (B : Type).
+  Variable f : A -> B.
+ +
+  Fixpoint map (l:list A) : list B :=
+    match l with
+      | nil => nil
+      | a :: l => (f a) :: (map l)
+    end.
+ +
+End Map.
+ +
+Section NatSeq.
+ +
+
+ +
+seq computes the sequence of len contiguous integers + that starts at start. For instance, seq 2 3 is 2::3::4::nil. +
+
+ +
+  Fixpoint seq (start len:nat) : list nat :=
+    match len with
+      | 0 => nil
+      | S len => start :: seq (S start) len
+    end.
+ +
+End NatSeq.
+ +
+Section Repeat.
+ +
+  Variable A : Type.
+  Fixpoint repeat (x : A) (n: nat ) :=
+    match n with
+      | O => nil
+      | S k => x :: repeat x k
+    end.
+ +
+End Repeat.
+ +
+Section Elts.
+ +
+  Variable A : Type.
+ +
+
+ +
+

Nth element of a list

+ +
+
+ +
+  Fixpoint nth (n:nat) (l:list A) (default:A) {struct l} : A :=
+    match n, l with
+      | O, x :: l' => x
+      | O, nil => default
+      | S m, nil => default
+      | S m, x :: l' => nth m l' default
+    end.
+ +
+End Elts.
+ +
+Section Cutting.
+ +
+  Variable A : Type.
+ +
+  Fixpoint firstn (n:nat) (l:list A) : list A :=
+    match n with
+      | 0 => nil
+      | S n => match l with
+                 | nil => nil
+                 | a::l => a::(firstn n l)
+               end
+    end.
+ +
+  Fixpoint skipn (n:nat) (l:list A) : list A :=
+    match n with
+      | 0 => l
+      | S n => match l with
+                 | nil => nil
+                 | a::l => skipn n l
+               end
+    end.
+ +
+End Cutting.
+ +
+Section Exists_Forall.
+ +
+
+ +
+

Existential and universal predicates over lists

+ +
+
+ +
+  Variable A:Type.
+ +
+  Section One_predicate.
+ +
+    Variable P : A -> Prop.
+ +
+    Inductive Forall : list A -> Prop :=
+      | Forall_nil : Forall nil
+      | Forall_cons : forall x l, P x -> Forall l -> Forall (x :: l).
+ +
+  End One_predicate.
+ +
+End Exists_Forall.
+ +
+
+ +
+

List comparison

+ +
+
+ +
+Section Compare.
+ +
+  Variable A : Type.
+  Variable cmp : A -> A -> comparison.
+ +
+  Fixpoint list_compare (xs ys : list A) : comparison :=
+    match xs, ys with
+    | nil , nil => Eq
+    | nil , _ => Lt
+    | _ , nil => Gt
+    | x :: xs, y :: ys =>
+        match cmp x y with
+        | Eq => list_compare xs ys
+        | c => c
+        end
+    end%list.
+ +
+End Compare.
+ +
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Numbers.BinNums.html b/master/corelib/Corelib.Numbers.BinNums.html new file mode 100644 index 0000000000..ed8e53ceb6 --- /dev/null +++ b/master/corelib/Corelib.Numbers.BinNums.html @@ -0,0 +1,195 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Numbers.BinNums

+ +
+ +
+
+ +
+

Binary Numerical Datatypes

+ +
+
+ +
+Set Implicit Arguments.
+ +
+
+ +
+positive is a datatype representing the strictly positive integers + in a binary way. Starting from 1 (represented by xH), one can + add a new least significant digit via xO (digit 0) or xI (digit 1). + Numbers in positive will also be denoted using a decimal notation; + e.g. 6%positive will abbreviate xO (xI xH) +
+
+ +
+Inductive positive : Set :=
+  | xI : positive -> positive
+  | xO : positive -> positive
+  | xH : positive.
+ +
+Declare Scope positive_scope.
+Delimit Scope positive_scope with positive.
+Bind Scope positive_scope with positive.
+Arguments xO _%_positive.
+Arguments xI _%_positive.
+ +
+Declare Scope hex_positive_scope.
+Delimit Scope hex_positive_scope with xpositive.
+ +
+Register positive as num.pos.type.
+Register xI as num.pos.xI.
+Register xO as num.pos.xO.
+Register xH as num.pos.xH.
+ +
+
+ +
+N is a datatype representing natural numbers in a binary way, + by extending the positive datatype with a zero. + Numbers in N will also be denoted using a decimal notation; + e.g. 6%N will abbreviate Npos (xO (xI xH)) +
+
+ +
+Inductive N : Set :=
+  | N0 : N
+  | Npos : positive -> N.
+ +
+Declare Scope N_scope.
+Delimit Scope N_scope with N.
+Bind Scope N_scope with N.
+Arguments Npos _%_positive.
+ +
+Declare Scope hex_N_scope.
+Delimit Scope hex_N_scope with xN.
+ +
+Register N as num.N.type.
+Register N0 as num.N.N0.
+Register Npos as num.N.Npos.
+ +
+
+ +
+Z is a datatype representing the integers in a binary way. + An integer is either zero or a strictly positive number + (coded as a positive) or a strictly negative number + (whose opposite is stored as a positive value). + Numbers in Z will also be denoted using a decimal notation; + e.g. (-6)%Z will abbreviate Zneg (xO (xI xH)) +
+
+ +
+Inductive Z : Set :=
+  | Z0 : Z
+  | Zpos : positive -> Z
+  | Zneg : positive -> Z.
+ +
+Declare Scope Z_scope.
+Delimit Scope Z_scope with Z.
+Bind Scope Z_scope with Z.
+Arguments Zpos _%_positive.
+Arguments Zneg _%_positive.
+ +
+Declare Scope hex_Z_scope.
+Delimit Scope hex_Z_scope with xZ.
+ +
+Register Z as num.Z.type.
+Register Z0 as num.Z.Z0.
+Register Zpos as num.Z.Zpos.
+Register Zneg as num.Z.Zneg.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Numbers.Cyclic.Int63.CarryType.html b/master/corelib/Corelib.Numbers.Cyclic.Int63.CarryType.html new file mode 100644 index 0000000000..5eae1d07b3 --- /dev/null +++ b/master/corelib/Corelib.Numbers.Cyclic.Int63.CarryType.html @@ -0,0 +1,90 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Numbers.Cyclic.Int63.CarryType

+ +
+ +
+Set Implicit Arguments.
+ +
+#[universes(template)]
+Variant carry (A : Type) :=
+| C0 : A -> carry A
+| C1 : A -> carry A.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Numbers.Cyclic.Int63.PrimInt63.html b/master/corelib/Corelib.Numbers.Cyclic.Int63.PrimInt63.html new file mode 100644 index 0000000000..4d06000677 --- /dev/null +++ b/master/corelib/Corelib.Numbers.Cyclic.Int63.PrimInt63.html @@ -0,0 +1,238 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Numbers.Cyclic.Int63.PrimInt63

+ +
+ +
+Require Export CarryType.
+ +
+Register bool as kernel.ind_bool.
+Register prod as kernel.ind_pair.
+Register carry as kernel.ind_carry.
+Register comparison as kernel.ind_cmp.
+ +
+Primitive int := #int63_type.
+Register int as num.int63.type.
+Variant pos_neg_int63 := Pos (d:int) | Neg (d:int).
+Register pos_neg_int63 as num.int63.pos_neg_int63.
+Declare Scope uint63_scope.
+Definition id_int : int -> int := fun x => x.
+Record int_wrapper := wrap_int {int_wrap : int}.
+Register int_wrapper as num.int63.int_wrapper.
+Register wrap_int as num.int63.wrap_int.
+Definition printer (x : int_wrapper) : pos_neg_int63 := Pos (int_wrap x).
+Definition parser (x : pos_neg_int63) : option int :=
+  match x with
+  | Pos p => Some p
+  | Neg _ => None
+  end.
+ +
+Declare Scope int63_scope.
+Module Import Int63NotationsInternalA.
+Delimit Scope int63_scope with int63.
+End Int63NotationsInternalA.
+Number Notation int parser printer : int63_scope.
+ +
+Module Import Uint63NotationsInternalA.
+Delimit Scope uint63_scope with uint63.
+Bind Scope uint63_scope with int.
+End Uint63NotationsInternalA.
+Number Notation int parser printer : uint63_scope.
+ +
+Primitive lsl := #int63_lsl.
+ +
+Primitive lsr := #int63_lsr.
+ +
+Primitive land := #int63_land.
+ +
+Primitive lor := #int63_lor.
+ +
+Primitive lxor := #int63_lxor.
+ +
+Primitive asr := #int63_asr.
+ +
+Primitive add := #int63_add.
+ +
+Primitive sub := #int63_sub.
+ +
+Primitive mul := #int63_mul.
+ +
+Primitive mulc := #int63_mulc.
+ +
+Primitive div := #int63_div.
+ +
+Primitive mod := #int63_mod.
+ +
+Primitive divs := #int63_divs.
+ +
+Primitive mods := #int63_mods.
+ +
+Primitive eqb := #int63_eq.
+Register eqb as num.int63.eqb.
+ +
+Primitive ltb := #int63_lt.
+ +
+Primitive leb := #int63_le.
+ +
+Primitive ltsb := #int63_lts.
+ +
+Primitive lesb := #int63_les.
+ +
+
+ +
+Exact arithmetic operations +
+
+ +
+Primitive addc := #int63_addc.
+ +
+Primitive addcarryc := #int63_addcarryc.
+ +
+Primitive subc := #int63_subc.
+ +
+Primitive subcarryc := #int63_subcarryc.
+ +
+Primitive diveucl := #int63_diveucl.
+ +
+Primitive diveucl_21 := #int63_div21.
+ +
+Primitive addmuldiv := #int63_addmuldiv.
+ +
+
+ +
+Comparison +
+
+Primitive compare := #int63_compare.
+ +
+Primitive compares := #int63_compares.
+ +
+
+ +
+Exotic operations +
+
+ +
+Primitive head0 := #int63_head0.
+Primitive tail0 := #int63_tail0.
+ +
+Module Export PrimInt63Notations.
+  Export Int63NotationsInternalA.
+  Export Uint63NotationsInternalA.
+End PrimInt63Notations.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Numbers.Cyclic.Int63.Sint63Axioms.html b/master/corelib/Corelib.Numbers.Cyclic.Int63.Sint63Axioms.html new file mode 100644 index 0000000000..622f56b8ba --- /dev/null +++ b/master/corelib/Corelib.Numbers.Cyclic.Int63.Sint63Axioms.html @@ -0,0 +1,136 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Numbers.Cyclic.Int63.Sint63Axioms

+ +
+ +
+From Corelib Require Import BinNums PosDef IntDef.
+From Corelib Require Export PrimInt63 Uint63Axioms.
+ +
+Local Open Scope Z_scope.
+ +
+Local Notation "2" := (Zpos 2) : Z_scope.
+Local Infix "^" := Z.pow : Z_scope.
+Local Notation "x <= y" := (Z.compare x y <> Gt) : Z_scope.
+Local Notation "x < y" := (Z.compare x y = Lt) : Z_scope.
+ +
+Definition min_int := Eval vm_compute in (lsl 1 62).
+ +
+
+ +
+Translation to and from Z +
+
+Definition to_Z (i : int) :=
+  if ltb i min_int then to_Z i
+  else Z.opp (to_Z (sub 0 i)).
+ +
+
+ +
+Specification of operations that differ on signed and unsigned ints +
+
+ +
+Axiom asr_spec : forall x p, to_Z (asr x p) = Z.div (to_Z x) (2 ^ (to_Z p)).
+ +
+Axiom div_spec : forall x y,
+    to_Z x <> to_Z min_int \/ to_Z y <> Zneg 1 ->
+  to_Z (divs x y) = Z.quot (to_Z x) (to_Z y).
+ +
+Axiom mod_spec : forall x y, to_Z (mods x y) = Z.rem (to_Z x) (to_Z y).
+ +
+Axiom ltb_spec : forall x y, ltsb x y = true <-> to_Z x < to_Z y.
+ +
+Axiom leb_spec : forall x y, lesb x y = true <-> to_Z x <= to_Z y.
+ +
+Axiom compare_spec : forall x y, compares x y = Z.compare (to_Z x) (to_Z y).
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Numbers.Cyclic.Int63.Uint63Axioms.html b/master/corelib/Corelib.Numbers.Cyclic.Int63.Uint63Axioms.html new file mode 100644 index 0000000000..e06c1afd22 --- /dev/null +++ b/master/corelib/Corelib.Numbers.Cyclic.Int63.Uint63Axioms.html @@ -0,0 +1,330 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Numbers.Cyclic.Int63.Uint63Axioms

+ +
+ +
+From Corelib Require Import BinNums PosDef IntDef.
+From Corelib Require Export PrimInt63.
+ +
+Local Open Scope Z_scope.
+ +
+Local Notation "0" := Z0 : Z_scope.
+Local Notation "1" := (Zpos 1) : Z_scope.
+Local Notation "2" := (Zpos 2) : Z_scope.
+Local Infix "+" := Z.add : Z_scope.
+Local Infix "-" := Z.sub : Z_scope.
+Local Infix "*" := Z.mul : Z_scope.
+Local Infix "^" := Z.pow : Z_scope.
+Local Infix "<=" := Z.le : Z_scope.
+Local Infix "<" := Z.lt : Z_scope.
+Local Notation "x <= y < z" := (x <= y /\ y < z) : Z_scope.
+ +
+Definition size := 63%nat.
+ +
+
+ +
+The number of digits as an int +
+
+Definition digits := 63%uint63.
+ +
+
+ +
+The biggest int +
+
+Definition max_int := Eval vm_compute in sub 0 1.
+ +
+
+ +
+Access to the nth digits +
+
+Definition get_digit x p := ltb 0 (land x (lsl 1 p)).
+ +
+Definition set_digit x p (b:bool) :=
+  if if leb 0 p then ltb p digits else false then
+    if b then lor x (lsl 1 p)
+    else land x (lxor max_int (lsl 1 p))
+  else x.
+ +
+
+ +
+Translation to Z +
+
+Definition is_zero (i:int) := eqb i 0.
+Definition is_even (i:int) := is_zero (land i 1).
+Fixpoint to_Z_rec (n:nat) (i:int) :=
+  match n with
+  | O => 0
+  | S n =>
+      (if is_even i then Z.double else Z.succ_double) (to_Z_rec n (lsr i 1))
+  end.
+ +
+Definition to_Z := to_Z_rec size.
+ +
+Fixpoint of_pos_rec (n:nat) (p:positive) {struct p} :=
+  match n, p with
+  | O, _ => 0%uint63
+  | S n, xH => 1%uint63
+  | S n, xO p => lsl (of_pos_rec n p) 1
+  | S n, xI p => lor (lsl (of_pos_rec n p) 1) 1
+  end.
+ +
+Definition of_pos := of_pos_rec size.
+ +
+Definition of_Z z :=
+  match z with
+  | Zpos p => of_pos p
+  | 0 => 0%uint63
+  | Zneg p => sub 0 (of_pos p)
+  end.
+ +
+Definition wB := 2 ^ (Z.of_nat size).
+ +
+ +
+Axiom of_to_Z : forall x, of_Z (to_Z x) = x.
+ +
+
+ +
+Specification of logical operations +
+
+ +
+Axiom lsl_spec : forall x p, to_Z (lsl x p) = Z.modulo (to_Z x * 2 ^ to_Z p) wB.
+ +
+Axiom lsr_spec : forall x p, to_Z (lsr x p) = Z.div (to_Z x) (2 ^ to_Z p).
+ +
+Definition bit i n := negb (is_zero (lsl (lsr i n) (sub digits 1))).
+ +
+Axiom land_spec : forall x y i, bit (land x y) i = andb (bit x i) (bit y i).
+ +
+Axiom lor_spec : forall x y i, bit (lor x y) i = orb (bit x i) (bit y i).
+ +
+Axiom lxor_spec : forall x y i, bit (lxor x y) i = xorb (bit x i) (bit y i).
+ +
+
+ +
+Specification of basic opetations +
+
+ +
+ +
+ +
+Axiom add_spec : forall x y, to_Z (add x y) = Z.modulo (to_Z x + to_Z y) wB.
+ +
+Axiom sub_spec : forall x y, to_Z (sub x y) = Z.modulo (to_Z x - to_Z y) wB.
+ +
+Axiom mul_spec : forall x y, to_Z (mul x y) = Z.modulo (to_Z x * to_Z y) wB.
+ +
+Axiom mulc_spec : forall x y,
+  to_Z x * to_Z y = to_Z (fst (mulc x y)) * wB + to_Z (snd (mulc x y)).
+ +
+Axiom div_spec : forall x y, to_Z (div x y) = Z.div (to_Z x) (to_Z y).
+ +
+Axiom mod_spec : forall x y,
+  to_Z (PrimInt63.mod x y) = Z.modulo (to_Z x) (to_Z y).
+ +
+Axiom eqb_correct : forall i j, eqb i j = true -> i = j.
+ +
+Axiom eqb_refl : forall x, eqb x x = true.
+ +
+Axiom ltb_spec : forall x y, ltb x y = true <-> to_Z x < to_Z y.
+ +
+Axiom leb_spec : forall x y, leb x y = true <-> to_Z x <= to_Z y.
+ +
+
+ +
+Exotic operations +
+ + Axioms on operations which are just short cut +
+
+ +
+Definition compare_def x y :=
+  if ltb x y then Lt else if eqb x y then Eq else Gt.
+ +
+Axiom compare_def_spec : forall x y, compare x y = compare_def x y.
+ +
+Axiom head0_spec : forall x, 0 < to_Z x ->
+  Z.div wB 2 <= 2 ^ (to_Z (head0 x)) * to_Z x < wB.
+ +
+Axiom tail0_spec : forall x, 0 < to_Z x ->
+  exists y, Z0 <= y /\ to_Z x = (2 * y + 1) * (2 ^ to_Z (tail0 x)).
+ +
+Definition addc_def x y :=
+  let r := add x y in
+  if ltb r x then C1 r else C0 r.
+ +
+Axiom addc_def_spec : forall x y, addc x y = addc_def x y.
+ +
+Definition addcarry i j := add (add i j) 1.
+Definition addcarryc_def x y :=
+  let r := addcarry x y in
+  if leb r x then C1 r else C0 r.
+ +
+Axiom addcarryc_def_spec : forall x y, addcarryc x y = addcarryc_def x y.
+ +
+Definition subc_def x y := if leb y x then C0 (sub x y) else C1 (sub x y).
+ +
+Axiom subc_def_spec : forall x y, subc x y = subc_def x y.
+ +
+Definition subcarryc_def x y :=
+  if ltb y x then C0 (sub (sub x y) 1) else C1 (sub (sub x y) 1).
+ +
+Axiom subcarryc_def_spec : forall x y, subcarryc x y = subcarryc_def x y.
+ +
+Definition diveucl_def x y := (div x y, PrimInt63.mod x y).
+ +
+Axiom diveucl_def_spec : forall x y, diveucl x y = diveucl_def x y.
+ +
+Axiom diveucl_21_spec : forall a1 a2 b,
+  let (q,r) := diveucl_21 a1 a2 b in
+  let (q',r') := Z.div_eucl (to_Z a1 * wB + to_Z a2) (to_Z b) in
+  to_Z a1 < to_Z b -> to_Z q = q' /\ to_Z r = r'.
+ +
+Definition addmuldiv_def p x y :=
+  lor (lsl x p) (lsr y (sub digits p)).
+ +
+Axiom addmuldiv_def_spec : forall p x y,
+  addmuldiv p x y = addmuldiv_def p x y.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Program.Basics.html b/master/corelib/Corelib.Program.Basics.html new file mode 100644 index 0000000000..6faa19cda4 --- /dev/null +++ b/master/corelib/Corelib.Program.Basics.html @@ -0,0 +1,188 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Program.Basics

+ +
+
+ +
+Standard functions and combinators. + +
+ + Proofs about them require functional extensionality and can be found + in Combinators. + +
+ + Author: Matthieu Sozeau + Institution: LRI, CNRS UMR 8623 - University Paris Sud + +
+ + The polymorphic identity function is defined in Datatypes. +
+
+ +
+Arguments id {A} x.
+ +
+
+ +
+Function composition. +
+
+ +
+Definition compose {A B C} (g : B -> C) (f : A -> B) :=
+  fun x : A => g (f x).
+ +
+#[global]
+Hint Unfold compose : core.
+ +
+Declare Scope program_scope.
+ +
+Notation " g ∘ f " := (compose g f)
+  (at level 40, left associativity) : program_scope.
+ +
+Local Open Scope program_scope.
+ +
+
+ +
+The non-dependent function space between A and B. +
+
+ +
+Definition arrow (A B : Type) := A -> B.
+Register arrow as core.arrow.
+ +
+
+ +
+Logical implication. +
+
+ +
+Definition impl (A B : Prop) : Prop := A -> B.
+Register impl as core.impl.
+ +
+
+ +
+The constant function const a always returns a. +
+
+ +
+Definition const {A B} (a : A) := fun _ : B => a.
+ +
+
+ +
+The flip combinator reverses the first two arguments of a function. +
+
+ +
+Definition flip {A B C} (f : A -> B -> C) x y := f y x.
+Register flip as core.flip.
+ +
+
+ +
+Application as a combinator. +
+
+ +
+Definition apply {A B} (f : A -> B) (x : A) := f x.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Program.Tactics.html b/master/corelib/Corelib.Program.Tactics.html new file mode 100644 index 0000000000..e6e77b7ffc --- /dev/null +++ b/master/corelib/Corelib.Program.Tactics.html @@ -0,0 +1,616 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Program.Tactics

+ +
+ +
+
+ +
+This module implements various tactics used to simplify the goals produced by Program, + which are also generally useful. +
+ + Debugging tactics to show the goal during evaluation. +
+
+ +
+Ltac show_goal := match goal with [ |- ?T ] => idtac T end.
+ +
+Ltac show_hyp id :=
+  match goal with
+    | [ H := ?b : ?T |- _ ] =>
+      match H with
+        | id => idtac id ":=" b ":" T
+      end
+    | [ H : ?T |- _ ] =>
+      match H with
+        | id => idtac id ":" T
+      end
+  end.
+ +
+Ltac show_hyps :=
+  try match reverse goal with
+        | [ H : ?T |- _ ] => show_hyp H ; fail
+      end.
+ +
+
+ +
+The do tactic but using a Rocq-side nat. +
+
+ +
+Ltac do_nat n tac :=
+  match n with
+    | 0 => idtac
+    | S ?n' => tac ; do_nat n' tac
+  end.
+ +
+
+ +
+Do something on the last hypothesis, or fail +
+
+ +
+Ltac on_last_hyp tac :=
+  lazymatch goal with [ H : _ |- _ ] => tac H end.
+ +
+
+ +
+Destructs one pair, without care regarding naming. +
+
+ +
+Ltac destruct_one_pair :=
+ match goal with
+   | [H : (_ /\ _) |- _] => destruct H
+   | [H : prod _ _ |- _] => destruct H
+ end.
+ +
+
+ +
+Repeateadly destruct pairs. +
+
+ +
+Ltac destruct_pairs := repeat (destruct_one_pair).
+ +
+
+ +
+Destruct one existential package, keeping the name of the hypothesis for the first component. +
+
+ +
+Ltac destruct_one_ex :=
+  let tac H := let ph := fresh "H" in (destruct H as [H ph]) in
+  let tac2 H := let ph := fresh "H" in let ph' := fresh "H" in
+    (destruct H as [H ph ph'])
+  in
+  let tacT H := let ph := fresh "X" in (destruct H as [H ph]) in
+  let tacT2 H := let ph := fresh "X" in let ph' := fresh "X" in
+    (destruct H as [H ph ph'])
+  in
+    match goal with
+      | [H : (ex _) |- _] => tac H
+      | [H : (sig ?P) |- _ ] => tac H
+      | [H : (sigT ?P) |- _ ] => tacT H
+      | [H : (ex2 _ _) |- _] => tac2 H
+      | [H : (sig2 ?P _) |- _ ] => tac2 H
+      | [H : (sigT2 ?P _) |- _ ] => tacT2 H
+    end.
+ +
+
+ +
+Repeateadly destruct existentials. +
+
+ +
+Ltac destruct_exists := repeat (destruct_one_ex).
+ +
+
+ +
+Repeateadly destruct conjunctions and existentials. +
+
+ +
+Ltac destruct_conjs := repeat (destruct_one_pair || destruct_one_ex).
+ +
+
+ +
+Destruct an existential hypothesis t keeping its name for the first component + and using Ht for the second +
+
+ +
+Tactic Notation "destruct" "exist" ident(t) ident(Ht) := destruct t as [t Ht].
+ +
+
+ +
+Destruct a disjunction keeping its name in both subgoals. +
+
+ +
+Tactic Notation "destruct" "or" ident(H) := destruct H as [H|H].
+ +
+
+ +
+Discriminate that also work on a x <> x hypothesis. +
+
+ +
+Ltac discriminates :=
+  match goal with
+    | [ H : ?x <> ?x |- _ ] => elim H ; reflexivity
+    | _ => discriminate
+  end.
+ +
+
+ +
+Revert the last hypothesis. +
+
+ +
+Ltac revert_last :=
+  match goal with
+    [ H : _ |- _ ] => revert H
+  end.
+ +
+
+ +
+Repeatedly reverse the last hypothesis, putting everything in the goal. +
+
+ +
+Ltac reverse := repeat revert_last.
+ +
+
+ +
+Reverse everything up to hypothesis id (not included). +
+
+ +
+Ltac revert_until id :=
+  on_last_hyp ltac:(fun id' =>
+    match id' with
+      | id => idtac
+      | _ => revert id' ; revert_until id
+    end).
+ +
+
+ +
+Clear duplicated hypotheses +
+
+ +
+Ltac clear_dup :=
+  match goal with
+    | [ H : ?X |- _ ] =>
+      match goal with
+        | [ H' : ?Y |- _ ] =>
+          match H with
+            | H' => fail 2
+            | _ => unify X Y ; (clear H' || clear H)
+          end
+      end
+  end.
+ +
+Ltac clear_dups := repeat clear_dup.
+ +
+
+ +
+Try to clear everything except some hyp +
+
+ +
+Ltac clear_except hyp :=
+  repeat match goal with [ H : _ |- _ ] =>
+           match H with
+             | hyp => fail 1
+             | _ => clear H
+           end
+         end.
+ +
+
+ +
+A non-failing subst that substitutes as much as possible. +
+
+ +
+Ltac subst_no_fail :=
+  repeat (match goal with
+            [ H : ?X = ?Y |- _ ] => subst X || subst Y
+          end).
+ +
+Tactic Notation "subst" "*" := subst_no_fail.
+ +
+Ltac on_application f tac T :=
+  match T with
+    | context [f ?x ?y ?z ?w ?v ?u ?a ?b ?c] => tac (f x y z w v u a b c)
+    | context [f ?x ?y ?z ?w ?v ?u ?a ?b] => tac (f x y z w v u a b)
+    | context [f ?x ?y ?z ?w ?v ?u ?a] => tac (f x y z w v u a)
+    | context [f ?x ?y ?z ?w ?v ?u] => tac (f x y z w v u)
+    | context [f ?x ?y ?z ?w ?v] => tac (f x y z w v)
+    | context [f ?x ?y ?z ?w] => tac (f x y z w)
+    | context [f ?x ?y ?z] => tac (f x y z)
+    | context [f ?x ?y] => tac (f x y)
+    | context [f ?x] => tac (f x)
+  end.
+ +
+
+ +
+Tactical on_call f tac applies tac on any application of f in the hypothesis or goal. +
+
+ +
+Ltac on_call f tac :=
+  match goal with
+    | |- ?T => on_application f tac T
+    | H : ?T |- _ => on_application f tac T
+  end.
+ +
+ +
+Ltac destruct_call f :=
+  let tac t := (destruct t) in on_call f tac.
+ +
+Ltac destruct_calls f := repeat destruct_call f.
+ +
+Ltac destruct_call_in f H :=
+  let tac t := (destruct t) in
+  let T := type of H in
+    on_application f tac T.
+ +
+Ltac destruct_call_as f l :=
+  let tac t := (destruct t as l) in on_call f tac.
+ +
+Ltac destruct_call_as_in f l H :=
+  let tac t := (destruct t as l) in
+  let T := type of H in
+    on_application f tac T.
+ +
+Tactic Notation "destruct_call" constr(f) := destruct_call f.
+ +
+
+ +
+Permit to name the results of destructing the call to f. +
+
+ +
+Tactic Notation "destruct_call" constr(f) "as" simple_intropattern(l) :=
+  destruct_call_as f l.
+ +
+
+ +
+Specify the hypothesis in which the call occurs as well. +
+
+ +
+Tactic Notation "destruct_call" constr(f) "in" hyp(id) :=
+  destruct_call_in f id.
+ +
+Tactic Notation "destruct_call" constr(f) "as" simple_intropattern(l) "in" hyp(id) :=
+  destruct_call_as_in f l id.
+ +
+
+ +
+A marker for prototypes to destruct. +
+
+ +
+Definition fix_proto {A : Type} (a : A) := a.
+ +
+Register fix_proto as program.tactic.fix_proto.
+ +
+Ltac destruct_rec_calls :=
+  match goal with
+    | [ H : fix_proto _ |- _ ] => destruct_calls H ; clear H
+  end.
+ +
+Ltac destruct_all_rec_calls :=
+  repeat destruct_rec_calls ; unfold fix_proto in *.
+ +
+
+ +
+Try to inject any potential constructor equality hypothesis. +
+
+ +
+Ltac autoinjection tac :=
+  match goal with
+    | [ H : ?f ?a = ?f' ?a' |- _ ] => tac H
+  end.
+ +
+Ltac inject H := progress (inversion H ; subst*; clear_dups) ; clear H.
+ +
+Ltac autoinjections := repeat (clear_dups ; autoinjection ltac:(inject)).
+ +
+
+ +
+Destruct an hypothesis by first copying it to avoid dependencies. +
+
+ +
+Ltac destruct_nondep H := let H0 := fresh "H" in assert(H0 := H); destruct H0.
+ +
+
+ +
+If bang appears in the goal, it means that we have a proof of False and the goal is solved. +
+
+ +
+Ltac bang :=
+  match goal with
+    | |- ?x =>
+      match x with
+        | context [False_rect _ ?p] => elim p
+      end
+  end.
+ +
+
+ +
+A tactic to show contradiction by first asserting an automatically provable hypothesis. +
+
+Tactic Notation "contradiction" "by" constr(t) :=
+  let H := fresh in assert t as H by auto with * ; contradiction.
+ +
+
+ +
+A tactic that adds H:=p:typeof(p) to the context if no hypothesis of the same type appears in the goal. + Useful to do saturation using tactics. +
+
+ +
+Ltac add_hypothesis H' p :=
+  match type of p with
+    ?X =>
+    match goal with
+      | [ H : X |- _ ] => fail 1
+      | _ => set (H':=p) ; try (change p with H') ; clearbody H'
+    end
+  end.
+ +
+
+ +
+A tactic to replace an hypothesis by another term. +
+
+ +
+Ltac replace_hyp H c :=
+  let H' := fresh "H" in
+    assert(H' := c) ; clear H ; rename H' into H.
+ +
+
+ +
+A tactic to refine an hypothesis by supplying some of its arguments. +
+
+ +
+Ltac refine_hyp c :=
+  let tac H := replace_hyp H c in
+    match c with
+      | ?H _ => tac H
+      | ?H _ _ => tac H
+      | ?H _ _ _ => tac H
+      | ?H _ _ _ _ => tac H
+      | ?H _ _ _ _ _ => tac H
+      | ?H _ _ _ _ _ _ => tac H
+      | ?H _ _ _ _ _ _ _ => tac H
+      | ?H _ _ _ _ _ _ _ _ => tac H
+    end.
+ +
+
+ +
+The default simplification tactic used by Program is defined by program_simpl, sometimes auto + is not enough, better rebind using Obligation Tactic := tac in this case, + possibly using program_simplify to use standard goal-cleaning tactics. +
+
+ +
+Ltac program_simplify :=
+simpl; intros ; destruct_all_rec_calls ; repeat (destruct_conjs; simpl proj1_sig in * );
+  subst*; autoinjections ; try discriminates ;
+    try (solve [ red ; intros ; destruct_conjs ; autoinjections ; discriminates ]).
+ +
+
+ +
+Restrict automation to propositional obligations. +
+
+ +
+Ltac program_solve_wf :=
+  match goal with
+    | |- well_founded _ => auto with *
+    | |- ?T => match type of T with Prop => auto end
+  end.
+ +
+Create HintDb program discriminated.
+ +
+Ltac program_simpl := program_simplify ; try typeclasses eauto 10 with program ; try program_solve_wf.
+ +
+#[global] Obligation Tactic := program_simpl.
+#[export] Obligation Tactic := program_simpl.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Program.Utils.html b/master/corelib/Corelib.Program.Utils.html new file mode 100644 index 0000000000..3d90d1c1f7 --- /dev/null +++ b/master/corelib/Corelib.Program.Utils.html @@ -0,0 +1,171 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Program.Utils

+ +
+ +
+
+ +
+Various syntactic shorthands that are useful with Program. +
+
+ +
+Require Export Corelib.Program.Tactics.
+ +
+Set Implicit Arguments.
+ +
+
+ +
+A simpler notation for subsets defined on a cartesian product. +
+
+ +
+Notation "{ ( x , y ) : A | P }" :=
+  (sig (fun anonymous : A => let (x,y) := anonymous in P))
+  (x name, y name) : type_scope.
+ +
+Declare Scope program_scope.
+Delimit Scope program_scope with prg.
+ +
+
+ +
+Generates an obligation to prove False. +
+
+ +
+Notation " ! " := (False_rect _ _) : program_scope.
+ +
+
+ +
+Abbreviation for first projection and hiding of proofs of subset objects. +
+
+ +
+Notation " ` t " := (proj1_sig t) (at level 10, t at next level) : program_scope.
+ +
+
+ +
+Coerces objects to their support before comparing them. +
+ + Construct a dependent disjunction from a boolean. +
+
+ +
+Notation dec := sumbool_of_bool.
+ +
+
+ +
+The notations in_right and in_left construct objects of a dependent disjunction. +
+ + Hide proofs and generates obligations when put in a term. +
+
+ +
+Notation in_left := (@left _ _ _).
+Notation in_right := (@right _ _ _).
+ +
+
+ +
+Extraction directives +
+
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Program.Wf.html b/master/corelib/Corelib.Program.Wf.html new file mode 100644 index 0000000000..d8088fa4be --- /dev/null +++ b/master/corelib/Corelib.Program.Wf.html @@ -0,0 +1,261 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Program.Wf

+ +
+
+ +
+Reformulation of the Wf module using subsets where possible, providing + the support for Program's treatment of well-founded definitions. +
+
+ +
+Require Import Corelib.Init.Wf.
+Require Import Corelib.Program.Utils.
+ +
+Local Open Scope program_scope.
+ +
+Section Well_founded.
+  Variable A : Type.
+  Variable R : A -> A -> Prop.
+  Hypothesis Rwf : well_founded R.
+ +
+  Variable P : A -> Type.
+ +
+  Variable F_sub : forall x:A, (forall y: { y : A | R y x }, P (proj1_sig y)) -> P x.
+ +
+  Fixpoint Fix_F_sub (x : A) (r : Acc R x) : P x :=
+    F_sub x (fun y: { y : A | R y x} => Fix_F_sub (proj1_sig y)
+      (Acc_inv r (proj2_sig y))).
+ +
+  Definition Fix_sub (x : A) := Fix_F_sub x (Rwf x).
+ +
+  Register Fix_sub as program.wf.fix_sub.
+ +
+ +
+  Hypothesis F_ext :
+    forall (x:A) (f g:forall y:{y:A | R y x}, P (`y)),
+      (forall y:{y : A | R y x}, f y = g y) -> F_sub x f = F_sub x g.
+ +
+  Lemma Fix_F_eq :
+    forall (x:A) (r:Acc R x),
+      F_sub x (fun y:{y:A | R y x} => Fix_F_sub (`y) (Acc_inv r (proj2_sig y))) = Fix_F_sub x r.
+ +
+  Lemma Fix_F_inv : forall (x:A) (r s:Acc R x), Fix_F_sub x r = Fix_F_sub x s.
+ +
+  Lemma Fix_eq : forall x:A, Fix_sub x = F_sub x (fun y:{ y:A | R y x} => Fix_sub (proj1_sig y)).
+ +
+  Lemma fix_sub_eq :
+    forall x : A,
+      Fix_sub x =
+      let f_sub := F_sub in
+        f_sub x (fun y: {y : A | R y x} => Fix_sub (`y)).
+ +
+End Well_founded.
+ +
+Set Implicit Arguments.
+ +
+
+ +
+Reasoning about well-founded fixpoints on measures. +
+
+ +
+Section Measure_well_founded.
+ +
+ +
+  Variables T M: Type.
+  Variable R: M -> M -> Prop.
+  Hypothesis wf: well_founded R.
+  Variable m: T -> M.
+ +
+  Definition MR (x y: T): Prop := R (m x) (m y).
+ +
+  Register MR as program.wf.mr.
+ +
+  Lemma measure_wf: well_founded MR.
+ +
+End Measure_well_founded.
+ +
+#[global]
+Hint Resolve measure_wf : core.
+ +
+Section Fix_rects.
+ +
+  Variable A: Type.
+  Variable P: A -> Type.
+  Variable R : A -> A -> Prop.
+  Variable Rwf : well_founded R.
+  Variable f: forall (x : A), (forall y: { y: A | R y x }, P (proj1_sig y)) -> P x.
+ +
+  Lemma F_unfold x r:
+    Fix_F_sub A R P f x r =
+    f (fun y => Fix_F_sub A R P f (proj1_sig y) (Acc_inv r (proj2_sig y))).
+ +
+ +
+  Lemma Fix_F_sub_rect
+    (Q: forall x, P x -> Type)
+    (inv: forall x: A,
+     (forall (y: A) (H: R y x) (a: Acc R y),
+        Q y (Fix_F_sub A R P f y a)) ->
+        forall (a: Acc R x),
+          Q x (f (fun y: {y: A | R y x} =>
+            Fix_F_sub A R P f (proj1_sig y) (Acc_inv a (proj2_sig y)))))
+    : forall x a, Q _ (Fix_F_sub A R P f x a).
+ +
+ +
+  Hypothesis equiv_lowers:
+    forall x0 (g h: forall x: {y: A | R y x0}, P (proj1_sig x)),
+    (forall x p p', g (exist (fun y: A => R y x0) x p) = h (exist (fun y => R y x0) x p')) ->
+      f g = f h.
+ +
+ +
+  Lemma eq_Fix_F_sub x (a a': Acc R x):
+    Fix_F_sub A R P f x a =
+    Fix_F_sub A R P f x a'.
+ +
+ +
+  Lemma Fix_sub_rect
+    (Q: forall x, P x -> Type)
+    (inv: forall
+      (x: A)
+      (H: forall (y: A), R y x -> Q y (Fix_sub A R Rwf P f y))
+      (a: Acc R x),
+        Q x (f (fun y: {y: A | R y x} => Fix_sub A R Rwf P f (proj1_sig y))))
+    : forall x, Q _ (Fix_sub A R Rwf P f x).
+ +
+End Fix_rects.
+ +
+
+ +
+Tactic to fold a definition based on Fix_measure_sub. +
+
+ +
+Ltac fold_sub f :=
+  match goal with
+    | [ |- ?T ] =>
+      match T with
+        context C [ @Fix_sub _ _ _ _ _ ?arg ] =>
+        let app := context C [ f arg ] in
+          change app
+      end
+  end.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Relations.Relation_Definitions.html b/master/corelib/Corelib.Relations.Relation_Definitions.html new file mode 100644 index 0000000000..3887aabce7 --- /dev/null +++ b/master/corelib/Corelib.Relations.Relation_Definitions.html @@ -0,0 +1,169 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Relations.Relation_Definitions

+ +
+ +
+Section Relation_Definition.
+ +
+  Variable A : Type.
+ +
+  Definition relation := A -> A -> Prop.
+ +
+  Variable R : relation.
+ +
+  Section General_Properties_of_Relations.
+ +
+    Definition reflexive : Prop := forall x:A, R x x.
+    Definition transitive : Prop := forall x y z:A, R x y -> R y z -> R x z.
+    Definition symmetric : Prop := forall x y:A, R x y -> R y x.
+    Definition antisymmetric : Prop := forall x y:A, R x y -> R y x -> x = y.
+ +
+    Definition equiv := reflexive /\ transitive /\ symmetric.
+ +
+  End General_Properties_of_Relations.
+ +
+  Section Sets_of_Relations.
+ +
+    Record preorder : Prop :=
+      { preord_refl : reflexive; preord_trans : transitive}.
+ +
+    Record order : Prop :=
+      { ord_refl : reflexive;
+        ord_trans : transitive;
+        ord_antisym : antisymmetric}.
+ +
+    Record equivalence : Prop :=
+      { equiv_refl : reflexive;
+        equiv_trans : transitive;
+        equiv_sym : symmetric}.
+ +
+    Record PER : Prop := {per_sym : symmetric; per_trans : transitive}.
+ +
+  End Sets_of_Relations.
+ +
+  Section Relations_of_Relations.
+ +
+    Definition inclusion (R1 R2:relation) : Prop :=
+      forall x y:A, R1 x y -> R2 x y.
+ +
+    Definition same_relation (R1 R2:relation) : Prop :=
+      inclusion R1 R2 /\ inclusion R2 R1.
+ +
+    Definition commut (R1 R2:relation) : Prop :=
+      forall x y:A,
+        R1 y x -> forall z:A, R2 z y -> exists2 y' : A, R2 y' x & R1 z y'.
+ +
+  End Relations_of_Relations.
+ +
+End Relation_Definition.
+ +
+#[global]
+Hint Unfold reflexive transitive antisymmetric symmetric: sets.
+ +
+#[global]
+Hint Resolve Build_preorder Build_order Build_equivalence Build_PER
+  preord_refl preord_trans ord_refl ord_trans ord_antisym equiv_refl
+  equiv_trans equiv_sym per_sym per_trans: sets.
+ +
+#[global]
+Hint Unfold inclusion same_relation commut: sets.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Setoids.Setoid.html b/master/corelib/Corelib.Setoids.Setoid.html new file mode 100644 index 0000000000..54e77b6882 --- /dev/null +++ b/master/corelib/Corelib.Setoids.Setoid.html @@ -0,0 +1,155 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Setoids.Setoid

+ +
+ +
+Require Export Corelib.Classes.SetoidTactics.
+ +
+Export Morphisms.ProperNotations.
+ +
+Require Corelib.ssr.ssrsetoid.
+ +
+
+ +
+For backward compatibility +
+
+ +
+Definition Setoid_Theory := @Equivalence.
+Definition Build_Setoid_Theory := @Build_Equivalence.
+ +
+Register Build_Setoid_Theory as plugins.ring.Build_Setoid_Theory.
+ +
+Definition Seq_refl A Aeq (s : Setoid_Theory A Aeq) : forall x:A, Aeq x x.
+ +
+Definition Seq_sym A Aeq (s : Setoid_Theory A Aeq) : forall x y:A, Aeq x y -> Aeq y x.
+ +
+Definition Seq_trans A Aeq (s : Setoid_Theory A Aeq) : forall x y z:A, Aeq x y -> Aeq y z -> Aeq x z.
+ +
+
+ +
+Some tactics for manipulating Setoid Theory not officially + declared as Setoid. +
+
+ +
+Ltac trans_st x :=
+  idtac "trans_st on Setoid_Theory is OBSOLETE";
+  idtac "use transitivity on Equivalence instead";
+  match goal with
+    | H : Setoid_Theory _ ?eqA |- ?eqA _ _ =>
+      apply (Seq_trans _ _ H) with x; auto
+  end.
+ +
+Ltac sym_st :=
+  idtac "sym_st on Setoid_Theory is OBSOLETE";
+  idtac "use symmetry on Equivalence instead";
+  match goal with
+    | H : Setoid_Theory _ ?eqA |- ?eqA _ _ =>
+      apply (Seq_sym _ _ H); auto
+  end.
+ +
+Ltac refl_st :=
+  idtac "refl_st on Setoid_Theory is OBSOLETE";
+  idtac "use reflexivity on Equivalence instead";
+  match goal with
+    | H : Setoid_Theory _ ?eqA |- ?eqA _ _ =>
+      apply (Seq_refl _ _ H); auto
+  end.
+ +
+Definition gen_st : forall A : Set, Setoid_Theory _ (@eq A).
+ +
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Strings.PrimString.html b/master/corelib/Corelib.Strings.PrimString.html new file mode 100644 index 0000000000..0b26cd1888 --- /dev/null +++ b/master/corelib/Corelib.Strings.PrimString.html @@ -0,0 +1,142 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Strings.PrimString

+ +
+Require Import PrimInt63.
+ +
+Definition char63 := int.
+ +
+Primitive string := #string_type.
+ +
+Primitive max_length : int := #string_max_length.
+ +
+Primitive make : int -> char63 -> string := #string_make.
+ +
+Primitive length : string -> int := #string_length.
+ +
+Primitive get : string -> int -> char63 := #string_get.
+ +
+Primitive sub : string -> int -> int -> string := #string_sub.
+ +
+Primitive cat : string -> string -> string := #string_cat.
+ +
+Primitive compare : string -> string -> comparison := #string_compare.
+ +
+Module Export PStringNotations.
+  Record string_wrapper := wrap_string {string_wrap : string}.
+  Definition id_string (s : string) : string := s.
+  Register string as strings.pstring.type.
+  Register string_wrapper as strings.pstring.string_wrapper.
+  Register wrap_string as strings.pstring.wrap_string.
+ +
+  Declare Scope pstring_scope.
+  Delimit Scope pstring_scope with pstring.
+  Bind Scope pstring_scope with string.
+  String Notation string id_string id_string : pstring_scope.
+End PStringNotations.
+ +
+Record char63_wrapper := wrap_char63 { char63_wrap : char63 }.
+ +
+Module Export Char63Notations.
+  Coercion char63_wrap : char63_wrapper >-> char63.
+  Definition parse (s : string) : option char63_wrapper :=
+    if PrimInt63.eqb (length s) 1%uint63 then Some (wrap_char63 (get s 0)) else None.
+  Definition print (i : char63_wrapper) : option string :=
+    if PrimInt63.ltb i.(char63_wrap) 256%uint63 then Some (make 1 i.(char63_wrap)) else None.
+ +
+  Declare Scope char63_scope.
+  Delimit Scope char63_scope with char63.
+  Bind Scope char63_scope with char63.
+  String Notation char63_wrapper parse print : char63_scope.
+End Char63Notations.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.Strings.PrimStringAxioms.html b/master/corelib/Corelib.Strings.PrimStringAxioms.html new file mode 100644 index 0000000000..7ecc232a4d --- /dev/null +++ b/master/corelib/Corelib.Strings.PrimStringAxioms.html @@ -0,0 +1,174 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.Strings.PrimStringAxioms

+ +
+From Corelib Require Import BinNums PosDef IntDef ListDef.
+From Corelib Require Export PrimInt63 Uint63Axioms.
+From Corelib Require Export PrimString.
+ +
+Definition char63_valid (c : char63) :=
+  PrimInt63.land c 255%uint63 = c.
+ +
+
+ +
+

Conversion to / from lists

+ +
+
+ +
+Notation of_nat n := (of_Z (Z.of_nat n)).
+Notation to_nat i := (Z.to_nat (to_Z i)).
+ +
+Definition to_list (s : string) : list char63 :=
+  ListDef.map (fun i => get s (of_nat i)) (ListDef.seq 0 (to_nat (length s))).
+ +
+Fixpoint of_list (cs : list char63) : string :=
+  match cs with
+  | nil => ""%pstring
+  | cons c cs => cat (make 1 c) (of_list cs)
+  end.
+ +
+Axiom of_to_list :
+  forall (s : string),
+    of_list (to_list s) = s.
+ +
+Axiom to_list_length :
+  forall (s : string),
+    Datatypes.length (to_list s) <= to_nat max_length.
+ +
+Axiom to_list_char63_valid :
+  forall (s : string),
+    ListDef.Forall char63_valid (to_list s).
+ +
+
+ +
+

Axioms relating string operations with list operations

+ +
+
+ +
+Axiom length_spec :
+  forall (s : string),
+    to_nat (length s) = Datatypes.length (to_list s).
+ +
+Axiom get_spec :
+  forall (s : string) (i : int),
+    get s i = ListDef.nth (to_nat i) (to_list s) 0%uint63.
+ +
+Axiom make_spec :
+  forall (i : int) (c : char63),
+    to_list (make i c) =
+      ListDef.repeat (PrimInt63.land c 255%uint63)
+        (Nat.min (to_nat i) (to_nat max_length)).
+ +
+Axiom sub_spec :
+  forall (s : string) (off len : int),
+    to_list (sub s off len) =
+      ListDef.firstn (to_nat len) (ListDef.skipn (to_nat off) (to_list s)).
+ +
+Axiom cat_spec :
+  forall (s1 s2 : string),
+    to_list (cat s1 s2) =
+      ListDef.firstn (to_nat max_length) (to_list s1 ++ to_list s2).
+ +
+Notation char63_compare := PrimInt63.compare (only parsing).
+ +
+Axiom compare_spec :
+  forall (s1 s2 : string),
+    compare s1 s2 =
+      ListDef.list_compare char63_compare (to_list s1) (to_list s2).
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.derive.Derive.html b/master/corelib/Corelib.derive.Derive.html new file mode 100644 index 0000000000..b5ace9899c --- /dev/null +++ b/master/corelib/Corelib.derive.Derive.html @@ -0,0 +1,81 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.derive.Derive

+ +
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.extraction.ExtrHaskellBasic.html b/master/corelib/Corelib.extraction.ExtrHaskellBasic.html new file mode 100644 index 0000000000..8b0dadc68d --- /dev/null +++ b/master/corelib/Corelib.extraction.ExtrHaskellBasic.html @@ -0,0 +1,107 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.extraction.ExtrHaskellBasic

+ +
+
+ +
+Extraction to Haskell : use of basic Haskell types +
+
+ +
+Require Corelib.extraction.Extraction.
+ +
+Extract Inductive bool => "Prelude.Bool" [ "Prelude.True" "Prelude.False" ].
+Extract Inductive option => "Prelude.Maybe" [ "Prelude.Just" "Prelude.Nothing" ].
+Extract Inductive unit => "()" [ "()" ].
+Extract Inductive list => "([])" [ "([])" "(:)" ].
+Extract Inductive prod => "(,)" [ "(,)" ].
+ +
+Extract Inductive sumbool => "Prelude.Bool" [ "Prelude.True" "Prelude.False" ].
+Extract Inductive sumor => "Prelude.Maybe" [ "Prelude.Just" "Prelude.Nothing" ].
+Extract Inductive sum => "Prelude.Either" [ "Prelude.Left" "Prelude.Right" ].
+ +
+Extract Inlined Constant andb => "(Prelude.&&)".
+Extract Inlined Constant orb => "(Prelude.||)".
+Extract Inlined Constant negb => "Prelude.not".
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.extraction.ExtrOcamlBasic.html b/master/corelib/Corelib.extraction.ExtrOcamlBasic.html new file mode 100644 index 0000000000..5b8972e782 --- /dev/null +++ b/master/corelib/Corelib.extraction.ExtrOcamlBasic.html @@ -0,0 +1,133 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.extraction.ExtrOcamlBasic

+ +
+ +
+Require Corelib.extraction.Extraction.
+ +
+
+ +
+Extraction to Ocaml : use of basic Ocaml types +
+
+ +
+Extract Inductive bool => bool [ true false ].
+Extract Inductive option => option [ Some None ].
+Extract Inductive unit => unit [ "()" ].
+Extract Inductive list => list [ "[]" "( :: )" ].
+Extract Inductive prod => "( * )" [ "" ].
+ +
+
+ +
+NB: The "" above is a hack, but produce nicer code than "(,)" +
+ + Mapping sumbool to bool and sumor to option is not always nicer, + but it helps when realizing stuff like lt_eq_lt_dec +
+
+ +
+Extract Inductive sumbool => bool [ true false ].
+Extract Inductive sumor => option [ Some None ].
+ +
+
+ +
+Restore laziness of andb, orb. + NB: without these Extract Constant, andb/orb would be inlined + by extraction in order to have laziness, producing inelegant + (if ... then ... else false) and (if ... then true else ...). + +
+
+ +
+Extract Inlined Constant andb => "(&&)".
+Extract Inlined Constant orb => "(||)".
+ +
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.extraction.Extraction.html b/master/corelib/Corelib.extraction.Extraction.html new file mode 100644 index 0000000000..831aa24a99 --- /dev/null +++ b/master/corelib/Corelib.extraction.Extraction.html @@ -0,0 +1,83 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.extraction.Extraction

+ +
+ +
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.ssr.ssrbool.html b/master/corelib/Corelib.ssr.ssrbool.html new file mode 100644 index 0000000000..4f966604b3 --- /dev/null +++ b/master/corelib/Corelib.ssr.ssrbool.html @@ -0,0 +1,2882 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.ssr.ssrbool

+ +
+ +
+ +
+
+ +
+ +
+
+ +
+Require Import ssreflect ssrfun.
+ +
+
+ +
+ A theory of boolean predicates and operators. A large part of this file is + concerned with boolean reflection. + Definitions and notations: + is_true b == the coercion of b : bool to Prop (:= b = true). + This is just input and displayed as `b''. + reflect P b == the reflection inductive predicate, asserting + that the logical proposition P : Prop holds iff + the formula b : bool is equal to true. Lemmas + asserting reflect P b are often referred to as + "views". + iffP, appP, sameP, rwP :: lemmas for direct manipulation of reflection + views: iffP is used to prove reflection from + logical equivalence, appP to compose views, and + sameP and rwP to perform boolean and setoid + rewriting. + elimT :: coercion reflect >-> Funclass, which allows the + direct application of `reflect' views to + boolean assertions. + decidable P <-> P is effectively decidable (:= {P} + {~ P}). + contra, contraL, ... :: contraposition lemmas. + altP my_viewP :: natural alternative for reflection; given + lemma myviewP: reflect my_Prop my_formula, + have [myP | not_myP] := altP my_viewP. + generates two subgoals, in which my_formula has + been replaced by true and false, resp., with + new assumptions myP : my_Prop and + not_myP: ~~ my_formula. + Caveat: my_formula must be an APPLICATION, not + a variable, constant, let-in, etc. (due to the + poor behaviour of dependent index matching). + boolP my_formula :: boolean disjunction, equivalent to + altP (idP my_formula) but circumventing the + dependent index capture issue; destructing + boolP my_formula generates two subgoals with + assumptions my_formula and ~~ my_formula. As + with altP, my_formula must be an application. + \unless C, P <-> we can assume property P when a something that + holds under condition C (such as C itself). + := forall G : Prop, (C -> G) -> (P -> G) -> G. + This is just C \/ P or rather its impredicative + encoding, whose usage better fits the above + description: given a lemma UCP whose conclusion + is \unless C, P we can assume P by writing: + wlog hP: / P by apply/UCP; (prove C -> goal). + or even apply: UCP id _ => hP if the goal is C. + classically P <-> we can assume P when proving is_true b. + := forall b : bool, (P -> b) -> b. + This is equivalent to ~ (~ P) when P : Prop. + implies P Q == wrapper variant type that coerces to P -> Q and + can be used as a P -> Q view unambiguously. + Useful to avoid spurious insertion of <-> views + when Q is a conjunction of foralls, as in Lemma + all_and2 below; conversely, avoids confusion in + apply views for impredicative properties, such + as \unless C, P. Also supports contrapositives. + a && b == the boolean conjunction of a and b. + a || b == the boolean disjunction of a and b. + a ==> b == the boolean implication of b by a. + ~~ a == the boolean negation of a. + a (+) b == the boolean exclusive or (or sum) of a and b. + [ /\ P1 , P2 & P3 ] == multiway logical conjunction, up to 5 terms. + [ \/ P1 , P2 | P3 ] == multiway logical disjunction, up to 4 terms. + [&& a, b, c & d] == iterated, right associative boolean conjunction + with arbitrary arity. + [|| a, b, c | d] == iterated, right associative boolean disjunction + with arbitrary arity. + [==> a, b, c => d] == iterated, right associative boolean implication + with arbitrary arity. + and3P, ... == specific reflection lemmas for iterated + connectives. + andTb, orbAC, ... == systematic names for boolean connective + properties (see suffix conventions below). + prop_congr == a tactic to move a boolean equality from + its coerced form in Prop to the equality + in bool. + bool_congr == resolution tactic for blindly weeding out + like terms from boolean equalities (can fail). + This file provides a theory of boolean predicates and relations: + pred T == the type of bool predicates (:= T -> bool). + simpl_pred T == the type of simplifying bool predicates, based on + the simpl_fun type from ssrfun.v. + mem_pred T == a specialized form of simpl_pred for "collective" + predicates (see below). + rel T == the type of bool relations. + := T -> pred T or T -> T -> bool. + simpl_rel T == type of simplifying relations. + := T -> simpl_pred T + predType == the generic predicate interface, supported for + for lists and sets. + pred_sort == the predType >-> Type projection; pred_sort is + itself a Coercion target class. Declaring a + coercion to pred_sort is an alternative way of + equipping a type with a predType structure, which + interoperates better with coercion subtyping. + This is used, e.g., for finite sets, so that finite + groups inherit the membership operation by + coercing to sets. + {pred T} == a type convertible to pred T, but whose head + constant is pred_sort. This type should be used + for parameters that can be used as collective + predicates (see below), as this will allow passing + in directly collections that implement predType + by coercion as described above, e.g., finite sets. + := pred_sort (predPredType T) + If P is a predicate the proposition "x satisfies P" can be written + applicatively as (P x), or using an explicit connective as (x \in P); in + the latter case we say that P is a "collective" predicate. We use A, B + rather than P, Q for collective predicates: + x \in A == x satisfies the (collective) predicate A. + x \notin A == x doesn't satisfy the (collective) predicate A. + The pred T type can be used as a generic predicate type for either kind, + but the two kinds of predicates should not be confused. When a "generic" + pred T value of one type needs to be passed as the other the following + conversions should be used explicitly: + SimplPred P == a (simplifying) applicative equivalent of P. + mem A == an applicative equivalent of collective predicate A: + mem A x simplifies to x \in A, as mem A has in + fact type mem_pred T. +> In user notation collective predicates only occur as arguments to mem: + A only appears as (mem A). This is hidden by notation, e.g., + x \in A := in_mem x (mem A) here, enum A := enum_mem (mem A) in fintype. + This makes it possible to unify the various ways in which A can be + interpreted as a predicate, for both pattern matching and display. + Alternatively one can use the syntax for explicit simplifying predicates + and relations (in the following x is bound in E): + [pred x | E] == simplifying (see ssrfun) predicate x => E. + [pred x : T | E] == predicate x => E, with a cast on the argument. + [pred : T | P] == constant predicate P on type T. + [pred x | E1 & E2] == [pred x | E1 && E2]; an x : T cast is allowed. + [pred x in A] == [pred x | x in A]. + [pred x in A | E] == [pred x | x in A & E]. + [pred x in A | E1 & E2] == [pred x in A | E1 && E2]. + [predU A & B] == union of two collective predicates A and B. + [predI A & B] == intersection of collective predicates A and B. + [predD A & B] == difference of collective predicates A and B. + [predC A] == complement of the collective predicate A. + [preim f of A] == preimage under f of the collective predicate A. + predU P Q, ..., preim f P == union, etc of applicative predicates. + pred_oapp A == the predicate A lifted to the option type + := [pred x | oapp (mem A) false x]. + pred0 == the empty predicate. + predT == the total (always true) predicate. + if T : predArgType, then T coerces to predT. + {: T} == T cast to predArgType (e.g., {: bool * nat}). + In the following, x and y are bound in E: + [rel x y | E] == simplifying relation x, y => E. + [rel x y : T | E] == simplifying relation with arguments cast. + [rel x y in A & B | E] == [rel x y | [&& x \in A, y \in B & E] ]. + [rel x y in A & B] == [rel x y | (x \in A) && (y \in B) ]. + [rel x y in A | E] == [rel x y in A & A | E]. + [rel x y in A] == [rel x y in A & A]. + relU R S == union of relations R and S. + relpre f R == preimage of relation R under f. + xpredU, ..., xrelpre == lambda terms implementing predU, ..., etc. + Explicit values of type pred T (i.e., lamdba terms) should always be used + applicatively, while values of collection types implementing the predType + interface, such as sequences or sets should always be used as collective + predicates. Defined constants and functions of type pred T or simpl_pred T + as well as the explicit simpl_pred T values described below, can generally + be used either way. Note however that x \in A will not auto-simplify when + A is an explicit simpl_pred T value; the generic simplification rule inE + must be used (when A : pred T, the unfold_in rule can be used). Constants + of type pred T with an explicit simpl_pred value do not auto-simplify when + used applicatively, but can still be expanded with inE. This behavior can + be controlled as follows: + Let A : collective_pred T := [pred x | ... ]. + The collective_pred T type is just an alias for pred T, but this cast + stops rewrite inE from expanding the definition of A, thus treating A + into an abstract collection (unfold_in or in_collective can be used to + expand manually). + Let A : applicative_pred T := [pred x | ... ]. + This cast causes inE to turn x \in A into the applicative A x form; + A will then have to be unfolded explicitly with the /A rule. This will + also apply to any definition that reduces to A (e.g., Let B := A). + Canonical A_app_pred := ApplicativePred A. + This declaration, given after definition of A, similarly causes inE to + turn x \in A into A x, but in addition allows the app_predE rule to + turn A x back into x \in A; it can be used for any definition of type + pred T, which makes it especially useful for ambivalent predicates + as the relational transitive closure connect, that are used in both + applicative and collective styles. + Purely for aesthetics, we provide a subtype of collective predicates: + qualifier q T == a pred T pretty-printing wrapper. An A : qualifier q T + coerces to pred_sort and thus behaves as a collective + predicate, but x \in A and x \notin A are displayed as: + x \is A and x \isn't A when q = 0, + x \is a A and x \isn't a A when q = 1, + x \is an A and x \isn't an A when q = 2, respectively. + [qualify x | P] := Qualifier 0 (fun x => P), constructor for the above. + [qualify x : T | P], [qualify a x | P], [qualify an X | P], etc. + variants of the above with type constraints and different + values of q. + We provide an internal interface to support attaching properties (such as + being multiplicative) to predicates: + pred_key p == phantom type that will serve as a support for properties + to be attached to p : {pred _}; instances should be + created with Fact/Qed so as to be opaque. + KeyedPred k_p == an instance of the interface structure that attaches + (k_p : pred_key P) to P; the structure projection is a + coercion to pred_sort. + KeyedQualifier k_q == an instance of the interface structure that attaches + (k_q : pred_key q) to (q : qualifier n T). + DefaultPredKey p == a default value for pred_key p; the vernacular command + Import DefaultKeying attaches this key to all predicates + that are not explicitly keyed. + Keys can be used to attach properties to predicates, qualifiers and + generic nouns in a way that allows them to be used transparently. The key + projection of a predicate property structure such as unsignedPred should + be a pred_key, not a pred, and corresponding lemmas will have the form + Lemma rpredN R S (oppS : @opprPred R S) (kS : keyed_pred oppS) : + {mono -%R: x / x \in kS}. + Because x \in kS will be displayed as x \in S (or x \is S, etc), the + canonical instance of opprPred will not normally be exposed (it will also + be erased by /= simplification). In addition each predicate structure + should have a DefaultPredKey Canonical instance that simply issues the + property as a proof obligation (which can be caught by the Prop-irrelevant + feature of the ssreflect plugin). + Some properties of predicates and relations: + A =i B <-> A and B are extensionally equivalent. + {subset A <= B} <-> A is a (collective) subpredicate of B. + subpred P Q <-> P is an (applicative) subpredicate or Q. + subrel R S <-> R is a subrelation of S. + In the following R is in rel T: + reflexive R <-> R is reflexive. + irreflexive R <-> R is irreflexive. + symmetric R <-> R (in rel T) is symmetric (equation). + pre_symmetric R <-> R is symmetric (implication). + antisymmetric R <-> R is antisymmetric. + total R <-> R is total. + transitive R <-> R is transitive. + left_transitive R <-> R is a congruence on its left hand side. + right_transitive R <-> R is a congruence on its right hand side. + equivalence_rel R <-> R is an equivalence relation. + Localization of (Prop) predicates; if P1 is convertible to forall x, Qx, + P2 to forall x y, Qxy and P3 to forall x y z, Qxyz : + {for y, P1} <-> Qx{y / x}. + {in A, P1} <-> forall x, x \in A -> Qx. + {in A1 & A2, P2} <-> forall x y, x \in A1 -> y \in A2 -> Qxy. + {in A &, P2} <-> forall x y, x \in A -> y \in A -> Qxy. + {in A1 & A2 & A3, Q3} <-> forall x y z, + x \in A1 -> y \in A2 -> z \in A3 -> Qxyz. + {in A1 & A2 &, Q3} := {in A1 & A2 & A2, Q3}. + {in A1 && A3, Q3} := {in A1 & A1 & A3, Q3}. + {in A &&, Q3} := {in A & A & A, Q3}. + {in A, bijective f} <-> f has a right inverse in A. + {on C, P1} <-> forall x, (f x) \in C -> Qx + when P1 is also convertible to Pf f, e.g., + {on C, involutive f}. + {on C &, P2} == forall x y, f x \in C -> f y \in C -> Qxy + when P2 is also convertible to Pf f, e.g., + {on C &, injective f}. + {on C, P1' & g} == forall x, (f x) \in cd -> Qx + when P1' is convertible to Pf f + and P1' g is convertible to forall x, Qx, e.g., + {on C, cancel f & g}. + {on C, bijective f} == f has a right inverse on C. + This file extends the lemma name suffix conventions of ssrfun as follows: + A -- associativity, as in andbA : associative andb. + AC -- right commutativity. + ACA -- self-interchange (inner commutativity), e.g., + orbACA : (a || b) || (c || d) = (a || c) || (b || d). + b -- a boolean argument, as in andbb : idempotent andb. + C -- commutativity, as in andbC : commutative andb, + or predicate complement, as in predC. + CA -- left commutativity. + D -- predicate difference, as in predD. + E -- elimination, as in negbFE : ~~ b = false -> b. + F or f -- boolean false, as in andbF : b && false = false. + I -- left/right injectivity, as in addbI : right_injective addb, + or predicate intersection, as in predI. + l -- a left-hand operation, as andb_orl : left_distributive andb orb. + N or n -- boolean negation, as in andbN : a && (~~ a) = false. + P -- a characteristic property, often a reflection lemma, as in + andP : reflect (a /\ b) (a && b). + r -- a right-hand operation, as orb_andr : right_distributive orb andb. + T or t -- boolean truth, as in andbT: right_id true andb. + U -- predicate union, as in predU. + W -- weakening, as in in1W : (forall x, P) -> {in D, forall x, P}. +
+
+ +
+Set Implicit Arguments.
+ +
+Notation reflect := Datatypes.reflect.
+Notation ReflectT := Datatypes.ReflectT.
+Notation ReflectF := Datatypes.ReflectF.
+ +
+Reserved Notation "~~ b" (at level 35, right associativity).
+Reserved Notation "b ==> c" (at level 55, right associativity).
+Reserved Notation "b1 (+) b2" (at level 50, left associativity).
+ +
+Reserved Notation "x \in A" (at level 70, no associativity,
+  format "'[hv' x '/ ' \in A ']'").
+Reserved Notation "x \notin A" (at level 70, no associativity,
+  format "'[hv' x '/ ' \notin A ']'").
+Reserved Notation "x \is A" (at level 70, no associativity,
+  format "'[hv' x '/ ' \is A ']'").
+Reserved Notation "x \isn't A" (at level 70, no associativity,
+  format "'[hv' x '/ ' \isn't A ']'").
+Reserved Notation "x \is 'a' A" (at level 70, no associativity,
+  format "'[hv' x '/ ' \is 'a' A ']'").
+Reserved Notation "x \isn't 'a' A" (at level 70, no associativity,
+  format "'[hv' x '/ ' \isn't 'a' A ']'").
+Reserved Notation "x \is 'an' A" (at level 70, no associativity,
+  format "'[hv' x '/ ' \is 'an' A ']'").
+Reserved Notation "x \isn't 'an' A" (at level 70, no associativity,
+  format "'[hv' x '/ ' \isn't 'an' A ']'").
+Reserved Notation "p1 =i p2" (at level 70, no associativity,
+  format "'[hv' p1 '/ ' =i p2 ']'").
+Reserved Notation "{ 'subset' A <= B }" (at level 0, A, B at level 69,
+  format "'[hv' { 'subset' A '/ ' <= B } ']'").
+ +
+Reserved Notation "{ : T }" (at level 0, format "{ : T }").
+Reserved Notation "{ 'pred' T }" (at level 0, format "{ 'pred' T }").
+Reserved Notation "[ 'predType' 'of' T ]" (at level 0,
+  format "[ 'predType' 'of' T ]").
+ +
+Reserved Notation "[ 'pred' : T | E ]" (at level 0,
+  format "'[hv' [ 'pred' : T | '/ ' E ] ']'").
+Reserved Notation "[ 'pred' x | E ]" (at level 0, x name,
+  format "'[hv' [ 'pred' x | '/ ' E ] ']'").
+Reserved Notation "[ 'pred' x : T | E ]" (at level 0, x name,
+  format "'[hv' [ 'pred' x : T | '/ ' E ] ']'").
+Reserved Notation "[ 'pred' x | E1 & E2 ]" (at level 0, x name,
+  format "'[hv' [ 'pred' x | '/ ' E1 & '/ ' E2 ] ']'").
+Reserved Notation "[ 'pred' x : T | E1 & E2 ]" (at level 0, x name,
+  format "'[hv' [ 'pred' x : T | '/ ' E1 & E2 ] ']'").
+Reserved Notation "[ 'pred' x 'in' A ]" (at level 0, x name,
+  format "'[hv' [ 'pred' x 'in' A ] ']'").
+Reserved Notation "[ 'pred' x 'in' A | E ]" (at level 0, x name,
+  format "'[hv' [ 'pred' x 'in' A | '/ ' E ] ']'").
+Reserved Notation "[ 'pred' x 'in' A | E1 & E2 ]" (at level 0, x name,
+  format "'[hv' [ 'pred' x 'in' A | '/ ' E1 & '/ ' E2 ] ']'").
+ +
+Reserved Notation "[ 'qualify' x | P ]" (at level 0, x at level 99,
+  format "'[hv' [ 'qualify' x | '/ ' P ] ']'").
+Reserved Notation "[ 'qualify' x : T | P ]" (at level 0, x at level 99,
+  format "'[hv' [ 'qualify' x : T | '/ ' P ] ']'").
+Reserved Notation "[ 'qualify' 'a' x | P ]" (at level 0, x at level 99,
+  format "'[hv' [ 'qualify' 'a' x | '/ ' P ] ']'").
+Reserved Notation "[ 'qualify' 'a' x : T | P ]" (at level 0, x at level 99,
+  format "'[hv' [ 'qualify' 'a' x : T | '/ ' P ] ']'").
+Reserved Notation "[ 'qualify' 'an' x | P ]" (at level 0, x at level 99,
+  format "'[hv' [ 'qualify' 'an' x | '/ ' P ] ']'").
+Reserved Notation "[ 'qualify' 'an' x : T | P ]" (at level 0, x at level 99,
+  format "'[hv' [ 'qualify' 'an' x : T | '/ ' P ] ']'").
+ +
+Reserved Notation "[ 'rel' x y | E ]" (at level 0, x name, y name,
+  format "'[hv' [ 'rel' x y | '/ ' E ] ']'").
+Reserved Notation "[ 'rel' x y : T | E ]" (at level 0, x name, y name,
+  format "'[hv' [ 'rel' x y : T | '/ ' E ] ']'").
+Reserved Notation "[ 'rel' x y 'in' A & B | E ]" (at level 0, x name, y name,
+  format "'[hv' [ 'rel' x y 'in' A & B | '/ ' E ] ']'").
+Reserved Notation "[ 'rel' x y 'in' A & B ]" (at level 0, x name, y name,
+  format "'[hv' [ 'rel' x y 'in' A & B ] ']'").
+Reserved Notation "[ 'rel' x y 'in' A | E ]" (at level 0, x name, y name,
+  format "'[hv' [ 'rel' x y 'in' A | '/ ' E ] ']'").
+Reserved Notation "[ 'rel' x y 'in' A ]" (at level 0, x name, y name,
+  format "'[hv' [ 'rel' x y 'in' A ] ']'").
+ +
+Reserved Notation "[ 'mem' A ]" (at level 0, format "[ 'mem' A ]").
+Reserved Notation "[ 'predI' A & B ]" (at level 0,
+  format "[ 'predI' A & B ]").
+Reserved Notation "[ 'predU' A & B ]" (at level 0,
+  format "[ 'predU' A & B ]").
+Reserved Notation "[ 'predD' A & B ]" (at level 0,
+  format "[ 'predD' A & B ]").
+Reserved Notation "[ 'predC' A ]" (at level 0,
+  format "[ 'predC' A ]").
+Reserved Notation "[ 'preim' f 'of' A ]" (at level 0,
+  format "[ 'preim' f 'of' A ]").
+ +
+Reserved Notation "\unless C , P" (at level 200, C at level 100,
+  format "'[hv' \unless C , '/ ' P ']'").
+ +
+Reserved Notation "{ 'for' x , P }" (at level 0,
+  format "'[hv' { 'for' x , '/ ' P } ']'").
+Reserved Notation "{ 'in' d , P }" (at level 0,
+  format "'[hv' { 'in' d , '/ ' P } ']'").
+Reserved Notation "{ 'in' d1 & d2 , P }" (at level 0,
+  format "'[hv' { 'in' d1 & d2 , '/ ' P } ']'").
+Reserved Notation "{ 'in' d & , P }" (at level 0,
+  format "'[hv' { 'in' d & , '/ ' P } ']'").
+Reserved Notation "{ 'in' d1 & d2 & d3 , P }" (at level 0,
+  format "'[hv' { 'in' d1 & d2 & d3 , '/ ' P } ']'").
+Reserved Notation "{ 'in' d1 & & d3 , P }" (at level 0,
+  format "'[hv' { 'in' d1 & & d3 , '/ ' P } ']'").
+Reserved Notation "{ 'in' d1 & d2 & , P }" (at level 0,
+  format "'[hv' { 'in' d1 & d2 & , '/ ' P } ']'").
+Reserved Notation "{ 'in' d & & , P }" (at level 0,
+  format "'[hv' { 'in' d & & , '/ ' P } ']'").
+Reserved Notation "{ 'on' cd , P }" (at level 0,
+  format "'[hv' { 'on' cd , '/ ' P } ']'").
+Reserved Notation "{ 'on' cd & , P }" (at level 0,
+  format "'[hv' { 'on' cd & , '/ ' P } ']'").
+Reserved Notation "{ 'on' cd , P & g }" (at level 0, g at level 8,
+  format "'[hv' { 'on' cd , '/ ' P & g } ']'").
+Reserved Notation "{ 'in' d , 'bijective' f }" (at level 0, f at level 8,
+   format "'[hv' { 'in' d , '/ ' 'bijective' f } ']'").
+Reserved Notation "{ 'on' cd , 'bijective' f }" (at level 0, f at level 8,
+   format "'[hv' { 'on' cd , '/ ' 'bijective' f } ']'").
+ +
+
+ +
+ We introduce a number of n-ary "list-style" notations that share a common + format, namely + [op arg1, arg2, ... last_separator last_arg] + This usually denotes a right-associative applications of op, e.g., + [&& a, b, c & d] denotes a && (b && (c && d)) + The last_separator must be a non-operator token. Here we use &, | or =>; + our default is &, but we try to match the intended meaning of op. The + separator is a workaround for limitations of the parsing engine; the same + limitations mean the separator cannot be omitted even when last_arg can. + The Notation declarations are complicated by the separate treatment for + some fixed arities (binary for bool operators, and all arities for Prop + operators). + We also use the square brackets in comprehension-style notations + [type var separator expr] + where "type" is the type of the comprehension (e.g., pred) and "separator" + is | or => . It is important that in other notations a leading square + bracket [ is always followed by an operator symbol or a fixed identifier. +
+
+ +
+Reserved Notation "[ /\ P1 & P2 ]" (at level 0).
+Reserved Notation "[ /\ P1 , P2 & P3 ]" (at level 0, format
+  "'[hv' [ /\ '[' P1 , '/' P2 ']' '/ ' & P3 ] ']'").
+Reserved Notation "[ /\ P1 , P2 , P3 & P4 ]" (at level 0, format
+  "'[hv' [ /\ '[' P1 , '/' P2 , '/' P3 ']' '/ ' & P4 ] ']'").
+Reserved Notation "[ /\ P1 , P2 , P3 , P4 & P5 ]" (at level 0, format
+  "'[hv' [ /\ '[' P1 , '/' P2 , '/' P3 , '/' P4 ']' '/ ' & P5 ] ']'").
+ +
+Reserved Notation "[ \/ P1 | P2 ]" (at level 0).
+Reserved Notation "[ \/ P1 , P2 | P3 ]" (at level 0, format
+  "'[hv' [ \/ '[' P1 , '/' P2 ']' '/ ' | P3 ] ']'").
+Reserved Notation "[ \/ P1 , P2 , P3 | P4 ]" (at level 0, format
+  "'[hv' [ \/ '[' P1 , '/' P2 , '/' P3 ']' '/ ' | P4 ] ']'").
+ +
+Reserved Notation "[ && b1 & c ]" (at level 0).
+Reserved Notation "[ && b1 , b2 , .. , bn & c ]" (at level 0, format
+  "'[hv' [ && '[' b1 , '/' b2 , '/' .. , '/' bn ']' '/ ' & c ] ']'").
+ +
+Reserved Notation "[ || b1 | c ]" (at level 0).
+Reserved Notation "[ || b1 , b2 , .. , bn | c ]" (at level 0, format
+  "'[hv' [ || '[' b1 , '/' b2 , '/' .. , '/' bn ']' '/ ' | c ] ']'").
+ +
+Reserved Notation "[ ==> b1 => c ]" (at level 0).
+Reserved Notation "[ ==> b1 , b2 , .. , bn => c ]" (at level 0, format
+  "'[hv' [ ==> '[' b1 , '/' b2 , '/' .. , '/' bn ']' '/' => c ] ']'").
+ +
+
+ +
+ Shorter delimiter +
+
+Delimit Scope bool_scope with B.
+Open Scope bool_scope.
+ +
+
+ +
+ An alternative to xorb that behaves somewhat better wrt simplification. +
+
+Definition addb b := if b then negb else id.
+ +
+
+ +
+ Notation for && and || is declared in Init.Datatypes. +
+
+Notation "~~ b" := (negb b) : bool_scope.
+Notation "b ==> c" := (implb b c) : bool_scope.
+Notation "b1 (+) b2" := (addb b1 b2) : bool_scope.
+ +
+
+ +
+ Constant is_true b := b = true is defined in Init.Datatypes. +
+
+Coercion is_true : bool >-> Sortclass. +
+Lemma prop_congr : forall b b' : bool, b = b' -> b = b' :> Prop.
+ +
+Ltac prop_congr := apply: prop_congr.
+ +
+
+ +
+ Lemmas for trivial. +
+
+Lemma is_true_true : true.
+Lemma not_false_is_true : ~ false.
+Lemma is_true_locked_true : locked true.
+#[global]
+Hint Resolve is_true_true not_false_is_true is_true_locked_true : core.
+ +
+
+ +
+ Shorter names. +
+
+Definition isT := is_true_true.
+Definition notF := not_false_is_true.
+ +
+
+ +
+ Negation lemmas. +
+ + +
+ + We generally take NEGATION as the standard form of a false condition: + negative boolean hypotheses should be of the form ~~ b, rather than ~ b or + b = false, as much as possible. +
+
+ +
+Lemma negbT b : b = false -> ~~ b.
+Lemma negbTE b : ~~ b -> b = false.
+Lemma negbF b : (b : bool) -> ~~ b = false.
+Lemma negbFE b : ~~ b = false -> b.
+Lemma negbK : involutive negb.
+Lemma negbNE b : ~~ ~~ b -> b.
+ +
+Lemma negb_inj : injective negb.
+Lemma negbLR b c : b = ~~ c -> ~~ b = c.
+Lemma negbRL b c : ~~ b = c -> b = ~~ c.
+ +
+Lemma contra (c b : bool) : (c -> b) -> ~~ b -> ~~ c.
+ Definition contraNN := contra.
+ +
+Lemma contraL (c b : bool) : (c -> ~~ b) -> b -> ~~ c.
+ Definition contraTN := contraL.
+ +
+Lemma contraR (c b : bool) : (~~ c -> b) -> ~~ b -> c.
+ Definition contraNT := contraR.
+ +
+Lemma contraLR (c b : bool) : (~~ c -> ~~ b) -> b -> c.
+ Definition contraTT := contraLR.
+ +
+Lemma contraT b : (~~ b -> false) -> b.
+ +
+Lemma wlog_neg b : (~~ b -> b) -> b.
+ +
+Lemma contraFT (c b : bool) : (~~ c -> b) -> b = false -> c.
+ +
+Lemma contraFN (c b : bool) : (c -> b) -> b = false -> ~~ c.
+ +
+Lemma contraTF (c b : bool) : (c -> ~~ b) -> b -> c = false.
+ +
+Lemma contraNF (c b : bool) : (c -> b) -> ~~ b -> c = false.
+ +
+Lemma contraFF (c b : bool) : (c -> b) -> b = false -> c = false.
+ +
+Lemma contra_not (P Q : Prop) : (Q -> P) -> (~ P -> ~ Q).
+ +
+Lemma contraPnot (P Q : Prop) : (Q -> ~ P) -> (P -> ~ Q).
+ +
+Lemma contraTnot (b : bool) (P : Prop) : (P -> ~~ b) -> (b -> ~ P).
+ +
+Lemma contraNnot (P : Prop) (b : bool) : (P -> b) -> (~~ b -> ~ P).
+ +
+Lemma contraPT (P : Prop) (b : bool) : (~~ b -> ~ P) -> P -> b.
+ +
+Lemma contra_notT (P : Prop) (b : bool) : (~~ b -> P) -> ~ P -> b.
+ +
+Lemma contra_notN (P : Prop) (b : bool) : (b -> P) -> ~ P -> ~~ b.
+ +
+Lemma contraPN (P : Prop) (b : bool) : (b -> ~ P) -> (P -> ~~ b).
+ +
+Lemma contraFnot (P : Prop) (b : bool) : (P -> b) -> b = false -> ~ P.
+ +
+Lemma contraPF (P : Prop) (b : bool) : (b -> ~ P) -> P -> b = false.
+ +
+Lemma contra_notF (P : Prop) (b : bool) : (b -> P) -> ~ P -> b = false.
+ +
+
+ +
+ Coercion of sum-style datatypes into bool, which makes it possible + to use ssr's boolean if rather than Rocq's "generic" if. +
+
+ +
+Coercion isSome T (u : option T) := if u is Some _ then true else false.
+ +
+Coercion is_inl A B (u : A + B) := if u is inl _ then true else false.
+ +
+Coercion is_left A B (u : {A} + {B}) := if u is left _ then true else false.
+ +
+Coercion is_inleft A B (u : A + {B}) := if u is inleft _ then true else false.
+ +
+ +
+Definition decidable P := {P} + {~ P}.
+ +
+
+ +
+ Lemmas for ifs with large conditions, which allow reasoning about the + condition without repeating it inside the proof (the latter IS + preferable when the condition is short). + Usage : + if the goal contains (if cond then ...) = ... + case: ifP => Hcond. + generates two subgoal, with the assumption Hcond : cond = true/false + Rewrite if_same eliminates redundant ifs + Rewrite (fun_if f) moves a function f inside an if + Rewrite if_arg moves an argument inside a function-valued if +
+
+ +
+Section BoolIf.
+ +
+Variables (A B : Type) (x : A) (f : A -> B) (b : bool) (vT vF : A).
+ +
+Variant if_spec (not_b : Prop) : bool -> A -> Set :=
+  | IfSpecTrue of b : if_spec not_b true vT
+  | IfSpecFalse of not_b : if_spec not_b false vF.
+ +
+Lemma ifP : if_spec (b = false) b (if b then vT else vF).
+ +
+Lemma ifPn : if_spec (~~ b) b (if b then vT else vF).
+ +
+Lemma ifT : b -> (if b then vT else vF) = vT.
+Lemma ifF : b = false -> (if b then vT else vF) = vF.
+Lemma ifN : ~~ b -> (if b then vT else vF) = vF.
+ +
+Lemma if_same : (if b then vT else vT) = vT.
+ +
+Lemma if_neg : (if ~~ b then vT else vF) = if b then vF else vT.
+ +
+Lemma fun_if : f (if b then vT else vF) = if b then f vT else f vF.
+ +
+Lemma if_arg (fT fF : A -> B) :
+  (if b then fT else fF) x = if b then fT x else fF x.
+ +
+
+ +
+ Turning a boolean "if" form into an application. +
+
+Definition if_expr := if b then vT else vF.
+Lemma ifE : (if b then vT else vF) = if_expr.
+ +
+End BoolIf.
+ +
+
+ +
+ Core (internal) reflection lemmas, used for the three kinds of views. +
+
+ +
+Section ReflectCore.
+ +
+Variables (P Q : Prop) (b c : bool).
+ +
+Hypothesis Hb : reflect P b.
+ +
+Lemma introNTF : (if c then ~ P else P) -> ~~ b = c.
+ +
+Lemma introTF : (if c then P else ~ P) -> b = c.
+ +
+Lemma elimNTF : ~~ b = c -> if c then ~ P else P.
+ +
+Lemma elimTF : b = c -> if c then P else ~ P.
+ +
+Lemma equivPif : (Q -> P) -> (P -> Q) -> if b then Q else ~ Q.
+ +
+Lemma xorPif : Q \/ P -> ~ (Q /\ P) -> if b then ~ Q else Q.
+ +
+End ReflectCore.
+ +
+
+ +
+ Internal negated reflection lemmas +
+
+Section ReflectNegCore.
+ +
+Variables (P Q : Prop) (b c : bool).
+Hypothesis Hb : reflect P (~~ b).
+ +
+Lemma introTFn : (if c then ~ P else P) -> b = c.
+ +
+Lemma elimTFn : b = c -> if c then ~ P else P.
+ +
+Lemma equivPifn : (Q -> P) -> (P -> Q) -> if b then ~ Q else Q.
+ +
+Lemma xorPifn : Q \/ P -> ~ (Q /\ P) -> if b then Q else ~ Q.
+ +
+End ReflectNegCore.
+ +
+
+ +
+ User-oriented reflection lemmas +
+
+Section Reflect.
+ +
+Variables (P Q : Prop) (b b' c : bool).
+Hypotheses (Pb : reflect P b) (Pb' : reflect P (~~ b')).
+ +
+Lemma introT : P -> b.
+Lemma introF : ~ P -> b = false.
+Lemma introN : ~ P -> ~~ b.
+Lemma introNf : P -> ~~ b = false.
+Lemma introTn : ~ P -> b'.
+Lemma introFn : P -> b' = false.
+ +
+Lemma elimT : b -> P.
+Lemma elimF : b = false -> ~ P.
+Lemma elimN : ~~ b -> ~P.
+Lemma elimNf : ~~ b = false -> P.
+Lemma elimTn : b' -> ~ P.
+Lemma elimFn : b' = false -> P.
+ +
+Lemma introP : (b -> Q) -> (~~ b -> ~ Q) -> reflect Q b.
+ +
+Lemma iffP : (P -> Q) -> (Q -> P) -> reflect Q b.
+ +
+Lemma equivP : (P <-> Q) -> reflect Q b.
+ +
+Lemma sumboolP (decQ : decidable Q) : reflect Q decQ.
+ +
+Lemma appP : reflect Q b -> P -> Q.
+ +
+Lemma sameP : reflect P c -> b = c.
+ +
+Lemma decPcases : if b then P else ~ P.
+ +
+Definition decP : decidable P.
+ +
+Lemma rwP : P <-> b.
+ +
+Lemma rwP2 : reflect Q b -> (P <-> Q).
+ +
+
+ +
+ Predicate family to reflect excluded middle in bool. +
+
+Variant alt_spec : bool -> Type :=
+  | AltTrue of P : alt_spec true
+  | AltFalse of ~~ b : alt_spec false.
+ +
+Lemma altP : alt_spec b.
+ +
+Lemma eqbLR (b1 b2 : bool) : b1 = b2 -> b1 -> b2.
+ +
+Lemma eqbRL (b1 b2 : bool) : b1 = b2 -> b2 -> b1.
+ +
+End Reflect.
+ +
+ +
+ +
+ +
+
+ +
+ Allow the direct application of a reflection lemma to a boolean assertion. +
+
+Coercion elimT : reflect >-> Funclass.
+ +
+#[universes(template)]
+Variant implies P Q := Implies of P -> Q.
+Lemma impliesP P Q : implies P Q -> P -> Q.
+Lemma impliesPn (P Q : Prop) : implies P Q -> ~ Q -> ~ P.
+ Coercion impliesP : implies >-> Funclass.
+ +
+
+ +
+ Impredicative or, which can emulate a classical not-implies. +
+
+Definition unless condition property : Prop :=
+ forall goal : Prop, (condition -> goal) -> (property -> goal) -> goal.
+ +
+Notation "\unless C , P" := (unless C P) : type_scope.
+ +
+Lemma unlessL C P : implies C (\unless C, P).
+ +
+Lemma unlessR C P : implies P (\unless C, P).
+ +
+Lemma unless_sym C P : implies (\unless C, P) (\unless P, C).
+ +
+Lemma unlessP (C P : Prop) : (\unless C, P) <-> C \/ P.
+ +
+Lemma bind_unless C P {Q} : implies (\unless C, P) (\unless (\unless C, Q), P).
+ +
+Lemma unless_contra b C : implies (~~ b -> C) (\unless C, b).
+ +
+
+ +
+ Classical reasoning becomes directly accessible for any bool subgoal. + Note that we cannot use "unless" here for lack of universe polymorphism. +
+
+Definition classically P : Prop := forall b : bool, (P -> b) -> b.
+ +
+Lemma classicP (P : Prop) : classically P <-> ~ ~ P.
+ +
+Lemma classicW P : P -> classically P.
+ +
+Lemma classic_bind P Q : (P -> classically Q) -> classically P -> classically Q.
+ +
+Lemma classic_EM P : classically (decidable P).
+ +
+Lemma classic_pick T P : classically ({x : T | P x} + (forall x, ~ P x)).
+ +
+Lemma classic_imply P Q : (P -> classically Q) -> classically (P -> Q).
+ +
+Lemma classic_sigW T (P : T -> Prop) :
+  classically (exists x, P x) <-> classically ({x | P x}).
+ +
+Lemma classic_ex T (P : T -> Prop) :
+  ~ (forall x, ~ P x) -> classically (exists x, P x).
+ +
+
+ +
+ List notations for wider connectives; the Prop connectives have a fixed + width so as to avoid iterated destruction (we go up to width 5 for /\, and + width 4 for or). The bool connectives have arbitrary widths, but denote + expressions that associate to the RIGHT. This is consistent with the right + associativity of list expressions and thus more convenient in most proofs. +
+
+ +
+Inductive and3 (P1 P2 P3 : Prop) : Prop := And3 of P1 & P2 & P3.
+ +
+Inductive and4 (P1 P2 P3 P4 : Prop) : Prop := And4 of P1 & P2 & P3 & P4.
+ +
+Inductive and5 (P1 P2 P3 P4 P5 : Prop) : Prop :=
+  And5 of P1 & P2 & P3 & P4 & P5.
+ +
+Inductive or3 (P1 P2 P3 : Prop) : Prop := Or31 of P1 | Or32 of P2 | Or33 of P3.
+ +
+Inductive or4 (P1 P2 P3 P4 : Prop) : Prop :=
+  Or41 of P1 | Or42 of P2 | Or43 of P3 | Or44 of P4.
+ +
+Notation "[ /\ P1 & P2 ]" := (and P1 P2) (only parsing) : type_scope.
+Notation "[ /\ P1 , P2 & P3 ]" := (and3 P1 P2 P3) : type_scope.
+Notation "[ /\ P1 , P2 , P3 & P4 ]" := (and4 P1 P2 P3 P4) : type_scope.
+Notation "[ /\ P1 , P2 , P3 , P4 & P5 ]" := (and5 P1 P2 P3 P4 P5) : type_scope.
+ +
+Notation "[ \/ P1 | P2 ]" := (or P1 P2) (only parsing) : type_scope.
+Notation "[ \/ P1 , P2 | P3 ]" := (or3 P1 P2 P3) : type_scope.
+Notation "[ \/ P1 , P2 , P3 | P4 ]" := (or4 P1 P2 P3 P4) : type_scope.
+ +
+Notation "[ && b1 & c ]" := (b1 && c) (only parsing) : bool_scope.
+Notation "[ && b1 , b2 , .. , bn & c ]" := (b1 && (b2 && .. (bn && c) .. ))
+  : bool_scope.
+ +
+Notation "[ || b1 | c ]" := (b1 || c) (only parsing) : bool_scope.
+Notation "[ || b1 , b2 , .. , bn | c ]" := (b1 || (b2 || .. (bn || c) .. ))
+  : bool_scope.
+ +
+Notation "[ ==> b1 , b2 , .. , bn => c ]" :=
+   (b1 ==> (b2 ==> .. (bn ==> c) .. )) : bool_scope.
+Notation "[ ==> b1 => c ]" := (b1 ==> c) (only parsing) : bool_scope.
+ +
+Section AllAnd.
+ +
+Variables (T : Type) (P1 P2 P3 P4 P5 : T -> Prop).
+Local Notation a P := (forall x, P x).
+ +
+Lemma all_and2 : implies (forall x, [/\ P1 x & P2 x]) [/\ a P1 & a P2].
+ +
+Lemma all_and3 : implies (forall x, [/\ P1 x, P2 x & P3 x])
+                         [/\ a P1, a P2 & a P3].
+ +
+Lemma all_and4 : implies (forall x, [/\ P1 x, P2 x, P3 x & P4 x])
+                         [/\ a P1, a P2, a P3 & a P4].
+ +
+Lemma all_and5 : implies (forall x, [/\ P1 x, P2 x, P3 x, P4 x & P5 x])
+                         [/\ a P1, a P2, a P3, a P4 & a P5].
+ +
+End AllAnd.
+ +
+Arguments all_and2 {T P1 P2}.
+Arguments all_and3 {T P1 P2 P3}.
+Arguments all_and4 {T P1 P2 P3 P4}.
+Arguments all_and5 {T P1 P2 P3 P4 P5}.
+ +
+Lemma pair_andP P Q : P /\ Q <-> P * Q.
+ +
+Section ReflectConnectives.
+ +
+Variable b1 b2 b3 b4 b5 : bool.
+ +
+Lemma idP : reflect b1 b1.
+ +
+Lemma boolP : alt_spec b1 b1 b1.
+ +
+Lemma idPn : reflect (~~ b1) (~~ b1).
+ +
+Lemma negP : reflect (~ b1) (~~ b1).
+ +
+Lemma negPn : reflect b1 (~~ ~~ b1).
+ +
+Lemma negPf : reflect (b1 = false) (~~ b1).
+ +
+Lemma andP : reflect (b1 /\ b2) (b1 && b2).
+ +
+Lemma and3P : reflect [/\ b1, b2 & b3] [&& b1, b2 & b3].
+ +
+Lemma and4P : reflect [/\ b1, b2, b3 & b4] [&& b1, b2, b3 & b4].
+ +
+Lemma and5P : reflect [/\ b1, b2, b3, b4 & b5] [&& b1, b2, b3, b4 & b5].
+ +
+Lemma orP : reflect (b1 \/ b2) (b1 || b2).
+ +
+Lemma or3P : reflect [\/ b1, b2 | b3] [|| b1, b2 | b3].
+ +
+Lemma or4P : reflect [\/ b1, b2, b3 | b4] [|| b1, b2, b3 | b4].
+ +
+Lemma nandP : reflect (~~ b1 \/ ~~ b2) (~~ (b1 && b2)).
+ +
+Lemma norP : reflect (~~ b1 /\ ~~ b2) (~~ (b1 || b2)).
+ +
+Lemma implyP : reflect (b1 -> b2) (b1 ==> b2).
+ +
+End ReflectConnectives.
+ +
+Arguments idP {b1}.
+Arguments idPn {b1}.
+Arguments negP {b1}.
+Arguments negPn {b1}.
+Arguments negPf {b1}.
+Arguments andP {b1 b2}.
+Arguments and3P {b1 b2 b3}.
+Arguments and4P {b1 b2 b3 b4}.
+Arguments and5P {b1 b2 b3 b4 b5}.
+Arguments orP {b1 b2}.
+Arguments or3P {b1 b2 b3}.
+Arguments or4P {b1 b2 b3 b4}.
+Arguments nandP {b1 b2}.
+Arguments norP {b1 b2}.
+Arguments implyP {b1 b2}.
+ +
+Section ReflectCombinators.
+ +
+Variables (P Q : Prop) (p q : bool).
+ +
+Hypothesis rP : reflect P p.
+Hypothesis rQ : reflect Q q.
+ +
+Lemma negPP : reflect (~ P) (~~ p).
+ +
+Lemma andPP : reflect (P /\ Q) (p && q).
+ +
+Lemma orPP : reflect (P \/ Q) (p || q).
+ +
+Lemma implyPP : reflect (P -> Q) (p ==> q).
+ +
+End ReflectCombinators.
+Arguments negPP {P p}.
+Arguments andPP {P Q p q}.
+Arguments orPP {P Q p q}.
+Arguments implyPP {P Q p q}.
+ +
+
+ +
+ Shorter, more systematic names for the boolean connectives laws. +
+
+ +
+Lemma andTb : left_id true andb.
+Lemma andFb : left_zero false andb.
+Lemma andbT : right_id true andb.
+Lemma andbF : right_zero false andb.
+Lemma andbb : idempotent andb.
+Lemma andbC : commutative andb.
+Lemma andbA : associative andb.
+Lemma andbCA : left_commutative andb.
+Lemma andbAC : right_commutative andb.
+Lemma andbACA : interchange andb andb.
+ +
+Lemma orTb : forall b, true || b.
+Lemma orFb : left_id false orb.
+Lemma orbT : forall b, b || true.
+Lemma orbF : right_id false orb.
+Lemma orbb : idempotent orb.
+Lemma orbC : commutative orb.
+Lemma orbA : associative orb.
+Lemma orbCA : left_commutative orb.
+Lemma orbAC : right_commutative orb.
+Lemma orbACA : interchange orb orb.
+ +
+Lemma andbN b : b && ~~ b = false.
+Lemma andNb b : ~~ b && b = false.
+Lemma orbN b : b || ~~ b = true.
+Lemma orNb b : ~~ b || b = true.
+ +
+Lemma andb_orl : left_distributive andb orb.
+Lemma andb_orr : right_distributive andb orb.
+Lemma orb_andl : left_distributive orb andb.
+Lemma orb_andr : right_distributive orb andb.
+ +
+Lemma andb_idl (a b : bool) : (b -> a) -> a && b = b.
+ Lemma andb_idr (a b : bool) : (a -> b) -> a && b = a.
+ Lemma andb_id2l (a b c : bool) : (a -> b = c) -> a && b = a && c.
+ Lemma andb_id2r (a b c : bool) : (b -> a = c) -> a && b = c && b.
+ +
+Lemma orb_idl (a b : bool) : (a -> b) -> a || b = b.
+ Lemma orb_idr (a b : bool) : (b -> a) -> a || b = a.
+ Lemma orb_id2l (a b c : bool) : (~~ a -> b = c) -> a || b = a || c.
+ Lemma orb_id2r (a b c : bool) : (~~ b -> a = c) -> a || b = c || b.
+ +
+Lemma negb_and (a b : bool) : ~~ (a && b) = ~~ a || ~~ b.
+ +
+Lemma negb_or (a b : bool) : ~~ (a || b) = ~~ a && ~~ b.
+ +
+
+ +
+ Pseudo-cancellation -- i.e, absorption +
+
+ +
+Lemma andbK a b : a && b || a = a.
+Lemma andKb a b : a || b && a = a.
+Lemma orbK a b : (a || b) && a = a.
+Lemma orKb a b : a && (b || a) = a.
+ +
+
+ +
+ Imply +
+
+ +
+Lemma implybT b : b ==> true.
+Lemma implybF b : (b ==> false) = ~~ b.
+Lemma implyFb b : false ==> b.
+Lemma implyTb b : (true ==> b) = b.
+Lemma implybb b : b ==> b.
+ +
+Lemma negb_imply a b : ~~ (a ==> b) = a && ~~ b.
+ +
+Lemma implybE a b : (a ==> b) = ~~ a || b.
+ +
+Lemma implyNb a b : (~~ a ==> b) = a || b.
+ +
+Lemma implybN a b : (a ==> ~~ b) = (b ==> ~~ a).
+ +
+Lemma implybNN a b : (~~ a ==> ~~ b) = b ==> a.
+ +
+Lemma implyb_idl (a b : bool) : (~~ a -> b) -> (a ==> b) = b.
+ Lemma implyb_idr (a b : bool) : (b -> ~~ a) -> (a ==> b) = ~~ a.
+ Lemma implyb_id2l (a b c : bool) : (a -> b = c) -> (a ==> b) = (a ==> c).
+ +
+
+ +
+ Addition (xor) +
+
+ +
+Lemma addFb : left_id false addb.
+Lemma addbF : right_id false addb.
+Lemma addbb : self_inverse false addb.
+Lemma addbC : commutative addb.
+Lemma addbA : associative addb.
+Lemma addbCA : left_commutative addb.
+Lemma addbAC : right_commutative addb.
+Lemma addbACA : interchange addb addb.
+Lemma andb_addl : left_distributive andb addb.
+Lemma andb_addr : right_distributive andb addb.
+Lemma addKb : left_loop id addb.
+Lemma addbK : right_loop id addb.
+Lemma addIb : left_injective addb.
+Lemma addbI : right_injective addb.
+ +
+Lemma addTb b : true (+) b = ~~ b.
+Lemma addbT b : b (+) true = ~~ b.
+ +
+Lemma addbN a b : a (+) ~~ b = ~~ (a (+) b).
+ Lemma addNb a b : ~~ a (+) b = ~~ (a (+) b).
+ +
+Lemma addbP a b : reflect (~~ a = b) (a (+) b).
+ Arguments addbP {a b}.
+ +
+
+ +
+ Resolution tactic for blindly weeding out common terms from boolean + equalities. When faced with a goal of the form (andb/orb/addb b1 b2) = b3 + they will try to locate b1 in b3 and remove it. This can fail! +
+
+ +
+Ltac bool_congr :=
+  match goal with
+  | |- (?X1 && ?X2 = ?X3) => first
+  [ symmetry; rewrite -1?(andbC X1) -?(andbCA X1); congr 1 (andb X1); symmetry
+  | case: (X1); [ rewrite ?andTb ?andbT // | by rewrite ?andbF /= ] ]
+  | |- (?X1 || ?X2 = ?X3) => first
+  [ symmetry; rewrite -1?(orbC X1) -?(orbCA X1); congr 1 (orb X1); symmetry
+  | case: (X1); [ by rewrite ?orbT //= | rewrite ?orFb ?orbF ] ]
+  | |- (?X1 (+) ?X2 = ?X3) =>
+    symmetry; rewrite -1?(addbC X1) -?(addbCA X1); congr 1 (addb X1); symmetry
+  | |- (~~ ?X1 = ?X2) => congr 1 negb
+  end.
+ +
+
+ +
+ Predicates, i.e., packaged functions to bool. +
    +
  • pred T, the basic type for predicates over a type T, is simply an alias + +
    • +
+ for T -> bool. + We actually distinguish two kinds of predicates, which we call applicative + and collective, based on the syntax used to test them at some x in T: +
    +
  • For an applicative predicate P, one uses prefix syntax: + P x + Also, most operations on applicative predicates use prefix syntax as + well (e.g., predI P Q). + +
    • +
  • For a collective predicate A, one uses infix syntax: + x \in A + and all operations on collective predicates use infix syntax as well + (e.g., [predI A & B]). + +
    • +
+ There are only two kinds of applicative predicates: +
    +
  • pred T, the alias for T -> bool mentioned above + +
    • +
  • simpl_pred T, an alias for simpl_fun T bool with a coercion to pred T + that auto-simplifies on application (see ssrfun). + +
    • +
+ On the other hand, the set of collective predicate types is open-ended via +
    +
  • predType T, a Structure that can be used to put Canonical collective + predicate interpretation on other types, such as lists, tuples, + finite sets, etc. + +
    • +
+ Indeed, we define such interpretations for applicative predicate types, + which can therefore also be used with the infix syntax, e.g., + x \in predI P Q + Moreover these infix forms are convertible to their prefix counterpart + (e.g., predI P Q x which in turn simplifies to P x && Q x). The converse + is not true, however; collective predicate types cannot, in general, be + used applicatively, because of restrictions on implicit coercions. + However, we do define an explicit generic coercion +
    +
  • mem : forall (pT : predType), pT -> mem_pred T + where mem_pred T is a variant of simpl_pred T that preserves the infix + syntax, i.e., mem A x auto-simplifies to x \in A. + +
    • +
+ Indeed, the infix "collective" operators are notation for a prefix + operator with arguments of type mem_pred T or pred T, applied to coerced + collective predicates, e.g., + Notation "x \in A" := (in_mem x (mem A)). + This prevents the variability in the predicate type from interfering with + the application of generic lemmas. Moreover this also makes it much easier + to define generic lemmas, because the simplest type -- pred T -- can be + used as the type of generic collective predicates, provided one takes care + not to use it applicatively; this avoids the burden of having to declare a + different predicate type for each predicate parameter of each section or + lemma. + In detail, we ensure that the head normal form of mem A is always of the + eta-long MemPred (fun x => pA x) form, where pA is the pred interpretation of + A following its predType pT, i.e., the expansion of topred A. For a pred T + evar ?P, (mem ?P) converts MemPred (fun x => ?P x), whose argument is a Miller + pattern and therefore always unify: unifying (mem A) with (mem ?P) always + yields ?P = pA, because the rigid constant MemPred aligns the unification. + Furthermore, we ensure pA is always either A or toP .... A where toP ... is + the expansion of @topred T pT, and toP is declared as a Coercion, so pA will + display as A in either case, and the instances of @mem T (predPredType T) pA + appearing in the premises or right-hand side of a generic lemma parameterized + by ?P will be indistinguishable from @mem T pT A. + Users should take care not to inadvertently "strip" (mem A) down to the + coerced A, since this will expose the internal toP coercion: Rocq could then + display terms A x that cannot be typed as such. The topredE lemma can be used + to restore the x \in A syntax in this case. While -topredE can conversely be + used to change x \in P into P x for an applicative P, it is safer to use the + inE, unfold_in or and memE lemmas instead, as they do not run the risk of + exposing internal coercions. As a consequence it is better to explicitly + cast a generic applicative predicate to simpl_pred using the SimplPred + constructor when it is used as a collective predicate (see, e.g., + Lemma eq_big in bigop). + We also sometimes "instantiate" the predType structure by defining a + coercion to the sort of the predPredType structure, conveniently denoted + {pred T}. This works better for types such as {set T} that have subtypes that + coerce to them, since the same coercion will be inserted by the application + of mem, or of any lemma that expects a generic collective predicates with + type {pred T} := pred_sort (predPredType T) = pred T; thus {pred T} should be + the preferred type for generic collective predicate parameters. + This device also lets us turn any Type aT : predArgType into the total + predicate over that type, i.e., fun _: aT => true. This allows us to write, + e.g., #|'I_n| for the cardinal of the (finite) type of integers less than n. + +
+ + Boolean predicates. +
+
+ +
+Definition pred T := T -> bool.
+Identity Coercion fun_of_pred : pred >-> Funclass.
+ +
+Definition subpred T (p1 p2 : pred T) := forall x : T, p1 x -> p2 x.
+ +
+ +
+Notation xpred0 := (fun=> false).
+Notation xpredT := (fun=> true).
+Notation xpredI := (fun (p1 p2 : pred _) x => p1 x && p2 x).
+Notation xpredU := (fun (p1 p2 : pred _) x => p1 x || p2 x).
+Notation xpredC := (fun (p : pred _) x => ~~ p x).
+Notation xpredD := (fun (p1 p2 : pred _) x => ~~ p2 x && p1 x).
+Notation xpreim := (fun f (p : pred _) x => p (f x)).
+ +
+
+ +
+The packed class interface for pred-like types. +
+
+ +
+Structure predType T :=
+   PredType {pred_sort :> Type; topred : pred_sort -> pred T}.
+ +
+Definition clone_pred T U :=
+  fun pT & @pred_sort T pT -> U =>
+  fun toP (pT' := @PredType T U toP) & phant_id pT' pT => pT'.
+Notation "[ 'predType' 'of' T ]" := (@clone_pred _ T _ id _ id) : form_scope.
+ +
+Canonical predPredType T := PredType (@id (pred T)).
+Canonical boolfunPredType T := PredType (@id (T -> bool)).
+ +
+
+ +
+The type of abstract collective predicates. + While {pred T} is convertible to pred T, it presents the pred_sort coercion + class, which crucially does not coerce to Funclass. Term whose type P coerces + to {pred T} cannot be applied to arguments, but they can be used as if P + had a canonical predType instance, as the coercion will be inserted if the + unification P =~= pred_sort ?pT fails, changing the problem into the trivial + {pred T} =~= pred_sort ?pT (solution ?pT := predPredType P). + Additional benefits of this approach are that any type coercing to P will + also inherit this behaviour, and that the coercion will be apparent in the + elaborated expression. The latter may be important if the coercion is also + a canonical structure projector - see mathcomp/fingroup/fingroup.v. The + main drawback of implementing predType by coercion in this way is that the + type of the value must be known when the unification constraint is imposed: + if we only register the constraint and then later discover later that the + expression had type P it will be too late to insert a coercion, whereas a + canonical instance of predType for P would have solved the deferred constraint. + Finally, definitions, lemmas and sections should use type {pred T} for + their generic collective type parameters, as this will make it possible to + apply such definitions and lemmas directly to values of types that implement + predType by coercion to {pred T} (values of types that implement predType + without coercing to {pred T} will have to be coerced explicitly using topred). + +
+
+Notation "{ 'pred' T }" := (pred_sort (predPredType T)) : type_scope.
+ +
+
+ +
+The type of self-simplifying collective predicates. +
+
+Definition simpl_pred T := simpl_fun T bool.
+Definition SimplPred {T} (p : pred T) : simpl_pred T := SimplFun p.
+ +
+
+ +
+Some simpl_pred constructors. +
+
+ +
+Definition pred0 {T} := @SimplPred T xpred0.
+Definition predT {T} := @SimplPred T xpredT.
+Definition predI {T} (p1 p2 : pred T) := SimplPred (xpredI p1 p2).
+Definition predU {T} (p1 p2 : pred T) := SimplPred (xpredU p1 p2).
+Definition predC {T} (p : pred T) := SimplPred (xpredC p).
+Definition predD {T} (p1 p2 : pred T) := SimplPred (xpredD p1 p2).
+Definition preim {aT rT} (f : aT -> rT) (d : pred rT) := SimplPred (xpreim f d).
+ +
+Notation "[ 'pred' : T | E ]" := (SimplPred (fun _ : T => E%B)) :
+  function_scope.
+Notation "[ 'pred' x | E ]" := (SimplPred (fun x => E%B)) : function_scope.
+Notation "[ 'pred' x | E1 & E2 ]" := [pred x | E1 && E2 ] : function_scope.
+Notation "[ 'pred' x : T | E ]" :=
+  (SimplPred (fun x : T => E%B)) (only parsing) : function_scope.
+Notation "[ 'pred' x : T | E1 & E2 ]" :=
+  [pred x : T | E1 && E2 ] (only parsing) : function_scope.
+ +
+
+ +
+Coercions for simpl_pred. + As simpl_pred T values are used both applicatively and collectively we + need simpl_pred to coerce to both pred T and {pred T}. However it is + undesirable to have two distinct constants for what are essentially identical + coercion functions, as this confuses the SSReflect keyed matching algorithm. + While the Rocq Coercion declarations appear to disallow such Coercion aliasing, + it is possible to work around this limitation with a combination of modules + and functors, which we do below. + In addition we also give a predType instance for simpl_pred, which will + be preferred to the {pred T} coercion to solve simpl_pred T =~= pred_sort ?pT + constraints; note however that the pred_of_simpl coercion will be used + when a simpl_pred T is passed as a {pred T}, since the simplPredType T + structure for simpl_pred T is not convertible to predPredType T. +
+
+ +
+Module PredOfSimpl.
+Definition coerce T (sp : simpl_pred T) : pred T := fun_of_simpl sp.
+End PredOfSimpl.
+Notation pred_of_simpl := PredOfSimpl.coerce.
+Coercion pred_of_simpl : simpl_pred >-> pred.
+Canonical simplPredType T := PredType (@pred_of_simpl T).
+ +
+Module Type PredSortOfSimplSignature.
+Parameter coerce : forall T, simpl_pred T -> {pred T}.
+End PredSortOfSimplSignature.
+Module DeclarePredSortOfSimpl (PredSortOfSimpl : PredSortOfSimplSignature).
+Coercion PredSortOfSimpl.coerce : simpl_pred >-> pred_sort.
+End DeclarePredSortOfSimpl.
+Module Export PredSortOfSimplCoercion := DeclarePredSortOfSimpl PredOfSimpl.
+ +
+
+ +
+Type to pred coercion. + This lets us use types of sort predArgType as a synonym for their universal + predicate. We define this predicate as a simpl_pred T rather than a pred T or + a {pred T} so that /= and inE reduce (T x) and x \in T to true, respectively. + Unfortunately, this can't be used for existing types like bool whose sort + is already fixed (at least, not without redefining bool, true, false and + all bool operations and lemmas); we provide syntax to recast a given type + in predArgType as a workaround. +
+
+Definition predArgType := Type.
+Bind Scope type_scope with predArgType.
+Identity Coercion sort_of_predArgType : predArgType >-> Sortclass.
+Coercion pred_of_argType (T : predArgType) : simpl_pred T := predT.
+Notation "{ : T }" := (T%type : predArgType) : type_scope.
+ +
+
+ +
+Boolean relations. + Simplifying relations follow the coding pattern of 2-argument simplifying + functions: the simplifying type constructor is applied to the last + argument. This design choice will let the in_simpl component of inE expand + membership in simpl_rel as well. We provide an explicit coercion to rel T + to avoid eta-expansion during coercion; this coercion self-simplifies so it + should be invisible. + +
+
+ +
+Definition rel T := T -> pred T.
+Identity Coercion fun_of_rel : rel >-> Funclass.
+ +
+Definition subrel T (r1 r2 : rel T) := forall x y : T, r1 x y -> r2 x y.
+ +
+Definition simpl_rel T := T -> simpl_pred T.
+ +
+Coercion rel_of_simpl T (sr : simpl_rel T) : rel T := fun x : T => sr x.
+Arguments rel_of_simpl {T} sr x /.
+ +
+Notation xrelU := (fun (r1 r2 : rel _) x y => r1 x y || r2 x y).
+Notation xrelpre := (fun f (r : rel _) x y => r (f x) (f y)).
+ +
+Definition SimplRel {T} (r : rel T) : simpl_rel T := fun x => SimplPred (r x).
+Definition relU {T} (r1 r2 : rel T) := SimplRel (xrelU r1 r2).
+Definition relpre {aT rT} (f : aT -> rT) (r : rel rT) := SimplRel (xrelpre f r).
+ +
+Notation "[ 'rel' x y | E ]" := (SimplRel (fun x y => E%B))
+  (only parsing) : function_scope.
+Notation "[ 'rel' x y : T | E ]" :=
+  (SimplRel (fun x y : T => E%B)) (only parsing) : function_scope.
+ +
+Lemma subrelUl T (r1 r2 : rel T) : subrel r1 (relU r1 r2).
+ +
+Lemma subrelUr T (r1 r2 : rel T) : subrel r2 (relU r1 r2).
+ +
+
+ +
+Variant of simpl_pred specialised to the membership operator. +
+
+ +
+Variant mem_pred T := Mem of pred T.
+ +
+
+ +
+ We mainly declare pred_of_mem as a coercion so that it is not displayed. + Similarly to pred_of_simpl, it will usually not be inserted by type + inference, as all mem_pred mp =~= pred_sort ?pT unification problems will + be solve by the memPredType instance below; pred_of_mem will however + be used if a mem_pred T is used as a {pred T}, which is desirable as it + will avoid a redundant mem in a collective, e.g., passing (mem A) to a lemma + exception a generic collective predicate p : {pred T} and premise x \in P + will display a subgoal x \in A rather than x \in mem A. + Conversely, pred_of_mem will not if it is used id (mem A) is used + applicatively or as a pred T; there the simpl_of_mem coercion defined below + will be used, resulting in a subgoal that displays as mem A x by simplifies + to x \in A. + +
+
+Coercion pred_of_mem {T} mp : {pred T} := let: Mem p := mp in [eta p].
+Canonical memPredType T := PredType (@pred_of_mem T).
+ +
+Definition in_mem {T} (x : T) mp := pred_of_mem mp x.
+Definition eq_mem {T} mp1 mp2 := forall x : T, in_mem x mp1 = in_mem x mp2.
+Definition sub_mem {T} mp1 mp2 := forall x : T, in_mem x mp1 -> in_mem x mp2.
+ +
+Arguments in_mem {T} x mp : simpl never.
+Global Typeclasses Opaque eq_mem sub_mem.
+ +
+
+ +
+The simpl_of_mem; pred_of_simpl path provides a new mem_pred >-> pred + coercion, but does not override the pred_of_mem : mem_pred >-> pred_sort + explicit coercion declaration above. + +
+
+Coercion simpl_of_mem {T} mp := SimplPred (fun x : T => in_mem x mp).
+ +
+Lemma sub_refl T (mp : mem_pred T) : sub_mem mp mp.
+Arguments sub_refl {T mp} [x] mp_x.
+ +
+
+ +
+ It is essential to interlock the production of the Mem constructor inside + the branch of the predType match, to ensure that unifying mem A with + Mem eta ?p sets ?p := toP A (or ?p := P if toP = id and A = eta P), + rather than topred pT A, had we put mem A := Mem (topred A). + +
+
+Definition mem T (pT : predType T) : pT -> mem_pred T :=
+  let: PredType toP := pT in fun A => Mem [eta toP A].
+Arguments mem {T pT} A : rename, simpl never.
+ +
+Notation "x \in A" := (in_mem x (mem A)) (only parsing) : bool_scope.
+Notation "x \in A" := (in_mem x (mem A)) (only printing) : bool_scope.
+Notation "x \notin A" := (~~ (x \in A)) : bool_scope.
+Notation "A =i B" := (eq_mem (mem A) (mem B)) : type_scope.
+Notation "{ 'subset' A <= B }" := (sub_mem (mem A) (mem B)) : type_scope.
+ +
+Notation "[ 'in' A ]" := (in_mem^~ (mem A))
+  (at level 0, format "[ 'in' A ]") : function_scope.
+ +
+Notation "[ 'mem' A ]" :=
+  (pred_of_simpl (simpl_of_mem (mem A))) (only parsing) : function_scope.
+ +
+Notation "[ 'predI' A & B ]" := (predI [in A] [in B]) : function_scope.
+Notation "[ 'predU' A & B ]" := (predU [in A] [in B]) : function_scope.
+Notation "[ 'predD' A & B ]" := (predD [in A] [in B]) : function_scope.
+Notation "[ 'predC' A ]" := (predC [in A]) : function_scope.
+Notation "[ 'preim' f 'of' A ]" := (preim f [in A]) : function_scope.
+ +
+Notation "[ 'pred' x 'in' A ]" := [pred x | x \in A] : function_scope.
+Notation "[ 'pred' x 'in' A | E ]" := [pred x | x \in A & E] : function_scope.
+Notation "[ 'pred' x 'in' A | E1 & E2 ]" :=
+  [pred x | x \in A & E1 && E2 ] : function_scope.
+ +
+Notation "[ 'rel' x y 'in' A & B | E ]" :=
+  [rel x y | (x \in A) && (y \in B) && E] : function_scope.
+Notation "[ 'rel' x y 'in' A & B ]" :=
+  [rel x y | (x \in A) && (y \in B)] : function_scope.
+Notation "[ 'rel' x y 'in' A | E ]" := [rel x y in A & A | E] : function_scope.
+Notation "[ 'rel' x y 'in' A ]" := [rel x y in A & A] : function_scope.
+ +
+
+ +
+Aliases of pred T that let us tag instances of simpl_pred as applicative + or collective, via bespoke coercions. This tagging will give control over + the simplification behaviour of inE and other rewriting lemmas below. + For this control to work it is crucial that collective_of_simpl not + be convertible to either applicative_of_simpl or pred_of_simpl. Indeed + they differ here by a commutative conversion (of the match and lambda). + +
+
+Definition applicative_pred T := pred T.
+Definition collective_pred T := pred T.
+Coercion applicative_pred_of_simpl T (sp : simpl_pred T) : applicative_pred T :=
+  fun_of_simpl sp.
+Coercion collective_pred_of_simpl T (sp : simpl_pred T) : collective_pred T :=
+  let: SimplFun p := sp in p.
+ +
+
+ +
+Explicit simplification rules for predicate application and membership. +
+
+Section PredicateSimplification.
+ +
+Variables T : Type.
+ +
+Implicit Types (p : pred T) (pT : predType T) (sp : simpl_pred T).
+Implicit Types (mp : mem_pred T).
+ +
+
+ +
+ The following four bespoke structures provide fine-grained control over + matching the various predicate forms. While all four follow a common pattern + of using a canonical projection to match a particular form of predicate + (in pred T, simpl_pred, mem_pred and mem_pred, respectively), and display + the matched predicate in the structure type, each is in fact used for a + different, specific purpose: +
    +
  • registered_applicative_pred: this user-facing structure is used to + declare values of type pred T meant to be used applicatively. The + structure parameter merely displays this same value, and is used to avoid + undesirable, visible occurrence of the structure in the right hand side + of rewrite rules such as app_predE. + There is a canonical instance of registered_applicative_pred for values + of the applicative_of_simpl coercion, which handles the + Definition Apred : applicative_pred T := pred x | ... idiom. + This instance is mainly intended for the in_applicative component of inE, + in conjunction with manifest_mem_pred and applicative_mem_pred. + +
    • +
  • manifest_simpl_pred: the only instance of this structure matches manifest + simpl_pred values of the form SimplPred p, displaying p in the structure + type. This structure is used in in_simpl to detect and selectively expand + collective predicates of this form. An explicit SimplPred p pattern would + NOT work for this purpose, as then the left-hand side of in_simpl would + reduce to in_mem ?x (Mem eta ?p) and would thus match any instance + of \in, not just those arising from a manifest simpl_pred. + +
    • +
  • manifest_mem_pred: similar to manifest_simpl_pred, the one instance of this + structure matches manifest mem_pred values of the form Mem eta ?p. The + purpose is different however: to match and display in ?p the actual + predicate appearing in an ... \in ... expression matched by the left hand + side of the in_applicative component of inE; then + +
    • +
  • applicative_mem_pred is a telescope refinement of manifest_mem_pred p with + a default constructor that checks that the predicate p is the value of a + registered_applicative_pred; any unfolding occurring during this check + does not affect the value of p passed to in_applicative, since that + has been fixed earlier by the manifest_mem_pred match. In particular the + definition of a predicate using the applicative_pred_of_simpl idiom above + will not be expanded - this very case is the reason in_applicative uses + a mem_pred telescope in its left hand side. The more straightforward + ?x \in applicative_pred_value ?ap (equivalent to in_mem ?x (Mem ?ap)) + with ?ap : registered_applicative_pred ?p would set ?p := pred x | ... + rather than ?p := Apred in the example above. + +
    • +
+ Also note that the in_applicative component of inE must be come before the + in_simpl one, as the latter also matches terms of the form x \in Apred. + Finally, no component of inE matches x \in Acoll, when + Definition Acoll : collective_pred T := pred x | .... + as the collective_pred_of_simpl is not convertible to pred_of_simpl. +
+
+ +
+Structure registered_applicative_pred p := RegisteredApplicativePred {
+  applicative_pred_value :> pred T;
+  _ : applicative_pred_value = p
+}.
+Definition ApplicativePred p := RegisteredApplicativePred (erefl p).
+Canonical applicative_pred_applicative sp :=
+  ApplicativePred (applicative_pred_of_simpl sp).
+ +
+Structure manifest_simpl_pred p := ManifestSimplPred {
+  simpl_pred_value :> simpl_pred T;
+  _ : simpl_pred_value = SimplPred p
+}.
+Canonical expose_simpl_pred p := ManifestSimplPred (erefl (SimplPred p)).
+ +
+Structure manifest_mem_pred p := ManifestMemPred {
+  mem_pred_value :> mem_pred T;
+  _ : mem_pred_value = Mem [eta p]
+}.
+Canonical expose_mem_pred p := ManifestMemPred (erefl (Mem [eta p])).
+ +
+Structure applicative_mem_pred p :=
+  ApplicativeMemPred {applicative_mem_pred_value :> manifest_mem_pred p}.
+Canonical check_applicative_mem_pred p (ap : registered_applicative_pred p) :=
+  [eta @ApplicativeMemPred ap].
+ +
+Lemma mem_topred pT (pp : pT) : mem (topred pp) = mem pp.
+ +
+Lemma topredE pT x (pp : pT) : topred pp x = (x \in pp).
+ +
+Lemma app_predE x p (ap : registered_applicative_pred p) : ap x = (x \in p).
+ +
+Lemma in_applicative x p (amp : applicative_mem_pred p) : in_mem x amp = p x.
+ +
+Lemma in_collective x p (msp : manifest_simpl_pred p) :
+  (x \in collective_pred_of_simpl msp) = p x.
+ +
+Lemma in_simpl x p (msp : manifest_simpl_pred p) :
+  in_mem x (Mem [eta pred_of_simpl msp]) = p x.
+ +
+
+ +
+ Because of the explicit eta expansion in the left-hand side, this lemma + should only be used in the left-to-right direction. + +
+
+Lemma unfold_in x p : (x \in ([eta p] : pred T)) = p x.
+ +
+Lemma simpl_predE p : SimplPred p =1 p.
+ +
+Definition inE := (in_applicative, in_simpl, simpl_predE). +
+Lemma mem_simpl sp : mem sp = sp :> pred T.
+ +
+Definition memE := mem_simpl. +
+Lemma mem_mem mp :
+  (mem mp = mp) * (mem (mp : simpl_pred T) = mp) * (mem (mp : pred T) = mp).
+ +
+End PredicateSimplification.
+ +
+
+ +
+ Qualifiers and keyed predicates. +
+
+ +
+Variant qualifier (q : nat) T := Qualifier of {pred T}.
+ +
+Coercion has_quality n T (q : qualifier n T) : {pred T} :=
+  fun x => let: Qualifier _ p := q in p x.
+Arguments has_quality n {T}.
+ +
+Lemma qualifE n T p x : (x \in @Qualifier n T p) = p x.
+ +
+Notation "x \is A" := (x \in has_quality 0 A) (only parsing) : bool_scope.
+Notation "x \is A" := (x \in has_quality 0 A) (only printing) : bool_scope.
+Notation "x \is 'a' A" := (x \in has_quality 1 A) (only parsing) : bool_scope.
+Notation "x \is 'a' A" := (x \in has_quality 1 A) (only printing) : bool_scope.
+Notation "x \is 'an' A" := (x \in has_quality 2 A) (only parsing) : bool_scope.
+Notation "x \is 'an' A" := (x \in has_quality 2 A) (only printing) : bool_scope.
+Notation "x \isn't A" := (x \notin has_quality 0 A) : bool_scope.
+Notation "x \isn't 'a' A" := (x \notin has_quality 1 A) : bool_scope.
+Notation "x \isn't 'an' A" := (x \notin has_quality 2 A) : bool_scope.
+Notation "[ 'qualify' x | P ]" := (Qualifier 0 (fun x => P%B)) : form_scope.
+Notation "[ 'qualify' x : T | P ]" :=
+  (Qualifier 0 (fun x : T => P%B)) (only parsing) : form_scope.
+Notation "[ 'qualify' 'a' x | P ]" := (Qualifier 1 (fun x => P%B)) : form_scope.
+Notation "[ 'qualify' 'a' x : T | P ]" :=
+  (Qualifier 1 (fun x : T => P%B)) (only parsing) : form_scope.
+Notation "[ 'qualify' 'an' x | P ]" :=
+  (Qualifier 2 (fun x => P%B)) : form_scope.
+Notation "[ 'qualify' 'an' x : T | P ]" :=
+  (Qualifier 2 (fun x : T => P%B)) (only parsing) : form_scope.
+ +
+
+ +
+ Keyed predicates: support for property-bearing predicate interfaces. +
+
+ +
+Section KeyPred.
+ +
+Variable T : Type.
+Variant pred_key (p : {pred T}) : Prop := DefaultPredKey.
+ +
+Variable p : {pred T}.
+Structure keyed_pred (k : pred_key p) :=
+  PackKeyedPred {unkey_pred :> {pred T}; _ : unkey_pred =i p}.
+ +
+Variable k : pred_key p.
+Definition KeyedPred := @PackKeyedPred k p (frefl _).
+ +
+Variable k_p : keyed_pred k.
+Lemma keyed_predE : k_p =i p.
+ +
+
+ +
+ Instances that strip the mem cast; the first one has "pred_of_mem" as its + projection head value, while the second has "pred_of_simpl". The latter + has the side benefit of preempting accidental misdeclarations. + Note: pred_of_mem is the registered mem >-> pred_sort coercion, while + simpl_of_mem; pred_of_simpl is the mem >-> pred >=> Funclass coercion. We + must write down the coercions explicitly as the Canonical head constant + computation does not strip casts. +
+
+Canonical keyed_mem :=
+  @PackKeyedPred k (pred_of_mem (mem k_p)) keyed_predE.
+Canonical keyed_mem_simpl :=
+  @PackKeyedPred k (pred_of_simpl (mem k_p)) keyed_predE.
+ +
+End KeyPred.
+ +
+Local Notation in_unkey x S := (x \in @unkey_pred _ S _ _) (only parsing).
+Notation "x \in S" := (in_unkey x S) (only printing) : bool_scope.
+ +
+Section KeyedQualifier.
+ +
+Variables (T : Type) (n : nat) (q : qualifier n T).
+ +
+Structure keyed_qualifier (k : pred_key q) :=
+  PackKeyedQualifier {unkey_qualifier; _ : unkey_qualifier = q}.
+Definition KeyedQualifier k := PackKeyedQualifier k (erefl q).
+Variables (k : pred_key q) (k_q : keyed_qualifier k).
+Fact keyed_qualifier_suproof : unkey_qualifier k_q =i q.
+ Canonical keyed_qualifier_keyed := PackKeyedPred k keyed_qualifier_suproof.
+ +
+End KeyedQualifier.
+ +
+Notation "x \is A" :=
+  (in_unkey x (has_quality 0 A)) (only printing) : bool_scope.
+Notation "x \is 'a' A" :=
+  (in_unkey x (has_quality 1 A)) (only printing) : bool_scope.
+Notation "x \is 'an' A" :=
+  (in_unkey x (has_quality 2 A)) (only printing) : bool_scope.
+ +
+Module DefaultKeying.
+ +
+Canonical default_keyed_pred T p := KeyedPred (@DefaultPredKey T p).
+Canonical default_keyed_qualifier T n (q : qualifier n T) :=
+  KeyedQualifier (DefaultPredKey q).
+ +
+End DefaultKeying.
+ +
+
+ +
+ Skolemizing with conditions. +
+
+ +
+Lemma all_tag_cond_dep I T (C : pred I) U :
+    (forall x, T x) -> (forall x, C x -> {y : T x & U x y}) ->
+  {f : forall x, T x & forall x, C x -> U x (f x)}.
+ +
+Lemma all_tag_cond I T (C : pred I) U :
+    T -> (forall x, C x -> {y : T & U x y}) ->
+  {f : I -> T & forall x, C x -> U x (f x)}.
+ +
+Lemma all_sig_cond_dep I T (C : pred I) P :
+    (forall x, T x) -> (forall x, C x -> {y : T x | P x y}) ->
+  {f : forall x, T x | forall x, C x -> P x (f x)}.
+ +
+Lemma all_sig_cond I T (C : pred I) P :
+    T -> (forall x, C x -> {y : T | P x y}) ->
+  {f : I -> T | forall x, C x -> P x (f x)}.
+ +
+Lemma all_sig2_cond {I T} (C : pred I) P Q :
+  T -> (forall x, C x -> {y : T | P x y & Q x y}) ->
+  {f : I -> T | forall x, C x -> P x (f x) & forall x, C x -> Q x (f x)}.
+ +
+Section RelationProperties.
+ +
+
+ +
+ Caveat: reflexive should not be used to state lemmas, as auto and trivial + will not expand the constant. +
+
+ +
+Variable T : Type.
+ +
+Variable R : rel T.
+ +
+Definition total := forall x y, R x y || R y x.
+Definition transitive := forall y x z, R x y -> R y z -> R x z.
+ +
+Definition symmetric := forall x y, R x y = R y x.
+Definition antisymmetric := forall x y, R x y && R y x -> x = y.
+Definition pre_symmetric := forall x y, R x y -> R y x.
+ +
+Lemma symmetric_from_pre : pre_symmetric -> symmetric.
+ +
+Definition reflexive := forall x, R x x.
+Definition irreflexive := forall x, R x x = false.
+ +
+Definition left_transitive := forall x y, R x y -> R x =1 R y.
+Definition right_transitive := forall x y, R x y -> R^~ x =1 R^~ y.
+ +
+Section PER.
+ +
+Hypotheses (symR : symmetric) (trR : transitive).
+ +
+Lemma sym_left_transitive : left_transitive.
+ +
+Lemma sym_right_transitive : right_transitive.
+ +
+End PER.
+ +
+
+ +
+ We define the equivalence property with prenex quantification so that it + can be localized using the {in ..., ..} form defined below. +
+
+ +
+Definition equivalence_rel := forall x y z, R z z * (R x y -> R x z = R y z).
+ +
+Lemma equivalence_relP : equivalence_rel <-> reflexive /\ left_transitive.
+ +
+End RelationProperties.
+ +
+Lemma rev_trans T (R : rel T) : transitive R -> transitive (fun x y => R y x).
+ +
+
+ +
+ Property localization +
+
+ +
+Local Notation "{ 'all1' P }" := (forall x, P x : Prop) (at level 0).
+Local Notation "{ 'all2' P }" := (forall x y, P x y : Prop) (at level 0).
+Local Notation "{ 'all3' P }" := (forall x y z, P x y z: Prop) (at level 0).
+Local Notation ph := (phantom _).
+ +
+Section LocalProperties.
+ +
+Variables T1 T2 T3 : Type.
+ +
+Variables (d1 : mem_pred T1) (d2 : mem_pred T2) (d3 : mem_pred T3).
+Local Notation ph := (phantom Prop).
+ +
+Definition prop_for (x : T1) P & ph {all1 P} := P x.
+ +
+Lemma forE x P phP : @prop_for x P phP = P x.
+ +
+Definition prop_in1 P & ph {all1 P} :=
+  forall x, in_mem x d1 -> P x.
+ +
+Definition prop_in11 P & ph {all2 P} :=
+  forall x y, in_mem x d1 -> in_mem y d2 -> P x y.
+ +
+Definition prop_in2 P & ph {all2 P} :=
+  forall x y, in_mem x d1 -> in_mem y d1 -> P x y.
+ +
+Definition prop_in111 P & ph {all3 P} :=
+  forall x y z, in_mem x d1 -> in_mem y d2 -> in_mem z d3 -> P x y z.
+ +
+Definition prop_in12 P & ph {all3 P} :=
+  forall x y z, in_mem x d1 -> in_mem y d2 -> in_mem z d2 -> P x y z.
+ +
+Definition prop_in21 P & ph {all3 P} :=
+  forall x y z, in_mem x d1 -> in_mem y d1 -> in_mem z d2 -> P x y z.
+ +
+Definition prop_in3 P & ph {all3 P} :=
+  forall x y z, in_mem x d1 -> in_mem y d1 -> in_mem z d1 -> P x y z.
+ +
+Variable f : T1 -> T2.
+ +
+Definition prop_on1 Pf P & phantom T3 (Pf f) & ph {all1 P} :=
+  forall x, in_mem (f x) d2 -> P x.
+ +
+Definition prop_on2 Pf P & phantom T3 (Pf f) & ph {all2 P} :=
+  forall x y, in_mem (f x) d2 -> in_mem (f y) d2 -> P x y.
+ +
+End LocalProperties.
+ +
+Definition inPhantom := Phantom Prop.
+Definition onPhantom {T} P (x : T) := Phantom Prop (P x).
+ +
+Definition bijective_in aT rT (d : mem_pred aT) (f : aT -> rT) :=
+  exists2 g, prop_in1 d (inPhantom (cancel f g))
+           & prop_on1 d (Phantom _ (cancel g)) (onPhantom (cancel g) f).
+ +
+Definition bijective_on aT rT (cd : mem_pred rT) (f : aT -> rT) :=
+  exists2 g, prop_on1 cd (Phantom _ (cancel f)) (onPhantom (cancel f) g)
+           & prop_in1 cd (inPhantom (cancel g f)).
+ +
+Notation "{ 'for' x , P }" := (prop_for x (inPhantom P)) : type_scope.
+Notation "{ 'in' d , P }" := (prop_in1 (mem d) (inPhantom P)) : type_scope.
+Notation "{ 'in' d1 & d2 , P }" :=
+  (prop_in11 (mem d1) (mem d2) (inPhantom P)) : type_scope.
+Notation "{ 'in' d & , P }" := (prop_in2 (mem d) (inPhantom P)) : type_scope.
+Notation "{ 'in' d1 & d2 & d3 , P }" :=
+  (prop_in111 (mem d1) (mem d2) (mem d3) (inPhantom P)) : type_scope.
+Notation "{ 'in' d1 & & d3 , P }" :=
+  (prop_in21 (mem d1) (mem d3) (inPhantom P)) : type_scope.
+Notation "{ 'in' d1 & d2 & , P }" :=
+  (prop_in12 (mem d1) (mem d2) (inPhantom P)) : type_scope.
+Notation "{ 'in' d & & , P }" := (prop_in3 (mem d) (inPhantom P)) : type_scope.
+Notation "{ 'on' cd , P }" :=
+  (prop_on1 (mem cd) (inPhantom P) (inPhantom P)) : type_scope.
+ +
+Notation "{ 'on' cd & , P }" :=
+  (prop_on2 (mem cd) (inPhantom P) (inPhantom P)) : type_scope.
+ +
+Local Arguments onPhantom : clear scopes.
+Notation "{ 'on' cd , P & g }" :=
+  (prop_on1 (mem cd) (Phantom (_ -> Prop) P) (onPhantom P g)) : type_scope.
+Notation "{ 'in' d , 'bijective' f }" := (bijective_in (mem d) f) : type_scope.
+Notation "{ 'on' cd , 'bijective' f }" :=
+  (bijective_on (mem cd) f) : type_scope.
+ +
+
+ +
+ Weakening and monotonicity lemmas for localized predicates. + Note that using these lemmas in backward reasoning will force expansion of + the predicate definition, as Rocq needs to expose the quantifier to apply + these lemmas. We define a few specialized variants to avoid this for some + of the ssrfun predicates. +
+
+ +
+Section LocalGlobal.
+ +
+Variables T1 T2 T3 : predArgType.
+Variables (D1 : {pred T1}) (D2 : {pred T2}) (D3 : {pred T3}).
+Variables (d1 d1' : mem_pred T1) (d2 d2' : mem_pred T2) (d3 d3' : mem_pred T3).
+Variables (f f' : T1 -> T2) (g : T2 -> T1) (h : T3).
+Variables (P1 : T1 -> Prop) (P2 : T1 -> T2 -> Prop).
+Variable P3 : T1 -> T2 -> T3 -> Prop.
+Variable Q1 : (T1 -> T2) -> T1 -> Prop.
+Variable Q1l : (T1 -> T2) -> T3 -> T1 -> Prop.
+Variable Q2 : (T1 -> T2) -> T1 -> T1 -> Prop.
+ +
+Hypothesis sub1 : sub_mem d1 d1'.
+Hypothesis sub2 : sub_mem d2 d2'.
+Hypothesis sub3 : sub_mem d3 d3'.
+ +
+Lemma in1W : {all1 P1} -> {in D1, {all1 P1}}.
+ Lemma in2W : {all2 P2} -> {in D1 & D2, {all2 P2}}.
+ Lemma in3W : {all3 P3} -> {in D1 & D2 & D3, {all3 P3}}.
+ +
+Lemma in1T : {in T1, {all1 P1}} -> {all1 P1}.
+ Lemma in2T : {in T1 & T2, {all2 P2}} -> {all2 P2}.
+ Lemma in3T : {in T1 & T2 & T3, {all3 P3}} -> {all3 P3}.
+ +
+Lemma sub_in1 (Ph : ph {all1 P1}) : prop_in1 d1' Ph -> prop_in1 d1 Ph.
+ +
+Lemma sub_in11 (Ph : ph {all2 P2}) : prop_in11 d1' d2' Ph -> prop_in11 d1 d2 Ph.
+ +
+Lemma sub_in111 (Ph : ph {all3 P3}) :
+  prop_in111 d1' d2' d3' Ph -> prop_in111 d1 d2 d3 Ph.
+ +
+Let allQ1 f'' := {all1 Q1 f''}.
+Let allQ1l f'' h' := {all1 Q1l f'' h'}.
+Let allQ2 f'' := {all2 Q2 f''}.
+ +
+Lemma on1W : allQ1 f -> {on D2, allQ1 f}.
+ +
+Lemma on1lW : allQ1l f h -> {on D2, allQ1l f & h}.
+ +
+Lemma on2W : allQ2 f -> {on D2 &, allQ2 f}.
+ +
+Lemma on1T : {on T2, allQ1 f} -> allQ1 f.
+ +
+Lemma on1lT : {on T2, allQ1l f & h} -> allQ1l f h.
+ +
+Lemma on2T : {on T2 &, allQ2 f} -> allQ2 f.
+ +
+Lemma subon1 (Phf : ph (allQ1 f)) (Ph : ph (allQ1 f)) :
+  prop_on1 d2' Phf Ph -> prop_on1 d2 Phf Ph.
+ +
+Lemma subon1l (Phf : ph (allQ1l f)) (Ph : ph (allQ1l f h)) :
+  prop_on1 d2' Phf Ph -> prop_on1 d2 Phf Ph.
+ +
+Lemma subon2 (Phf : ph (allQ2 f)) (Ph : ph (allQ2 f)) :
+  prop_on2 d2' Phf Ph -> prop_on2 d2 Phf Ph.
+ +
+Lemma can_in_inj : {in D1, cancel f g} -> {in D1 &, injective f}.
+ +
+Lemma canLR_in x y : {in D1, cancel f g} -> y \in D1 -> x = f y -> g x = y.
+ +
+Lemma canRL_in x y : {in D1, cancel f g} -> x \in D1 -> f x = y -> x = g y.
+ +
+Lemma on_can_inj : {on D2, cancel f & g} -> {on D2 &, injective f}.
+ +
+Lemma canLR_on x y : {on D2, cancel f & g} -> f y \in D2 -> x = f y -> g x = y.
+ +
+Lemma canRL_on x y : {on D2, cancel f & g} -> f x \in D2 -> f x = y -> x = g y.
+ +
+Lemma inW_bij : bijective f -> {in D1, bijective f}.
+ +
+Lemma onW_bij : bijective f -> {on D2, bijective f}.
+ +
+Lemma inT_bij : {in T1, bijective f} -> bijective f.
+ +
+Lemma onT_bij : {on T2, bijective f} -> bijective f.
+ +
+Lemma sub_in_bij (D1' : pred T1) :
+  {subset D1 <= D1'} -> {in D1', bijective f} -> {in D1, bijective f}.
+ +
+Lemma subon_bij (D2' : pred T2) :
+  {subset D2 <= D2'} -> {on D2', bijective f} -> {on D2, bijective f}.
+ +
+Lemma in_on1P : {in D1, {on D2, allQ1 f}} <->
+                {in [pred x in D1 | f x \in D2], allQ1 f}.
+ +
+Lemma in_on1lP : {in D1, {on D2, allQ1l f & h}} <->
+                {in [pred x in D1 | f x \in D2], allQ1l f h}.
+ +
+Lemma in_on2P : {in D1 &, {on D2 &, allQ2 f}} <->
+                {in [pred x in D1 | f x \in D2] &, allQ2 f}.
+ +
+Lemma on1W_in : {in D1, allQ1 f} -> {in D1, {on D2, allQ1 f}}.
+ +
+Lemma on1lW_in : {in D1, allQ1l f h} -> {in D1, {on D2, allQ1l f & h}}.
+ +
+Lemma on2W_in : {in D1 &, allQ2 f} -> {in D1 &, {on D2 &, allQ2 f}}.
+ +
+Lemma in_on1W : allQ1 f -> {in D1, {on D2, allQ1 f}}.
+ +
+Lemma in_on1lW : allQ1l f h -> {in D1, {on D2, allQ1l f & h}}.
+ +
+Lemma in_on2W : allQ2 f -> {in D1 &, {on D2 &, allQ2 f}}.
+ +
+Lemma on1S : (forall x, f x \in D2) -> {on D2, allQ1 f} -> allQ1 f.
+ +
+Lemma on1lS : (forall x, f x \in D2) -> {on D2, allQ1l f & h} -> allQ1l f h.
+ +
+Lemma on2S : (forall x, f x \in D2) -> {on D2 &, allQ2 f} -> allQ2 f.
+ +
+Lemma on1S_in : {homo f : x / x \in D1 >-> x \in D2} ->
+  {in D1, {on D2, allQ1 f}} -> {in D1, allQ1 f}.
+ +
+Lemma on1lS_in : {homo f : x / x \in D1 >-> x \in D2} ->
+  {in D1, {on D2, allQ1l f & h}} -> {in D1, allQ1l f h}.
+ +
+Lemma on2S_in : {homo f : x / x \in D1 >-> x \in D2} ->
+  {in D1 &, {on D2 &, allQ2 f}} -> {in D1 &, allQ2 f}.
+ +
+Lemma in_on1S : (forall x, f x \in D2) -> {in T1, {on D2, allQ1 f}} -> allQ1 f.
+ +
+Lemma in_on1lS : (forall x, f x \in D2) ->
+  {in T1, {on D2, allQ1l f & h}} -> allQ1l f h.
+ +
+Lemma in_on2S : (forall x, f x \in D2) ->
+  {in T1 &, {on D2 &, allQ2 f}} -> allQ2 f.
+ +
+End LocalGlobal.
+Arguments in_on1P {T1 T2 D1 D2 f Q1}.
+Arguments in_on1lP {T1 T2 T3 D1 D2 f h Q1l}.
+Arguments in_on2P {T1 T2 D1 D2 f Q2}.
+Arguments on1W_in {T1 T2 D1} D2 {f Q1}.
+Arguments on1lW_in {T1 T2 T3 D1} D2 {f h Q1l}.
+Arguments on2W_in {T1 T2 D1} D2 {f Q2}.
+Arguments in_on1W {T1 T2} D1 D2 {f Q1}.
+Arguments in_on1lW {T1 T2 T3} D1 D2 {f h Q1l}.
+Arguments in_on2W {T1 T2} D1 D2 {f Q2}.
+Arguments on1S {T1 T2} D2 {f Q1}.
+Arguments on1lS {T1 T2 T3} D2 {f h Q1l}.
+Arguments on2S {T1 T2} D2 {f Q2}.
+Arguments on1S_in {T1 T2 D1} D2 {f Q1}.
+Arguments on1lS_in {T1 T2 T3 D1} D2 {f h Q1l}.
+Arguments on2S_in {T1 T2 D1} D2 {f Q2}.
+Arguments in_on1S {T1 T2} D2 {f Q1}.
+Arguments in_on1lS {T1 T2 T3} D2 {f h Q1l}.
+Arguments in_on2S {T1 T2} D2 {f Q2}.
+ +
+Lemma can_in_pcan [rT aT : Type] (A : {pred aT}) [f : aT -> rT] [g : rT -> aT] :
+  {in A, cancel f g} -> {in A, pcancel f (fun y : rT => Some (g y))}.
+ +
+Lemma pcan_in_inj [rT aT : Type] [A : {pred aT}]
+  [f : aT -> rT] [g : rT -> option aT] :
+  {in A, pcancel f g} -> {in A &, injective f}.
+ +
+Lemma in_inj_comp A B C (f : B -> A) (h : C -> B) (P : pred B) (Q : pred C) :
+  {in P &, injective f} -> {in Q &, injective h} -> {homo h : x / Q x >-> P x} ->
+  {in Q &, injective (f \o h)}.
+ +
+Lemma can_in_comp [A B C : Type] (D : {pred B}) (D' : {pred C})
+  [f : B -> A] [h : C -> B] [f' : A -> B] [h' : B -> C] :
+  {homo h : x / x \in D' >-> x \in D} ->
+  {in D, cancel f f'} -> {in D', cancel h h'} ->
+  {in D', cancel (f \o h) (h' \o f')}.
+ +
+Lemma pcan_in_comp [A B C : Type] (D : {pred B}) (D' : {pred C})
+  [f : B -> A] [h : C -> B] [f' : A -> option B] [h' : B -> option C] :
+  {homo h : x / x \in D' >-> x \in D} ->
+  {in D, pcancel f f'} -> {in D', pcancel h h'} ->
+  {in D', pcancel (f \o h) (obind h' \o f')}.
+ +
+Definition pred_oapp T (D : {pred T}) : pred (option T) :=
+  [pred x | oapp (mem D) false x].
+ +
+Lemma ocan_in_comp [A B C : Type] (D : {pred B}) (D' : {pred C})
+    [f : B -> option A] [h : C -> option B] [f' : A -> B] [h' : B -> C] :
+  {homo h : x / x \in D' >-> x \in pred_oapp D} ->
+  {in D, ocancel f f'} -> {in D', ocancel h h'} ->
+  {in D', ocancel (obind f \o h) (h' \o f')}.
+ +
+Section in_sig.
+ +
+Variables T1 T2 T3 : Type.
+Variables (D1 : {pred T1}) (D2 : {pred T2}) (D3 : {pred T3}).
+Variable P1 : T1 -> Prop.
+Variable P2 : T1 -> T2 -> Prop.
+Variable P3 : T1 -> T2 -> T3 -> Prop.
+ +
+Lemma in1_sig : {in D1, {all1 P1}} -> forall x : sig D1, P1 (sval x).
+ +
+Lemma in2_sig : {in D1 & D2, {all2 P2}} ->
+  forall (x : sig D1) (y : sig D2), P2 (sval x) (sval y).
+ +
+Lemma in3_sig : {in D1 & D2 & D3, {all3 P3}} ->
+  forall (x : sig D1) (y : sig D2) (z : sig D3), P3 (sval x) (sval y) (sval z).
+ +
+End in_sig.
+Arguments in1_sig {T1 D1 P1}.
+Arguments in2_sig {T1 T2 D1 D2 P2}.
+Arguments in3_sig {T1 T2 T3 D1 D2 D3 P3}.
+ +
+Lemma sub_in2 T d d' (P : T -> T -> Prop) :
+  sub_mem d d' -> forall Ph : ph {all2 P}, prop_in2 d' Ph -> prop_in2 d Ph.
+ +
+Lemma sub_in3 T d d' (P : T -> T -> T -> Prop) :
+  sub_mem d d' -> forall Ph : ph {all3 P}, prop_in3 d' Ph -> prop_in3 d Ph.
+ +
+Lemma sub_in12 T1 T d1 d1' d d' (P : T1 -> T -> T -> Prop) :
+  sub_mem d1 d1' -> sub_mem d d' ->
+  forall Ph : ph {all3 P}, prop_in12 d1' d' Ph -> prop_in12 d1 d Ph.
+ +
+Lemma sub_in21 T T3 d d' d3 d3' (P : T -> T -> T3 -> Prop) :
+  sub_mem d d' -> sub_mem d3 d3' ->
+  forall Ph : ph {all3 P}, prop_in21 d' d3' Ph -> prop_in21 d d3 Ph.
+ +
+Lemma equivalence_relP_in T (R : rel T) (A : pred T) :
+  {in A & &, equivalence_rel R}
+   <-> {in A, reflexive R} /\ {in A &, forall x y, R x y -> {in A, R x =1 R y}}.
+ +
+Section MonoHomoMorphismTheory.
+ +
+Variables (aT rT sT : Type) (f : aT -> rT) (g : rT -> aT).
+Variables (aP : pred aT) (rP : pred rT) (aR : rel aT) (rR : rel rT).
+ +
+Lemma monoW : {mono f : x / aP x >-> rP x} -> {homo f : x / aP x >-> rP x}.
+ +
+Lemma mono2W :
+  {mono f : x y / aR x y >-> rR x y} -> {homo f : x y / aR x y >-> rR x y}.
+ +
+Hypothesis fgK : cancel g f.
+ +
+Lemma homoRL :
+  {homo f : x y / aR x y >-> rR x y} -> forall x y, aR (g x) y -> rR x (f y).
+ +
+Lemma homoLR :
+  {homo f : x y / aR x y >-> rR x y} -> forall x y, aR x (g y) -> rR (f x) y.
+ +
+Lemma homo_mono :
+    {homo f : x y / aR x y >-> rR x y} -> {homo g : x y / rR x y >-> aR x y} ->
+  {mono g : x y / rR x y >-> aR x y}.
+ +
+Lemma monoLR :
+  {mono f : x y / aR x y >-> rR x y} -> forall x y, rR (f x) y = aR x (g y).
+ +
+Lemma monoRL :
+  {mono f : x y / aR x y >-> rR x y} -> forall x y, rR x (f y) = aR (g x) y.
+ +
+Lemma can_mono :
+  {mono f : x y / aR x y >-> rR x y} -> {mono g : x y / rR x y >-> aR x y}.
+ +
+End MonoHomoMorphismTheory.
+ +
+Section MonoHomoMorphismTheory_in.
+ +
+Variables (aT rT : predArgType) (f : aT -> rT) (g : rT -> aT).
+Variables (aD : {pred aT}) (rD : {pred rT}).
+Variable (aP : pred aT) (rP : pred rT) (aR : rel aT) (rR : rel rT).
+ +
+Lemma mono1W_in :
+    {in aD, {mono f : x / aP x >-> rP x}} ->
+  {in aD, {homo f : x / aP x >-> rP x}}.
+ #[deprecated(since="Coq 8.16", note="Use mono1W_in instead.")]
+Notation mono2W_in := mono1W_in.
+ +
+Lemma monoW_in :
+    {in aD &, {mono f : x y / aR x y >-> rR x y}} ->
+  {in aD &, {homo f : x y / aR x y >-> rR x y}}.
+ +
+Hypothesis fgK : {in rD, {on aD, cancel g & f}}.
+Hypothesis mem_g : {homo g : x / x \in rD >-> x \in aD}.
+ +
+Lemma homoRL_in :
+    {in aD &, {homo f : x y / aR x y >-> rR x y}} ->
+  {in rD & aD, forall x y, aR (g x) y -> rR x (f y)}.
+ +
+Lemma homoLR_in :
+    {in aD &, {homo f : x y / aR x y >-> rR x y}} ->
+  {in aD & rD, forall x y, aR x (g y) -> rR (f x) y}.
+ +
+Lemma homo_mono_in :
+    {in aD &, {homo f : x y / aR x y >-> rR x y}} ->
+    {in rD &, {homo g : x y / rR x y >-> aR x y}} ->
+  {in rD &, {mono g : x y / rR x y >-> aR x y}}.
+ +
+Lemma monoLR_in :
+    {in aD &, {mono f : x y / aR x y >-> rR x y}} ->
+  {in aD & rD, forall x y, rR (f x) y = aR x (g y)}.
+ +
+Lemma monoRL_in :
+    {in aD &, {mono f : x y / aR x y >-> rR x y}} ->
+  {in rD & aD, forall x y, rR x (f y) = aR (g x) y}.
+ +
+Lemma can_mono_in :
+    {in aD &, {mono f : x y / aR x y >-> rR x y}} ->
+  {in rD &, {mono g : x y / rR x y >-> aR x y}}.
+ +
+End MonoHomoMorphismTheory_in.
+Arguments homoRL_in {aT rT f g aD rD aR rR}.
+Arguments homoLR_in {aT rT f g aD rD aR rR}.
+Arguments homo_mono_in {aT rT f g aD rD aR rR}.
+Arguments monoLR_in {aT rT f g aD rD aR rR}.
+Arguments monoRL_in {aT rT f g aD rD aR rR}.
+Arguments can_mono_in {aT rT f g aD rD aR rR}.
+ +
+Section HomoMonoMorphismFlip.
+Variables (aT rT : Type) (aR : rel aT) (rR : rel rT) (f : aT -> rT).
+Variable (aD aD' : {pred aT}).
+ +
+Lemma homo_sym : {homo f : x y / aR x y >-> rR x y} ->
+  {homo f : y x / aR x y >-> rR x y}.
+ +
+Lemma mono_sym : {mono f : x y / aR x y >-> rR x y} ->
+  {mono f : y x / aR x y >-> rR x y}.
+ +
+Lemma homo_sym_in : {in aD &, {homo f : x y / aR x y >-> rR x y}} ->
+  {in aD &, {homo f : y x / aR x y >-> rR x y}}.
+ +
+Lemma mono_sym_in : {in aD &, {mono f : x y / aR x y >-> rR x y}} ->
+  {in aD &, {mono f : y x / aR x y >-> rR x y}}.
+ +
+Lemma homo_sym_in11 : {in aD & aD', {homo f : x y / aR x y >-> rR x y}} ->
+  {in aD' & aD, {homo f : y x / aR x y >-> rR x y}}.
+ +
+Lemma mono_sym_in11 : {in aD & aD', {mono f : x y / aR x y >-> rR x y}} ->
+  {in aD' & aD, {mono f : y x / aR x y >-> rR x y}}.
+ +
+End HomoMonoMorphismFlip.
+Arguments homo_sym {aT rT} [aR rR f].
+Arguments mono_sym {aT rT} [aR rR f].
+Arguments homo_sym_in {aT rT} [aR rR f aD].
+Arguments mono_sym_in {aT rT} [aR rR f aD].
+Arguments homo_sym_in11 {aT rT} [aR rR f aD aD'].
+Arguments mono_sym_in11 {aT rT} [aR rR f aD aD'].
+ +
+Section CancelOn.
+ +
+Variables (aT rT : predArgType) (aD : {pred aT}) (rD : {pred rT}).
+Variables (f : aT -> rT) (g : rT -> aT).
+ +
+Lemma onW_can : cancel g f -> {on aD, cancel g & f}.
+ +
+Lemma onW_can_in : {in rD, cancel g f} -> {in rD, {on aD, cancel g & f}}.
+ +
+Lemma in_onW_can : cancel g f -> {in rD, {on aD, cancel g & f}}.
+ +
+Lemma onS_can : (forall x, g x \in aD) -> {on aD, cancel g & f} -> cancel g f.
+ +
+Lemma onS_can_in : {homo g : x / x \in rD >-> x \in aD} ->
+  {in rD, {on aD, cancel g & f}} -> {in rD, cancel g f}.
+ +
+Lemma in_onS_can : (forall x, g x \in aD) ->
+  {in rT, {on aD, cancel g & f}} -> cancel g f.
+ +
+End CancelOn.
+Arguments onW_can {aT rT} aD {f g}.
+Arguments onW_can_in {aT rT} aD {rD f g}.
+Arguments in_onW_can {aT rT} aD rD {f g}.
+Arguments onS_can {aT rT} aD {f g}.
+Arguments onS_can_in {aT rT} aD {rD f g}.
+Arguments in_onS_can {aT rT} aD {f g}.
+ +
+Section inj_can_sym_in_on.
+Variables (aT rT : predArgType) (aD : {pred aT}) (rD : {pred rT}).
+Variables (f : aT -> rT) (g : rT -> aT).
+ +
+Lemma inj_can_sym_in_on :
+    {homo f : x / x \in aD >-> x \in rD} -> {in aD, {on rD, cancel f & g}} ->
+  {in rD &, {on aD &, injective g}} -> {in rD, {on aD, cancel g & f}}.
+ +
+Lemma inj_can_sym_on : {in aD, cancel f g} ->
+  {on aD &, injective g} -> {on aD, cancel g & f}.
+ +
+Lemma inj_can_sym_in : {homo f \o g : x / x \in rD} -> {on rD, cancel f & g} ->
+  {in rD &, injective g} -> {in rD, cancel g f}.
+ +
+End inj_can_sym_in_on.
+Arguments inj_can_sym_in_on {aT rT aD rD f g}.
+Arguments inj_can_sym_on {aT rT aD f g}.
+Arguments inj_can_sym_in {aT rT rD f g}.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.ssr.ssrclasses.html b/master/corelib/Corelib.ssr.ssrclasses.html new file mode 100644 index 0000000000..ae8ec7e8e1 --- /dev/null +++ b/master/corelib/Corelib.ssr.ssrclasses.html @@ -0,0 +1,120 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.ssr.ssrclasses

+ +
+ +
+
+ +
+ +
+ + Compatibility layer for under and setoid_rewrite. + +
+ + Note: this file does not require ssreflect; it is both required by + ssrsetoid and required by ssrunder. + +
+ + Redefine Corelib.Classes.RelationClasses.Reflexive here, so that doing + Require Import ssreflect does not Require Import RelationClasses, + and conversely. +
+
+ +
+Section Defs.
+  Context {A : Type}.
+  Class Reflexive (R : A -> A -> Prop) :=
+    reflexivity : forall x : A, R x x.
+End Defs.
+ +
+Register Reflexive as plugins.ssreflect.reflexive_type.
+Register reflexivity as plugins.ssreflect.reflexive_proof.
+ +
+#[global]
+Instance eq_Reflexive {A : Type} : Reflexive (@eq A) := @eq_refl A.
+#[global]
+Instance iff_Reflexive : Reflexive iff := iff_refl.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.ssr.ssreflect.html b/master/corelib/Corelib.ssr.ssreflect.html new file mode 100644 index 0000000000..b8a298e2e9 --- /dev/null +++ b/master/corelib/Corelib.ssr.ssreflect.html @@ -0,0 +1,1061 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.ssr.ssreflect

+ +
+ +
+ +
+
+ +
+ +
+
+ +
+Require Import ssrmatching.
+ +
+
+ +
+ This file is the Gallina part of the ssreflect plugin implementation. + Files that use the ssreflect plugin should always Require ssreflect and + either Import ssreflect or Import ssreflect.SsrSyntax. + Part of the contents of this file is technical and will only interest + advanced developers; in addition the following are defined: + [the str of v by f] == the Canonical s : str such that f s = v. + [the str of v] == the Canonical s : str that coerces to v. + argumentType c == the T such that c : forall x : T, P x. + returnType c == the R such that c : T -> R. + {type of c for s} == P s where c : forall x : T, P x. + nonPropType == an interface for non-Prop Types: a nonPropType coerces + to a Type, and only types that do not have sort + Prop are canonical nonPropType instances. This is + useful for applied views (see mid-file comment). + notProp T == the nonPropType instance for type T. + phantom T v == singleton type with inhabitant Phantom T v. + phant T == singleton type with inhabitant Phant v. + =^~ r == the converse of rewriting rule r (e.g., in a + rewrite multirule). + unkeyed t == t, but treated as an unkeyed matching pattern by + the ssreflect matching algorithm. + nosimpl t == t, but on the right-hand side of Definition C := + nosimpl disables expansion of C by /=. + locked t == t, but locked t is not convertible to t. + locked_with k t == t, but not convertible to t or locked_with k' t + unless k = k' (with k : unit). Rocq type-checking + will be much more efficient if locked_with with a + bespoke k is used for sealed definitions. + unlockable v == interface for sealed constant definitions of v. + Unlockable def == the unlockable that registers def : C = v. + [unlockable of C] == a clone for C of the canonical unlockable for the + definition of C (e.g., if it uses locked_with). + [unlockable fun C] == [unlockable of C] with the expansion forced to be + an explicit lambda expression. +
    +
  • > The usage pattern for ADT operations is: + Definition foo_def x1 .. xn := big_foo_expression. + Fact foo_key : unit. Proof. by [ ]. Qed. + Definition foo := locked_with foo_key foo_def. + Canonical foo_unlockable := [unlockable fun foo]. + This minimizes the comparison overhead for foo, while still allowing + rewrite unlock to expose big_foo_expression. + +
    + + [elaborate x] == triggers Rocq elaboration to fill the holes of the term x + The main use case is to trigger typeclass inference in + the body of a ssreflect have := [elaborate body]. + +
    • +
+ +
+ + Additionally we provide default intro pattern ltac views: +
    +
  • top of the stack actions: + => /[apply] := => hyp {}/hyp + => /[swap] := => x y; move: y x + (also swap and preserves let bindings) + => /[dup] := => x; have copy := x; move: copy x + (also copies and preserves let bindings) + +
    • +
  • calling rewrite from an intro pattern, use with parsimony: + => /[1! rules] := rewrite rules + => /[! rules] := rewrite !rules + +
    • +
+ +
+ + More information about these definitions and their use can be found in the + ssreflect manual, and in specific comments below. +
+
+ +
+Set Implicit Arguments.
+ +
+Module SsrSyntax.
+ +
+
+ +
+ Declare Ssr keywords: 'is' 'of' '//' '/=' and '//='. We also declare the + parsing level 8, as a workaround for a notation grammar factoring problem. + Arguments of application-style notations (at level 10) should be declared + at level 8 rather than 9 or the camlp5 grammar will not factor properly. +
+
+ +
+Reserved Notation "(* x 'is' y 'of' z 'isn't' // /= //= *)".
+ +
+
+ +
+ Non ambiguous keyword to check if the SsrSyntax module is imported +
+
+Reserved Notation "(* Use to test if 'SsrSyntax_is_Imported' *)".
+ +
+Reserved Notation "<hidden n >" (at level 0, n at level 0,
+  format "<hidden n >").
+#[warning="-postfix-notation-not-level-1"]
+Reserved Notation "T (* n *)" (at level 200, format "T (* n *)").
+ +
+End SsrSyntax.
+ +
+Export SsrMatchingSyntax.
+Export SsrSyntax.
+ +
+
+ +
+Save primitive notation that will be overloaded. +
+
+Local Notation RocqGenericIf c vT vF := (if c then vT else vF) (only parsing).
+Local Notation RocqGenericDependentIf c x R vT vF :=
+  (if c as x return R then vT else vF) (only parsing).
+ +
+
+ +
+Reserve notation that introduced in this file. +
+
+Reserved Notation "'if' c 'then' vT 'else' vF" (at level 200,
+  c, vT, vF at level 200).
+Reserved Notation "'if' c 'return' R 'then' vT 'else' vF" (at level 200,
+  c, R, vT, vF at level 200).
+Reserved Notation "'if' c 'as' x 'return' R 'then' vT 'else' vF" (at level 200,
+  c, R, vT, vF at level 200, x name).
+ +
+Reserved Notation "[ 'the' sT 'of' v 'by' f ]" (at level 0,
+  format "[ 'the' sT 'of' v 'by' f ]").
+Reserved Notation "[ 'the' sT 'of' v ]" (at level 0,
+  format "[ 'the' sT 'of' v ]").
+Reserved Notation "{ 'type' 'of' c 'for' s }" (at level 0,
+  format "{ 'type' 'of' c 'for' s }").
+ +
+Reserved Notation "=^~ r" (at level 100, format "=^~ r").
+ +
+Reserved Notation "[ 'unlockable' 'of' C ]" (at level 0,
+  format "[ 'unlockable' 'of' C ]").
+Reserved Notation "[ 'unlockable' 'fun' C ]" (at level 0,
+  format "[ 'unlockable' 'fun' C ]").
+ +
+Reserved Notation "[ 'elaborate' x ]" (at level 0).
+ +
+
+ +
+ To define notations for tactic in intro patterns. + When "=> /t" is parsed, "t: +
+
+Declare Scope ssripat_scope.
+Delimit Scope ssripat_scope with ssripat.
+ +
+
+ +
+ Make the general "if" into a notation, so that we can override it below. + The notations are "only parsing" because the Rocq decompiler will not + recognize the expansion of the boolean if; using the default printer + avoids a spurious trailing %GEN_IF. +
+
+ +
+Declare Scope general_if_scope.
+Delimit Scope general_if_scope with GEN_IF.
+ +
+Notation "'if' c 'then' vT 'else' vF" :=
+  (RocqGenericIf c vT vF) (only parsing) : general_if_scope.
+ +
+Notation "'if' c 'return' R 'then' vT 'else' vF" :=
+  (RocqGenericDependentIf c c R vT vF) (only parsing) : general_if_scope.
+ +
+Notation "'if' c 'as' x 'return' R 'then' vT 'else' vF" :=
+  (RocqGenericDependentIf c x R vT vF) (only parsing) : general_if_scope.
+ +
+
+ +
+ Force boolean interpretation of simple if expressions. +
+
+ +
+Declare Scope boolean_if_scope.
+Delimit Scope boolean_if_scope with BOOL_IF.
+ +
+Notation "'if' c 'return' R 'then' vT 'else' vF" :=
+  (if c is true as c in bool return R then vT else vF) : boolean_if_scope.
+ +
+Notation "'if' c 'then' vT 'else' vF" :=
+  (if c%bool is true as _ in bool return _ then vT else vF) : boolean_if_scope.
+ +
+Notation "'if' c 'as' x 'return' R 'then' vT 'else' vF" :=
+  (if c%bool is true as x in bool return R then vT else vF) : boolean_if_scope.
+ +
+Open Scope boolean_if_scope.
+ +
+
+ +
+ To allow a wider variety of notations without reserving a large number of + of identifiers, the ssreflect library systematically uses "forms" to + enclose complex mixfix syntax. A "form" is simply a mixfix expression + enclosed in square brackets and introduced by a keyword: + [keyword ... ] + Because the keyword follows a bracket it does not need to be reserved. + Non-ssreflect libraries that do not respect the form syntax (e.g., the Rocq + Lists library) should be loaded before ssreflect so that their notations + do not mask all ssreflect forms. +
+
+Declare Scope form_scope.
+Delimit Scope form_scope with FORM.
+Open Scope form_scope.
+ +
+
+ +
+ Constants for abstract: and [: name ] intro pattern +
+
+Definition abstract_lock := unit.
+Definition abstract_key := tt.
+ +
+Definition abstract (statement : Type) (id : nat) (lock : abstract_lock) :=
+  let: tt := lock in statement.
+ +
+Declare Scope ssr_scope.
+Notation "<hidden n >" := (abstract _ n _) : ssr_scope.
+Notation "T (* n *)" := (abstract T n abstract_key) : ssr_scope.
+Open Scope ssr_scope.
+ +
+Register abstract_lock as plugins.ssreflect.abstract_lock.
+Register abstract_key as plugins.ssreflect.abstract_key.
+Register abstract as plugins.ssreflect.abstract.
+ +
+
+ +
+ Constants for tactic-views +
+
+Inductive external_view : Type := tactic_view of Type.
+ +
+
+ +
+ Syntax for referring to canonical structures: + [the struct_type of proj_val by proj_fun] + This form denotes the Canonical instance s of the Structure type + struct_type whose proj_fun projection is proj_val, i.e., such that + proj_fun s = proj_val. + Typically proj_fun will be A record field accessors of struct_type, but + this need not be the case; it can be, for instance, a field of a record + type to which struct_type coerces; proj_val will likewise be coerced to + the return type of proj_fun. In all but the simplest cases, proj_fun + should be eta-expanded to allow for the insertion of implicit arguments. + In the common case where proj_fun itself is a coercion, the "by" part + can be omitted entirely; in this case it is inferred by casting s to the + inferred type of proj_val. Obviously the latter can be fixed by using an + explicit cast on proj_val, and it is highly recommended to do so when the + return type intended for proj_fun is "Type", as the type inferred for + proj_val may vary because of sort polymorphism (it could be Set or Prop). + Note when using the [the _ of _ ] form to generate a substructure from a + telescopes-style canonical hierarchy (implementing inheritance with + coercions), one should always project or coerce the value to the BASE + structure, because Rocq will only find a Canonical derived structure for + the Canonical base structure -- not for a base structure that is specific + to proj_value. +
+
+ +
+Module TheCanonical.
+ +
+Variant put vT sT (v1 v2 : vT) (s : sT) : Prop := Put.
+ +
+Definition get vT sT v s (p : @put vT sT v v s) := let: Put _ _ _ := p in s.
+ +
+Definition get_by vT sT of sT -> vT := @get vT sT.
+ +
+End TheCanonical.
+ +
+Import TheCanonical. +
+Local Arguments get_by _%_type_scope _%_type_scope _ _ _ _.
+ +
+Notation "[ 'the' sT 'of' v 'by' f ]" :=
+  (@get_by _ sT f _ _ ((fun v' (s : sT) => Put v' (f s) s) v _))
+  (only parsing) : form_scope.
+ +
+Notation "[ 'the' sT 'of' v ]" := (get ((fun s : sT => Put v s s) _))
+  (only parsing) : form_scope.
+ +
+
+ +
+ The following are "format only" versions of the above notations. + We need to do this to prevent the formatter from being be thrown off by + application collapsing, coercion insertion and beta reduction in the right + hand side of the notations above. +
+
+ +
+Notation "[ 'the' sT 'of' v 'by' f ]" := (@get_by _ sT f v _ _)
+  (only printing) : form_scope.
+ +
+Notation "[ 'the' sT 'of' v ]" := (@get _ sT v _ _)
+  (only printing) : form_scope.
+ +
+
+ +
+ We would like to recognize +Notation " [ 'the' sT 'of' v : 'Type' ]" := (@get Type sT v _ ) + (at level 0, format " [ 'the' sT 'of' v : 'Type' ]") : form_scope. + +
+ + +
+ + Helper notation for canonical structure inheritance support. + This is a workaround for the poor interaction between delta reduction and + canonical projections in Rocq's unification algorithm, by which transparent + definitions hide canonical instances, i.e., in + Canonical a_type_struct := @Struct a_type ... + Definition my_type := a_type. + my_type doesn't effectively inherit the struct structure from a_type. Our + solution is to redeclare the instance as follows + Canonical my_type_struct := Eval hnf in [struct of my_type]. + The special notation [str of _ ] must be defined for each Structure "str" + with constructor "Str", typically as follows + Definition clone_str s := + let: Str _ x y ... z := s return {type of Str for s} -> str in + fun k => k _ x y ... z. + Notation " [ 'str' 'of' T 'for' s ]" := (@clone_str s (@Str T)) + (at level 0, format " [ 'str' 'of' T 'for' s ]") : form_scope. + Notation " [ 'str' 'of' T ]" := (repack_str (fun x => @Str T x)) + (at level 0, format " [ 'str' 'of' T ]") : form_scope. + The notation for the match return predicate is defined below; the eta + expansion in the second form serves both to distinguish it from the first + and to avoid the delta reduction problem. + There are several variations on the notation and the definition of the + the "clone" function, for telescopes, mixin classes, and join (multiple + inheritance) classes. We describe a different idiom for clones in ssrfun; + it uses phantom types (see below) and static unification; see fintype and + ssralg for examples. +
+
+ +
+Definition argumentType T P & forall x : T, P x := T.
+Definition dependentReturnType T P & forall x : T, P x := P.
+Definition returnType aT rT & aT -> rT := rT.
+ +
+Notation "{ 'type' 'of' c 'for' s }" := (dependentReturnType c s) : type_scope.
+ +
+
+ +
+ A generic "phantom" type (actually, a unit type with a phantom parameter). + This type can be used for type definitions that require some Structure + on one of their parameters, to allow Rocq to infer said structure so it + does not have to be supplied explicitly or via the " [the _ of _ ]" notation + (the latter interacts poorly with other Notation). + The definition of a (co)inductive type with a parameter p : p_type, that + needs to use the operations of a structure + Structure p_str : Type := p_Str {p_repr :> p_type; p_op : p_repr -> ...} + should be given as + Inductive indt_type (p : p_str) := Indt ... . + Definition indt_of (p : p_str) & phantom p_type p := indt_type p. + Notation "{ 'indt' p }" := (indt_of (Phantom p)). + Definition indt p x y ... z : {indt p} := @Indt p x y ... z. + Notation " [ 'indt' x y ... z ]" := (indt x y ... z). + That is, the concrete type and its constructor should be shadowed by + definitions that use a phantom argument to infer and display the true + value of p (in practice, the "indt" constructor often performs additional + functions, like "locking" the representation -- see below). + We also define a simpler version ("phant" / "Phant") of phantom for the + common case where p_type is Type. +
+
+ +
+Variant phantom T (p : T) : Prop := Phantom.
+Arguments phantom : clear implicits.
+Arguments Phantom : clear implicits.
+Variant phant (p : Type) : Prop := Phant.
+ +
+
+ +
+ Internal tagging used by the implementation of the ssreflect elim. +
+
+ +
+Definition protect_term (A : Type) (x : A) : A := x.
+ +
+Register protect_term as plugins.ssreflect.protect_term.
+ +
+
+ +
+ The ssreflect idiom for a non-keyed pattern: +
    +
  • unkeyed t will match any subterm that unifies with t, regardless of + whether it displays the same head symbol as t. + +
    • +
  • unkeyed t a b will match any application of a term f unifying with t, + to two arguments unifying with a and b, respectively, regardless of + apparent head symbols. + +
    • +
  • unkeyed x where x is a variable will match any subterm with the same + type as x (when x would raise the 'indeterminate pattern' error). + +
    • +
+
+
+ +
+Notation unkeyed x := (let flex := x in flex).
+ +
+
+ +
+ Ssreflect converse rewrite rule rule idiom. +
+
+Definition ssr_converse R (r : R) := (Logic.I, r).
+Notation "=^~ r" := (ssr_converse r) : form_scope.
+ +
+
+ +
+ Term tagging (user-level). + The ssreflect library uses four strengths of term tagging to restrict + convertibility during type checking: + nosimpl t simplifies to t EXCEPT in a definition; more precisely, given + Definition foo := nosimpl bar, foo (or foo t') will NOT be expanded by + the /= and //= switches unless it is in a forcing context (e.g., in + match foo t' with ... end, foo t' will be reduced if this allows the + match to be reduced). Note that nosimpl bar is simply notation for a + a term that beta-iota reduces to bar; hence rewrite /foo will replace + foo by bar, and rewrite -/foo will replace bar by foo. + CAVEAT: nosimpl should not be used inside a Section, because the end of + section "cooking" removes the iota redex. + locked t is provably equal to t, but is not convertible to t; 'locked' + provides support for selective rewriting, via the lock t : t = locked t + Lemma, and the ssreflect unlock tactic. + locked_with k t is equal but not convertible to t, much like locked t, + but supports explicit tagging with a value k : unit. This is used to + mitigate a flaw in the term comparison heuristic of the Rocq kernel, + which treats all terms of the form locked t as equal and compares their + arguments recursively, leading to an exponential blowup of comparison. + For this reason locked_with should be used rather than locked when + defining ADT operations. The unlock tactic does not support locked_with + but the unlock rewrite rule does, via the unlockable interface. + we also use Module Type ascription to create truly opaque constants, + because simple expansion of constants to reveal an unreducible term + doubles the time complexity of a negative comparison. Such opaque + constants can be expanded generically with the unlock rewrite rule. + See the definition of card and subset in fintype for examples of this. +
+
+ +
+Notation nosimpl t := (let: tt := tt in t).
+ +
+Lemma master_key : unit.
+Definition locked A := let: tt := master_key in fun x : A => x.
+ +
+Register master_key as plugins.ssreflect.master_key.
+Register locked as plugins.ssreflect.locked.
+ +
+Lemma lock A x : x = locked x :> A.
+ +
+
+ +
+ The basic closing tactic "done". +
+
+Ltac done :=
+  trivial; hnf; intros; solve
+   [ do ![solve [trivial | simple refine (@sym_equal _ _ _ _); trivial]
+         | discriminate | contradiction | split]
+   | match goal with H : ~ _ |- _ => solve [case H; trivial] end ].
+ +
+
+ +
+ Quicker done tactic not including split, syntax: /0/ +
+
+Ltac ssrdone0 :=
+  trivial; hnf; intros; solve
+   [ do ![solve [trivial | apply: sym_equal; trivial]
+         | discriminate | contradiction ]
+   | match goal with H : ~ _ |- _ => solve [case H; trivial] end ].
+ +
+
+ +
+ To unlock opaque constants. +
+
+#[universes(template)]
+Structure unlockable T v := Unlockable {unlocked : T; _ : unlocked = v}.
+Lemma unlock T x C : @unlocked T x C = x.
+ +
+Notation "[ 'unlockable' 'of' C ]" :=
+  (@Unlockable _ _ C (unlock _)) : form_scope.
+ +
+Notation "[ 'unlockable' 'fun' C ]" :=
+  (@Unlockable _ (fun _ => _) C (unlock _)) : form_scope.
+ +
+
+ +
+ Generic keyed constant locking. +
+ + The argument order ensures that k is always compared before T. +
+
+Definition locked_with k := let: tt := k in fun T x => x : T.
+ +
+
+ +
+ This can be used as a cheap alternative to cloning the unlockable instance + below, but with caution as unkeyed matching can be expensive. +
+
+Lemma locked_withE T k x : unkeyed (locked_with k x) = x :> T.
+ +
+
+ +
+ Intensionaly, this instance will not apply to locked u. +
+
+Canonical locked_with_unlockable T k x :=
+  @Unlockable T x (locked_with k x) (locked_withE k x).
+ +
+
+ +
+ More accurate variant of unlock, and safer alternative to locked_withE. +
+
+Lemma unlock_with T k x : unlocked (locked_with_unlockable k x) = x :> T.
+ +
+
+ +
+ Notation to trigger Rocq elaboration to fill the holes +
+
+Notation "[ 'elaborate' x ]" := (ltac:(refine x)) (only parsing).
+ +
+
+ +
+ The internal lemmas for the have tactics. +
+
+ +
+Lemma ssr_have
+  (Plemma : Prop) (Pgoal : Prop)
+  (step : Plemma) (rest : Plemma -> Pgoal) : Pgoal.
+ +
+Register ssr_have as plugins.ssreflect.ssr_have.
+ +
+Polymorphic Lemma ssr_have_upoly@{s1 s2|u1 u2|}
+  (Plemma : Type@{s1|u1}) (Pgoal : Type@{s2|u2})
+  (step : Plemma) (rest : Plemma -> Pgoal) : Pgoal.
+ +
+Register ssr_have_upoly as plugins.ssreflect.ssr_have_upoly.
+ +
+
+ +
+ Internal N-ary congruence lemmas for the congr tactic. +
+
+ +
+Fixpoint nary_congruence_statement (n : nat)
+         : (forall B, (B -> B -> Prop) -> Prop) -> Prop :=
+  match n with
+  | O => fun k => forall B, k B (fun x1 x2 : B => x1 = x2)
+  | S n' =>
+    let k' A B e (f1 f2 : A -> B) :=
+      forall x1 x2, x1 = x2 -> (e (f1 x1) (f2 x2) : Prop) in
+    fun k => forall A, nary_congruence_statement n' (fun B e => k _ (k' A B e))
+  end.
+ +
+Lemma nary_congruence n (k := fun B e => forall y : B, (e y y : Prop)) :
+  nary_congruence_statement n k.
+ +
+Lemma ssr_congr_arrow Plemma Pgoal : Plemma = Pgoal -> Plemma -> Pgoal.
+ Arguments ssr_congr_arrow : clear implicits.
+ +
+Register nary_congruence as plugins.ssreflect.nary_congruence.
+Register ssr_congr_arrow as plugins.ssreflect.ssr_congr_arrow.
+ +
+
+ +
+ View lemmas that don't use reflection. +
+
+ +
+Section ApplyIff.
+ +
+Variables P Q : Prop.
+Hypothesis eqPQ : P <-> Q.
+ +
+Lemma iffLR : P -> Q.
+Lemma iffRL : Q -> P.
+ +
+Lemma iffLRn : ~P -> ~Q.
+Lemma iffRLn : ~Q -> ~P.
+ +
+End ApplyIff.
+ +
+ +
+
+ +
+ To focus non-ssreflect tactics on a subterm, eg vm_compute. + Usage: + elim/abstract_context: (pattern) => G defG. + vm_compute; rewrite {}defG {G}. + Note that vm_cast are not stored in the proof term + for reductions occurring in the context, hence + set here := pattern; vm_compute in (value of here) + blows up at Qed time. +
+
+Lemma abstract_context T (P : T -> Type) x :
+  (forall Q, Q = P -> Q x) -> P x.
+ +
+ +
+Require Export ssrunder.
+ +
+#[global]
+Hint Extern 0 (@Under_rel.Over_rel _ _ _ _) =>
+  solve [ apply: Under_rel.over_rel_done ] : core.
+#[global]
+Hint Resolve Under_rel.over_rel_done : core.
+ +
+Register Under_rel.Under_rel as plugins.ssreflect.Under_rel.
+Register Under_rel.Under_rel_from_rel as plugins.ssreflect.Under_rel_from_rel.
+ +
+
+ +
+Closing rewrite rule +
+
+Definition over := over_rel.
+ +
+
+ +
+Closing tactic +
+
+Ltac over :=
+  by [ apply: Under_rel.under_rel_done
+     | rewrite over
+     ].
+ +
+
+ +
+Convenience rewrite rule to unprotect evars, e.g., to instantiate + them in another way than with reflexivity. +
+
+Definition UnderE := Under_relE.
+ +
+ +
+
+ +
+An interface for non-Prop types; used to avoid improper instantiation + of polymorphic lemmas with on-demand implicits when they are used as views. + For example: Some_inj {T} : forall x y : T, Some x = Some y -> x = y. + Using move/Some_inj on a goal of the form Some n = Some 0 will fail: + SSReflect will interpret the view as @Some_inj ?T top_assumption + since this is the well-typed application of the view with the minimal + number of inserted evars (taking ?T := Some n = Some 0), and then will + later complain that it cannot erase top_assumption after having + abstracted the viewed assumption. Making x and y maximal implicits + would avoid this and force the intended @Some_inj nat x y top_assumption + interpretation, but is undesirable as it makes it harder to use Some_inj + with the many SSReflect and MathComp lemmas that have an injectivity + premise. Specifying {T : nonPropType} solves this more elegantly, as then + (?T : Type) no longer unifies with (Some n = Some 0), which has sort Prop. + +
+
+ +
+Module NonPropType.
+ +
+
+ +
+Implementation notes: + We rely on three interface Structures: +
    +
  • test_of r, the middle structure, performs the actual check: it has two + canonical instances whose 'condition' projection are maybeProj (?P : Prop) + and tt, and which set r := true and r := false, respectively. Unifying + condition (?t : test_of ?r) with maybeProj T will thus set ?r to true if + T is in Prop as the test_Prop T instance will apply, and otherwise simplify + maybeProp T to tt and use the test_negative instance and set ?r to false. + +
    • +
  • call_of c r sets up a call to test_of on condition c with expected result r. + It has a default instance for its 'callee' projection to Type, which + sets c := maybeProj T and r := false when unifying with a type T. + +
    • +
  • type is a telescope on call_of c r, which checks that unifying test_of ?r1 + with c indeed sets ?r1 := r; the type structure bundles the 'test' instance + and its 'result' value along with its call_of c r projection. The default + instance essentially provides eta-expansion for 'type'. This is only + essential for the first 'result' projection to bool; using the instance + for other projection merely avoids spurious delta expansions that would + spoil the notProp T notation. + +
    • +
+ In detail, unifying T =~= ?S with ?S : nonPropType, i.e., + (1) T =~= @callee (@condition (result ?S) (test ?S)) (result ?S) (frame ?S) + first uses the default call instance with ?T := T to reduce (1) to + (2a) @condition (result ?S) (test ?S) =~= maybeProp T + (3) result ?S =~= false + (4) frame ?S =~= call T + along with some trivial universe-related checks which are irrelevant here. + Then the unification tries to use the test_Prop instance to reduce (2a) to + (6a) result ?S =~= true + (7a) ?P =~= T with ?P : Prop + (8a) test ?S =~= test_Prop ?P + Now the default 'check' instance with ?result := true resolves (6a) as + (9a) ?S := @check true ?test ?frame + Then (7a) can be solved precisely if T has sort at most (hence exactly) Prop, + and then (8a) is solved by the check instance, yielding ?test := test_Prop T, + and completing the solution of (2a), and committing to it. But now (3) is + inconsistent with (9a), and this makes the entire problem (1) fails. + If on the other hand T does not have sort Prop then (7a) fails and the + unification resorts to delta expanding (2a), which gives + (2b) @condition (result ?S) (test ?S) =~= tt + which is then reduced, using the test_negative instance, to + (6b) result ?S =~= false + (8b) test ?S =~= test_negative + Both are solved using the check default instance, as in the (2a) branch, giving + (9b) ?S := @check false test_negative ?frame + Then (3) and (4) are similarly solved using check, giving the final assignment + (9) ?S := notProp T + Observe that we must perform the actual test unification on the arguments + of the initial canonical instance, and not on the instance itself as we do + in mathcomp/matrix and mathcomp/vector, because we want the unification to + fail when T has sort Prop. If both the test_of and the result check + unifications were done as part of the structure telescope then the latter + would be a sub-problem of the former, and thus failing the check would merely + make the test_of unification backtrack and delta-expand and we would not get + failure. + +
+
+ +
+Structure call_of (condition : unit) (result : bool) := Call {callee : Type}.
+Definition maybeProp (T : Type) := tt.
+Definition call T := Call (maybeProp T) false T.
+ +
+Structure test_of (result : bool) := Test {condition :> unit}.
+Definition test_Prop (P : Prop) := Test true (maybeProp P).
+Definition test_negative := Test false tt.
+ +
+Structure type :=
+  Check {result : bool; test : test_of result; frame : call_of test result}.
+Definition check result test frame := @Check result test frame.
+ +
+Module Exports.
+Canonical call.
+Canonical test_Prop.
+Canonical test_negative.
+Canonical check.
+Notation nonPropType := type.
+Coercion callee : call_of >-> Sortclass.
+Coercion frame : type >-> call_of.
+Notation notProp T := (@check false test_negative (call T)).
+End Exports.
+ +
+End NonPropType.
+Export NonPropType.Exports.
+ +
+Module Export ipat.
+ +
+Notation "'[' 'apply' ']'" := (ltac:(let f := fresh "_top_" in move=> f {}/f))
+  (at level 0, only parsing) : ssripat_scope.
+ +
+Notation "'[' 'swap' ']'" := (ltac:(move;
+  let x := lazymatch goal with
+    | |- forall (x : _), _ => fresh x | |- let x := _ in _ => fresh x | _ => fresh "_top_"
+  end in intro x; move;
+  let y := lazymatch goal with
+    | |- forall (y : _), _ => fresh y | |- let y := _ in _ => fresh y | _ => fresh "_top_"
+  end in intro y; revert x; revert y))
+  (at level 0, only parsing) : ssripat_scope.
+ +
+Notation "'[' 'dup' ']'" := (ltac:(move;
+  lazymatch goal with
+  | |- forall (x : _), _ =>
+    let x := fresh x in intro x;
+    let copy := fresh x in have copy := x; revert x; revert copy
+  | |- let x := _ in _ =>
+    let x := fresh x in intro x;
+    let copy := fresh x in pose copy := x;
+    do [unfold x in (value of copy)]; revert x; revert copy
+  | |- _ =>
+    let x := fresh "_top_" in move=> x;
+    let copy := fresh "_top" in have copy := x; revert x; revert copy
+  end))
+  (at level 0, only parsing) : ssripat_scope.
+ +
+Notation "'[' '1' '!' rules ']'" := (ltac:(rewrite rules))
+  (at level 0, rules at level 200, only parsing) : ssripat_scope.
+Notation "'[' '!' rules ']'" := (ltac:(rewrite !rules))
+  (at level 0, rules at level 200, only parsing) : ssripat_scope.
+ +
+End ipat.
+ +
+ +
+Class vm_compute_eq {T : Type} (x y : T) := vm_compute : x = y.
+ +
+#[global]
+Hint Extern 0 (@vm_compute_eq _ _ _) =>
+       vm_compute; reflexivity : typeclass_instances.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.ssr.ssrfun.html b/master/corelib/Corelib.ssr.ssrfun.html new file mode 100644 index 0000000000..c7f27dbc16 --- /dev/null +++ b/master/corelib/Corelib.ssr.ssrfun.html @@ -0,0 +1,1209 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.ssr.ssrfun

+ +
+ +
+ +
+
+ +
+ +
+
+ +
+Require Import ssreflect.
+ +
+
+ +
+ This file contains the basic definitions and notations for working with + functions. The definitions provide for: + +
+ +
    +
  • Pair projections: + p.1 == first element of a pair + p.2 == second element of a pair + These notations also apply to p : P /\ Q, via an and >-> pair coercion. + +
    + + +
    • +
  • Simplifying functions, beta-reduced by /= and simpl: + [fun : T => E] == constant function from type T that returns E + [fun x => E] == unary function + [fun x : T => E] == unary function with explicit domain type + [fun x y => E] == binary function + [fun x y : T => E] == binary function with common domain type + [fun (x : T) y => E] \ + +
    • +
+ [fun (x : xT) (y : yT) => E] | == binary function with (some) explicit, + [fun x (y : T) => E] / independent domain types for each argument + +
+ +
    +
  • Partial functions using option type: + oapp f d ox == if ox is Some x returns f x, d otherwise + odflt d ox == if ox is Some x returns x, d otherwise + obind f ox == if ox is Some x returns f x, None otherwise + omap f ox == if ox is Some x returns Some (f x), None otherwise + olift f := Some \o f + +
    + + +
    • +
  • Singleton types: + all_equal_to x0 == x0 is the only value in its type, so any such value + can be rewritten to x0. + +
    + + +
    • +
  • A generic wrapper type: + wrapped T == the inductive type with values Wrap x for x : T. + unwrap w == the projection of w : wrapped T on T. + wrap x == the canonical injection of x : T into wrapped T; it is + equivalent to Wrap x, but is declared as a (default) + Canonical Structure, which lets the Rocq HO unification + automatically expand x into unwrap (wrap x). The delta + reduction of wrap x to Wrap can be exploited to + introduce controlled nondeterminism in Canonical + Structure inference, as in the implementation of + the mxdirect predicate in matrix.v. + +
    + + +
    • +
  • The empty type: + void == a notation for the Empty_set type of the standard library. + of_void T == the canonical injection void -> T. + +
    + + +
    • +
  • Sigma types: + tag w == the i of w : {i : I & T i}. + tagged w == the T i component of w : {i : I & T i}. + Tagged T x == the {i : I & T i} with component x : T i. + tag2 w == the i of w : {i : I & T i & U i}. + tagged2 w == the T i component of w : {i : I & T i & U i}. + tagged2' w == the U i component of w : {i : I & T i & U i}. + +
    • +
+ Tagged2 T U x y == the {i : I & T i} with components x : T i and y : U i. + sval u == the x of u : {x : T | P x}. + s2val u == the x of u : {x : T | P x & Q x}. + The properties of sval u, s2val u are given by lemmas svalP, s2valP, and + s2valP'. We provide coercions sigT2 >-> sigT and sig2 >-> sig >-> sigT. + A suite of lemmas (all_sig, ...) let us skolemize sig, sig2, sigT, sigT2 + and pair, e.g., + have /all_sig[f fP] (x : T): {y : U | P y} by ... + yields an f : T -> U such that fP : forall x, P (f x). +
    +
  • Identity functions: + id == NOTATION for the explicit identity function fun x => x. + @id T == notation for the explicit identity at type T. + idfun == an expression with a head constant, convertible to id; + idfun x simplifies to x. + @idfun T == the expression above, specialized to type T. + phant_id x y == the function type phantom _ x -> phantom _ y. + +
    • +
+ *** In addition to their casual use in functional programming, identity + functions are often used to trigger static unification as part of the + construction of dependent Records and Structures. For example, if we need + a structure sT over a type T, we take as arguments T, sT, and a "dummy" + function T -> sort sT: + Definition foo T sT & T -> sort sT := ... + We can avoid specifying sT directly by calling foo (@id T), or specify + the call completely while still ensuring the consistency of T and sT, by + calling @foo T sT idfun. The phant_id type allows us to extend this trick + to non-Type canonical projections. It also allows us to sidestep + dependent type constraints when building explicit records, e.g., given + Record r := R {x; y : T(x)}. + if we need to build an r from a given y0 while inferring some x0, such + that y0 : T(x0), we pose + Definition mk_r .. y .. (x := ...) y' & phant_id y y' := R x y'. + Calling @mk_r .. y0 .. id will cause Rocq to use y' := y0, while checking + the dependent type constraint y0 : T(x0). + +
+ +
    +
  • Extensional equality for functions and relations (i.e. functions of two + arguments): + f1 =1 f2 == f1 x is equal to f2 x for all x. + f1 =1 f2 :> A == ... and f2 is explicitly typed. + f1 =2 f2 == f1 x y is equal to f2 x y for all x y. + f1 =2 f2 :> A == ... and f2 is explicitly typed. + +
    + + +
    • +
  • Composition for total and partial functions: + f^~ y == function f with second argument specialised to y, + i.e., fun x => f x y + CAVEAT: conditional (non-maximal) implicit arguments + of f are NOT inserted in this context + @^~ x == application at x, i.e., fun f => f x + [eta f] == the explicit eta-expansion of f, i.e., fun x => f x + CAVEAT: conditional (non-maximal) implicit arguments + of f are NOT inserted in this context. + fun=> v := the constant function fun _ => v. + f1 \o f2 == composition of f1 and f2. + Note: (f1 \o f2) x simplifies to f1 (f2 x). + f1 \; f2 == categorical composition of f1 and f2. This expands to + to f2 \o f1 and (f1 \; f2) x simplifies to f2 (f1 x). + pcomp f1 f2 == composition of partial functions f1 and f2. + +
    • +
+ +
+ + +
+ +
    +
  • Properties of functions: + injective f <-> f is injective. + cancel f g <-> g is a left inverse of f / f is a right inverse of g. + pcancel f g <-> g is a left inverse of f where g is partial. + ocancel f g <-> g is a left inverse of f where f is partial. + bijective f <-> f is bijective (has a left and right inverse). + involutive f <-> f is involutive. + +
    + + +
    • +
  • Properties for operations. + left_id e op <-> e is a left identity for op (e op x = x). + right_id e op <-> e is a right identity for op (x op e = x). + left_inverse e inv op <-> inv is a left inverse for op wrt identity e, + i.e., (inv x) op x = e. + right_inverse e inv op <-> inv is a right inverse for op wrt identity e + i.e., x op (i x) = e. + self_inverse e op <-> each x is its own op-inverse (x op x = e). + idempotent op <-> op is idempotent for op (x op x = x). + associative op <-> op is associative, i.e., + x op (y op z) = (x op y) op z. + commutative op <-> op is commutative (x op y = y op x). + left_commutative op <-> op is left commutative, i.e., + x op (y op z) = y op (x op z). + right_commutative op <-> op is right commutative, i.e., + (x op y) op z = (x op z) op y. + left_zero z op <-> z is a left zero for op (z op x = z). + right_zero z op <-> z is a right zero for op (x op z = z). + left_distributive op1 op2 <-> op1 distributes over op2 to the left: + (x op2 y) op1 z = (x op1 z) op2 (y op1 z). + +
    • +
+ right_distributive op1 op2 <-> op distributes over add to the right: + x op1 (y op2 z) = (x op1 z) op2 (x op1 z). + interchange op1 op2 <-> op1 and op2 satisfy an interchange law: + (x op2 y) op1 (z op2 t) = (x op1 z) op2 (y op1 t). + Note that interchange op op is a commutativity property. + left_injective op <-> op is injective in its left argument: + x op y = z op y -> x = z. + right_injective op <-> op is injective in its right argument: + x op y = x op z -> y = z. + left_loop inv op <-> op, inv obey the inverse loop left axiom: + (inv x) op (x op y) = y for all x, y, i.e., + op (inv x) is always a left inverse of op x + rev_left_loop inv op <-> op, inv obey the inverse loop reverse left + axiom: x op ((inv x) op y) = y, for all x, y. + right_loop inv op <-> op, inv obey the inverse loop right axiom: + (x op y) op (inv y) = x for all x, y. + rev_right_loop inv op <-> op, inv obey the inverse loop reverse right + axiom: (x op (inv y)) op y = x for all x, y. + Note that familiar "cancellation" identities like x + y - y = x or + x - y + y = x are respectively instances of right_loop and rev_right_loop + The corresponding lemmas will use the K and NK/VK suffixes, respectively. + +
+ +
    +
  • Morphisms for functions and relations: + {morph f : x / a >-> r} <-> f is a morphism with respect to functions + (fun x => a) and (fun x => r); if r == R[x], + this states that f a = R[f x] for all x. + {morph f : x / a} <-> f is a morphism with respect to the + function expression (fun x => a). This is + shorthand for {morph f : x / a >-> a}; note + that the two instances of a are often + interpreted at different types. + {morph f : x y / a >-> r} <-> f is a morphism with respect to functions + (fun x y => a) and (fun x y => r). + {morph f : x y / a} <-> f is a morphism with respect to the + function expression (fun x y => a). + {homo f : x / a >-> r} <-> f is a homomorphism with respect to the + predicates (fun x => a) and (fun x => r); + if r == R[x], this states that a -> R[f x] + for all x. + {homo f : x / a} <-> f is a homomorphism with respect to the + predicate expression (fun x => a). + {homo f : x y / a >-> r} <-> f is a homomorphism with respect to the + relations (fun x y => a) and (fun x y => r). + {homo f : x y / a} <-> f is a homomorphism with respect to the + relation expression (fun x y => a). + {mono f : x / a >-> r} <-> f is monotone with respect to projectors + (fun x => a) and (fun x => r); if r == R[x], + this states that R[f x] = a for all x. + {mono f : x / a} <-> f is monotone with respect to the projector + expression (fun x => a). + {mono f : x y / a >-> r} <-> f is monotone with respect to relators + (fun x y => a) and (fun x y => r). + {mono f : x y / a} <-> f is monotone with respect to the relator + expression (fun x y => a). + +
    • +
+ +
+ + The file also contains some basic lemmas for the above concepts. + Lemmas relative to cancellation laws use some abbreviated suffixes: + K - a cancellation rule like esymK : cancel (@esym T x y) (@esym T y x). + LR - a lemma moving an operation from the left hand side of a relation to + the right hand side, like canLR: cancel g f -> x = g y -> f x = y. + RL - a lemma moving an operation from the right to the left, e.g., canRL. + Beware that the LR and RL orientations refer to an "apply" (back chaining) + usage; when using the same lemmas with "have" or "move" (forward chaining) + the directions will be reversed!. +
+
+ +
+Set Implicit Arguments.
+ +
+
+ +
+Parsing / printing declarations. +
+
+Reserved Notation "f ^~ y" (at level 10, y at level 8, no associativity,
+  format "f ^~ y").
+Reserved Notation "@^~ x" (at level 10, x at level 8, no associativity,
+  format "@^~ x").
+Reserved Notation "[ 'eta' f ]" (at level 0, format "[ 'eta' f ]").
+Reserved Notation "'fun' => E" (at level 200, format "'fun' => E").
+ +
+Reserved Notation "[ 'fun' : T => E ]" (at level 0,
+  format "'[hv' [ 'fun' : T => '/ ' E ] ']'").
+Reserved Notation "[ 'fun' x => E ]" (at level 0,
+  x name, format "'[hv' [ 'fun' x => '/ ' E ] ']'").
+Reserved Notation "[ 'fun' x : T => E ]" (at level 0,
+  x name, format "'[hv' [ 'fun' x : T => '/ ' E ] ']'").
+Reserved Notation "[ 'fun' x y => E ]" (at level 0,
+  x name, y name, format "'[hv' [ 'fun' x y => '/ ' E ] ']'").
+Reserved Notation "[ 'fun' x y : T => E ]" (at level 0,
+  x name, y name, format "'[hv' [ 'fun' x y : T => '/ ' E ] ']'").
+Reserved Notation "[ 'fun' ( x : T ) y => E ]" (at level 0,
+  x name, y name, format "'[hv' [ 'fun' ( x : T ) y => '/ ' E ] ']'").
+Reserved Notation "[ 'fun' x ( y : T ) => E ]" (at level 0,
+  x name, y name, format "'[hv' [ 'fun' x ( y : T ) => '/ ' E ] ']'").
+Reserved Notation "[ 'fun' ( x : T ) ( y : U ) => E ]" (at level 0,
+  x name, y name, format "[ 'fun' ( x : T ) ( y : U ) => E ]" ).
+ +
+Reserved Notation "f =1 g" (at level 70, no associativity).
+Reserved Notation "f =1 g :> A" (at level 70, g at next level, A at level 90).
+Reserved Notation "f =2 g" (at level 70, no associativity).
+Reserved Notation "f =2 g :> A" (at level 70, g at next level, A at level 90).
+Reserved Notation "f \o g" (at level 50, format "f \o '/ ' g").
+Reserved Notation "f \; g" (at level 60, right associativity,
+  format "f \; '/ ' g").
+ +
+Reserved Notation "{ 'morph' f : x / a >-> r }" (at level 0, f at level 99,
+  x name, format "{ 'morph' f : x / a >-> r }").
+Reserved Notation "{ 'morph' f : x / a }" (at level 0, f at level 99,
+  x name, format "{ 'morph' f : x / a }").
+Reserved Notation "{ 'morph' f : x y / a >-> r }" (at level 0, f at level 99,
+  x name, y name, format "{ 'morph' f : x y / a >-> r }").
+Reserved Notation "{ 'morph' f : x y / a }" (at level 0, f at level 99,
+  x name, y name, format "{ 'morph' f : x y / a }").
+Reserved Notation "{ 'homo' f : x / a >-> r }" (at level 0, f at level 99,
+  x name, format "{ 'homo' f : x / a >-> r }").
+Reserved Notation "{ 'homo' f : x / a }" (at level 0, f at level 99,
+  x name, format "{ 'homo' f : x / a }").
+Reserved Notation "{ 'homo' f : x y / a >-> r }" (at level 0, f at level 99,
+  x name, y name, format "{ 'homo' f : x y / a >-> r }").
+Reserved Notation "{ 'homo' f : x y / a }" (at level 0, f at level 99,
+  x name, y name, format "{ 'homo' f : x y / a }").
+Reserved Notation "{ 'homo' f : x y /~ a }" (at level 0, f at level 99,
+  x name, y name, format "{ 'homo' f : x y /~ a }").
+Reserved Notation "{ 'mono' f : x / a >-> r }" (at level 0, f at level 99,
+  x name, format "{ 'mono' f : x / a >-> r }").
+Reserved Notation "{ 'mono' f : x / a }" (at level 0, f at level 99,
+  x name, format "{ 'mono' f : x / a }").
+Reserved Notation "{ 'mono' f : x y / a >-> r }" (at level 0, f at level 99,
+  x name, y name, format "{ 'mono' f : x y / a >-> r }").
+Reserved Notation "{ 'mono' f : x y / a }" (at level 0, f at level 99,
+  x name, y name, format "{ 'mono' f : x y / a }").
+Reserved Notation "{ 'mono' f : x y /~ a }" (at level 0, f at level 99,
+  x name, y name, format "{ 'mono' f : x y /~ a }").
+ +
+Reserved Notation "@ 'id' T" (at level 10, T at level 8, format "@ 'id' T").
+#[warning="-closed-notation-not-level-0"]
+Reserved Notation "@ 'sval'" (at level 10, format "@ 'sval'").
+ +
+
+ +
+ Syntax for defining auxiliary recursive function. + Usage: + Section FooDefinition. + Variables (g1 : T1) (g2 : T2). (globals) + Fixoint foo_auxiliary (a3 : T3) ... := + body, using [rec e3, ... ] for recursive calls + where " [ 'rec' a3 , a4 , ... ]" := foo_auxiliary. + Definition foo x y .. := [rec e1, ... ]. + + proofs about foo + End FooDefinition. +
+
+ +
+Reserved Notation "[ 'rec' a ]" (at level 0,
+  format "[ 'rec' a ]").
+Reserved Notation "[ 'rec' a , b ]" (at level 0,
+  format "[ 'rec' a , b ]").
+Reserved Notation "[ 'rec' a , b , c ]" (at level 0,
+  format "[ 'rec' a , b , c ]").
+Reserved Notation "[ 'rec' a , b , c , d ]" (at level 0,
+  format "[ 'rec' a , b , c , d ]").
+Reserved Notation "[ 'rec' a , b , c , d , e ]" (at level 0,
+  format "[ 'rec' a , b , c , d , e ]").
+Reserved Notation "[ 'rec' a , b , c , d , e , f ]" (at level 0,
+  format "[ 'rec' a , b , c , d , e , f ]").
+Reserved Notation "[ 'rec' a , b , c , d , e , f , g ]" (at level 0,
+  format "[ 'rec' a , b , c , d , e , f , g ]").
+Reserved Notation "[ 'rec' a , b , c , d , e , f , g , h ]" (at level 0,
+  format "[ 'rec' a , b , c , d , e , f , g , h ]").
+Reserved Notation "[ 'rec' a , b , c , d , e , f , g , h , i ]" (at level 0,
+  format "[ 'rec' a , b , c , d , e , f , g , h , i ]").
+Reserved Notation "[ 'rec' a , b , c , d , e , f , g , h , i , j ]" (at level 0,
+  format "[ 'rec' a , b , c , d , e , f , g , h , i , j ]").
+ +
+Declare Scope pair_scope.
+Delimit Scope pair_scope with PAIR.
+Open Scope pair_scope.
+ +
+
+ +
+ Notations for pair/conjunction projections +
+
+Notation "p .1" := (fst p) : pair_scope.
+Notation "p .2" := (snd p) : pair_scope.
+ +
+Coercion pair_of_and P Q (PandQ : P /\ Q) := (proj1 PandQ, proj2 PandQ).
+ +
+Definition all_pair I T U (w : forall i : I, T i * U i) :=
+  (fun i => (w i).1, fun i => (w i).2).
+ +
+
+ +
+ Complements on the option type constructor, used below to + encode partial functions. +
+
+ +
+Module Option.
+ +
+Definition apply aT rT (f : aT -> rT) x u := if u is Some y then f y else x.
+ +
+Definition default T := apply (fun x : T => x).
+ +
+Definition bind aT rT (f : aT -> option rT) := apply f None.
+ +
+Definition map aT rT (f : aT -> rT) := bind (fun x => Some (f x)).
+ +
+Definition lift aT rT (f : aT -> rT) := fun x => Some (f x).
+ +
+End Option.
+ +
+Notation oapp := Option.apply.
+Notation odflt := Option.default.
+Notation obind := Option.bind.
+Notation omap := Option.map.
+Notation olift := Option.lift.
+Notation some := (@Some _) (only parsing).
+ +
+
+ +
+ Shorthand for some basic equality lemmas. +
+
+ +
+Notation erefl := refl_equal.
+Notation ecast i T e x := (let: erefl in _ = i := e return T in x).
+Definition esym := sym_eq.
+Definition nesym := sym_not_eq.
+Definition etrans := trans_eq.
+Definition congr1 := f_equal.
+Definition congr2 := f_equal2.
+
+ +
+ Force at least one implicit when used as a view. +
+
+ +
+
+ +
+ A predicate for singleton types. +
+
+Definition all_equal_to T (x0 : T) := forall x, unkeyed x = x0.
+ +
+Lemma unitE : all_equal_to tt.
+ +
+
+ +
+ A generic wrapper type +
+
+ +
+#[universes(template)]
+Structure wrapped T := Wrap {unwrap : T}.
+Canonical wrap T x := @Wrap T x.
+ +
+ +
+
+ +
+ fun_scope below is deprecated and should eventually be + removed. Use function_scope instead. +
+
+Declare Scope fun_scope.
+Delimit Scope fun_scope with FUN.
+Open Scope fun_scope.
+Open Scope function_scope.
+ +
+
+ +
+ Notations for argument transpose +
+
+Notation "f ^~ y" := (fun x => f x y) : function_scope.
+Notation "@^~ x" := (fun f => f x) : function_scope.
+ +
+
+ +
+ Definitions and notation for explicit functions with simplification, + i.e., which simpl and /= beta expand (this is complementary to nosimpl). +
+
+ +
+#[universes(template)]
+Variant simpl_fun (aT rT : Type) := SimplFun of aT -> rT.
+ +
+Section SimplFun.
+ +
+Variables aT rT : Type.
+ +
+Definition fun_of_simpl (f : simpl_fun aT rT) := fun x => let: SimplFun lam := f in lam x.
+ +
+End SimplFun.
+ +
+Coercion fun_of_simpl : simpl_fun >-> Funclass.
+ +
+Notation "[ 'fun' : T => E ]" := (SimplFun (fun _ : T => E)) : function_scope.
+Notation "[ 'fun' x => E ]" := (SimplFun (fun x => E)) : function_scope.
+Notation "[ 'fun' x y => E ]" := (fun x => [fun y => E]) : function_scope.
+Notation "[ 'fun' x : T => E ]" := (SimplFun (fun x : T => E))
+  (only parsing) : function_scope.
+Notation "[ 'fun' x y : T => E ]" := (fun x : T => [fun y : T => E])
+  (only parsing) : function_scope.
+Notation "[ 'fun' ( x : T ) y => E ]" := (fun x : T => [fun y => E])
+  (only parsing) : function_scope.
+Notation "[ 'fun' x ( y : T ) => E ]" := (fun x => [fun y : T => E])
+  (only parsing) : function_scope.
+Notation "[ 'fun' ( x : T ) ( y : U ) => E ]" := (fun x : T => [fun y : U => E])
+  (only parsing) : function_scope.
+ +
+
+ +
+ For delta functions in eqtype.v. +
+
+Definition SimplFunDelta aT rT (f : aT -> aT -> rT) := [fun z => f z z].
+ +
+
+ +
+ Extensional equality, for unary and binary functions, including syntactic + sugar. +
+
+ +
+Section ExtensionalEquality.
+ +
+Variables A B C : Type.
+ +
+Definition eqfun (f g : B -> A) : Prop := forall x, f x = g x.
+ +
+Definition eqrel (r s : C -> B -> A) : Prop := forall x y, r x y = s x y.
+ +
+Lemma frefl f : eqfun f f.
+Lemma fsym f g : eqfun f g -> eqfun g f.
+ +
+Lemma ftrans f g h : eqfun f g -> eqfun g h -> eqfun f h.
+ +
+Lemma rrefl r : eqrel r r.
+ +
+End ExtensionalEquality.
+ +
+Global Typeclasses Opaque eqfun eqrel.
+ +
+#[global]
+Hint Resolve frefl rrefl : core.
+ +
+Notation "f1 =1 f2" := (eqfun f1 f2) : type_scope.
+Notation "f1 =1 f2 :> A" := (f1 =1 (f2 : A)) : type_scope.
+Notation "f1 =2 f2" := (eqrel f1 f2) : type_scope.
+Notation "f1 =2 f2 :> A" := (f1 =2 (f2 : A)) : type_scope.
+ +
+Section Composition.
+ +
+Variables A B C : Type.
+ +
+Definition comp (f : B -> A) (g : C -> B) x := f (g x).
+Definition catcomp g f := comp f g.
+Definition pcomp (f : B -> option A) (g : C -> option B) x := obind f (g x).
+ +
+Lemma eq_comp f f' g g' : f =1 f' -> g =1 g' -> comp f g =1 comp f' g'.
+ +
+End Composition.
+ +
+Arguments comp {A B C} f g x /.
+Arguments catcomp {A B C} g f x /.
+Notation "f1 \o f2" := (comp f1 f2) : function_scope.
+Notation "f1 \; f2" := (catcomp f1 f2) : function_scope.
+ +
+Lemma compA {A B C D : Type} (f : B -> A) (g : C -> B) (h : D -> C) :
+  f \o (g \o h) = (f \o g) \o h.
+ +
+Notation "[ 'eta' f ]" := (fun x => f x) : function_scope.
+ +
+Notation "'fun' => E" := (fun _ => E) : function_scope.
+ +
+Notation id := (fun x => x).
+ +
+Notation "@ 'id' T" := (fun x : T => x) (only parsing) : function_scope.
+ +
+Definition idfun T x : T := x.
+Arguments idfun {T} x /.
+ +
+Definition phant_id T1 T2 v1 v2 := phantom T1 v1 -> phantom T2 v2.
+ +
+Section OptionTheory.
+ +
+Variables (aT rT sT : Type) (f : aT -> rT) (g : rT -> sT).
+ +
+Lemma obindEapp (fo : aT -> option rT) : obind fo = oapp fo None.
+ +
+Lemma omapEbind : omap f = obind (olift f).
+ +
+Lemma omapEapp : omap f = oapp (olift f) None.
+ +
+Lemma oappEmap (y0 : rT) x : oapp f y0 x = odflt y0 (omap f x).
+ +
+Lemma omap_comp : omap (g \o f) =1 omap g \o omap f.
+ +
+Lemma oapp_comp x : oapp (g \o f) x =1 (@oapp _ _)^~ x g \o omap f.
+ +
+Lemma oapp_comp_f (x : rT) : oapp (g \o f) (g x) =1 g \o oapp f x.
+ +
+Lemma olift_comp : olift (g \o f) = olift g \o f.
+ +
+End OptionTheory.
+ +
+
+ +
+The empty type. +
+
+ +
+Notation void := Empty_set.
+ +
+Definition of_void T (x : void) : T := match x with end.
+ +
+
+ +
+ Strong sigma types. +
+
+ +
+Section Tag.
+ +
+Variables (I : Type) (i : I) (T_ U_ : I -> Type).
+ +
+Definition tag := projT1.
+Definition tagged : forall w, T_(tag w) := @projT2 I [eta T_].
+Definition Tagged x := @existT I [eta T_] i x.
+ +
+Definition tag2 (w : @sigT2 I T_ U_) := let: existT2 _ _ i _ _ := w in i.
+Definition tagged2 w : T_(tag2 w) := let: existT2 _ _ _ x _ := w in x.
+Definition tagged2' w : U_(tag2 w) := let: existT2 _ _ _ _ y := w in y.
+Definition Tagged2 x y := @existT2 I [eta T_] [eta U_] i x y.
+ +
+End Tag.
+ +
+Arguments Tagged [I i].
+Arguments Tagged2 [I i].
+ +
+Coercion tag_of_tag2 I T_ U_ (w : @sigT2 I T_ U_) :=
+  Tagged (fun i => T_ i * U_ i)%type (tagged2 w, tagged2' w).
+ +
+Lemma all_tag I T U :
+   (forall x : I, {y : T x & U x y}) ->
+  {f : forall x, T x & forall x, U x (f x)}.
+ +
+Lemma all_tag2 I T U V :
+    (forall i : I, {y : T i & U i y & V i y}) ->
+  {f : forall i, T i & forall i, U i (f i) & forall i, V i (f i)}.
+ +
+
+ +
+ Refinement types. +
+ + Prenex Implicits and renaming. +
+
+Notation sval := (@proj1_sig _ _).
+Notation "@ 'sval'" := (@proj1_sig) (only parsing) : function_scope.
+ +
+Section Sig.
+ +
+Variables (T : Type) (P Q : T -> Prop).
+ +
+Lemma svalP (u : sig P) : P (sval u).
+ +
+Definition s2val (u : sig2 P Q) := let: exist2 _ _ x _ _ := u in x.
+ +
+Lemma s2valP u : P (s2val u).
+ +
+Lemma s2valP' u : Q (s2val u).
+ +
+End Sig.
+ +
+ +
+Coercion tag_of_sig I P (u : @sig I P) := Tagged P (svalP u).
+ +
+Coercion sig_of_sig2 I P Q (u : @sig2 I P Q) :=
+  exist (fun i => P i /\ Q i) (s2val u) (conj (s2valP u) (s2valP' u)).
+ +
+Lemma all_sig I T P :
+    (forall x : I, {y : T x | P x y}) ->
+  {f : forall x, T x | forall x, P x (f x)}.
+ +
+Lemma all_sig2 I T P Q :
+    (forall x : I, {y : T x | P x y & Q x y}) ->
+  {f : forall x, T x | forall x, P x (f x) & forall x, Q x (f x)}.
+ +
+Section Morphism.
+ +
+Variables (aT rT sT : Type) (f : aT -> rT).
+ +
+
+ +
+ Morphism property for unary and binary functions +
+
+Definition morphism_1 aF rF := forall x, f (aF x) = rF (f x).
+Definition morphism_2 aOp rOp := forall x y, f (aOp x y) = rOp (f x) (f y).
+ +
+
+ +
+ Homomorphism property for unary and binary relations +
+
+Definition homomorphism_1 (aP rP : _ -> Prop) := forall x, aP x -> rP (f x).
+Definition homomorphism_2 (aR rR : _ -> _ -> Prop) :=
+  forall x y, aR x y -> rR (f x) (f y).
+ +
+
+ +
+ Stability property for unary and binary relations +
+
+Definition monomorphism_1 (aP rP : _ -> sT) := forall x, rP (f x) = aP x.
+Definition monomorphism_2 (aR rR : _ -> _ -> sT) :=
+  forall x y, rR (f x) (f y) = aR x y.
+ +
+End Morphism.
+ +
+Notation "{ 'morph' f : x / a >-> r }" :=
+  (morphism_1 f (fun x => a) (fun x => r)) : type_scope.
+Notation "{ 'morph' f : x / a }" :=
+  (morphism_1 f (fun x => a) (fun x => a)) : type_scope.
+Notation "{ 'morph' f : x y / a >-> r }" :=
+  (morphism_2 f (fun x y => a) (fun x y => r)) : type_scope.
+Notation "{ 'morph' f : x y / a }" :=
+  (morphism_2 f (fun x y => a) (fun x y => a)) : type_scope.
+Notation "{ 'homo' f : x / a >-> r }" :=
+  (homomorphism_1 f (fun x => a) (fun x => r)) : type_scope.
+Notation "{ 'homo' f : x / a }" :=
+  (homomorphism_1 f (fun x => a) (fun x => a)) : type_scope.
+Notation "{ 'homo' f : x y / a >-> r }" :=
+  (homomorphism_2 f (fun x y => a) (fun x y => r)) : type_scope.
+Notation "{ 'homo' f : x y / a }" :=
+  (homomorphism_2 f (fun x y => a) (fun x y => a)) : type_scope.
+Notation "{ 'homo' f : x y /~ a }" :=
+  (homomorphism_2 f (fun y x => a) (fun x y => a)) : type_scope.
+Notation "{ 'mono' f : x / a >-> r }" :=
+  (monomorphism_1 f (fun x => a) (fun x => r)) : type_scope.
+Notation "{ 'mono' f : x / a }" :=
+  (monomorphism_1 f (fun x => a) (fun x => a)) : type_scope.
+Notation "{ 'mono' f : x y / a >-> r }" :=
+  (monomorphism_2 f (fun x y => a) (fun x y => r)) : type_scope.
+Notation "{ 'mono' f : x y / a }" :=
+  (monomorphism_2 f (fun x y => a) (fun x y => a)) : type_scope.
+Notation "{ 'mono' f : x y /~ a }" :=
+  (monomorphism_2 f (fun y x => a) (fun x y => a)) : type_scope.
+ +
+
+ +
+ In an intuitionistic setting, we have two degrees of injectivity. The + weaker one gives only simplification, and the strong one provides a left + inverse (we show in `fintype' that they coincide for finite types). + We also define an intermediate version where the left inverse is only a + partial function. +
+
+ +
+Section Injections.
+ +
+Variables (rT aT : Type) (f : aT -> rT).
+ +
+Definition injective := forall x1 x2, f x1 = f x2 -> x1 = x2.
+ +
+Definition cancel g := forall x, g (f x) = x.
+ +
+Definition pcancel g := forall x, g (f x) = Some x.
+ +
+Definition ocancel (g : aT -> option rT) h := forall x, oapp h x (g x) = x.
+ +
+Lemma can_pcan g : cancel g -> pcancel (fun y => Some (g y)).
+ +
+Lemma pcan_inj g : pcancel g -> injective.
+ +
+Lemma can_inj g : cancel g -> injective.
+ +
+Lemma canLR g x y : cancel g -> x = f y -> g x = y.
+ +
+Lemma canRL g x y : cancel g -> f x = y -> x = g y.
+ +
+End Injections.
+ +
+Lemma Some_inj {T : nonPropType} : injective (@Some T).
+ +
+Lemma of_voidK T : pcancel (of_void T) [fun _ => None].
+ +
+
+ +
+ cancellation lemmas for dependent type casts. +
+
+Lemma esymK T x y : cancel (@esym T x y) (@esym T y x).
+ +
+Lemma etrans_id T x y (eqxy : x = y :> T) : etrans (erefl x) eqxy = eqxy.
+ +
+Section InjectionsTheory.
+ +
+Variables (A B C : Type) (f g : B -> A) (h : C -> B).
+ +
+Lemma inj_id : injective (@id A).
+ +
+Lemma inj_can_sym f' : cancel f f' -> injective f' -> cancel f' f.
+ +
+Lemma inj_comp : injective f -> injective h -> injective (f \o h).
+ +
+Lemma inj_compr : injective (f \o h) -> injective h.
+ +
+Lemma can_comp f' h' : cancel f f' -> cancel h h' -> cancel (f \o h) (h' \o f').
+ +
+Lemma pcan_pcomp f' h' :
+  pcancel f f' -> pcancel h h' -> pcancel (f \o h) (pcomp h' f').
+ +
+Lemma ocan_comp [fo : B -> option A] [ho : C -> option B]
+    [f' : A -> B] [h' : B -> C] :
+  ocancel fo f' -> ocancel ho h' -> ocancel (obind fo \o ho) (h' \o f').
+ +
+Lemma eq_inj : injective f -> f =1 g -> injective g.
+ +
+Lemma eq_can f' g' : cancel f f' -> f =1 g -> f' =1 g' -> cancel g g'.
+ +
+Lemma inj_can_eq f' : cancel f f' -> injective f' -> cancel g f' -> f =1 g.
+ +
+End InjectionsTheory.
+ +
+Section Bijections.
+ +
+Variables (A B : Type) (f : B -> A).
+ +
+Variant bijective : Prop := Bijective g of cancel f g & cancel g f.
+ +
+Hypothesis bijf : bijective.
+ +
+Lemma bij_inj : injective f.
+ +
+Lemma bij_can_sym f' : cancel f' f <-> cancel f f'.
+ +
+Lemma bij_can_eq f' f'' : cancel f f' -> cancel f f'' -> f' =1 f''.
+ +
+End Bijections.
+ +
+Section BijectionsTheory.
+ +
+Variables (A B C : Type) (f : B -> A) (h : C -> B).
+ +
+Lemma eq_bij : bijective f -> forall g, f =1 g -> bijective g.
+ +
+Lemma bij_comp : bijective f -> bijective h -> bijective (f \o h).
+ +
+Lemma bij_can_bij : bijective f -> forall f', cancel f f' -> bijective f'.
+ +
+End BijectionsTheory.
+ +
+Section Involutions.
+ +
+Variables (A : Type) (f : A -> A).
+ +
+Definition involutive := cancel f f.
+ +
+Hypothesis Hf : involutive.
+ +
+Lemma inv_inj : injective f.
+Lemma inv_bij : bijective f.
+ +
+End Involutions.
+ +
+Section OperationProperties.
+ +
+Variables S T R : Type.
+ +
+Section SopTisR.
+Implicit Type op : S -> T -> R.
+Definition left_inverse e inv op := forall x, op (inv x) x = e.
+Definition right_inverse e inv op := forall x, op x (inv x) = e.
+Definition left_injective op := forall x, injective (op^~ x).
+Definition right_injective op := forall y, injective (op y).
+End SopTisR.
+ +
+Section SopTisS.
+Implicit Type op : S -> T -> S.
+Definition right_id e op := forall x, op x e = x.
+Definition left_zero z op := forall x, op z x = z.
+Definition right_commutative op := forall x y z, op (op x y) z = op (op x z) y.
+Definition left_distributive op add :=
+  forall x y z, op (add x y) z = add (op x z) (op y z).
+Definition right_loop inv op := forall y, cancel (op^~ y) (op^~ (inv y)).
+Definition rev_right_loop inv op := forall y, cancel (op^~ (inv y)) (op^~ y).
+End SopTisS.
+ +
+Section SopTisT.
+Implicit Type op : S -> T -> T.
+Definition left_id e op := forall x, op e x = x.
+Definition right_zero z op := forall x, op x z = z.
+Definition left_commutative op := forall x y z, op x (op y z) = op y (op x z).
+Definition right_distributive op add :=
+  forall x y z, op x (add y z) = add (op x y) (op x z).
+Definition left_loop inv op := forall x, cancel (op x) (op (inv x)).
+Definition rev_left_loop inv op := forall x, cancel (op (inv x)) (op x).
+End SopTisT.
+ +
+Section SopSisT.
+Implicit Type op : S -> S -> T.
+Definition self_inverse e op := forall x, op x x = e.
+Definition commutative op := forall x y, op x y = op y x.
+End SopSisT.
+ +
+Section SopSisS.
+Implicit Type op : S -> S -> S.
+Definition idempotent op := forall x, op x x = x.
+Definition associative op := forall x y z, op x (op y z) = op (op x y) z.
+Definition interchange op1 op2 :=
+  forall x y z t, op1 (op2 x y) (op2 z t) = op2 (op1 x z) (op1 y t).
+End SopSisS.
+ +
+End OperationProperties.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.ssr.ssrsetoid.html b/master/corelib/Corelib.ssr.ssrsetoid.html new file mode 100644 index 0000000000..9a2835b428 --- /dev/null +++ b/master/corelib/Corelib.ssr.ssrsetoid.html @@ -0,0 +1,133 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.ssr.ssrsetoid

+ +
+ +
+
+ +
+ +
+ + Compatibility layer for under and setoid_rewrite. + +
+ + This file is intended to be required by Require Import Setoid. + +
+ + In particular, we can use the under tactic with other relations + than eq or iff, e.g. a RewriteRelation, by doing: + Require Import ssreflect. Require Setoid. + +
+ + This file's instances have priority 12 > other stdlib instances. + +
+ + (Note: this file could be skipped when porting under to stdlib2.) + +
+
+ +
+Require Import ssrclasses.
+Require Import ssrunder.
+Require Import RelationClasses.
+Require Import Relation_Definitions.
+ +
+
+ +
+Reconcile Corelib.Classes.RelationClasses.Reflexive with + Corelib.ssr.ssrclasses.Reflexive +
+
+ +
+#[global]
+Instance compat_Reflexive :
+  forall {A} {R : relation A},
+    RelationClasses.Reflexive R ->
+    ssrclasses.Reflexive R | 12.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.ssr.ssrunder.html b/master/corelib/Corelib.ssr.ssrunder.html new file mode 100644 index 0000000000..14190df671 --- /dev/null +++ b/master/corelib/Corelib.ssr.ssrunder.html @@ -0,0 +1,168 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.ssr.ssrunder

+ +
+ +
+
+ +
+ +
+ + Constants for under/over, to rewrite under binders using "context lemmas" + +
+ + Note: this file does not require ssreflect; it is both required by + ssrsetoid and *exported* by ssrunder. + +
+ + This preserves the following feature: we can use Setoid without + requiring ssreflect and use ssreflect without requiring Setoid. + +
+
+ +
+Require Import ssrclasses.
+ +
+Module Type UNDER_REL.
+Parameter Under_rel :
+  forall (A : Type) (eqA : A -> A -> Prop), A -> A -> Prop.
+Parameter Under_rel_from_rel :
+  forall (A : Type) (eqA : A -> A -> Prop) (x y : A),
+    @Under_rel A eqA x y -> eqA x y.
+Parameter Under_relE :
+  forall (A : Type) (eqA : A -> A -> Prop),
+    @Under_rel A eqA = eqA.
+ +
+
+ +
+Over_rel, over_rel, over_rel_done: for "by rewrite over_rel" +
+
+Parameter Over_rel :
+  forall (A : Type) (eqA : A -> A -> Prop), A -> A -> Prop.
+Parameter over_rel :
+  forall (A : Type) (eqA : A -> A -> Prop) (x y : A),
+    @Under_rel A eqA x y = @Over_rel A eqA x y.
+Parameter over_rel_done :
+  forall (A : Type) (eqA : A -> A -> Prop) (EeqA : Reflexive eqA) (x : A),
+    @Over_rel A eqA x x.
+ +
+
+ +
+under_rel_done: for Ltac-style over +
+
+Parameter under_rel_done :
+  forall (A : Type) (eqA : A -> A -> Prop) (EeqA : Reflexive eqA) (x : A),
+    @Under_rel A eqA x x.
+Notation "''Under[' x ]" := (@Under_rel _ _ x _)
+  (at level 8, format "''Under[' x ]", only printing).
+End UNDER_REL.
+ +
+Module Export Under_rel : UNDER_REL.
+Definition Under_rel (A : Type) (eqA : A -> A -> Prop) :=
+  eqA.
+Lemma Under_rel_from_rel :
+  forall (A : Type) (eqA : A -> A -> Prop) (x y : A),
+    @Under_rel A eqA x y -> eqA x y.
+ Lemma Under_relE (A : Type) (eqA : A -> A -> Prop) :
+  @Under_rel A eqA = eqA.
+ Definition Over_rel := Under_rel.
+Lemma over_rel :
+  forall (A : Type) (eqA : A -> A -> Prop) (x y : A),
+    @Under_rel A eqA x y = @Over_rel A eqA x y.
+ Lemma over_rel_done :
+  forall (A : Type) (eqA : A -> A -> Prop) (EeqA : Reflexive eqA) (x : A),
+    @Over_rel A eqA x x.
+ Lemma under_rel_done :
+  forall (A : Type) (eqA : A -> A -> Prop) (EeqA : Reflexive eqA) (x : A),
+    @Under_rel A eqA x x.
+ End Under_rel.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Corelib.ssrmatching.ssrmatching.html b/master/corelib/Corelib.ssrmatching.ssrmatching.html new file mode 100644 index 0000000000..750e88c146 --- /dev/null +++ b/master/corelib/Corelib.ssrmatching.ssrmatching.html @@ -0,0 +1,114 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Corelib.ssrmatching.ssrmatching

+ +
+ +
+ +
+ +
+Module SsrMatchingSyntax.
+ +
+Reserved Notation "( a 'in' b )" (at level 0).
+Reserved Notation "( a 'as' b )" (at level 0).
+Reserved Notation "( a 'in' b 'in' c )" (at level 0).
+Reserved Notation "( a 'as' b 'in' c )" (at level 0).
+ +
+Declare Scope ssrpatternscope.
+Delimit Scope ssrpatternscope with pattern.
+ +
+Notation "( X 'in' t )" := (_ : fun X => t) (only parsing) : ssrpatternscope.
+ +
+Notation RHS := (X in _ = X)%pattern.
+Notation LHS := (X in X = _)%pattern.
+ +
+End SsrMatchingSyntax.
+ +
+Export SsrMatchingSyntax.
+ +
+Tactic Notation "ssrpattern" ssrpatternarg(p) := ssrpattern p .
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Array.html b/master/corelib/Ltac2.Array.html new file mode 100644 index 0000000000..9a5e4d2342 --- /dev/null +++ b/master/corelib/Ltac2.Array.html @@ -0,0 +1,345 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Array

+ +
+ +
+ +
+ +
+Require Import Ltac2.Init.
+Require Ltac2.Int.
+Require Ltac2.Control.
+Require Ltac2.Bool.
+Require Ltac2.Message.
+ +
+ +
+Ltac2 @external empty : 'a array := "rocq-runtime.plugins.ltac2" "array_empty".
+Ltac2 @external make : int -> 'a -> 'a array := "rocq-runtime.plugins.ltac2" "array_make".
+Ltac2 @external length : 'a array -> int := "rocq-runtime.plugins.ltac2" "array_length".
+Ltac2 @external get : 'a array -> int -> 'a := "rocq-runtime.plugins.ltac2" "array_get".
+Ltac2 @external set : 'a array -> int -> 'a -> unit := "rocq-runtime.plugins.ltac2" "array_set".
+Ltac2 @external lowlevel_blit : 'a array -> int -> 'a array -> int -> int -> unit := "rocq-runtime.plugins.ltac2" "array_blit".
+Ltac2 @external lowlevel_fill : 'a array -> int -> int -> 'a -> unit := "rocq-runtime.plugins.ltac2" "array_fill".
+Ltac2 @external concat : ('a array) list -> 'a array := "rocq-runtime.plugins.ltac2" "array_concat".
+ +
+ +
+Ltac2 lowlevel_sub (arr : 'a array) (start : int) (len : int) :=
+  let l := length arr in
+  match Int.equal l 0 with
+  | true => empty
+  | false =>
+      let newarr:=make len (get arr 0) in
+      lowlevel_blit arr start newarr 0 len;
+      newarr
+  end.
+ +
+ +
+Ltac2 init (l : int) (f : int->'a) :=
+  let rec init_aux (dst : 'a array) (pos : int) (len : int) (f : int->'a) :=
+    match Int.equal len 0 with
+    | true => ()
+    | false =>
+        set dst pos (f pos);
+        init_aux dst (Int.add pos 1) (Int.sub len 1) f
+    end
+  in
+  match Int.le l 0 with
+  | true => empty
+  | false =>
+      let arr:=make l (f 0) in
+      init_aux arr 1 (Int.sub l 1) f;
+      arr
+  end.
+ +
+Ltac2 make_matrix (sx : int) (sy : int) (v : 'a) :=
+  let init1 _ := v in
+  let initr _ := init sy init1 in
+  init sx initr.
+ +
+Ltac2 copy a := lowlevel_sub a 0 (length a).
+ +
+Ltac2 append (a1 : 'a array) (a2 : 'a array) :=
+  match Int.equal (length a1) 0 with
+  | true => copy a2
+  | false => match Int.equal (length a2) 0 with
+             | true => copy a1
+             | false =>
+                 let newarr:=make (Int.add (length a1) (length a2)) (get a1 0) in
+                 lowlevel_blit a1 0 newarr 0 (length a1);
+                 lowlevel_blit a2 0 newarr (length a1) (length a2);
+                 newarr
+             end
+  end.
+ +
+Ltac2 sub (a : 'a array) (ofs : int) (len : int) :=
+  Control.assert_valid_argument "Array.sub ofs<0" (Int.ge ofs 0);
+  Control.assert_valid_argument "Array.sub len<0" (Int.ge len 0);
+  Control.assert_bounds "Array.sub" (Int.le ofs (Int.sub (length a) len));
+  lowlevel_sub a ofs len.
+ +
+Ltac2 fill (a : 'a array) (ofs : int) (len : int) (v : 'a) :=
+  Control.assert_valid_argument "Array.fill ofs<0" (Int.ge ofs 0);
+  Control.assert_valid_argument "Array.fill len<0" (Int.ge len 0);
+  Control.assert_bounds "Array.fill" (Int.le ofs (Int.sub (length a) len));
+  lowlevel_fill a ofs len v.
+ +
+Ltac2 blit (a1 : 'a array) (ofs1 : int) (a2 : 'a array) (ofs2 : int) (len : int) :=
+  Control.assert_valid_argument "Array.blit ofs1<0" (Int.ge ofs1 0);
+  Control.assert_valid_argument "Array.blit ofs2<0" (Int.ge ofs2 0);
+  Control.assert_valid_argument "Array.blit len<0" (Int.ge len 0);
+  Control.assert_bounds "Array.blit ofs1+len>len a1" (Int.le ofs1 (Int.sub (length a1) len));
+  Control.assert_bounds "Array.blit ofs2+len>len a2" (Int.le ofs2 (Int.sub (length a2) len));
+  lowlevel_blit a1 ofs1 a2 ofs2 len.
+ +
+Ltac2 rec iter_aux (f : 'a -> unit) (a : 'a array) (pos : int) (len : int) :=
+  match Int.equal len 0 with
+  | true => ()
+  | false => f (get a pos); iter_aux f a (Int.add pos 1) (Int.sub len 1)
+  end.
+ +
+Ltac2 iter (f : 'a -> unit) (a : 'a array) := iter_aux f a 0 (length a).
+ +
+Ltac2 rec iter2_aux (f : 'a -> 'b -> unit) (a : 'a array) (b : 'b array) (pos : int) (len : int) :=
+  match Int.equal len 0 with
+  | true => ()
+  | false => f (get a pos) (get b pos); iter2_aux f a b (Int.add pos 1) (Int.sub len 1)
+  end.
+ +
+Ltac2 rec iter2 (f : 'a -> 'b -> unit) (a : 'a array) (b : 'b array) :=
+  Control.assert_valid_argument "Array.iter2" (Int.equal (length a) (length b));
+  iter2_aux f a b 0 (length a).
+ +
+Ltac2 map (f : 'a -> 'b) (a : 'a array) :=
+  init (length a) (fun i => f (get a i)).
+ +
+Ltac2 map2 (f : 'a -> 'b -> 'c) (a : 'a array) (b : 'b array) :=
+  Control.assert_valid_argument "Array.map2" (Int.equal (length a) (length b));
+  init (length a) (fun i => f (get a i) (get b i)).
+ +
+Ltac2 rec iteri_aux (f : int -> 'a -> unit) (a : 'a array) (pos : int) (len : int) :=
+  match Int.equal len 0 with
+  | true => ()
+  | false => f pos (get a pos); iteri_aux f a (Int.add pos 1) (Int.sub len 1)
+  end.
+ +
+Ltac2 iteri (f : int -> 'a -> unit) (a : 'a array) := iteri_aux f a 0 (length a).
+ +
+Ltac2 mapi (f : int -> 'a -> 'b) (a : 'a array) :=
+  init (length a) (fun i => f i (get a i)).
+ +
+Ltac2 rec to_list_aux (a : 'a array) (pos : int) (len : int) :=
+  match Int.equal len 0 with
+  | true => []
+  | false => get a pos :: to_list_aux a (Int.add pos 1) (Int.sub len 1)
+  end.
+ +
+Ltac2 to_list (a : 'a array) := to_list_aux a 0 (length a).
+ +
+Ltac2 rec of_list_aux (ls : 'a list) (dst : 'a array) (pos : int) :=
+  match ls with
+  | [] => ()
+  | hd::tl =>
+      set dst pos hd;
+      of_list_aux tl dst (Int.add pos 1)
+  end.
+ +
+Ltac2 of_list (ls : 'a list) :=
+  
+  let rec list_length (ls : 'a list) :=
+    match ls with
+    | [] => 0
+    | _ :: tl => Int.add 1 (list_length tl)
+    end in
+  match ls with
+  | [] => empty
+  | hd :: _ =>
+      let anew := make (list_length ls) hd in
+      of_list_aux ls anew 0;
+      anew
+  end.
+ +
+Ltac2 rec fold_left_aux (f : 'a -> 'b -> 'a) (x : 'a) (a : 'b array) (pos : int) (len : int) :=
+  match Int.equal len 0 with
+  | true => x
+  | false => fold_left_aux f (f x (get a pos)) a (Int.add pos 1) (Int.sub len 1)
+  end.
+ +
+Ltac2 fold_left (f : 'a -> 'b -> 'a) (x : 'a) (a : 'b array) : 'a :=
+  fold_left_aux f x a 0 (length a).
+ +
+Ltac2 rec fold_right_aux (f : 'a -> 'b -> 'b) (a : 'a array) (x : 'b) (pos : int) (len : int) :=
+  
+  match Int.equal len 0 with
+  | true => x
+  | false => fold_right_aux f a (f (get a pos) x) (Int.sub pos 1) (Int.sub len 1)
+  end.
+ +
+Ltac2 fold_right (f : 'a -> 'b -> 'b) (a : 'a array) (x : 'b) : 'b :=
+  fold_right_aux f a x (Int.sub (length a) 1) (length a).
+ +
+Ltac2 rec exist_aux (p : 'a -> bool) (a : 'a array) (pos : int) (len : int) :=
+  match Int.equal len 0 with
+  | true => false
+  | false => match p (get a pos) with
+             | true => true
+             | false => exist_aux p a (Int.add pos 1) (Int.sub len 1)
+             end
+  end.
+ +
+Ltac2 exist (p : 'a -> bool) (a : 'a array) := exist_aux p a 0 (length a).
+ +
+Ltac2 rec for_all_aux (p : 'a -> bool) (a : 'a array) (pos : int) (len : int) :=
+  match Int.equal len 0 with
+  | true => true
+  | false => match p (get a pos) with
+             | true => for_all_aux p a (Int.add pos 1) (Int.sub len 1)
+             | false => false
+             end
+  end.
+ +
+Ltac2 for_all (p : 'a -> bool) (a : 'a array) := for_all_aux p a 0 (length a).
+ +
+Ltac2 mem (eq : 'a -> 'a -> bool) (x : 'a) (a : 'a array) :=
+  exist (eq x) a.
+ +
+Ltac2 rec for_all2_aux (p : 'a -> 'b -> bool) (a : 'a array) (b : 'b array) (pos : int) (len : int) :=
+  if Int.equal len 0
+  then true
+  else if p (get a pos) (get b pos)
+       then for_all2_aux p a b (Int.add pos 1) (Int.sub len 1)
+       else false.
+ +
+Ltac2 for_all2 p a b :=
+  let lena := length a in
+  let lenb := length b in
+  if Int.equal lena lenb
+  then for_all2_aux p a b 0 lena
+  else Control.throw_invalid_argument "Array.for_all2".
+ +
+Ltac2 equal p a b :=
+  let lena := length a in
+  let lenb := length b in
+  if Int.equal lena lenb
+  then for_all2_aux p a b 0 lena
+  else false.
+ +
+Ltac2 rev (ar : 'a array) : 'a array :=
+  let len := length ar in
+  init len (fun i => get ar (Int.sub (Int.sub len i) 1)).
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Bool.html b/master/corelib/Ltac2.Bool.html new file mode 100644 index 0000000000..becb109db6 --- /dev/null +++ b/master/corelib/Ltac2.Bool.html @@ -0,0 +1,181 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Bool

+ +
+ +
+Require Import Ltac2.Init.
+ +
+
+ +
+

Boolean operators

+ +
+
+ +
+Ltac2 and x y :=
+  match x with
+  | true => y
+  | false => false
+  end.
+ +
+Ltac2 or x y :=
+  match x with
+  | true => true
+  | false => y
+  end.
+ +
+Ltac2 impl x y :=
+  match x with
+  | true => y
+  | false => true
+  end.
+ +
+Ltac2 neg x :=
+  match x with
+  | true => false
+  | false => true
+  end.
+ +
+Ltac2 xor x y :=
+  match x with
+  | true
+    => match y with
+       | true => false
+       | false => true
+       end
+  | false
+    => match y with
+       | true => true
+       | false => false
+       end
+  end.
+ +
+Ltac2 equal x y :=
+  match x with
+  | true
+    => match y with
+       | true => true
+       | false => false
+       end
+  | false
+    => match y with
+       | true => false
+       | false => true
+       end
+  end.
+ +
+
+ +
+

Boolean operators with lazy evaluation of the second argument

+ +
+ + We place the notations in a separate module so that we can import them separately +
+
+Module Export BoolNotations.
+ +
+Ltac2 Notation x(self) "&&" y(thunk(self)) : 2 :=
+  match x with
+  | true => y ()
+  | false => false
+  end.
+ +
+Ltac2 Notation x(self) "||" y(thunk(self)) : 3 :=
+  match x with
+  | true => true
+  | false => y ()
+  end.
+ +
+End BoolNotations.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Char.html b/master/corelib/Ltac2.Char.html new file mode 100644 index 0000000000..42b25ba4e4 --- /dev/null +++ b/master/corelib/Ltac2.Char.html @@ -0,0 +1,101 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Char

+ +
+ +
+Require Import Ltac2.Init.
+Require Ltac2.Int.
+ +
+Ltac2 @external of_int : int -> char := "rocq-runtime.plugins.ltac2" "char_of_int".
+
+ +
+Throws if the integer is not a valid char (in range 0-255). +
+
+ +
+Ltac2 @external to_int : char -> int := "rocq-runtime.plugins.ltac2" "char_to_int".
+ +
+Ltac2 equal (x : char) (y : char) : bool := Int.equal (to_int x) (to_int y).
+Ltac2 compare (x : char) (y : char) : int := Int.compare (to_int x) (to_int y).
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Compat.Coq818.html b/master/corelib/Ltac2.Compat.Coq818.html new file mode 100644 index 0000000000..a0bf34e6c9 --- /dev/null +++ b/master/corelib/Ltac2.Compat.Coq818.html @@ -0,0 +1,95 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Compat.Coq818

+ +
+ +
+Require Export Ltac2.Compat.Coq819.
+ +
+Require Ltac2.Array.
+ +
+Module Export Ltac2.
+  Module Array.
+    Export Ltac2.Array.
+    Ltac2 empty () := empty.
+  End Array.
+End Ltac2.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Compat.Coq819.html b/master/corelib/Ltac2.Compat.Coq819.html new file mode 100644 index 0000000000..ffd5e9ee6f --- /dev/null +++ b/master/corelib/Ltac2.Compat.Coq819.html @@ -0,0 +1,85 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Compat.Coq819

+ +
+Require Ltac2.Init.
+ +
+#[export] Unset Ltac2 Typed Notations.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Constant.html b/master/corelib/Ltac2.Constant.html new file mode 100644 index 0000000000..fd1df4996e --- /dev/null +++ b/master/corelib/Ltac2.Constant.html @@ -0,0 +1,97 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Constant

+ +
+ +
+Require Import Ltac2.Init.
+ +
+Ltac2 Type t := constant.
+ +
+Ltac2 @ external equal : constant -> constant -> bool := "rocq-runtime.plugins.ltac2" "constant_equal".
+
+ +
+Constants obtained through module aliases or Include are not + considered equal by this function. +
+
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Constr.html b/master/corelib/Ltac2.Constr.html new file mode 100644 index 0000000000..af5cbe8be2 --- /dev/null +++ b/master/corelib/Ltac2.Constr.html @@ -0,0 +1,802 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Constr

+ +
+ +
+Require Import Ltac2.Init.
+Require Ltac2.Ind Ltac2.Array.
+ +
+Ltac2 @ external type : constr -> constr := "rocq-runtime.plugins.ltac2" "constr_type".
+
+ +
+Return the type of a term +
+
+ +
+Ltac2 @ external equal : constr -> constr -> bool := "rocq-runtime.plugins.ltac2" "constr_equal".
+
+ +
+Strict syntactic equality: only up to α-conversion and evar expansion +
+
+ +
+Module Binder.
+ +
+Ltac2 Type relevance_var.
+Ltac2 Type relevance := [ Relevant | Irrelevant | RelevanceVar (relevance_var) ].
+ +
+Ltac2 @ external make : ident option -> constr -> binder := "rocq-runtime.plugins.ltac2" "constr_binder_make".
+
+ +
+Create a binder given the name and the type of the bound variable. + Fails if the type is not a type in the current goal. +
+
+ +
+Ltac2 @ external unsafe_make : ident option -> relevance -> constr -> binder := "rocq-runtime.plugins.ltac2" "constr_binder_unsafe_make".
+
+ +
+Create a binder given the name and the type and relevance of the bound variable. +
+
+ +
+Ltac2 @ external name : binder -> ident option := "rocq-runtime.plugins.ltac2" "constr_binder_name".
+
+ +
+Retrieve the name of a binder. +
+
+ +
+Ltac2 @ external type : binder -> constr := "rocq-runtime.plugins.ltac2" "constr_binder_type".
+
+ +
+Retrieve the type of a binder. +
+
+ +
+Ltac2 @ external relevance : binder -> relevance := "rocq-runtime.plugins.ltac2" "constr_binder_relevance".
+
+ +
+Retrieve the relevance of a binder. +
+
+ +
+End Binder.
+ +
+Module Unsafe.
+ +
+
+ +
+Low-level access to kernel terms. Use with care! +
+
+ +
+Ltac2 Type case.
+ +
+Ltac2 Type case_invert := [
+| NoInvert
+| CaseInvert (constr array)
+].
+ +
+Ltac2 Type kind := [
+| Rel (int)
+| Var (ident)
+| Meta (meta)
+| Evar (evar, constr array)
+| Sort (sort)
+| Cast (constr, cast, constr)
+| Prod (binder, constr)
+| Lambda (binder, constr)
+| LetIn (binder, constr, constr)
+| App (constr, constr array)
+| Constant (constant, instance)
+| Ind (inductive, instance)
+| Constructor (constructor, instance)
+| Case (case, (constr * Binder.relevance), case_invert, constr, constr array)
+| Fix (int array, int, binder array, constr array)
+| CoFix (int, binder array, constr array)
+| Proj (projection, Binder.relevance, constr)
+| Uint63 (uint63)
+| Float (float)
+| String (pstring)
+| Array (instance, constr array, constr, constr)
+].
+ +
+Ltac2 @ external kind : constr -> kind := "rocq-runtime.plugins.ltac2" "constr_kind".
+ +
+Ltac2 rec kind_nocast c :=
+  match kind c with
+  | Cast c _ _ => kind_nocast c
+  | k => k
+  end.
+ +
+Ltac2 @ external make : kind -> constr := "rocq-runtime.plugins.ltac2" "constr_make".
+ +
+Ltac2 @ external check : constr -> constr result := "rocq-runtime.plugins.ltac2" "constr_check".
+
+ +
+Checks that a constr generated by unsafe means is indeed safe in the + current environment, and returns it, or the error otherwise. Panics if + not focused. +
+
+ +
+Ltac2 @ external liftn : int -> int -> constr -> constr := "rocq-runtime.plugins.ltac2" "constr_liftn".
+
+ +
+liftn n k c lifts by n indices greater than or equal to k in c + Note that with respect to substitution calculi's terminology, n + is the shift and k is the lift. +
+
+ +
+Ltac2 @ external substnl : constr list -> int -> constr -> constr := "rocq-runtime.plugins.ltac2" "constr_substnl".
+
+ +
+substnl [r₁;...;rₙ] k c substitutes in parallel Rel(k+1); ...; Rel(k+n) with + r₁;...;rₙ in c. +
+
+ +
+Ltac2 @ external closenl : ident list -> int -> constr -> constr := "rocq-runtime.plugins.ltac2" "constr_closenl".
+
+ +
+closenl [x₁;...;xₙ] k c abstracts over variables x₁;...;xₙ and replaces them with + Rel(k); ...; Rel(k+n-1) in c. If two names are identical, the one of least index is kept. +
+
+ +
+Ltac2 @ external closedn : int -> constr -> bool := "rocq-runtime.plugins.ltac2" "constr_closedn".
+
+ +
+closedn n c is true iff c is a closed term under n binders +
+
+ +
+Ltac2 is_closed (c : constr) : bool := closedn 0 c.
+
+ +
+is_closed c is true iff c is a closed term (contains no Rels) +
+
+ +
+Ltac2 @ external noccur_between : int -> int -> constr -> bool := "rocq-runtime.plugins.ltac2" "constr_noccur_between".
+
+ +
+noccur_between n m c returns true iff Rel p does not occur in term c + for n <= p < n+m +
+
+ +
+#[deprecated(since="9.0", note="occur_between currently behaves as noccur_between. +Use noccur_between instead if you want [true] for variables which do not occur in the term +and its negation if you want [false].")]
+Ltac2 occur_between := noccur_between.
+ +
+Ltac2 noccurn (n : int) (c : constr) : bool := noccur_between n 1 c.
+
+ +
+noccurn n c returns true iff Rel n does not occur in term c +
+
+ +
+#[deprecated(since="9.0", note="occurn currently behaves as noccurn. +Use noccurn instead if you want [true] for variables which do not occur in the term +and its negation if you want [false].")]
+Ltac2 occurn (n : int) (c : constr) : bool := noccur_between n 1 c.
+ +
+Ltac2 @ external case : inductive -> case := "rocq-runtime.plugins.ltac2" "constr_case".
+
+ +
+Generate the case information for a given inductive type. +
+
+ +
+Ltac2 constructor (ind : inductive) (i : int) : constructor :=
+  Ind.get_constructor (Ind.data ind) i.
+
+ +
+Generate the i-th constructor for a given inductive type. Indexing starts + at 0. Panics if there is no such constructor. +
+
+ +
+Module Case.
+  Ltac2 @ external equal : case -> case -> bool := "rocq-runtime.plugins.ltac2" "constr_case_equal".
+
+ +
+Checks equality of the inductive components of the + case info. When comparing the inductives, those obtained through + module aliases or Include are not considered equal by this + function. +
+
+ +
+End Case.
+ +
+
+ +
+Open recursion combinators +
+
+ +
+Local Ltac2 iter_invert (f : constr -> unit) (ci : case_invert) : unit :=
+  match ci with
+  | NoInvert => ()
+  | CaseInvert indices => Array.iter f indices
+  end.
+ +
+
+ +
+iter f c iterates f on the immediate subterms of c; it is + not recursive and the order with which subterms are processed is + not specified +
+
+Ltac2 iter (f : constr -> unit) (c : constr) : unit :=
+  match kind c with
+  | Rel _ | Meta _ | Var _ | Sort _ | Constant _ _ | Ind _ _
+  | Constructor _ _ | Uint63 _ | Float _ | String _ => ()
+  | Cast c _ t => f c; f t
+  | Prod b c => f (Binder.type b); f c
+  | Lambda b c => f (Binder.type b); f c
+  | LetIn b t c => f (Binder.type b); f t; f c
+  | App c l => f c; Array.iter f l
+  | Evar _ l => Array.iter f l
+  | Case _ x iv y bl =>
+      match x with (x,_) => f x end;
+      iter_invert f iv;
+      f y;
+      Array.iter f bl
+  | Proj _p _ c => f c
+  | Fix _ _ tl bl =>
+      Array.iter (fun b => f (Binder.type b)) tl;
+      Array.iter f bl
+  | CoFix _ tl bl =>
+      Array.iter (fun b => f (Binder.type b)) tl;
+      Array.iter f bl
+  | Array _u t def ty =>
+      f ty; Array.iter f t; f def
+  end.
+ +
+
+ +
+iter_with_binders g f n c iterates f n on the immediate + subterms of c; it carries an extra data n (typically a lift + index) which is processed by g (which typically add 1 to n) at + each binder traversal; it is not recursive and the order with which + subterms are processed is not specified +
+
+Ltac2 iter_with_binders (g : 'a -> binder -> 'a) (f : 'a -> constr -> unit) (n : 'a) (c : constr) : unit :=
+  match kind c with
+  | Rel _ | Meta _ | Var _ | Sort _ | Constant _ _ | Ind _ _
+  | Constructor _ _ | Uint63 _ | Float _ | String _ => ()
+  | Cast c _ t => f n c; f n t
+  | Prod b c => f n (Binder.type b); f (g n b) c
+  | Lambda b c => f n (Binder.type b); f (g n b) c
+  | LetIn b t c => f n (Binder.type b); f n t; f (g n b) c
+  | App c l => f n c; Array.iter (f n) l
+  | Evar _ l => Array.iter (f n) l
+  | Case _ x iv y bl =>
+      match x with (x,_) => f n x end;
+      iter_invert (f n) iv;
+      f n y;
+      Array.iter (f n) bl
+  | Proj _p _ c => f n c
+  | Fix _ _ tl bl =>
+      Array.iter (fun b => f n (Binder.type b)) tl;
+      let n := Array.fold_left g n tl in
+      Array.iter (f n) bl
+  | CoFix _ tl bl =>
+      Array.iter (fun b => f n (Binder.type b)) tl;
+      let n := Array.fold_left g n tl in
+      Array.iter (f n) bl
+  | Array _u t def ty =>
+      f n ty;
+      Array.iter (f n) t;
+      f n def
+  end.
+ +
+Local Ltac2 binder_map (f : constr -> constr) (b : binder) : binder :=
+  Binder.unsafe_make (Binder.name b) (Binder.relevance b) (f (Binder.type b)).
+ +
+Local Ltac2 map_invert (f : constr -> constr) (iv : case_invert) : case_invert :=
+  match iv with
+  | NoInvert => NoInvert
+  | CaseInvert indices => CaseInvert (Array.map f indices)
+  end.
+ +
+
+ +
+map f c maps f on the immediate subterms of c; it is + not recursive and the order with which subterms are processed is + not specified +
+
+Ltac2 map (f : constr -> constr) (c : constr) : constr :=
+  match kind c with
+  | Rel _ | Meta _ | Var _ | Sort _ | Constant _ _ | Ind _ _
+  | Constructor _ _ | Uint63 _ | Float _ | String _ => c
+  | Cast c k t =>
+      let c := f c
+      with t := f t in
+      make (Cast c k t)
+  | Prod b c =>
+      let b := binder_map f b
+      with c := f c in
+      make (Prod b c)
+  | Lambda b c =>
+      let b := binder_map f b
+      with c := f c in
+      make (Lambda b c)
+  | LetIn b t c =>
+      let b := binder_map f b
+      with t := f t
+      with c := f c in
+      make (LetIn b t c)
+  | App c l =>
+      let c := f c
+      with l := Array.map f l in
+      make (App c l)
+  | Evar e l =>
+      let l := Array.map f l in
+      make (Evar e l)
+  | Case info x iv y bl =>
+      let x := match x with (x,x') => (f x, x') end
+      with iv := map_invert f iv
+      with y := f y
+      with bl := Array.map f bl in
+      make (Case info x iv y bl)
+  | Proj p r c =>
+      let c := f c in
+      make (Proj p r c)
+  | Fix structs which tl bl =>
+      let tl := Array.map (binder_map f) tl
+      with bl := Array.map f bl in
+      make (Fix structs which tl bl)
+  | CoFix which tl bl =>
+      let tl := Array.map (binder_map f) tl
+      with bl := Array.map f bl in
+      make (CoFix which tl bl)
+  | Array u t def ty =>
+      let ty := f ty
+      with t := Array.map f t
+      with def := f def in
+      make (Array u t def ty)
+  end.
+ +
+
+ +
+map_with_binders g f n c maps f n on the immediate subterms of c; + it carries an extra data n (typically a lift index) which is processed by g + (which typically add 1 to n) at each binder traversal; + it is not recursive and the order with which subterms are processed is not specified. +
+
+Ltac2 map_with_binders (lift : 'a -> binder -> 'a) (f : 'a -> constr -> constr) (n : 'a) (c : constr) : constr :=
+  match kind c with
+  | Rel _ | Meta _ | Var _ | Sort _ | Constant _ _ | Ind _ _
+  | Constructor _ _ | Uint63 _ | Float _ | String _ => c
+  | Cast c k t =>
+      let c := f n c
+      with t := f n t in
+      make (Cast c k t)
+  | Prod b c =>
+      let b := binder_map (f n) b
+      with c := f (lift n b) c in
+      make (Prod b c)
+  | Lambda b c =>
+      let b := binder_map (f n) b
+      with c := f (lift n b) c in
+      make (Lambda b c)
+  | LetIn b t c =>
+      let b := binder_map (f n) b
+      with t := f n t
+      with c := f (lift n b) c in
+      make (LetIn b t c)
+  | App c l =>
+      let c := f n c
+      with l := Array.map (f n) l in
+      make (App c l)
+  | Evar e l =>
+      let l := Array.map (f n) l in
+      make (Evar e l)
+  | Case info x iv y bl =>
+      let x := match x with (x,x') => (f n x, x') end
+      with iv := map_invert (f n) iv
+      with y := f n y
+      with bl := Array.map (f n) bl in
+      make (Case info x iv y bl)
+  | Proj p r c =>
+      let c := f n c in
+      make (Proj p r c)
+  | Fix structs which tl bl =>
+      let tl := Array.map (binder_map (f n)) tl in
+      let n_bl := Array.fold_left lift n tl in
+      let bl := Array.map (f n_bl) bl in
+      make (Fix structs which tl bl)
+  | CoFix which tl bl =>
+      let tl := Array.map (binder_map (f n)) tl in
+      let n_bl := Array.fold_left lift n tl in
+      let bl := Array.map (f n_bl) bl in
+      make (CoFix which tl bl)
+  | Array u t def ty =>
+      let ty := f n ty
+      with t := Array.map (f n) t
+      with def := f n def in
+      make (Array u t def ty)
+  end.
+ +
+End Unsafe.
+ +
+Module Cast.
+ +
+  Ltac2 @ external default : cast := "rocq-runtime.plugins.ltac2" "constr_cast_default".
+  Ltac2 @ external vm : cast := "rocq-runtime.plugins.ltac2" "constr_cast_vm".
+  Ltac2 @ external native : cast := "rocq-runtime.plugins.ltac2" "constr_cast_native".
+ +
+  Ltac2 @ external equal : cast -> cast -> bool := "rocq-runtime.plugins.ltac2" "constr_cast_equal".
+ +
+End Cast.
+ +
+Ltac2 @ external in_context : ident -> constr -> (unit -> unit) -> constr := "rocq-runtime.plugins.ltac2" "constr_in_context".
+
+ +
+On a focused goal Γ ⊢ A, in_context id c tac evaluates tac in a + focused goal Γ, id : c ⊢ ?X and returns fun (id : c) => t where t is + the proof built by the tactic. +
+
+ +
+Module Pretype.
+  Module Flags.
+    Ltac2 Type t.
+ +
+    Ltac2 @ external constr_flags : t := "rocq-runtime.plugins.ltac2" "constr_flags".
+
+ +
+The flags used by constr:(). +
+
+ +
+    Ltac2 @external set_use_coercions : bool -> t -> t
+      := "rocq-runtime.plugins.ltac2" "pretype_flags_set_use_coercions".
+
+ +
+Use coercions during pretyping. true in constr_flags. +
+
+ +
+    Ltac2 @external set_use_typeclasses : bool -> t -> t
+      := "rocq-runtime.plugins.ltac2" "pretype_flags_set_use_typeclasses".
+
+ +
+Run typeclass inference at the end of pretyping and when + needed according to flag "Typeclass Resolution For Conversion". + true in constr_flags. +
+
+ +
+    Ltac2 @external set_allow_evars : bool -> t -> t
+      := "rocq-runtime.plugins.ltac2" "pretype_flags_set_allow_evars".
+
+ +
+Allow pretyping to produce new unresolved evars. + false in constr_flags. +
+
+ +
+    Ltac2 @external set_nf_evars : bool -> t -> t
+      := "rocq-runtime.plugins.ltac2" "pretype_flags_set_nf_evars".
+
+ +
+Evar-normalize the result of pretyping. This should not impact + anything other than performance. + true in constr_flags. +
+
+ +
+    Ltac2 Notation open_constr_flags_with_tc :=
+      set_nf_evars false (set_allow_evars true constr_flags).
+ +
+    Local Ltac2 open_constr_flags_with_tc_kn () := open_constr_flags_with_tc.
+
+ +
+Code generation uses this as using the notation is not convenient. +
+
+ +
+    Ltac2 Notation open_constr_flags_no_tc :=
+      set_use_typeclasses false open_constr_flags_with_tc.
+
+ +
+The flags used by open_constr:() and its alias '. +
+
+ +
+    #[deprecated(since="8.20", note="use open_constr_flags_with_tc (or no_tc as desired)")]
+    Ltac2 Notation open_constr_flags := open_constr_flags_with_tc.
+  End Flags.
+ +
+  Ltac2 Type expected_type.
+ +
+  Ltac2 @ external expected_istype : expected_type
+    := "rocq-runtime.plugins.ltac2" "expected_istype".
+ +
+  Ltac2 @ external expected_oftype : constr -> expected_type
+    := "rocq-runtime.plugins.ltac2" "expected_oftype".
+ +
+  Ltac2 @ external expected_without_type_constraint : expected_type
+    := "rocq-runtime.plugins.ltac2" "expected_without_type_constraint".
+ +
+  Ltac2 @ external pretype : Flags.t -> expected_type -> preterm -> constr
+    := "rocq-runtime.plugins.ltac2" "constr_pretype".
+
+ +
+Pretype the provided preterm. Assumes the goal to be focussed. +
+
+End Pretype.
+ +
+Ltac2 pretype (c : preterm) : constr :=
+  Pretype.pretype Pretype.Flags.constr_flags Pretype.expected_without_type_constraint c.
+
+ +
+Pretype the provided preterm. Assumes the goal to be focussed. +
+
+ +
+Ltac2 is_evar(c: constr) :=
+  match Unsafe.kind c with
+  | Unsafe.Evar _ _ => true
+  | _ => false
+  end.
+ +
+Ltac2 @ external has_evar : constr -> bool := "rocq-runtime.plugins.ltac2" "constr_has_evar".
+ +
+Ltac2 is_var(c: constr) :=
+  match Unsafe.kind c with
+  | Unsafe.Var _ => true
+  | _ => false
+  end.
+ +
+Ltac2 is_fix(c: constr) :=
+  match Unsafe.kind c with
+  | Unsafe.Fix _ _ _ _ => true
+  | _ => false
+  end.
+ +
+Ltac2 is_cofix(c: constr) :=
+  match Unsafe.kind c with
+  | Unsafe.CoFix _ _ _ => true
+  | _ => false
+  end.
+ +
+Ltac2 is_ind(c: constr) :=
+  match Unsafe.kind c with
+  | Unsafe.Ind _ _ => true
+  | _ => false
+  end.
+ +
+Ltac2 is_constructor(c: constr) :=
+  match Unsafe.kind c with
+  | Unsafe.Constructor _ _ => true
+  | _ => false
+  end.
+ +
+Ltac2 is_proj(c: constr) :=
+  match Unsafe.kind c with
+  | Unsafe.Proj _ _ _ => true
+  | _ => false
+  end.
+ +
+Ltac2 is_const(c: constr) :=
+  match Unsafe.kind c with
+  | Unsafe.Constant _ _ => true
+  | _ => false
+  end.
+ +
+Ltac2 is_float(c: constr) :=
+  match Unsafe.kind c with
+  | Unsafe.Float _ => true
+  | _ => false
+  end.
+ +
+Ltac2 is_uint63(c: constr) :=
+  match Unsafe.kind c with
+  | Unsafe.Uint63 _ => true
+  | _ => false
+  end.
+ +
+Ltac2 is_array(c: constr) :=
+  match Unsafe.kind c with
+  | Unsafe.Array _ _ _ _ => true
+  | _ => false
+  end.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Constructor.html b/master/corelib/Ltac2.Constructor.html new file mode 100644 index 0000000000..6beb2d8b00 --- /dev/null +++ b/master/corelib/Ltac2.Constructor.html @@ -0,0 +1,116 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Constructor

+ +
+ +
+Require Import Ltac2.Init.
+ +
+Ltac2 Type t := constructor.
+ +
+Ltac2 @ external equal : t -> t -> bool := "rocq-runtime.plugins.ltac2" "constructor_equal".
+
+ +
+Constructors obtained through module aliases or Include are not + considered equal by this function. +
+
+ +
+Ltac2 @ external inductive : t -> inductive := "rocq-runtime.plugins.ltac2" "constructor_inductive".
+
+ +
+Returns the inductive to which the given constructor belongs. +
+
+ +
+Ltac2 @ external index : t -> int := "rocq-runtime.plugins.ltac2" "constructor_index".
+
+ +
+Returns the index of the given constructor + (such that c is Ind.get_constructor (Ind.data (inductive c)) (index c)). +
+
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Control.html b/master/corelib/Ltac2.Control.html new file mode 100644 index 0000000000..b869efa7c6 --- /dev/null +++ b/master/corelib/Ltac2.Control.html @@ -0,0 +1,405 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Control

+ +
+ +
+Require Import Ltac2.Init.
+Require Ltac2.Message.
+ +
+
+ +
+Panic +
+
+ +
+Ltac2 @ external throw : exn -> 'a := "rocq-runtime.plugins.ltac2" "throw".
+
+ +
+Fatal exception throwing. This does not induce backtracking. +
+ + Generic backtracking control +
+
+ +
+Ltac2 @ external zero : exn -> 'a := "rocq-runtime.plugins.ltac2" "zero".
+Ltac2 @ external plus : (unit -> 'a) -> (exn -> 'a) -> 'a := "rocq-runtime.plugins.ltac2" "plus".
+Ltac2 @ external once : (unit -> 'a) -> 'a := "rocq-runtime.plugins.ltac2" "once".
+Ltac2 @ external case : (unit -> 'a) -> ('a * (exn -> 'a)) result := "rocq-runtime.plugins.ltac2" "case".
+ +
+Ltac2 once_plus (run : unit -> 'a) (handle : exn -> 'a) : 'a :=
+  once (fun () => plus run handle).
+ +
+
+ +
+Proof state manipulation +
+
+ +
+Ltac2 @ external numgoals : unit -> int := "rocq-runtime.plugins.ltac2" "numgoals".
+
+ +
+Return the number of goals currently focused. +
+
+ +
+Ltac2 @ external dispatch : (unit -> unit) list -> unit := "rocq-runtime.plugins.ltac2" "dispatch".
+Ltac2 @ external extend : (unit -> unit) list -> (unit -> unit) -> (unit -> unit) list -> unit := "rocq-runtime.plugins.ltac2" "extend".
+Ltac2 @ external enter : (unit -> unit) -> unit := "rocq-runtime.plugins.ltac2" "enter".
+ +
+Ltac2 @ external focus : int -> int -> (unit -> 'a) -> 'a := "rocq-runtime.plugins.ltac2" "focus".
+Ltac2 @ external shelve : unit -> unit := "rocq-runtime.plugins.ltac2" "shelve".
+Ltac2 @ external shelve_unifiable : unit -> unit := "rocq-runtime.plugins.ltac2" "shelve_unifiable".
+ +
+Ltac2 @ external new_goal : evar -> unit := "rocq-runtime.plugins.ltac2" "new_goal".
+
+ +
+Adds the given evar to the list of goals as the last one. If it is + already defined in the current state, don't do anything. Panics if the + evar is not in the current state. +
+
+ +
+Ltac2 @ external unshelve : (unit -> 'a) -> 'a := "rocq-runtime.plugins.ltac2" "unshelve".
+
+ +
+Runs the closure, then unshelves existential variables added to the + shelf by its execution, prepending them to the current goal. + Returns the value produced by the closure. +
+
+ +
+Ltac2 @ external progress : (unit -> 'a) -> 'a := "rocq-runtime.plugins.ltac2" "progress".
+ +
+
+ +
+Goal inspection +
+
+ +
+Ltac2 @ external goal : unit -> constr := "rocq-runtime.plugins.ltac2" "goal".
+
+ +
+Panics if there is not exactly one goal under focus. Otherwise returns + the conclusion of this goal. +
+
+ +
+Ltac2 @ external hyp : ident -> constr := "rocq-runtime.plugins.ltac2" "hyp".
+
+ +
+Panics if there is more than one goal under focus. If there is no + goal under focus, looks for the section variable with the given name. + If there is one, looks for the hypothesis with the given name. +
+
+ +
+Ltac2 @ external hyp_value : ident -> constr option := "rocq-runtime.plugins.ltac2" "hyp_value".
+
+ +
+Panics if there is more than one goal under focus. If there is no + goal under focus, looks for the section variable with the given + name and return its value ("v" in "H := v") if there is one. If + there is one, looks for the hypothesis with the given name and + return its value if there is one. +
+
+ +
+Ltac2 @ external hyps : unit -> (ident * constr option * constr) list := "rocq-runtime.plugins.ltac2" "hyps".
+
+ +
+Panics if there is more than one goal under focus. If there is no + goal under focus, returns the list of section variables. + If there is one, returns the list of hypotheses. In both cases, the + list is ordered with rightmost values being last introduced. +
+ + Refinement +
+
+ +
+Ltac2 @ external refine : (unit -> constr) -> unit := "rocq-runtime.plugins.ltac2" "refine".
+ +
+
+ +
+Evars +
+
+ +
+Ltac2 @ external with_holes : (unit -> 'a) -> ('a -> 'b) -> 'b := "rocq-runtime.plugins.ltac2" "with_holes".
+
+ +
+with_holes x f evaluates x, then apply f to the result, and fails if + all evars generated by the call to x have not been solved when f + returns. +
+ + Misc +
+
+ +
+Ltac2 @ external time : string option -> (unit -> 'a) -> 'a := "rocq-runtime.plugins.ltac2" "time".
+
+ +
+Displays the time taken by a tactic to evaluate. +
+
+ +
+Ltac2 @ external abstract : ident option -> (unit -> unit) -> unit := "rocq-runtime.plugins.ltac2" "abstract".
+
+ +
+Abstract a subgoal. +
+
+ +
+Ltac2 @ external check_interrupt : unit -> unit := "rocq-runtime.plugins.ltac2" "check_interrupt".
+
+ +
+For internal use. +
+ + Assertions throwing exceptions and short form throws +
+
+ +
+Ltac2 throw_invalid_argument (msg : string) :=
+  Control.throw (Invalid_argument (Some (Message.of_string msg))).
+ +
+Ltac2 throw_out_of_bounds (msg : string) :=
+  Control.throw (Out_of_bounds (Some (Message.of_string msg))).
+ +
+Ltac2 assert_valid_argument (msg : string) (test : bool) :=
+  match test with
+  | true => ()
+  | false => throw_invalid_argument msg
+  end.
+ +
+Ltac2 assert_bounds (msg : string) (test : bool) :=
+  match test with
+  | true => ()
+  | false => throw_out_of_bounds msg
+  end.
+ +
+Ltac2 assert_true b :=
+  if b then () else throw Assertion_failure.
+ +
+Ltac2 assert_false b :=
+  if b then throw Assertion_failure else ().
+ +
+
+ +
+Short form backtracks +
+
+ +
+Ltac2 backtrack_tactic_failure (msg : string) :=
+  Control.zero (Tactic_failure (Some (Message.of_string msg))).
+ +
+
+ +
+Backtraces. +
+ + throw_bt info e is similar to throw e, but raises e with the + backtrace represented by info. +
+
+Ltac2 @ external throw_bt : exn -> exninfo -> 'a :=
+  "rocq-runtime.plugins.ltac2" "throw_bt".
+ +
+
+ +
+zero_bt info e is similar to zero e, but raises e with the + backtrace represented by info. +
+
+Ltac2 @ external zero_bt : exn -> exninfo -> 'a :=
+  "rocq-runtime.plugins.ltac2" "zero_bt".
+ +
+
+ +
+plus_bt run handle is similar to plus run handle (up to the type + missmatch for handle), but it calls handle with an extra argument + representing the backtrace at the point of the exception. The handle + function can thus decide to re-attach that backtrace when using the + throw_bt or zero_bt functions. +
+
+Ltac2 @ external plus_bt : (unit -> 'a) -> (exn -> exninfo -> 'a) -> 'a :=
+  "rocq-runtime.plugins.ltac2" "plus_bt".
+ +
+
+ +
+once_plus_bt run handle is a non-backtracking variant of once_plus + that has backtrace support similar to that of plus_bt. +
+
+Ltac2 once_plus_bt (run : unit -> 'a) (handle : exn -> exninfo -> 'a) : 'a :=
+  once (fun _ => plus_bt run handle).
+ +
+Ltac2 @ external clear_err_info : err -> err :=
+  "rocq-runtime.plugins.ltac2" "clear_err_info".
+ +
+Ltac2 clear_exn_info (e : exn) : exn :=
+  match e with
+  | Init.Internal err => Init.Internal (clear_err_info err)
+  | e => e
+  end.
+ +
+
+ +
+Timeout. +
+ + timeout t thunk calls thunk () with a timeout of t seconds. +
+
+Ltac2 @ external timeout : int -> (unit -> 'a) -> 'a :=
+  "rocq-runtime.plugins.ltac2" "timeout".
+ +
+
+ +
+timeoutf t thunk calls thunk () with a timeout of t seconds. +
+
+Ltac2 @ external timeoutf : float -> (unit -> 'a) -> 'a :=
+  "rocq-runtime.plugins.ltac2" "timeoutf".
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Env.html b/master/corelib/Ltac2.Env.html new file mode 100644 index 0000000000..5cc50db195 --- /dev/null +++ b/master/corelib/Ltac2.Env.html @@ -0,0 +1,125 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Env

+ +
+ +
+From Ltac2 Require Import Init Std.
+ +
+Ltac2 @ external get : ident list -> Std.reference option := "rocq-runtime.plugins.ltac2" "env_get".
+
+ +
+Returns the global reference corresponding to the absolute name given as + argument if it exists. +
+
+ +
+Ltac2 @ external expand : ident list -> Std.reference list := "rocq-runtime.plugins.ltac2" "env_expand".
+
+ +
+Returns the list of all global references whose absolute name contains + the argument list as a suffix. +
+
+ +
+Ltac2 @ external path : Std.reference -> ident list := "rocq-runtime.plugins.ltac2" "env_path".
+
+ +
+Returns the absolute name of the given reference. Panics if the reference + does not exist. +
+
+ +
+Ltac2 @ external instantiate : Std.reference -> constr := "rocq-runtime.plugins.ltac2" "env_instantiate".
+
+ +
+Returns a fresh instance of the corresponding reference, in particular + generating fresh universe variables and constraints when this reference is + universe-polymorphic. +
+
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Evar.html b/master/corelib/Ltac2.Evar.html new file mode 100644 index 0000000000..25560a8549 --- /dev/null +++ b/master/corelib/Ltac2.Evar.html @@ -0,0 +1,90 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Evar

+ +
+ +
+Require Import Ltac2.Init.
+ +
+Ltac2 Type t := evar.
+ +
+Ltac2 @ external equal : t -> t -> bool := "rocq-runtime.plugins.ltac2" "evar_equal".
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.FMap.html b/master/corelib/Ltac2.FMap.html new file mode 100644 index 0000000000..eb30b080e7 --- /dev/null +++ b/master/corelib/Ltac2.FMap.html @@ -0,0 +1,124 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.FMap

+ +
+ +
+From Ltac2 Require Import Init.
+From Ltac2 Require FSet.
+ +
+Import FSet.Tags.
+ +
+Ltac2 Type ('k, 'v) t.
+ +
+Ltac2 @ external empty : 'k tag -> ('k, 'v) t := "rocq-runtime.plugins.ltac2" "fmap_empty".
+ +
+Ltac2 @ external is_empty : ('k, 'v) t -> bool := "rocq-runtime.plugins.ltac2" "fmap_is_empty".
+ +
+Ltac2 @ external mem : 'k -> ('k, 'v) t -> bool := "rocq-runtime.plugins.ltac2" "fmap_mem".
+ +
+Ltac2 @ external add : 'k -> 'v -> ('k, 'v) t -> ('k, 'v) t := "rocq-runtime.plugins.ltac2" "fmap_add".
+ +
+Ltac2 @ external remove : 'k -> ('k, 'v) t -> ('k, 'v) t := "rocq-runtime.plugins.ltac2" "fmap_remove".
+ +
+Ltac2 @ external find_opt : 'k -> ('k, 'v) t -> 'v option := "rocq-runtime.plugins.ltac2" "fmap_find_opt".
+ +
+Ltac2 @ external mapi : ('k -> 'v -> 'r) -> ('k, 'v) t -> ('k, 'r) t := "rocq-runtime.plugins.ltac2" "fmap_mapi".
+ +
+Ltac2 @ external fold : ('k -> 'v -> 'acc -> 'acc) -> ('k, 'v) t -> 'acc -> 'acc := "rocq-runtime.plugins.ltac2" "fmap_fold".
+ +
+Ltac2 @ external cardinal : ('k, 'v) t -> int := "rocq-runtime.plugins.ltac2" "fmap_cardinal".
+ +
+Ltac2 @ external bindings : ('k, 'v) t -> ('k * 'v) list := "rocq-runtime.plugins.ltac2" "fmap_bindings".
+ +
+Ltac2 @ external domain : ('k, 'v) t -> 'k FSet.t := "rocq-runtime.plugins.ltac2" "fmap_domain".
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.FSet.html b/master/corelib/Ltac2.FSet.html new file mode 100644 index 0000000000..f7336ff522 --- /dev/null +++ b/master/corelib/Ltac2.FSet.html @@ -0,0 +1,138 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.FSet

+ +
+ +
+From Ltac2 Require Import Init.
+ +
+Module Import Tags.
+  Ltac2 Type 'a tag.
+ +
+  Ltac2 @ external ident_tag : ident tag := "rocq-runtime.plugins.ltac2" "fmap_ident_tag".
+  Ltac2 @ external int_tag : int tag := "rocq-runtime.plugins.ltac2" "fmap_int_tag".
+  Ltac2 @ external inductive_tag : inductive tag := "rocq-runtime.plugins.ltac2" "fmap_inductive_tag".
+  Ltac2 @ external constructor_tag : constructor tag := "rocq-runtime.plugins.ltac2" "fmap_constructor_tag".
+  Ltac2 @ external constant_tag : constant tag := "rocq-runtime.plugins.ltac2" "fmap_constant_tag".
+ +
+  Ltac2 @ external string_tag : string tag := "rocq-runtime.plugins.ltac2" "fmap_string_tag".
+End Tags.
+ +
+Ltac2 Type 'a t.
+ +
+Ltac2 @ external empty : 'a tag -> 'a t := "rocq-runtime.plugins.ltac2" "fset_empty".
+ +
+Ltac2 @ external is_empty : 'a t -> bool := "rocq-runtime.plugins.ltac2" "fset_is_empty".
+ +
+Ltac2 @ external mem : 'a -> 'a t -> bool := "rocq-runtime.plugins.ltac2" "fset_mem".
+ +
+Ltac2 @ external add : 'a -> 'a t -> 'a t := "rocq-runtime.plugins.ltac2" "fset_add".
+ +
+Ltac2 @ external remove : 'a -> 'a t -> 'a t := "rocq-runtime.plugins.ltac2" "fset_remove".
+ +
+Ltac2 @ external union : 'a t -> 'a t -> 'a t := "rocq-runtime.plugins.ltac2" "fset_union".
+ +
+Ltac2 @ external inter : 'a t -> 'a t -> 'a t := "rocq-runtime.plugins.ltac2" "fset_inter".
+ +
+Ltac2 @ external diff : 'a t -> 'a t -> 'a t := "rocq-runtime.plugins.ltac2" "fset_diff".
+ +
+Ltac2 @ external equal : 'a t -> 'a t -> bool := "rocq-runtime.plugins.ltac2" "fset_equal".
+ +
+Ltac2 @ external subset : 'a t -> 'a t -> bool := "rocq-runtime.plugins.ltac2" "fset_subset".
+ +
+Ltac2 @ external cardinal : 'a t -> int := "rocq-runtime.plugins.ltac2" "fset_cardinal".
+ +
+Ltac2 @ external elements : 'a t -> 'a list := "rocq-runtime.plugins.ltac2" "fset_elements".
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Float.html b/master/corelib/Ltac2.Float.html new file mode 100644 index 0000000000..cc367d5613 --- /dev/null +++ b/master/corelib/Ltac2.Float.html @@ -0,0 +1,90 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Float

+ +
+ +
+Require Import Ltac2.Init.
+ +
+Ltac2 Type t := float.
+ +
+Ltac2 @ external equal : t -> t -> bool := "rocq-runtime.plugins.ltac2" "float_equal".
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Fresh.html b/master/corelib/Ltac2.Fresh.html new file mode 100644 index 0000000000..40c43fc2db --- /dev/null +++ b/master/corelib/Ltac2.Fresh.html @@ -0,0 +1,126 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Fresh

+ +
+ +
+Require Import Ltac2.Init.
+Require Ltac2.Control.
+Require Ltac2.List.
+ +
+Module Free.
+ +
+Ltac2 Type t.
+
+ +
+Type of sets of free variables +
+
+ +
+Ltac2 @ external union : t -> t -> t := "rocq-runtime.plugins.ltac2" "fresh_free_union".
+ +
+Ltac2 @ external of_ids : ident list -> t := "rocq-runtime.plugins.ltac2" "fresh_free_of_ids".
+ +
+Ltac2 @ external of_constr : constr -> t := "rocq-runtime.plugins.ltac2" "fresh_free_of_constr".
+ +
+Ltac2 of_goal () := of_ids (List.map (fun (id, _, _) => id) (Control.hyps ())).
+ +
+End Free.
+ +
+Ltac2 @ external fresh : Free.t -> ident -> ident := "rocq-runtime.plugins.ltac2" "fresh_fresh".
+
+ +
+Generate a fresh identifier with the given base name which is not a + member of the provided set of free variables. +
+
+ +
+Ltac2 in_goal id := Fresh.fresh (Free.of_goal ()) id.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Ident.html b/master/corelib/Ltac2.Ident.html new file mode 100644 index 0000000000..c84491af28 --- /dev/null +++ b/master/corelib/Ltac2.Ident.html @@ -0,0 +1,96 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Ident

+ +
+ +
+Require Import Ltac2.Init.
+ +
+Ltac2 Type t := ident.
+ +
+Ltac2 @ external equal : t -> t -> bool := "rocq-runtime.plugins.ltac2" "ident_equal".
+ +
+Ltac2 @ external of_string : string -> t option := "rocq-runtime.plugins.ltac2" "ident_of_string".
+ +
+Ltac2 @ external to_string : t -> string := "rocq-runtime.plugins.ltac2" "ident_to_string".
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Ind.html b/master/corelib/Ltac2.Ind.html new file mode 100644 index 0000000000..8d859cd53f --- /dev/null +++ b/master/corelib/Ltac2.Ind.html @@ -0,0 +1,184 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Ind

+ +
+ +
+From Ltac2 Require Import Init.
+ +
+Ltac2 Type t := inductive.
+ +
+Ltac2 @ external equal : t -> t -> bool := "rocq-runtime.plugins.ltac2" "ind_equal".
+
+ +
+Equality test. +
+
+ +
+Ltac2 Type data.
+
+ +
+Type of data representing inductive blocks. +
+
+ +
+Ltac2 @ external data : t -> data := "rocq-runtime.plugins.ltac2" "ind_data".
+
+ +
+Get the mutual blocks corresponding to an inductive type in the current + environment. Panics if there is no such inductive. +
+
+ +
+Ltac2 @ external repr : data -> t := "rocq-runtime.plugins.ltac2" "ind_repr".
+
+ +
+Returns the inductive corresponding to the block. Inverse of data. +
+
+ +
+Ltac2 @ external index : t -> int := "rocq-runtime.plugins.ltac2" "ind_index".
+
+ +
+Returns the index of the inductive type inside its mutual block. Guaranteed + to range between 0 and nblocks data - 1 where data was retrieved + using the above function. +
+
+ +
+Ltac2 @ external nblocks : data -> int := "rocq-runtime.plugins.ltac2" "ind_nblocks".
+
+ +
+Returns the number of inductive types appearing in a mutual block. +
+
+ +
+Ltac2 @ external nconstructors : data -> int := "rocq-runtime.plugins.ltac2" "ind_nconstructors".
+
+ +
+Returns the number of constructors appearing in the current block. +
+
+ +
+Ltac2 @ external get_block : data -> int -> data := "rocq-runtime.plugins.ltac2" "ind_get_block".
+
+ +
+Returns the block corresponding to the nth inductive type. Index must range + between 0 and nblocks data - 1, otherwise the function panics. +
+
+ +
+Ltac2 @ external get_constructor : data -> int -> constructor := "rocq-runtime.plugins.ltac2" "ind_get_constructor".
+
+ +
+Returns the nth constructor of the inductive type. Index must range between + 0 and nconstructors data - 1, otherwise the function panics. +
+
+ +
+Ltac2 @ external get_projections : data -> projection array option
+  := "rocq-runtime.plugins.ltac2" "ind_get_projections".
+
+ +
+Returns the list of projections for a primitive record, + or None if the inductive is not a primitive record. +
+
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Init.html b/master/corelib/Ltac2.Init.html new file mode 100644 index 0000000000..2d0eb15d6a --- /dev/null +++ b/master/corelib/Ltac2.Init.html @@ -0,0 +1,281 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Init

+ +
+ +
+ +
+#[export] Set Default Proof Mode "Ltac2".
+ +
+
+ +
+Primitive types +
+
+ +
+Ltac2 Type int.
+Ltac2 Type string.
+Ltac2 Type char.
+Ltac2 Type ident.
+Ltac2 Type uint63.
+Ltac2 Type float.
+Ltac2 Type pstring.
+ +
+
+ +
+Constr-specific built-in types +
+
+Ltac2 Type meta.
+Ltac2 Type evar.
+Ltac2 Type sort.
+Ltac2 Type cast.
+Ltac2 Type instance.
+Ltac2 Type constant.
+Ltac2 Type inductive.
+Ltac2 Type constructor.
+Ltac2 Type projection.
+Ltac2 Type pattern.
+Ltac2 Type constr.
+Ltac2 Type preterm.
+Ltac2 Type binder.
+ +
+Ltac2 Type message.
+Ltac2 Type ('a, 'b, 'c, 'd) format.
+Ltac2 Type exn := [ .. ].
+Ltac2 Type 'a array.
+ +
+
+ +
+Tuples +
+
+ +
+Ltac2 fst (p:'a * 'b) : 'a := let (x,_) := p in x.
+Ltac2 snd (p:'a * 'b) : 'b := let (_,y) := p in y.
+ +
+
+ +
+Pervasive types +
+
+ +
+Ltac2 Type 'a option := [ None | Some ('a) ].
+ +
+Ltac2 Type 'a ref := { mutable contents : 'a }.
+ +
+Ltac2 Type bool := [ true | false ].
+ +
+Ltac2 Type 'a result := [ Val ('a) | Err (exn) ].
+ +
+
+ +
+Pervasive exceptions +
+
+ +
+Ltac2 Type err.
+
+ +
+Rocq internal errors. Cannot be constructed, merely passed around. +
+
+ +
+Ltac2 Type exn ::= [ Internal (err) ].
+
+ +
+Wrapper around the errors raised by Rocq implementation. +
+
+ +
+Ltac2 Type exn ::= [ Out_of_bounds (message option) ].
+
+ +
+Used for bound checking, e.g. with String and Array. +
+
+ +
+Ltac2 Type exn ::= [ Not_focussed ].
+
+ +
+In Ltac2, the notion of "current environment" only makes sense when there is + at most one goal under focus. Contrarily to Ltac1, instead of dynamically + focussing when we need it, we raise this non-backtracking error when it does + not make sense. +
+
+ +
+Ltac2 Type exn ::= [ Not_found ].
+
+ +
+Used when something is missing. +
+
+ +
+Ltac2 Type exn ::= [ No_value ].
+
+ +
+Used for empty lists, None options and the like. +
+
+ +
+Ltac2 Type exn ::= [ Match_failure ].
+
+ +
+Used to signal a pattern didn't match a term. +
+
+ +
+Ltac2 Type exn ::= [ Invalid_argument (message option) ].
+
+ +
+Used to signal that an invalid argument was passed to a tactic. +
+
+ +
+Ltac2 Type exn ::= [ Tactic_failure (message option) ].
+
+ +
+Generic error for tactic failure. +
+
+ +
+Ltac2 Type exn ::= [ Assertion_failure ].
+
+ +
+Used to indicate that an Ltac2 function ran into a situation that should never occcur. +
+
+ +
+Ltac2 Type exn ::= [ Division_by_zero ].
+
+ +
+Int division by zero or modulus by zero +
+
+ +
+Ltac2 Type exninfo.
+
+ +
+Information attached to an exception (e.g., backtrace). +
+
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Int.html b/master/corelib/Ltac2.Int.html new file mode 100644 index 0000000000..3bfbe69a46 --- /dev/null +++ b/master/corelib/Ltac2.Int.html @@ -0,0 +1,127 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Int

+ +
+ +
+Require Import Ltac2.Init.
+ +
+Ltac2 Type t := int.
+ +
+Ltac2 @ external equal : int -> int -> bool := "rocq-runtime.plugins.ltac2" "int_equal".
+Ltac2 @ external compare : int -> int -> int := "rocq-runtime.plugins.ltac2" "int_compare".
+Ltac2 @ external add : int -> int -> int := "rocq-runtime.plugins.ltac2" "int_add".
+Ltac2 @ external sub : int -> int -> int := "rocq-runtime.plugins.ltac2" "int_sub".
+Ltac2 @ external mul : int -> int -> int := "rocq-runtime.plugins.ltac2" "int_mul".
+ +
+Ltac2 @ external div : int -> int -> int := "rocq-runtime.plugins.ltac2" "int_div".
+ +
+Ltac2 @ external mod : int -> int -> int := "rocq-runtime.plugins.ltac2" "int_mod".
+Ltac2 @ external neg : int -> int := "rocq-runtime.plugins.ltac2" "int_neg".
+Ltac2 @ external abs : int -> int := "rocq-runtime.plugins.ltac2" "int_abs".
+ +
+Ltac2 @ external asr : int -> int -> int := "rocq-runtime.plugins.ltac2" "int_asr".
+Ltac2 @ external lsl : int -> int -> int := "rocq-runtime.plugins.ltac2" "int_lsl".
+Ltac2 @ external lsr : int -> int -> int := "rocq-runtime.plugins.ltac2" "int_lsr".
+Ltac2 @ external land : int -> int -> int := "rocq-runtime.plugins.ltac2" "int_land".
+Ltac2 @ external lor : int -> int -> int := "rocq-runtime.plugins.ltac2" "int_lor".
+Ltac2 @ external lxor : int -> int -> int := "rocq-runtime.plugins.ltac2" "int_lxor".
+Ltac2 @ external lnot : int -> int := "rocq-runtime.plugins.ltac2" "int_lnot".
+ +
+Ltac2 lt (x : int) (y : int) := equal (compare x y) -1.
+Ltac2 gt (x : int) (y : int) := equal (compare x y) 1.
+Ltac2 le (x : int) (y : int) :=
+  
+  match equal x y with
+  | true => true
+  | false => lt x y
+  end.
+Ltac2 ge (x : int) (y : int) :=
+  
+  match equal x y with
+  | true => true
+  | false => gt x y
+  end.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Lazy.html b/master/corelib/Ltac2.Lazy.html new file mode 100644 index 0000000000..fa0ef45cb1 --- /dev/null +++ b/master/corelib/Ltac2.Lazy.html @@ -0,0 +1,214 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Lazy

+ +
+ +
+Require Import Ltac2.Init.
+Require Ltac2.Ref.
+Require Ltac2.Control.
+ +
+Ltac2 Type 'a lazy_data := [ Value ('a) | Thunk (unit -> 'a) ].
+ +
+
+ +
+Type of a lazy cell, similar to OCaml's 'a Lazy.t type. The functions of + this module do not have any specific backtracking support, so any function + passed to primitives of this module is handled as if it had one success at + most (potential other successes are ignored). +
+
+Ltac2 Type 'a t := 'a lazy_data Ref.ref.
+ +
+
+ +
+from_val v creates a new lazy cell storing (already-computed) value v. + Forcing (i.e., using the force function on) the produced cell gives back + value v, and never gives an exception. +
+
+Ltac2 from_val (v : 'a) : 'a t :=
+  Ref.ref (Value v).
+ +
+
+ +
+from_fun f creates a new lazy cell from the given thunk f. There is no + specific support for backtracking in the Lazy module, so if f has more + than one success, only the first one will be considered. +
+
+Ltac2 from_fun (f : unit -> 'a) : 'a t :=
+  Ref.ref (Thunk f).
+ +
+
+ +
+is_val r indicates whether the given lazy cell r holds a forced value. + In particular, is_val r always returns true if r was created via the + from_val function. If r was created using from_fun, then true will + only be returned if the value of r was previously forced (e.g., with the + force function), and if no exception was produced by said forcing. +
+
+Ltac2 is_val (r : 'a t) : bool :=
+  match Ref.get r with
+  | Value _ => true
+  | Thunk _ => false
+  end.
+ +
+
+ +
+Exception raised in case of a "cyclic" lazy cell. +
+
+Ltac2 Type exn ::= [ Undefined ].
+ +
+
+ +
+force r gives the value represented by the lazy cell r, which requires + forcing a thunk and updating r to the produced value if r does not yet + have a value. Note that if forcing produces an exception, subsequent calls + to force will immediately yield the same exception (without re-computing + the whole thunk). Additionally, the Undefined exception is produced (and + set to be produced by r on subsequent calls to force) if r relies on + its own value for its definition (i.e., if r is "cyclic"). +
+
+Ltac2 force (r : 'a t) : 'a :=
+  match Ref.get r with
+  | Value v => v
+  | Thunk f =>
+      Ref.set r (Thunk (fun () => Control.throw Undefined));
+      match Control.case f with
+      | Val (v, _) =>
+          Ref.set r (Value v);
+          v
+      | Err e =>
+          Ref.set r (Thunk (fun () => Control.zero e));
+          Control.zero e
+      end
+  end.
+ +
+
+ +
+map f r is equivalent to from_fun (fun () => f (force r)). +
+
+Ltac2 map (f : 'a -> 'b) (r : 'a t) : 'b t :=
+  from_fun (fun () => f (force r)).
+ +
+
+ +
+map_val f r is similar to map f r, but the function f is immediately + applied if r contains a forced value. If the immediate application gives + an exception, then any subsequent forcing of produced lazy cell will raise + the same exception. +
+
+Ltac2 map_val (f : 'a -> 'b) (r : 'a t) : 'b t :=
+  match Ref.get r with
+  | Value v =>
+      match Control.case (fun () => f v) with
+      | Val (v, _) => from_val v
+      | Err e => from_fun (fun () => Control.zero e)
+      end
+  | Thunk t => from_fun (fun () => f (t ()))
+  end.
+ +
+Module Export Notations.
+  Ltac2 Notation "lazy!" f(thunk(self)) := from_fun f.
+End Notations.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.List.html b/master/corelib/Ltac2.List.html new file mode 100644 index 0000000000..b2a8c55660 --- /dev/null +++ b/master/corelib/Ltac2.List.html @@ -0,0 +1,795 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.List

+ +
+ +
+ +
+ +
+Require Import Ltac2.Init.
+Require Ltac2.Int.
+Require Ltac2.Control.
+Require Ltac2.Bool.
+Require Ltac2.Message.
+ +
+Ltac2 rec length (ls : 'a list) :=
+  match ls with
+  | [] => 0
+  | _ :: xs => Int.add 1 (length xs)
+  end.
+ +
+Ltac2 rec compare_lengths (ls1 : 'a list) (ls2 : 'b list) :=
+  match ls1 with
+  | []
+    => match ls2 with
+       | [] => 0
+       | _ :: _ => -1
+       end
+  | _ :: ls1
+    => match ls2 with
+       | [] => 1
+       | _ :: ls2 => compare_lengths ls1 ls2
+       end
+  end.
+ +
+Ltac2 rec compare_length_with (ls : 'a list) (n : int) :=
+  match Int.lt n 0 with
+  | true => 1
+  | false
+    => match ls with
+       | [] => Int.compare 0 n
+       | _ :: ls => compare_length_with ls (Int.sub n 1)
+       end
+  end.
+ +
+Ltac2 cons (x : 'a) (xs : 'a list) :=
+  x :: xs.
+ +
+ +
+Ltac2 hd_opt (ls : 'a list) :=
+  match ls with
+  | [] => None
+  | x :: _ => Some x
+  end.
+ +
+Ltac2 hd (ls : 'a list) :=
+  match ls with
+  | [] => Control.throw_invalid_argument "List.hd"
+  | x :: _ => x
+  end.
+ +
+Ltac2 tl (ls : 'a list) :=
+  match ls with
+  | [] => []
+  | _ :: xs => xs
+  end.
+ +
+Ltac2 dest (xs : 'a list) : 'a * 'a list :=
+  match xs with
+  | x :: xs => (x, xs)
+  | [] => Control.throw_invalid_argument "List.dest: list empty"
+  end.
+ +
+Ltac2 is_empty (xs : 'a list) : bool :=
+  match xs with
+  | _ :: _ => false
+  | _ => true
+  end.
+ +
+Ltac2 rec last_opt (ls : 'a list) :=
+  match ls with
+  | [] => None
+  | x :: xs
+    => match xs with
+       | [] => Some x
+       | _ :: _ => last_opt xs
+       end
+  end.
+ +
+Ltac2 last (ls : 'a list) :=
+  match last_opt ls with
+  | None => Control.throw_invalid_argument "List.last"
+  | Some v => v
+  end.
+ +
+Ltac2 rec removelast (ls : 'a list) :=
+  match ls with
+  | [] => []
+  | x :: xs
+    => match xs with
+       | [] => []
+       | _ :: _ => x :: removelast xs
+       end
+  end.
+ +
+Ltac2 rec nth_opt_aux (ls : 'a list) (n : int) :=
+  match ls with
+  | [] => None
+  | x :: xs
+    => match Int.equal n 0 with
+       | true => Some x
+       | false => nth_opt_aux xs (Int.sub n 1)
+       end
+  end.
+ +
+Ltac2 nth_opt (ls : 'a list) (n : int) :=
+  Control.assert_valid_argument "List.nth" (Int.ge n 0);
+  nth_opt_aux ls n.
+ +
+Ltac2 nth (ls : 'a list) (n : int) :=
+  match nth_opt ls n with
+  | Some v => v
+  | None => Control.throw_out_of_bounds "List.nth"
+  end.
+ +
+Ltac2 rec rev_append (l1 : 'a list) (l2 : 'a list) :=
+  match l1 with
+  | [] => l2
+  | a :: l => rev_append l (a :: l2)
+  end.
+ +
+Ltac2 rev l := rev_append l [].
+ +
+Ltac2 rec append ls1 ls2 :=
+  match ls1 with
+  | [] => ls2
+  | x :: xs => x :: append xs ls2
+  end.
+ +
+Ltac2 rec concat (ls : 'a list list) :=
+  match ls with
+  | [] => []
+  | x :: xs => append x (concat xs)
+  end.
+ +
+Ltac2 flatten (ls : 'a list list) := concat ls.
+ +
+Ltac2 rec iter (f : 'a -> unit) (ls : 'a list) :=
+  match ls with
+  | [] => ()
+  | l :: ls => f l; iter f ls
+  end.
+ +
+Ltac2 rec iteri_aux (i : int) (f : int -> 'a -> unit) (ls : 'a list) :=
+  match ls with
+  | [] => ()
+  | l :: ls => f i l; iteri_aux (Int.add i 1) f ls
+  end.
+ +
+Ltac2 iteri (f : int -> 'a -> unit) (ls : 'a list) :=
+  iteri_aux 0 f ls.
+ +
+Ltac2 rec map (f : 'a -> 'b) (ls : 'a list) :=
+  match ls with
+  | [] => []
+  | l :: ls => f l :: map f ls
+  end.
+ +
+Ltac2 rec mapi_aux (i : int) (f : int -> 'a -> 'b) (ls : 'a list) :=
+  match ls with
+  | [] => []
+  | l :: ls => f i l :: mapi_aux (Int.add i 1) f ls
+  end.
+ +
+Ltac2 mapi (f : int -> 'a -> 'b) (ls : 'a list) :=
+  mapi_aux 0 f ls.
+ +
+Ltac2 rec flat_map (f : 'a -> 'b list) (xs : 'a list) :=
+  match xs with
+  | [] => []
+  | x :: xs => append (f x) (flat_map f xs)
+  end.
+ +
+Ltac2 rev_map (f : 'a -> 'b) (ls : 'a list) :=
+  let rec rmap_f accu ls :=
+      match ls with
+      | [] => accu
+      | a::l => rmap_f (f a :: accu) l
+      end in
+  rmap_f [] ls.
+ +
+Ltac2 rec fold_right (f : 'a -> 'b -> 'b) (ls : 'a list) (a : 'b) : 'b :=
+  match ls with
+  | [] => a
+  | l :: ls => f l (fold_right f ls a)
+  end.
+ +
+Ltac2 rec fold_left (f : 'a -> 'b -> 'a) (a : 'a) (xs : 'b list) : 'a :=
+  match xs with
+  | [] => a
+  | x :: xs => fold_left f (f a x) xs
+  end.
+ +
+Ltac2 fold_lefti (f : int -> 'a -> 'b -> 'a) (a : 'a) (xs : 'b list) : 'a :=
+  let rec go i a xs :=
+    match xs with
+    | [] => a
+    | x :: xs => go (Int.add i 1) (f i a x) xs
+    end
+  in go 0 a xs.
+ +
+Ltac2 rec iter2 (f : 'a -> 'b -> unit) (ls1 : 'a list) (ls2 : 'b list) :=
+  match ls1 with
+  | []
+    => match ls2 with
+       | [] => ()
+       | _ :: _ => Control.throw_invalid_argument "List.iter2"
+       end
+  | l1 :: ls1
+    => match ls2 with
+       | [] => Control.throw_invalid_argument "List.iter2"
+       | l2 :: ls2
+         => f l1 l2; iter2 f ls1 ls2
+       end
+  end.
+ +
+Ltac2 rec map2 (f : 'a -> 'b -> 'c) (ls1 : 'a list) (ls2 : 'b list) :=
+  match ls1 with
+  | []
+    => match ls2 with
+       | [] => []
+       | _ :: _ => Control.throw_invalid_argument "List.map2"
+       end
+  | l1 :: ls1
+    => match ls2 with
+       | [] => Control.throw_invalid_argument "List.map2"
+       | l2 :: ls2
+         => f l1 l2 :: map2 f ls1 ls2
+       end
+  end.
+ +
+Ltac2 rev_map2 (f : 'a -> 'b -> 'c) (ls1 : 'a list) (ls2 : 'b list) :=
+  let rec rmap2_f accu ls1 ls2 :=
+      match ls1 with
+      | []
+        => match ls2 with
+           | [] => accu
+           | _ :: _ => Control.throw_invalid_argument "List.rev_map2"
+           end
+      | l1 :: ls1
+        => match ls2 with
+           | [] => Control.throw_invalid_argument "List.rev_map2"
+           | l2 :: ls2
+             => rmap2_f (f l1 l2 :: accu) ls1 ls2
+           end
+      end in
+  rmap2_f [] ls1 ls2.
+ +
+Ltac2 rec fold_right2 (f : 'a -> 'b -> 'c -> 'c) (ls1 : 'a list) (ls2 : 'b list) (a : 'c) :=
+  match ls1 with
+  | []
+    => match ls2 with
+       | [] => a
+       | _ :: _ => Control.throw_invalid_argument "List.fold_right2"
+       end
+  | l1 :: ls1
+    => match ls2 with
+       | [] => Control.throw_invalid_argument "List.fold_right2"
+       | l2 :: ls2
+         => f l1 l2 (fold_right2 f ls1 ls2 a)
+       end
+  end.
+ +
+Ltac2 rec fold_left2 (f : 'a -> 'b -> 'c -> 'a) (a : 'a) (ls1 : 'b list) (ls2 : 'c list) :=
+  match ls1 with
+  | []
+    => match ls2 with
+       | [] => a
+       | _ :: _ => Control.throw_invalid_argument "List.fold_left2"
+       end
+  | l1 :: ls1
+    => match ls2 with
+       | [] => Control.throw_invalid_argument "List.fold_left2"
+       | l2 :: ls2
+         => fold_left2 f (f a l1 l2) ls1 ls2
+       end
+  end.
+ +
+Ltac2 rec for_all f ls :=
+  match ls with
+  | [] => true
+  | x :: xs => match f x with
+               | true => for_all f xs
+               | false => false
+               end
+  end.
+ +
+Ltac2 rec exist f ls :=
+  match ls with
+  | [] => false
+  | x :: xs => match f x with
+               | true => true
+               | false => exist f xs
+               end
+  end.
+ +
+Ltac2 rec for_all2_aux (on_length_mismatch : 'a list -> 'b list -> bool) f xs ys :=
+  match xs with
+  | [] => match ys with
+          | [] => true
+          | _ :: _ => on_length_mismatch xs ys
+          end
+  | x :: xs'
+    => match ys with
+       | [] => on_length_mismatch xs ys
+       | y :: ys'
+         => match f x y with
+            | true => for_all2_aux on_length_mismatch f xs' ys'
+            | false => false
+            end
+       end
+  end.
+ +
+Ltac2 for_all2 f xs ys := for_all2_aux (fun _ _ => Control.throw_invalid_argument "List.for_all2") f xs ys.
+Ltac2 equal f xs ys := for_all2_aux (fun _ _ => false) f xs ys.
+ +
+Ltac2 rec exist2 f xs ys :=
+  match xs with
+  | [] => match ys with
+          | [] => false
+          | _ :: _ => Control.throw_invalid_argument "List.exist2"
+          end
+  | x :: xs'
+    => match ys with
+       | [] => Control.throw_invalid_argument "List.exist2"
+       | y :: ys'
+         => match f x y with
+            | true => true
+            | false => exist2 f xs' ys'
+            end
+       end
+  end.
+ +
+Ltac2 rec find_opt f xs :=
+  match xs with
+  | [] => None
+  | x :: xs => match f x with
+               | true => Some x
+               | false => find_opt f xs
+               end
+  end.
+ +
+Ltac2 find f xs :=
+  match find_opt f xs with
+  | Some v => v
+  | None => Control.throw Not_found
+  end.
+ +
+Ltac2 rec find_rev_opt f xs :=
+  match xs with
+  | [] => None
+  | x :: xs => match find_rev_opt f xs with
+               | Some v => Some v
+               | None => match f x with
+                         | true => Some x
+                         | false => None
+                         end
+               end
+  end.
+ +
+Ltac2 find_rev f xs :=
+  match find_rev_opt f xs with
+  | Some v => v
+  | None => Control.throw Not_found
+  end.
+ +
+Ltac2 mem (eq : 'a -> 'a -> bool) (a : 'a) (ls : 'a list) :=
+  exist (eq a) ls.
+ +
+Ltac2 rec filter f xs :=
+  match xs with
+  | [] => []
+  | x :: xs
+    => match f x with
+       | true => x :: filter f xs
+       | false => filter f xs
+       end
+  end.
+ +
+Ltac2 rec filter_out f xs :=
+  filter (fun x => Bool.neg (f x)) xs.
+ +
+Ltac2 find_all (f : 'a -> bool) (ls : 'a list) := filter f ls.
+ +
+Ltac2 remove (eqb : 'a -> 'a -> bool) (x : 'a) (ls : 'a list) :=
+  filter_out (eqb x) ls.
+ +
+Ltac2 count_occ (eqb : 'a -> 'a -> bool) (x : 'a) (ls : 'a list) :=
+  length (filter (eqb x) ls).
+ +
+Ltac2 rec list_power (ls1 : 'a list) (ls2 : 'b list) :=
+  match ls1 with
+  | [] => [] :: []
+  | x :: t
+    => flat_map (fun f => map (fun y => (x, y) :: f) ls2)
+                (list_power t ls2)
+  end.
+ +
+Ltac2 rec partition (f : 'a -> bool) (l : 'a list) :=
+  match l with
+  | [] => ([], [])
+  | x :: tl
+    => let (g, d) := partition f tl in
+       match f x with
+       | true => ((x::g), d)
+       | false => (g, (x::d))
+       end
+  end.
+ +
+
+ +
+list_prod has the same signature as combine, but unlike + combine, it adds every possible pairs, not only those at the + same position. +
+
+ +
+Ltac2 rec list_prod (ls1 : 'a list) (ls2 : 'b list) :=
+  match ls1 with
+  | [] => []
+  | x :: t
+    => append (map (fun y => (x, y)) ls2) (list_prod t ls2)
+  end.
+ +
+Ltac2 rec firstn (n : int) (ls : 'a list) :=
+  Control.assert_valid_argument "List.firstn" (Int.ge n 0);
+  match Int.equal n 0 with
+  | true => []
+  | false
+    => match ls with
+       | [] => Control.throw_out_of_bounds "List.firstn"
+       | x :: xs
+         => x :: firstn (Int.sub n 1) xs
+       end
+  end.
+ +
+Ltac2 rec skipn (n : int) (ls : 'a list) :=
+  Control.assert_valid_argument "List.skipn" (Int.ge n 0);
+  match Int.equal n 0 with
+  | true => ls
+  | false
+    => match ls with
+       | [] => Control.throw_out_of_bounds "List.skipn"
+       | _ :: xs
+         => skipn (Int.sub n 1) xs
+       end
+  end.
+ +
+Ltac2 lastn (n : int) (ls : 'a list) :=
+  let l := length ls in
+  Control.assert_valid_argument "List.lastn" (Int.ge n 0);
+  Control.assert_bounds "List.lastn" (Int.le n l);
+  skipn (Int.sub l n) ls.
+ +
+Ltac2 rec nodup (eqb : 'a -> 'a -> bool) (ls : 'a list) :=
+  match ls with
+  | [] => []
+  | x :: xs
+    => match mem eqb x xs with
+       | true => nodup eqb xs
+       | false => x :: nodup eqb xs
+       end
+  end.
+ +
+Ltac2 rec seq (start : int) (step : int) (last : int) :=
+  match Int.lt (Int.sub last start) step with
+  | true
+    => []
+  | false
+    => start :: seq (Int.add start step) step last
+  end.
+ +
+Ltac2 init (len : int) (f : int -> 'a) :=
+  Control.assert_valid_argument "List.init" (Int.ge len 0);
+  map f (seq 0 1 len).
+ +
+Ltac2 repeat (x : 'a) (n : 'int) :=
+  init n (fun _ => x).
+ +
+Ltac2 assoc (eqk : 'k -> 'k -> bool) (k : 'k) (l : ('k * 'v) list) :=
+  let eq_key kv := let (k', _) := kv in eqk k k' in
+  let (_, v) := find eq_key l in
+  v.
+ +
+Ltac2 assoc_opt (eqk : 'k -> 'k -> bool) (k : 'k) (l : ('k * 'v) list) :=
+  let eq_key kv := let (k', _) := kv in eqk k k' in
+  match find_opt eq_key l with
+  | Some kv => let (_, v) := kv in Some v
+  | None => None
+  end.
+ +
+Ltac2 mem_assoc (eqk : 'k -> 'k -> bool) (k : 'k) (l : ('k * 'v) list) :=
+  let eq_key kv := let (k', _) := kv in eqk k k' in
+  exist eq_key l.
+ +
+Ltac2 remove_assoc (eqk : 'k -> 'k -> bool) (k : 'k) (l : ('k * 'v) list) :=
+  let eq_key kv := let (k', _) := kv in eqk k k' in
+  filter_out eq_key l.
+ +
+Ltac2 rec split (ls : ('a * 'b) list) :=
+  match ls with
+  | [] => ([], [])
+  | xy :: tl
+    => let (x, y) := xy in
+       let (left, right) := split tl in
+       ((x::left), (y::right))
+  end.
+ +
+Ltac2 rec combine (ls1 : 'a list) (ls2 : 'b list) :=
+  match ls1 with
+  | []
+    => match ls2 with
+       | [] => []
+       | _ :: _ => Control.throw_invalid_argument "List.combine"
+       end
+  | x :: xs
+    => match ls2 with
+       | y :: ys
+         => (x, y) :: combine xs ys
+       | [] => Control.throw_invalid_argument "List.combine"
+       end
+  end.
+ +
+Ltac2 enumerate (ls : 'a list) :=
+  combine (seq 0 1 (length ls)) ls.
+ +
+Ltac2 rec merge (cmp : 'a -> 'a -> int) (l1 : 'a list) (l2 : 'b list) :=
+  let rec merge_aux l2 :=
+      match l1 with
+      | [] => l2
+      | a1 :: l1'
+        => match l2 with
+           | [] => l1
+           | a2 :: l2'
+             => match Int.le (cmp a1 a2) 0 with
+                | true => a1 :: merge cmp l1' l2
+                | false => a2 :: merge_aux l2'
+                end
+           end
+      end in
+  merge_aux l2.
+ +
+Ltac2 rec merge_list_to_stack cmp stack l :=
+  match stack with
+  | [] => [Some l]
+  | l' :: stack'
+    => match l' with
+       | None => Some l :: stack'
+       | Some l'
+         => None :: merge_list_to_stack cmp stack' (merge cmp l' l)
+       end
+  end.
+ +
+Ltac2 rec merge_stack cmp stack :=
+  match stack with
+  | [] => []
+  | l :: stack'
+    => match l with
+       | None => merge_stack cmp stack'
+       | Some l => merge cmp l (merge_stack cmp stack')
+       end
+  end.
+ +
+Ltac2 rec iter_merge cmp stack l :=
+  match l with
+  | [] => merge_stack cmp stack
+  | a::l' => iter_merge cmp (merge_list_to_stack cmp stack [a]) l'
+  end.
+ +
+Ltac2 sort cmp l := iter_merge cmp [] l.
+ +
+Ltac2 sort_uniq (cmp : 'a -> 'a -> int) (l : 'a list) :=
+  let rec uniq l :=
+      match l with
+      | [] => []
+      | x1 :: xs
+        => match xs with
+           | [] => x1 :: xs
+           | x2 :: _
+             => match Int.equal (cmp x1 x2) 0 with
+                | true => uniq xs
+                | false => x1 :: uniq xs
+                end
+           end
+      end in
+  uniq (sort cmp l).
+ +
+Ltac2 inclusive_range (lb : int) (ub : int) : int list :=
+  let rec go lb ub :=
+    if Int.gt lb ub then [] else lb :: go (Int.add lb 1) ub
+  in
+  go lb ub.
+ +
+Ltac2 range (lb : int) (ub : int) : int list :=
+  inclusive_range lb (Int.sub ub 1).
+ +
+
+ +
+concat_rev [x1; ..; xN-1; xN] computes rev xN ++ rev xN-1 ++ .. x1. + Note that x1 is not reversed and appears in its original order. + concat_rev is faster than concat and should be preferred over concat + when the order of items does not matter. +
+
+Ltac2 concat_rev (ls : 'a list list) : 'a list :=
+  let rec go ls acc :=
+    match ls with
+    | [] => acc
+    | l :: ls => go ls (rev_append l acc)
+    end
+  in
+  match ls with
+  | [] => []
+  | l :: ls => go ls l
+  end.
+ +
+Ltac2 rec map_filter (f : 'a -> 'b option) (l : 'a list) : 'b list :=
+  match l with
+  | [] => []
+  | x :: l =>
+    match f x with
+    | Some y => y :: map_filter f l
+    | None => map_filter f l
+    end
+  end.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Ltac1.html b/master/corelib/Ltac2.Ltac1.html new file mode 100644 index 0000000000..1d60ebed17 --- /dev/null +++ b/master/corelib/Ltac2.Ltac1.html @@ -0,0 +1,215 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Ltac1

+ +
+ +
+
+ +
+This module defines the Ltac2 FFI to Ltac1 code. Due to intricate semantics + of the latter, the functions described here are voluntarily under-specified. + Not for the casual user, handle with care and expect undefined behaviours + otherwise. +
+
+ +
+Require Import Ltac2.Init Ltac2.Std Ltac2.Control.
+ +
+Ltac2 Type t.
+
+ +
+Dynamically-typed Ltac1 values. +
+
+ +
+Ltac2 @ external ref : ident list -> t := "rocq-runtime.plugins.ltac2_ltac1" "ltac1_ref".
+
+ +
+Returns the Ltac1 definition with the given absolute name. +
+
+ +
+Ltac2 @ external run : t -> unit := "rocq-runtime.plugins.ltac2_ltac1" "ltac1_run".
+
+ +
+Runs an Ltac1 value, assuming it is a 'tactic', i.e. not returning + anything. +
+
+ +
+Ltac2 @ external lambda : (t -> t) -> t := "rocq-runtime.plugins.ltac2_ltac1" "ltac1_lambda".
+
+ +
+Embed an Ltac2 function into Ltac1 values. Contrarily to the ltac1:(...) + quotation, this function allows both to capture an Ltac2 context inside the + closure and to return an Ltac1 value. Returning values in Ltac1 is a + intrepid endeavour prone to weird runtime semantics. +
+
+ +
+Ltac2 @ external apply : t -> t list -> (t -> unit) -> unit := "rocq-runtime.plugins.ltac2_ltac1" "ltac1_apply".
+
+ +
+Applies an Ltac1 value to a list of arguments, and provides the result in + CPS style. It does **not** run the returned value. +
+ + Conversion functions +
+
+ +
+Ltac2 @ external of_int : int -> t := "rocq-runtime.plugins.ltac2_ltac1" "ltac1_of_int".
+
+ +
+Converts an Ltac2 int into an Ltac1 value. +
+
+Ltac2 @ external to_int : t -> int option := "rocq-runtime.plugins.ltac2_ltac1" "ltac1_to_int".
+
+ +
+Converts an Ltac1 int into an Ltac2 value. +
+
+ +
+Ltac2 @ external of_constr : constr -> t := "rocq-runtime.plugins.ltac2_ltac1" "ltac1_of_constr".
+
+ +
+Converts an Ltac2 constr into an Ltac1 value. +
+
+Ltac2 @ external to_constr : t -> constr option := "rocq-runtime.plugins.ltac2_ltac1" "ltac1_to_constr".
+
+ +
+Converts an Ltac1 constr (which includes terms created via open_constr) into an Ltac2 value. +
+ + preterm is called uconstr in Ltac1. +
+
+Ltac2 @ external of_preterm : preterm -> t := "rocq-runtime.plugins.ltac2_ltac1" "ltac1_of_preterm".
+Ltac2 @ external to_preterm : t -> preterm option := "rocq-runtime.plugins.ltac2_ltac1" "ltac1_to_preterm".
+ +
+Ltac2 @ external of_ident : ident -> t := "rocq-runtime.plugins.ltac2_ltac1" "ltac1_of_ident".
+Ltac2 @ external to_ident : t -> ident option := "rocq-runtime.plugins.ltac2_ltac1" "ltac1_to_ident".
+ +
+Ltac2 @ external of_list : t list -> t := "rocq-runtime.plugins.ltac2_ltac1" "ltac1_of_list".
+Ltac2 @ external to_list : t -> t list option := "rocq-runtime.plugins.ltac2_ltac1" "ltac1_to_list".
+ +
+Ltac2 @ external of_intro_pattern : intro_pattern -> t := "rocq-runtime.plugins.ltac2_ltac1" "ltac1_of_intro_pattern".
+Ltac2 @ external to_intro_pattern : t -> intro_pattern option := "rocq-runtime.plugins.ltac2_ltac1" "ltac1_to_intro_pattern".
+ +
+
+ +
+Debug information +
+
+ +
+Ltac2 @ external tag_name : t -> string := "rocq-runtime.plugins.ltac2_ltac1" "ltac1_tag_name".
+
+ +
+Name of the ltac1 value class the argument belongs to. Should be + used only for error printing, typically "expected a constr but got a +
+
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Ltac2.html b/master/corelib/Ltac2.Ltac2.html new file mode 100644 index 0000000000..d8ee8c4b55 --- /dev/null +++ b/master/corelib/Ltac2.Ltac2.html @@ -0,0 +1,121 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Ltac2

+ +
+ +
+Require Export Ltac2.Init.
+ +
+Require Ltac2.Array.
+Require Ltac2.Bool.
+Require Ltac2.Char.
+Require Ltac2.Constant.
+Require Ltac2.Constr.
+Require Ltac2.Constructor.
+Require Ltac2.Control.
+Require Ltac2.Env.
+Require Ltac2.Evar.
+Require Ltac2.Float.
+Require Ltac2.Fresh.
+Require Ltac2.Ident.
+Require Ltac2.Ind.
+Require Ltac2.Int.
+Require Ltac2.Lazy.
+Require Ltac2.List.
+Require Ltac2.Ltac1.
+Require Ltac2.Message.
+Require Ltac2.Meta.
+Require Ltac2.Option.
+Require Ltac2.Pattern.
+Require Ltac2.Printf.
+Require Ltac2.Proj.
+Require Ltac2.RedFlags.
+Require Ltac2.Ref.
+Require Ltac2.Std.
+Require Ltac2.String.
+Require Ltac2.Uint63.
+Require Ltac2.FSet.
+Require Ltac2.FMap.
+Require Ltac2.TransparentState.
+Require Ltac2.Unification.
+ +
+Require Export Ltac2.Notations.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Message.html b/master/corelib/Ltac2.Message.html new file mode 100644 index 0000000000..478ccd57ae --- /dev/null +++ b/master/corelib/Ltac2.Message.html @@ -0,0 +1,253 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Message

+ +
+ +
+Require Import Ltac2.Init.
+ +
+Ltac2 @ external print : message -> unit := "rocq-runtime.plugins.ltac2" "print".
+ +
+Ltac2 @ external of_string : string -> message := "rocq-runtime.plugins.ltac2" "message_of_string".
+ +
+Ltac2 @ external to_string : message -> string := "rocq-runtime.plugins.ltac2" "message_to_string".
+ +
+Ltac2 @ external of_int : int -> message := "rocq-runtime.plugins.ltac2" "message_of_int".
+ +
+Ltac2 @ external of_ident : ident -> message := "rocq-runtime.plugins.ltac2" "message_of_ident".
+ +
+Ltac2 @ external of_constr : constr -> message := "rocq-runtime.plugins.ltac2" "message_of_constr".
+
+ +
+Panics if there is more than one goal under focus. +
+
+ +
+Ltac2 @ external of_exn : exn -> message := "rocq-runtime.plugins.ltac2" "message_of_exn".
+
+ +
+Panics if there is more than one goal under focus. +
+
+ +
+Ltac2 @ external concat : message -> message -> message := "rocq-runtime.plugins.ltac2" "message_concat".
+ +
+
+ +
+Boxing primitives. They are translated to OCaml "Format" boxes, + see https://ocaml.org/docs/formatting-text +
+
+ +
+Ltac2 @external force_new_line : message := "rocq-runtime.plugins.ltac2" "message_force_new_line".
+
+ +
+Force writing on a new line after this. + Warning: partially reinitialises the pretty-printing engine, + potentially leading to bad printing afterwards. + Prefer using a break hint inside a vertical box. +
+
+ +
+Ltac2 @external break : int -> int -> message := "rocq-runtime.plugins.ltac2" "message_break".
+
+ +
+General break hint: break n i either prints n spaces or splits + the line adding i to the current indentation. +
+
+ +
+Ltac2 @external space : message := "rocq-runtime.plugins.ltac2" "message_space".
+
+ +
+Breaking space. Equivalent to break 1 0. +
+
+ +
+Ltac2 @external hbox : message -> message := "rocq-runtime.plugins.ltac2" "message_hbox".
+
+ +
+Horizontal box. Break hints in a horizontal box never split the + line (nested boxes inside the horizontal box may allow line + splitting). +
+
+ +
+Ltac2 @external vbox : int -> message -> message := "rocq-runtime.plugins.ltac2" "message_vbox".
+
+ +
+Vertical box. Every break hint in a vertical box splits the line. + The int is added to the current indentation when splitting the line. +
+
+ +
+Ltac2 @external hvbox : int -> message -> message := "rocq-runtime.plugins.ltac2" "message_hvbox".
+
+ +
+Horizontal/vertical box. Behaves as a horizontal box if it fits on + a single line, otherwise behaves as a vertical box (using the + given int). +
+
+ +
+Ltac2 @external hovbox : int -> message -> message := "rocq-runtime.plugins.ltac2" "message_hovbox".
+
+ +
+Horizonal-or-vertical box. Prints as much as possible on each + line, splitting the line at break hints when there is no more room + on the line (see "Printing Width" option). The int is added to + the indentation when splitting the line. +
+
+ +
+Module Format.
+ +
+
+ +
+Only for internal use. +
+
+ +
+Ltac2 @ external stop : ('a, 'b, 'c, 'a) format := "rocq-runtime.plugins.ltac2" "format_stop".
+ +
+Ltac2 @ external string : ('a, 'b, 'c, 'd) format ->
+  (string -> 'a, 'b, 'c, 'd) format := "rocq-runtime.plugins.ltac2" "format_string".
+ +
+Ltac2 @ external int : ('a, 'b, 'c, 'd) format ->
+  (int -> 'a, 'b, 'c, 'd) format := "rocq-runtime.plugins.ltac2" "format_int".
+ +
+Ltac2 @ external constr : ('a, 'b, 'c, 'd) format ->
+  (constr -> 'a, 'b, 'c, 'd) format := "rocq-runtime.plugins.ltac2" "format_constr".
+ +
+Ltac2 @ external ident : ('a, 'b, 'c, 'd) format ->
+  (ident -> 'a, 'b, 'c, 'd) format := "rocq-runtime.plugins.ltac2" "format_ident".
+ +
+Ltac2 @ external literal : string -> ('a, 'b, 'c, 'd) format ->
+  ('a, 'b, 'c, 'd) format := "rocq-runtime.plugins.ltac2" "format_literal".
+ +
+Ltac2 @ external alpha : ('a, 'b, 'c, 'd) format ->
+  (('b -> 'r -> 'c) -> 'r -> 'a, 'b, 'c, 'd) format := "rocq-runtime.plugins.ltac2" "format_alpha".
+ +
+Ltac2 @ external kfprintf : (message -> 'r) -> ('a, unit, message, 'r) format -> 'a :=
+  "rocq-runtime.plugins.ltac2" "format_kfprintf".
+ +
+Ltac2 @ external ikfprintf : ('v -> 'r) -> 'v -> ('a, unit, 'v, 'r) format -> 'a :=
+  "rocq-runtime.plugins.ltac2" "format_ikfprintf".
+ +
+End Format.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Meta.html b/master/corelib/Ltac2.Meta.html new file mode 100644 index 0000000000..63efd5ae86 --- /dev/null +++ b/master/corelib/Ltac2.Meta.html @@ -0,0 +1,90 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Meta

+ +
+ +
+Require Import Ltac2.Init.
+ +
+Ltac2 Type t := meta.
+ +
+Ltac2 @ external equal : t -> t -> bool := "rocq-runtime.plugins.ltac2" "meta_equal".
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Notations.html b/master/corelib/Ltac2.Notations.html new file mode 100644 index 0000000000..1736448fb4 --- /dev/null +++ b/master/corelib/Ltac2.Notations.html @@ -0,0 +1,929 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Notations

+ +
+ +
+Require Import Ltac2.Init.
+Require Ltac2.Control Ltac2.Option Ltac2.Pattern Ltac2.Array Ltac2.Int Ltac2.Std Ltac2.Constr.
+ +
+
+ +
+Constr matching +
+
+ +
+Ltac2 Notation "lazy_match!" t(tactic(6)) "with" m(constr_matching) "end" :=
+  Pattern.lazy_match0 t m.
+ +
+Ltac2 Notation "multi_match!" t(tactic(6)) "with" m(constr_matching) "end" :=
+  Pattern.multi_match0 t m.
+ +
+Ltac2 Notation "match!" t(tactic(6)) "with" m(constr_matching) "end" :=
+  Pattern.one_match0 t m.
+ +
+
+ +
+Goal matching +
+
+ +
+Ltac2 Notation "lazy_match!" "goal" "with" m(goal_matching) "end" :=
+  Pattern.lazy_goal_match0 false m.
+ +
+Ltac2 Notation "multi_match!" "goal" "with" m(goal_matching) "end" :=
+  Pattern.multi_goal_match0 false m.
+ +
+Ltac2 Notation "match!" "goal" "with" m(goal_matching) "end" :=
+  Pattern.one_goal_match0 false m.
+ +
+Ltac2 Notation "lazy_match!" "reverse" "goal" "with" m(goal_matching) "end" :=
+  Pattern.lazy_goal_match0 true m.
+ +
+Ltac2 Notation "multi_match!" "reverse" "goal" "with" m(goal_matching) "end" :=
+  Pattern.multi_goal_match0 true m.
+ +
+Ltac2 Notation "match!" "reverse" "goal" "with" m(goal_matching) "end" :=
+  Pattern.one_goal_match0 true m.
+ +
+
+ +
+Tacticals +
+
+ +
+Ltac2 orelse t f :=
+match Control.case t with
+| Err e => f e
+| Val ans =>
+  let (x, k) := ans in
+  Control.plus (fun _ => x) k
+end.
+ +
+Ltac2 ifcatch t s f :=
+match Control.case t with
+| Err e => f e
+| Val ans =>
+  let (x, k) := ans in
+  Control.plus (fun _ => s x) (fun e => s (k e))
+end.
+ +
+Ltac2 fail0 (_ : unit) := Control.enter (fun _ => Control.zero (Tactic_failure None)).
+ +
+Ltac2 Notation fail := fail0 ().
+ +
+Ltac2 try0 t := Control.enter (fun _ => orelse t (fun _ => ())).
+ +
+Ltac2 Notation try := try0.
+ +
+Ltac2 rec repeat0 (t : unit -> unit) :=
+  Control.enter (fun () =>
+    ifcatch (fun _ => Control.progress t)
+      (fun _ => Control.check_interrupt (); repeat0 t) (fun _ => ())).
+ +
+Ltac2 Notation repeat := repeat0.
+ +
+Ltac2 dispatch0 t (head, tail) :=
+  match tail with
+  | None => Control.enter (fun _ => t (); Control.dispatch head)
+  | Some tacs =>
+    let (def, rem) := tacs in
+    Control.enter (fun _ => t (); Control.extend head def rem)
+  end.
+ +
+Ltac2 Notation t(thunk(self)) ">" "[" l(dispatch) "]" : 4 := dispatch0 t l.
+ +
+Ltac2 do0 n t :=
+  let rec aux n t := match Int.equal n 0 with
+  | true => ()
+  | false => t (); aux (Int.sub n 1) t
+  end in
+  aux (n ()) t.
+ +
+Ltac2 Notation do := do0.
+ +
+Ltac2 Notation once := Control.once.
+ +
+Ltac2 Notation unshelve := Control.unshelve.
+ +
+Ltac2 progress0 tac := Control.enter (fun _ => Control.progress tac).
+ +
+Ltac2 Notation progress := progress0.
+ +
+Ltac2 rec first0 tacs :=
+match tacs with
+| [] => Control.zero (Tactic_failure None)
+| tac :: tacs => Control.enter (fun _ => orelse tac (fun _ => first0 tacs))
+end.
+ +
+Ltac2 Notation "first" "[" tacs(list0(thunk(tactic(6)), "|")) "]" := first0 tacs.
+ +
+Ltac2 complete tac :=
+  let ans := tac () in
+  Control.enter (fun () => Control.zero (Tactic_failure None));
+  ans.
+ +
+Ltac2 rec solve0 tacs :=
+match tacs with
+| [] => Control.zero (Tactic_failure None)
+| tac :: tacs =>
+  Control.enter (fun _ => orelse (fun _ => complete tac) (fun _ => solve0 tacs))
+end.
+ +
+Ltac2 Notation "solve" "[" tacs(list0(thunk(tactic(6)), "|")) "]" := solve0 tacs.
+ +
+Ltac2 time0 tac := Control.time None tac.
+ +
+Ltac2 Notation time := time0.
+ +
+Ltac2 abstract0 tac := Control.abstract None tac.
+ +
+Ltac2 Notation abstract := abstract0.
+ +
+
+ +
+Base tactics +
+ + Note that we redeclare notations that can be parsed as mere identifiers + as abbreviations, so that it allows to parse them as function arguments + without having to write them within parentheses. +
+ + Enter and check evar resolution +
+
+Ltac2 enter_h ev f arg :=
+match ev with
+| true => Control.enter (fun () => f ev (arg ()))
+| false =>
+  Control.enter (fun () =>
+    Control.with_holes arg (fun x => f ev x))
+end.
+ +
+Ltac2 intros0 ev p :=
+  Control.enter (fun () => Std.intros ev p).
+ +
+Ltac2 Notation "intros" p(intropatterns) := intros0 false p.
+Ltac2 Notation intros := intros.
+ +
+Ltac2 Notation "eintros" p(intropatterns) := intros0 true p.
+Ltac2 Notation eintros := eintros.
+ +
+Ltac2 split0 ev bnd :=
+  enter_h ev Std.split bnd.
+ +
+Ltac2 Notation "split" bnd(thunk(with_bindings)) := split0 false bnd.
+Ltac2 Notation split := split.
+ +
+Ltac2 Notation "esplit" bnd(thunk(with_bindings)) := split0 true bnd.
+Ltac2 Notation esplit := esplit.
+ +
+Ltac2 exists0 ev bnds := match bnds with
+| [] => split0 ev (fun () => Std.NoBindings)
+| _ =>
+  let rec aux bnds := match bnds with
+  | [] => ()
+  | bnd :: bnds => split0 ev bnd; aux bnds
+  end in
+  aux bnds
+end.
+ +
+Ltac2 Notation "exists" bnd(list0(thunk(bindings), ",")) := exists0 false bnd.
+ +
+Ltac2 Notation "eexists" bnd(list0(thunk(bindings), ",")) := exists0 true bnd.
+Ltac2 Notation eexists := eexists.
+ +
+Ltac2 left0 ev bnd := enter_h ev Std.left bnd.
+ +
+Ltac2 Notation "left" bnd(thunk(with_bindings)) := left0 false bnd.
+Ltac2 Notation left := left.
+ +
+Ltac2 Notation "eleft" bnd(thunk(with_bindings)) := left0 true bnd.
+Ltac2 Notation eleft := eleft.
+ +
+Ltac2 right0 ev bnd := enter_h ev Std.right bnd.
+ +
+Ltac2 Notation "right" bnd(thunk(with_bindings)) := right0 false bnd.
+Ltac2 Notation right := right.
+ +
+Ltac2 Notation "eright" bnd(thunk(with_bindings)) := right0 true bnd.
+Ltac2 Notation eright := eright.
+ +
+Ltac2 constructor0 ev n bnd :=
+  enter_h ev (fun ev bnd => Std.constructor_n ev n bnd) bnd.
+ +
+Ltac2 Notation "constructor" := Control.enter (fun () => Std.constructor false).
+Ltac2 Notation constructor := constructor.
+Ltac2 Notation "constructor" n(tactic) bnd(thunk(with_bindings)) := constructor0 false n bnd.
+ +
+Ltac2 Notation "econstructor" := Control.enter (fun () => Std.constructor true).
+Ltac2 Notation econstructor := econstructor.
+Ltac2 Notation "econstructor" n(tactic) bnd(thunk(with_bindings)) := constructor0 true n bnd.
+ +
+Ltac2 specialize0 c pat :=
+  enter_h false (fun _ c => Std.specialize c pat) c.
+ +
+Ltac2 Notation "specialize" c(thunk(seq(constr, with_bindings))) ipat(opt(seq("as", intropattern))) :=
+  specialize0 c ipat.
+ +
+Ltac2 elim0 ev c bnd use :=
+  let f ev (c, bnd, use) := Std.elim ev (c, bnd) use in
+  enter_h ev f (fun () => c (), bnd (), use ()).
+ +
+Ltac2 Notation "elim" c(thunk(constr)) bnd(thunk(with_bindings))
+  use(thunk(opt(seq("using", constr, with_bindings)))) :=
+  elim0 false c bnd use.
+ +
+Ltac2 Notation "eelim" c(thunk(constr)) bnd(thunk(with_bindings))
+  use(thunk(opt(seq("using", constr, with_bindings)))) :=
+  elim0 true c bnd use.
+ +
+Ltac2 apply0 adv ev cb cl :=
+  Std.apply adv ev cb cl.
+ +
+Ltac2 Notation "eapply"
+  cb(list1(thunk(seq(open_constr, with_bindings)), ","))
+  cl(opt(seq("in", ident, opt(seq("as", intropattern))))) :=
+  apply0 true true cb cl.
+ +
+Ltac2 Notation "apply"
+  cb(list1(thunk(seq(open_constr, with_bindings)), ","))
+  cl(opt(seq("in", ident, opt(seq("as", intropattern))))) :=
+  apply0 true false cb cl.
+ +
+Ltac2 default_on_concl cl :=
+match cl with
+| None => { Std.on_hyps := Some []; Std.on_concl := Std.AllOccurrences }
+| Some cl => cl
+end.
+ +
+Ltac2 pose0 ev p :=
+  enter_h ev (fun _ (na, p) => Std.pose na p) p.
+ +
+Ltac2 Notation "pose" p(thunk(pose)) :=
+  pose0 false p.
+ +
+Ltac2 Notation "epose" p(thunk(pose)) :=
+  pose0 true p.
+ +
+Ltac2 Notation "set" p(thunk(pose)) cl(opt(clause)) :=
+  Std.set false p (default_on_concl cl).
+ +
+Ltac2 Notation "eset" p(thunk(pose)) cl(opt(clause)) :=
+  Std.set true p (default_on_concl cl).
+ +
+Ltac2 assert0 ev ast :=
+  enter_h ev (fun _ ast => Std.assert ast) ast.
+ +
+Ltac2 Notation "assert" ast(thunk(assert)) := assert0 false ast.
+ +
+Ltac2 Notation "eassert" ast(thunk(assert)) := assert0 true ast.
+ +
+Ltac2 enough_from_assertion(a : Std.assertion) :=
+  match a with
+  | Std.AssertType ip_opt term tac_opt => Std.enough term (Some tac_opt) ip_opt
+  | Std.AssertValue ident constr => Std.pose (Some ident) constr
+  end.
+ +
+Ltac2 enough0 ev ast :=
+  enter_h ev (fun _ ast => enough_from_assertion ast) ast.
+ +
+Ltac2 Notation "enough" ast(thunk(assert)) := enough0 false ast.
+ +
+Ltac2 Notation "eenough" ast(thunk(assert)) := enough0 true ast.
+ +
+Ltac2 default_everywhere cl :=
+match cl with
+| None => { Std.on_hyps := None; Std.on_concl := Std.AllOccurrences }
+| Some cl => cl
+end.
+ +
+Ltac2 Notation "remember"
+  c(thunk(open_constr))
+  na(opt(seq("as", ident)))
+  pat(opt(seq("eqn", ":", intropattern)))
+  cl(opt(clause)) :=
+  Std.remember false na c pat (default_everywhere cl).
+ +
+Ltac2 Notation "eremember"
+  c(thunk(open_constr))
+  na(opt(seq("as", ident)))
+  pat(opt(seq("eqn", ":", intropattern)))
+  cl(opt(clause)) :=
+  Std.remember true na c pat (default_everywhere cl).
+ +
+Ltac2 induction0 ev ic use :=
+  let f ev use := Std.induction ev ic use in
+  enter_h ev f use.
+ +
+Ltac2 Notation "induction"
+  ic(list1(induction_clause, ","))
+  use(thunk(opt(seq("using", constr, with_bindings)))) :=
+  induction0 false ic use.
+ +
+Ltac2 Notation "einduction"
+  ic(list1(induction_clause, ","))
+  use(thunk(opt(seq("using", constr, with_bindings)))) :=
+  induction0 true ic use.
+ +
+Ltac2 generalize0 gen :=
+  enter_h false (fun _ gen => Std.generalize gen) gen.
+ +
+Ltac2 Notation "generalize"
+  gen(thunk(list1(seq (open_constr, occurrences, opt(seq("as", ident))), ","))) :=
+  generalize0 gen.
+ +
+Ltac2 destruct0 ev ic use :=
+  let f ev use := Std.destruct ev ic use in
+  enter_h ev f use.
+ +
+Ltac2 Notation "destruct"
+  ic(list1(induction_clause, ","))
+  use(thunk(opt(seq("using", constr, with_bindings)))) :=
+  destruct0 false ic use.
+ +
+Ltac2 Notation "edestruct"
+  ic(list1(induction_clause, ","))
+  use(thunk(opt(seq("using", constr, with_bindings)))) :=
+  destruct0 true ic use.
+ +
+Ltac2 Notation "simple" "inversion"
+  arg(destruction_arg)
+  pat(opt(seq("as", intropattern)))
+  ids(opt(seq("in", list1(ident)))) :=
+  Std.inversion Std.SimpleInversion arg pat ids.
+ +
+Ltac2 Notation "inversion"
+  arg(destruction_arg)
+  pat(opt(seq("as", intropattern)))
+  ids(opt(seq("in", list1(ident)))) :=
+  Std.inversion Std.FullInversion arg pat ids.
+ +
+Ltac2 Notation "inversion_clear"
+  arg(destruction_arg)
+  pat(opt(seq("as", intropattern)))
+  ids(opt(seq("in", list1(ident)))) :=
+  Std.inversion Std.FullInversionClear arg pat ids.
+ +
+Ltac2 Notation "red" cl(opt(clause)) :=
+  Std.red (default_on_concl cl).
+Ltac2 Notation red := red.
+ +
+Ltac2 Notation "hnf" cl(opt(clause)) :=
+  Std.hnf (default_on_concl cl).
+Ltac2 Notation hnf := hnf.
+ +
+Ltac2 Notation "simpl" s(strategy) pl(opt(seq(pattern, occurrences))) cl(opt(clause)) :=
+  Std.simpl s pl (default_on_concl cl).
+Ltac2 Notation simpl := simpl.
+ +
+Ltac2 Notation "cbv" s(strategy) cl(opt(clause)) :=
+  Std.cbv s (default_on_concl cl).
+Ltac2 Notation cbv := cbv.
+ +
+Ltac2 Notation "cbn" s(strategy) cl(opt(clause)) :=
+  Std.cbn s (default_on_concl cl).
+Ltac2 Notation cbn := cbn.
+ +
+Ltac2 Notation "lazy" s(strategy) cl(opt(clause)) :=
+  Std.lazy s (default_on_concl cl).
+Ltac2 Notation lazy := lazy.
+ +
+Ltac2 Notation "unfold" pl(list1(seq(reference, occurrences), ",")) cl(opt(clause)) :=
+  Std.unfold pl (default_on_concl cl).
+ +
+Ltac2 fold0 pl cl :=
+  let cl := default_on_concl cl in
+  Control.enter (fun () => Control.with_holes pl (fun pl => Std.fold pl cl)).
+ +
+Ltac2 Notation "fold" pl(thunk(list1(open_constr))) cl(opt(clause)) :=
+  fold0 pl cl.
+ +
+Ltac2 Notation "pattern" pl(list1(seq(constr, occurrences), ",")) cl(opt(clause)) :=
+  Std.pattern pl (default_on_concl cl).
+ +
+Ltac2 Notation "vm_compute" pl(opt(seq(pattern, occurrences))) cl(opt(clause)) :=
+  Std.vm pl (default_on_concl cl).
+Ltac2 Notation vm_compute := vm_compute.
+ +
+Ltac2 Notation "native_compute" pl(opt(seq(pattern, occurrences))) cl(opt(clause)) :=
+  Std.native pl (default_on_concl cl).
+Ltac2 Notation native_compute := native_compute.
+ +
+Ltac2 Notation "eval" "red" "in" c(constr) :=
+  Std.eval_red c.
+ +
+Ltac2 Notation "eval" "hnf" "in" c(constr) :=
+  Std.eval_hnf c.
+ +
+Ltac2 Notation "eval" "simpl" s(strategy) pl(opt(seq(pattern, occurrences))) "in" c(constr) :=
+  Std.eval_simpl s pl c.
+ +
+Ltac2 Notation "eval" "cbv" s(strategy) "in" c(constr) :=
+  Std.eval_cbv s c.
+ +
+Ltac2 Notation "eval" "cbn" s(strategy) "in" c(constr) :=
+  Std.eval_cbn s c.
+ +
+Ltac2 Notation "eval" "lazy" s(strategy) "in" c(constr) :=
+  Std.eval_lazy s c.
+ +
+Ltac2 Notation "eval" "unfold" pl(list1(seq(reference, occurrences), ",")) "in" c(constr) :=
+  Std.eval_unfold pl c.
+ +
+Ltac2 Notation "eval" "fold" pl(thunk(list1(open_constr))) "in" c(constr) :=
+  Std.eval_fold (pl ()) c.
+ +
+Ltac2 Notation "eval" "pattern" pl(list1(seq(constr, occurrences), ",")) "in" c(constr) :=
+  Std.eval_pattern pl c.
+ +
+Ltac2 Notation "eval" "vm_compute" pl(opt(seq(pattern, occurrences))) "in" c(constr) :=
+  Std.eval_vm pl c.
+ +
+Ltac2 Notation "eval" "native_compute" pl(opt(seq(pattern, occurrences))) "in" c(constr) :=
+  Std.eval_native pl c.
+ +
+Ltac2 change0 p cl :=
+  let (pat, c) := p in
+  Std.change pat c (default_on_concl cl).
+ +
+Ltac2 Notation "change" c(conversion) cl(opt(clause)) := change0 c cl.
+ +
+Ltac2 rewrite0 ev rw cl tac :=
+  let cl := default_on_concl cl in
+  Std.rewrite ev rw cl tac.
+ +
+Ltac2 Notation "rewrite"
+  rw(list1(rewriting, ","))
+  cl(opt(clause))
+  tac(opt(seq("by", thunk(tactic)))) :=
+  rewrite0 false rw cl tac.
+ +
+Ltac2 Notation "setoid_rewrite"
+  ori(orient)
+  c(thunk(seq(open_constr, with_bindings)))
+  occs(occurrences)
+  id(opt(seq("in", ident))) :=
+  Std.setoid_rewrite (Option.default Std.LTR ori) c occs id.
+ +
+Ltac2 Notation "erewrite"
+  rw(list1(rewriting, ","))
+  cl(opt(clause))
+  tac(opt(seq("by", thunk(tactic)))) :=
+  rewrite0 true rw cl tac.
+ +
+
+ +
+coretactics +
+ + Provided for backwards compat +
+
+#[deprecated(since="8.19")]
+Ltac2 exact0 ev c :=
+  Control.enter (fun _ =>
+    match ev with
+    | true =>
+      let c := c () in
+      Control.refine (fun _ => c)
+    | false =>
+      Control.with_holes c (fun c => Control.refine (fun _ => c))
+    end
+  ).
+ +
+Ltac2 exact1 ev c :=
+  Control.enter (fun () =>
+    let c :=
+      Constr.Pretype.pretype
+        (if ev then Constr.Pretype.Flags.open_constr_flags_with_tc else Constr.Pretype.Flags.constr_flags)
+        (Constr.Pretype.expected_oftype (Control.goal()))
+        c
+    in
+    Std.exact_no_check c).
+ +
+Ltac2 Notation "exact" c(preterm) := exact1 false c.
+ +
+Ltac2 Notation "eexact" c(preterm) := exact1 true c.
+
+ +
+Like refine but new evars are shelved instead of becoming subgoals. +
+
+ +
+Ltac2 Notation "intro" id(opt(ident)) mv(opt(move_location)) := Std.intro id mv.
+Ltac2 Notation intro := intro.
+ +
+Ltac2 Notation "move" id(ident) mv(move_location) := Std.move id mv.
+ +
+Ltac2 Notation reflexivity := Std.reflexivity ().
+ +
+Ltac2 symmetry0 cl :=
+  Std.symmetry (default_on_concl cl).
+ +
+Ltac2 Notation "symmetry" cl(opt(clause)) := symmetry0 cl.
+Ltac2 Notation symmetry := symmetry.
+ +
+Ltac2 Notation "revert" ids(list1(ident)) := Std.revert ids.
+ +
+Ltac2 Notation assumption := Std.assumption ().
+ +
+Ltac2 Notation etransitivity := Std.etransitivity ().
+ +
+Ltac2 Notation admit := Std.admit ().
+ +
+Ltac2 clear0 ids := match ids with
+| [] => Std.keep []
+| _ => Std.clear ids
+end.
+ +
+Ltac2 Notation "clear" ids(list0(ident)) := clear0 ids.
+Ltac2 Notation "clear" "-" ids(list1(ident)) := Std.keep ids.
+Ltac2 Notation clear := clear.
+ +
+Ltac2 Notation refine := Control.refine.
+ +
+
+ +
+extratactics +
+
+ +
+Ltac2 absurd0 c := Control.enter (fun _ => Std.absurd (c ())).
+ +
+Ltac2 Notation "absurd" c(thunk(open_constr)) := absurd0 c.
+ +
+Ltac2 subst0 ids := match ids with
+| [] => Std.subst_all ()
+| _ => Std.subst ids
+end.
+ +
+Ltac2 Notation "subst" ids(list0(ident)) := subst0 ids.
+Ltac2 Notation subst := subst.
+ +
+Ltac2 Notation "discriminate" arg(opt(destruction_arg)) :=
+  Std.discriminate false arg.
+Ltac2 Notation discriminate := discriminate.
+ +
+Ltac2 Notation "ediscriminate" arg(opt(destruction_arg)) :=
+  Std.discriminate true arg.
+Ltac2 Notation ediscriminate := ediscriminate.
+ +
+Ltac2 Notation "injection" arg(opt(destruction_arg)) ipat(opt(seq("as", intropatterns))):=
+  Std.injection false ipat arg.
+ +
+Ltac2 Notation "einjection" arg(opt(destruction_arg)) ipat(opt(seq("as", intropatterns))):=
+  Std.injection true ipat arg.
+ +
+
+ +
+Auto +
+
+ +
+Ltac2 default_db dbs := match dbs with
+| None => Some []
+| Some dbs =>
+  match dbs with
+  | None => None
+  | Some l => Some l
+  end
+end.
+ +
+Ltac2 default_list use := match use with
+| None => []
+| Some use => use
+end.
+ +
+Ltac2 trivial0 use dbs :=
+  let dbs := default_db dbs in
+  let use := default_list use in
+  Std.trivial Std.Off use dbs.
+ +
+Ltac2 Notation "trivial"
+  use(opt(seq("using", list1(reference, ","))))
+  dbs(opt(seq("with", hintdb))) := trivial0 use dbs.
+ +
+Ltac2 Notation trivial := trivial.
+ +
+Ltac2 auto0 n use dbs :=
+  let dbs := default_db dbs in
+  let use := default_list use in
+  Std.auto Std.Off n use dbs.
+ +
+Ltac2 Notation "auto" n(opt(tactic(0)))
+  use(opt(seq("using", list1(reference, ","))))
+  dbs(opt(seq("with", hintdb))) := auto0 n use dbs.
+ +
+Ltac2 Notation auto := auto.
+ +
+Ltac2 eauto0 n use dbs :=
+  let dbs := default_db dbs in
+  let use := default_list use in
+  Std.eauto Std.Off n use dbs.
+ +
+Ltac2 Notation "eauto" n(opt(tactic(0)))
+  use(opt(seq("using", list1(reference, ","))))
+  dbs(opt(seq("with", hintdb))) := eauto0 n use dbs.
+ +
+Ltac2 Notation eauto := eauto.
+ +
+Ltac2 Notation "typeclasses_eauto" n(opt(tactic(0)))
+  dbs(opt(seq("with", list1(ident)))) := Std.typeclasses_eauto None n dbs.
+ +
+Ltac2 Notation "typeclasses_eauto" "bfs" n(opt(tactic(0)))
+  dbs(opt(seq("with", list1(ident)))) := Std.typeclasses_eauto (Some Std.BFS) n dbs.
+ +
+Ltac2 Notation typeclasses_eauto := typeclasses_eauto.
+ +
+Ltac2 Notation "unify" x(constr) y(constr) := Std.unify x y.
+ +
+
+ +
+Congruence +
+
+ +
+Ltac2 Notation "congruence" n(opt(tactic(0))) l(opt(seq("with", list1(constr)))) := Std.congruence n l.
+ +
+Ltac2 Notation "simple" "congruence" n(opt(tactic(0))) l(opt(seq("with", list1(constr)))) := Std.simple_congruence n l.
+ +
+Ltac2 f_equal0 () := ltac1:(f_equal).
+Ltac2 Notation f_equal := f_equal0 ().
+ +
+
+ +
+now +
+
+ +
+Ltac2 now0 t := t (); ltac1:(easy).
+Ltac2 Notation "now" t(thunk(self)) : 6 := now0 t.
+ +
+
+ +
+profiling +
+
+ +
+Ltac2 start_profiling () := ltac1:(start ltac profiling).
+Ltac2 stop_profiling () := ltac1:(stop ltac profiling).
+Ltac2 show_profile () := ltac1:(show ltac profile).
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Option.html b/master/corelib/Ltac2.Option.html new file mode 100644 index 0000000000..6351a3fde2 --- /dev/null +++ b/master/corelib/Ltac2.Option.html @@ -0,0 +1,155 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Option

+ +
+ +
+ +
+Require Import Ltac2.Init.
+Require Import Ltac2.Control.
+ +
+Ltac2 may (f : 'a -> unit) (ov : 'a option) :=
+  match ov with
+  | Some v => f v
+  | None => ()
+  end.
+ +
+Ltac2 map (f : 'a -> 'b) (ov : 'a option) :=
+  match ov with
+  | Some v => Some (f v)
+  | None => None
+  end.
+ +
+Ltac2 default (def : 'a) (ov : 'a option) :=
+  match ov with
+  | Some v => v
+  | None => def
+  end.
+ +
+Ltac2 map_default (f : 'a -> 'b) (def : 'b) (ov : 'a option) :=
+  match ov with
+  | Some v => f v
+  | None => def
+  end.
+ +
+Ltac2 get (ov : 'a option) :=
+  match ov with
+  | Some v => v
+  | None => Control.throw No_value
+  end.
+ +
+Ltac2 get_bt (ov : 'a option) :=
+  match ov with
+  | Some v => v
+  | None => Control.zero No_value
+  end.
+ +
+Ltac2 bind (x : 'a option) (f : 'a -> 'b option) :=
+  match x with
+  | Some x => f x
+  | None => None
+  end.
+ +
+Ltac2 ret (x : 'a) := Some x.
+ +
+Ltac2 lift (f : 'a -> 'b) (x : 'a option) := map f x.
+ +
+Ltac2 equal (eq : 'a -> 'b -> bool) (a : 'a option) (b : 'b option) : bool
+  := match a with
+     | None => match b with
+               | None => true
+               | _ => false
+               end
+     | Some a => match b with
+                 | Some b => eq a b
+                 | _ => false
+                 end
+     end.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Pattern.html b/master/corelib/Ltac2.Pattern.html new file mode 100644 index 0000000000..70bd592144 --- /dev/null +++ b/master/corelib/Ltac2.Pattern.html @@ -0,0 +1,299 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Pattern

+ +
+ +
+Require Import Ltac2.Init.
+Require Ltac2.Control.
+ +
+Ltac2 Type t := pattern.
+ +
+Ltac2 Type context.
+ +
+Ltac2 Type match_kind := [
+| MatchPattern
+| MatchContext
+].
+ +
+Ltac2 @ external empty_context : context :=
+  "rocq-runtime.plugins.ltac2" "pattern_empty_context".
+
+ +
+A trivial context only made of the hole. +
+
+ +
+Ltac2 @ external matches : t -> constr -> (ident * constr) list :=
+  "rocq-runtime.plugins.ltac2" "pattern_matches".
+
+ +
+If the term matches the pattern, returns the bound variables. If it doesn't, + fail with Match_failure. Panics if not focused. +
+
+ +
+Ltac2 @ external matches_subterm : t -> constr -> context * ((ident * constr) list) :=
+  "rocq-runtime.plugins.ltac2" "pattern_matches_subterm".
+
+ +
+Returns a stream of results corresponding to all of the subterms of the term + that matches the pattern as in matches. The stream is encoded as a + backtracking value whose last exception is Match_failure. The additional + value compared to matches is the context of the match, to be filled with + the instantiate function. +
+
+ +
+Ltac2 @ external matches_vect : t -> constr -> constr array :=
+  "rocq-runtime.plugins.ltac2" "pattern_matches_vect".
+
+ +
+Internal version of matches that does not return the identifiers. +
+
+ +
+Ltac2 @ external matches_subterm_vect : t -> constr -> context * constr array :=
+  "rocq-runtime.plugins.ltac2" "pattern_matches_subterm_vect".
+
+ +
+Internal version of matches_subterms that does not return the identifiers. +
+
+ +
+Ltac2 @ external matches_goal :
+  bool ->
+  ((match_kind * t) option * (match_kind * t)) list ->
+  (match_kind * t) ->
+  ident array * context array * context array * constr array * context :=
+  "rocq-runtime.plugins.ltac2" "pattern_matches_goal".
+
+ +
+Given a list of patterns hpats for hypotheses and one pattern cpat for the + conclusion, matches_goal rev hpats cpat produces (a stream of) tuples of: +
    +
  • An array of idents, whose size is the length of hpats, corresponding to the + name of matched hypotheses. + +
    • +
  • An array of contexts, whose size is the number of hpats which have non empty body pattern, + corresponding to the contexts matched for every body pattern. + In case the match kind of a body pattern was MatchPattern, + the corresponding context is ensured to be empty. + +
    • +
  • An array of contexts, whose size is the length of hpats, corresponding to + the contexts matched for every hypothesis pattern. In case the match kind of + a hypothesis was MatchPattern, the corresponding context is ensured to be empty. + +
    • +
  • An array of terms, whose size is the total number of pattern variables without + duplicates. Terms are ordered by identifier order, e.g. ?a comes before ?b. + +
    • +
  • A context corresponding to the conclusion, which is ensured to be empty if + the kind of cpat was MatchPattern. + +
    • +
+ This produces a backtracking stream of results containing all the possible + result combinations. The order of considered hypotheses is reversed if rev + is true. + +
+
+ +
+Ltac2 @ external instantiate : context -> constr -> constr :=
+  "rocq-runtime.plugins.ltac2" "pattern_instantiate".
+
+ +
+Fill the hole of a context with the given term. +
+ + Implementation of Ltac matching over terms and goals +
+
+ +
+Ltac2 Type 'a constr_matching := (match_kind * t * (context -> constr array -> 'a)) list.
+ +
+Ltac2 lazy_match0 t (pats:'a constr_matching) :=
+  let rec interp m := match m with
+  | [] => Control.zero Match_failure
+  | p :: m =>
+    let next _ := interp m in
+    let (knd, pat, f) := p in
+    let p := match knd with
+    | MatchPattern =>
+      (fun _ =>
+        let context := empty_context in
+        let bind := matches_vect pat t in
+        fun _ => f context bind)
+    | MatchContext =>
+      (fun _ =>
+        let (context, bind) := matches_subterm_vect pat t in
+        fun _ => f context bind)
+    end in
+    Control.plus p next
+  end in
+  Control.once (fun () => interp pats) ().
+ +
+Ltac2 multi_match0 t (pats:'a constr_matching) :=
+  let rec interp e m := match m with
+  | [] => Control.zero e
+  | p :: m =>
+    let next e := interp e m in
+    let (knd, pat, f) := p in
+    let p := match knd with
+    | MatchPattern =>
+      (fun _ =>
+        let context := empty_context in
+        let bind := matches_vect pat t in
+        f context bind)
+    | MatchContext =>
+      (fun _ =>
+        let (context, bind) := matches_subterm_vect pat t in
+        f context bind)
+    end in
+    Control.plus p next
+  end in
+  interp Match_failure pats.
+ +
+Ltac2 one_match0 t m := Control.once (fun _ => multi_match0 t m).
+ +
+Ltac2 Type 'a goal_matching :=
+  ((((match_kind * t) option * (match_kind * t)) list * (match_kind * t)) *
+     (ident array -> context array -> context array -> constr array -> context -> 'a)) list.
+ +
+Ltac2 lazy_goal_match0 rev (pats:'a goal_matching) :=
+  let rec interp m := match m with
+  | [] => Control.zero Match_failure
+  | p :: m =>
+    let next _ := interp m in
+    let (pat, f) := p in
+    let (phyps, pconcl) := pat in
+    let cur _ :=
+      let (hids, hbctx, hctx, subst, cctx) := matches_goal rev phyps pconcl in
+      fun _ => f hids hbctx hctx subst cctx
+    in
+    Control.plus cur next
+  end in
+  Control.once (fun () => interp pats) ().
+ +
+Ltac2 multi_goal_match0 rev (pats:'a goal_matching) :=
+  let rec interp e m := match m with
+  | [] => Control.zero e
+  | p :: m =>
+    let next e := interp e m in
+    let (pat, f) := p in
+    let (phyps, pconcl) := pat in
+    let cur _ :=
+      let (hids, hbctx, hctx, subst, cctx) := matches_goal rev phyps pconcl in
+      f hids hbctx hctx subst cctx
+    in
+    Control.plus cur next
+  end in
+  interp Match_failure pats.
+ +
+Ltac2 one_goal_match0 rev pats := Control.once (fun _ => multi_goal_match0 rev pats).
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Printf.html b/master/corelib/Ltac2.Printf.html new file mode 100644 index 0000000000..610790b102 --- /dev/null +++ b/master/corelib/Ltac2.Printf.html @@ -0,0 +1,181 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Printf

+ +
+ +
+Require Import Ltac2.Message.
+ +
+
+ +
+This file defines a printf notation for easiness of writing messages +
+ + +
+ + The built-in "format" notation scope can be used to create well-typed variadic + printing commands following a printf-like syntax. The "format" scope parses + quoted strings which contain either raw string data or printing + specifications. Raw strings will be output verbatim as if they were passed + to Ltac2.Message.of_string. + +
+ + Printing specifications are of the form + +
+ + '%' type + +
+ + where the type value defines which kind of arguments will be accepted and + how they will be printed. They can take the following values. + +
+ +
    +
  • i : takes an argument of type int and behaves as Message.of_int + +
    • +
  • I : takes an argument of type ident and behaves as Message.of_ident + +
    • +
  • s : takes an argument of type string and behaves as Message.of_string + +
    • +
  • t : takes an argument of type constr and behaves as Message.of_constr + +
    • +
  • a : takes two arguments f of type (unit -> 'a -> message) + and x of type 'a and behaves as f () x + +
    • +
  • % : outputs % verbatim + +
    • +
+ +
+ + TODO: add printing modifiers. + +
+ + +
+
+ +
+Ltac2 printf fmt := Format.kfprintf print fmt.
+Ltac2 fprintf fmt := Format.kfprintf (fun x => x) fmt.
+ +
+
+ +
+The two following notations are made available when this module is imported. + +
+ +
    +
  • printf will parse a format and generate a function taking the + corresponding arguments ant printing the resulting message as per + Message.print. In particular when fully applied it has type unit. + +
    • +
  • fprintf behaves similarly but return the message as a value instead of + printing it. + +
    • +
+ +
+ + +
+
+ +
+Ltac2 Notation "printf" fmt(format) := printf fmt.
+Ltac2 Notation "fprintf" fmt(format) := fprintf fmt.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Proj.html b/master/corelib/Ltac2.Proj.html new file mode 100644 index 0000000000..8db6f15ee5 --- /dev/null +++ b/master/corelib/Ltac2.Proj.html @@ -0,0 +1,163 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Proj

+ +
+ +
+Require Import Ltac2.Init.
+ +
+Ltac2 Type t := projection.
+
+ +
+Type of primitive projections. This includes the unfolding boolean. +
+
+ +
+Ltac2 @ external equal : t -> t -> bool := "rocq-runtime.plugins.ltac2" "projection_equal".
+
+ +
+Projections obtained through module aliases or Include are not + considered equal by this function. The unfolding boolean is not ignored. +
+
+ +
+Ltac2 @ external ind : t -> inductive := "rocq-runtime.plugins.ltac2" "projection_ind".
+
+ +
+Get the inductive to which the projectin belongs. +
+
+ +
+Ltac2 @ external index : t -> int := "rocq-runtime.plugins.ltac2" "projection_index".
+
+ +
+The index of the projection indicates which field it projects. +
+
+ +
+Ltac2 @ external unfolded : t -> bool := "rocq-runtime.plugins.ltac2" "projection_unfolded".
+
+ +
+Get the unfolding boolean. +
+
+ +
+Ltac2 @ external set_unfolded : t -> bool -> t
+  := "rocq-runtime.plugins.ltac2" "projection_set_unfolded".
+
+ +
+Set the unfolding boolean. +
+
+ +
+Ltac2 @ external of_constant : constant -> t option
+  := "rocq-runtime.plugins.ltac2" "projection_of_constant".
+
+ +
+Get the primitive projection associated to the constant. + The returned projection is folded. + Returns None when the constant is not associated to a primitive projection. +
+
+ +
+Ltac2 @ external to_constant : t -> constant option
+  := "rocq-runtime.plugins.ltac2" "projection_to_constant".
+
+ +
+Get the constant associated to the primitive projection. + Currently always returns Some but this may change in the future. +
+
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Pstring.html b/master/corelib/Ltac2.Pstring.html new file mode 100644 index 0000000000..6722ceae49 --- /dev/null +++ b/master/corelib/Ltac2.Pstring.html @@ -0,0 +1,108 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Pstring

+ +
+ +
+Require Import Ltac2.Init.
+ +
+Ltac2 Type t := pstring.
+ +
+Ltac2 Type char63 := uint63.
+ +
+Ltac2 @ external max_length : uint63 := "rocq-runtime.plugins.ltac2" "pstring_max_length".
+ +
+Ltac2 @ external to_string : t -> string := "rocq-runtime.plugins.ltac2" "pstring_to_string".
+Ltac2 @ external of_string : string -> t option := "rocq-runtime.plugins.ltac2" "pstring_of_string".
+ +
+Ltac2 @ external make : uint63 -> char63 -> t := "rocq-runtime.plugins.ltac2" "pstring_make".
+Ltac2 @ external length : t -> uint63 := "rocq-runtime.plugins.ltac2" "pstring_length".
+Ltac2 @ external get : t -> uint63 -> char63 := "rocq-runtime.plugins.ltac2" "pstring_get".
+Ltac2 @ external sub : t -> uint63 -> uint63 -> t := "rocq-runtime.plugins.ltac2" "pstring_sub".
+Ltac2 @ external cat : t -> t -> t := "rocq-runtime.plugins.ltac2" "pstring_cat".
+ +
+Ltac2 @ external equal : t -> t -> bool := "rocq-runtime.plugins.ltac2" "pstring_equal".
+Ltac2 @ external compare : t -> t -> int := "rocq-runtime.plugins.ltac2" "pstring_compare".
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.RedFlags.html b/master/corelib/Ltac2.RedFlags.html new file mode 100644 index 0000000000..d3888c6297 --- /dev/null +++ b/master/corelib/Ltac2.RedFlags.html @@ -0,0 +1,114 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.RedFlags

+ +
+ +
+Require Import Ltac2.Init.
+Require Import Ltac2.Std.
+ +
+Ltac2 Type t := Std.red_flags.
+ +
+Module Export Notations.
+Ltac2 Notation "red_flags:(" s(strategy) ")" : 0 := s.
+End Notations.
+ +
+Ltac2 none := {
+  rBeta := false; rMatch := false; rFix := false; rCofix := false;
+  rZeta := false; rDelta := false; rConst := []; rStrength := Norm;
+}.
+ +
+Ltac2 all : t := {
+  rBeta := true; rMatch := true; rFix := true; rCofix := true;
+  rZeta := true; rDelta := true; rConst := []; rStrength := Norm;
+}.
+ +
+Ltac2 beta : t := red_flags:(beta).
+Ltac2 beta_delta_zeta : t := red_flags:(beta delta zeta).
+Ltac2 beta_iota : t := red_flags:(beta iota).
+Ltac2 beta_iota_zeta : t := red_flags:(beta iota zeta).
+Ltac2 beta_zeta : t := red_flags:(beta zeta).
+Ltac2 delta : t := red_flags:(delta).
+Ltac2 zeta : t := red_flags:(zeta).
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Ref.html b/master/corelib/Ltac2.Ref.html new file mode 100644 index 0000000000..958dfbcb89 --- /dev/null +++ b/master/corelib/Ltac2.Ref.html @@ -0,0 +1,107 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Ref

+ +
+ +
+Require Import Ltac2.Init.
+Require Import Ltac2.Int.
+ +
+
+ +
+Type of a reference cell, similar to OCaml's 'a ref type. +
+
+Ltac2 Type 'a ref := 'a Init.ref.
+ +
+Ltac2 ref (v : 'a) : 'a ref := { contents := v}.
+Ltac2 get (r : 'a ref) : 'a := r.(contents).
+Ltac2 set (r : 'a ref) (v : 'a) : unit := r.(contents) := v.
+ +
+Ltac2 incr (r : int ref) : unit := r.(contents) := add (r.(contents)) 1.
+Ltac2 decr (r : int ref) : unit := r.(contents) := sub (r.(contents)) 1.
+ +
+Ltac2 update (r : 'a ref) (f : 'a -> 'a) : unit :=
+  r.(contents) := f (r.(contents)).
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Std.html b/master/corelib/Ltac2.Std.html new file mode 100644 index 0000000000..41cd34fd37 --- /dev/null +++ b/master/corelib/Ltac2.Std.html @@ -0,0 +1,458 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Std

+ +
+ +
+Require Import Ltac2.Init.
+ +
+
+ +
+ML-facing types +
+
+ +
+Ltac2 Type hypothesis := [ AnonHyp (int) | NamedHyp (ident) ].
+ +
+Ltac2 Type bindings := [
+| NoBindings
+| ImplicitBindings (constr list)
+| ExplicitBindings ((hypothesis * constr) list)
+].
+ +
+Ltac2 Type constr_with_bindings := constr * bindings.
+ +
+Ltac2 Type occurrences := [
+| AllOccurrences
+| AllOccurrencesBut (int list)
+| NoOccurrences
+| OnlyOccurrences (int list)
+].
+ +
+Ltac2 Type hyp_location_flag := [ InHyp | InHypTypeOnly | InHypValueOnly ].
+ +
+Ltac2 Type clause := {
+  on_hyps : (ident * occurrences * hyp_location_flag) list option;
+  on_concl : occurrences;
+}.
+ +
+Ltac2 Type reference := [
+| VarRef (ident)
+| ConstRef (constant)
+| IndRef (inductive)
+| ConstructRef (constructor)
+].
+ +
+Ltac2 Type strength := [ Norm | Head ].
+ +
+Ltac2 Type red_flags := {
+  rStrength : strength;
+  rBeta : bool;
+  rMatch : bool;
+  rFix : bool;
+  rCofix : bool;
+  rZeta : bool;
+  rDelta : bool;
+ +
+true = delta all but rConst; false = delta only on rConst +
+
+  rConst : reference list
+}.
+ +
+Ltac2 Type 'a not_implemented.
+ +
+Ltac2 Type rec intro_pattern := [
+| IntroForthcoming (bool)
+| IntroNaming (intro_pattern_naming)
+| IntroAction (intro_pattern_action)
+]
+with intro_pattern_naming := [
+| IntroIdentifier (ident)
+| IntroFresh (ident)
+| IntroAnonymous
+]
+with intro_pattern_action := [
+| IntroWildcard
+| IntroOrAndPattern (or_and_intro_pattern)
+| IntroInjection (intro_pattern list)
+| IntroApplyOn ((unit -> constr), intro_pattern)
+| IntroRewrite (bool)
+]
+with or_and_intro_pattern := [
+| IntroOrPattern (intro_pattern list list)
+| IntroAndPattern (intro_pattern list)
+].
+ +
+Ltac2 Type destruction_arg := [
+| ElimOnConstr (unit -> constr_with_bindings)
+| ElimOnIdent (ident)
+| ElimOnAnonHyp (int)
+].
+ +
+Ltac2 Type induction_clause := {
+  indcl_arg : destruction_arg;
+  indcl_eqn : intro_pattern_naming option;
+  indcl_as : or_and_intro_pattern option;
+  indcl_in : clause option;
+}.
+ +
+Ltac2 Type assertion := [
+| AssertType (intro_pattern option, constr, (unit -> unit) option)
+| AssertValue (ident, constr)
+].
+ +
+Ltac2 Type repeat := [
+| Precisely (int)
+| UpTo (int)
+| RepeatStar
+| RepeatPlus
+].
+ +
+Ltac2 Type orientation := [ LTR | RTL ].
+ +
+Ltac2 Type rewriting := {
+  rew_orient : orientation option;
+  rew_repeat : repeat;
+  rew_equatn : (unit -> constr_with_bindings);
+}.
+ +
+Ltac2 Type evar_flag := bool.
+Ltac2 Type advanced_flag := bool.
+ +
+Ltac2 Type move_location := [
+| MoveAfter (ident)
+| MoveBefore (ident)
+| MoveFirst
+| MoveLast
+].
+ +
+Ltac2 Type inversion_kind := [
+| SimpleInversion
+| FullInversion
+| FullInversionClear
+].
+ +
+
+ +
+Standard, built-in tactics. See Ltac1 for documentation. +
+
+ +
+Ltac2 @ external intros : evar_flag -> intro_pattern list -> unit := "rocq-runtime.plugins.ltac2" "tac_intros".
+ +
+Ltac2 @ external apply : advanced_flag -> evar_flag ->
+  (unit -> constr_with_bindings) list -> (ident * (intro_pattern option)) option -> unit := "rocq-runtime.plugins.ltac2" "tac_apply".
+ +
+Ltac2 @ external elim : evar_flag -> constr_with_bindings -> constr_with_bindings option -> unit := "rocq-runtime.plugins.ltac2" "tac_elim".
+Ltac2 @ external case : evar_flag -> constr_with_bindings -> unit := "rocq-runtime.plugins.ltac2" "tac_case".
+ +
+Ltac2 @ external generalize : (constr * occurrences * ident option) list -> unit := "rocq-runtime.plugins.ltac2" "tac_generalize".
+ +
+Ltac2 @ external assert : assertion -> unit := "rocq-runtime.plugins.ltac2" "tac_assert".
+Ltac2 @ external enough : constr -> (unit -> unit) option option -> intro_pattern option -> unit := "rocq-runtime.plugins.ltac2" "tac_enough".
+ +
+Ltac2 @ external pose : ident option -> constr -> unit := "rocq-runtime.plugins.ltac2" "tac_pose".
+Ltac2 @ external set : evar_flag -> (unit -> ident option * constr) -> clause -> unit := "rocq-runtime.plugins.ltac2" "tac_set".
+ +
+Ltac2 @ external remember : evar_flag -> ident option -> (unit -> constr) -> intro_pattern option -> clause -> unit := "rocq-runtime.plugins.ltac2" "tac_remember".
+ +
+Ltac2 @ external destruct : evar_flag -> induction_clause list ->
+  constr_with_bindings option -> unit := "rocq-runtime.plugins.ltac2" "tac_destruct".
+ +
+Ltac2 @ external induction : evar_flag -> induction_clause list ->
+  constr_with_bindings option -> unit := "rocq-runtime.plugins.ltac2" "tac_induction".
+ +
+Ltac2 @ external red : clause -> unit := "rocq-runtime.plugins.ltac2" "tac_red".
+Ltac2 @ external hnf : clause -> unit := "rocq-runtime.plugins.ltac2" "tac_hnf".
+Ltac2 @ external simpl : red_flags -> (pattern * occurrences) option -> clause -> unit := "rocq-runtime.plugins.ltac2" "tac_simpl".
+Ltac2 @ external cbv : red_flags -> clause -> unit := "rocq-runtime.plugins.ltac2" "tac_cbv".
+Ltac2 @ external cbn : red_flags -> clause -> unit := "rocq-runtime.plugins.ltac2" "tac_cbn".
+Ltac2 @ external lazy : red_flags -> clause -> unit := "rocq-runtime.plugins.ltac2" "tac_lazy".
+Ltac2 @ external unfold : (reference * occurrences) list -> clause -> unit := "rocq-runtime.plugins.ltac2" "tac_unfold".
+Ltac2 @ external fold : constr list -> clause -> unit := "rocq-runtime.plugins.ltac2" "tac_fold".
+Ltac2 @ external pattern : (constr * occurrences) list -> clause -> unit := "rocq-runtime.plugins.ltac2" "tac_pattern".
+Ltac2 @ external vm : (pattern * occurrences) option -> clause -> unit := "rocq-runtime.plugins.ltac2" "tac_vm".
+Ltac2 @ external native : (pattern * occurrences) option -> clause -> unit := "rocq-runtime.plugins.ltac2" "tac_native".
+ +
+Ltac2 @ external eval_red : constr -> constr := "rocq-runtime.plugins.ltac2" "eval_red".
+Ltac2 @ external eval_hnf : constr -> constr := "rocq-runtime.plugins.ltac2" "eval_hnf".
+Ltac2 @ external eval_red : constr -> constr := "rocq-runtime.plugins.ltac2" "eval_red".
+Ltac2 @ external eval_simpl : red_flags -> (pattern * occurrences) option -> constr -> constr := "rocq-runtime.plugins.ltac2" "eval_simpl".
+Ltac2 @ external eval_cbv : red_flags -> constr -> constr := "rocq-runtime.plugins.ltac2" "eval_cbv".
+Ltac2 @ external eval_cbn : red_flags -> constr -> constr := "rocq-runtime.plugins.ltac2" "eval_cbn".
+Ltac2 @ external eval_lazy : red_flags -> constr -> constr := "rocq-runtime.plugins.ltac2" "eval_lazy".
+Ltac2 @ external eval_unfold : (reference * occurrences) list -> constr -> constr := "rocq-runtime.plugins.ltac2" "eval_unfold".
+Ltac2 @ external eval_fold : constr list -> constr -> constr := "rocq-runtime.plugins.ltac2" "eval_fold".
+Ltac2 @ external eval_pattern : (constr * occurrences) list -> constr -> constr := "rocq-runtime.plugins.ltac2" "eval_pattern".
+Ltac2 @ external eval_vm : (pattern * occurrences) option -> constr -> constr := "rocq-runtime.plugins.ltac2" "eval_vm".
+Ltac2 @ external eval_native : (pattern * occurrences) option -> constr -> constr := "rocq-runtime.plugins.ltac2" "eval_native".
+ +
+Ltac2 @ external change : pattern option -> (constr array -> constr) -> clause -> unit := "rocq-runtime.plugins.ltac2" "tac_change".
+ +
+Ltac2 @ external rewrite : evar_flag -> rewriting list -> clause -> (unit -> unit) option -> unit := "rocq-runtime.plugins.ltac2" "tac_rewrite".
+ +
+Ltac2 @ external setoid_rewrite : orientation -> (unit -> constr_with_bindings) -> occurrences -> ident option -> unit := "rocq-runtime.plugins.ltac2" "tac_setoid_rewrite".
+ +
+Ltac2 @ external reflexivity : unit -> unit := "rocq-runtime.plugins.ltac2" "tac_reflexivity".
+ +
+Ltac2 @ external assumption : unit -> unit := "rocq-runtime.plugins.ltac2" "tac_assumption".
+ +
+Ltac2 @ external transitivity : constr -> unit := "rocq-runtime.plugins.ltac2" "tac_transitivity".
+ +
+Ltac2 @ external etransitivity : unit -> unit := "rocq-runtime.plugins.ltac2" "tac_etransitivity".
+ +
+Ltac2 @ external cut : constr -> unit := "rocq-runtime.plugins.ltac2" "tac_cut".
+ +
+Ltac2 @ external left : evar_flag -> bindings -> unit := "rocq-runtime.plugins.ltac2" "tac_left".
+Ltac2 @ external right : evar_flag -> bindings -> unit := "rocq-runtime.plugins.ltac2" "tac_right".
+ +
+Ltac2 @ external constructor : evar_flag -> unit := "rocq-runtime.plugins.ltac2" "tac_constructor".
+Ltac2 @ external split : evar_flag -> bindings -> unit := "rocq-runtime.plugins.ltac2" "tac_split".
+ +
+Ltac2 @ external constructor_n : evar_flag -> int -> bindings -> unit := "rocq-runtime.plugins.ltac2" "tac_constructorn".
+ +
+Ltac2 @ external intros_until : hypothesis -> unit := "rocq-runtime.plugins.ltac2" "tac_introsuntil".
+ +
+Ltac2 @ external symmetry : clause -> unit := "rocq-runtime.plugins.ltac2" "tac_symmetry".
+ +
+Ltac2 @ external rename : (ident * ident) list -> unit := "rocq-runtime.plugins.ltac2" "tac_rename".
+ +
+Ltac2 @ external revert : ident list -> unit := "rocq-runtime.plugins.ltac2" "tac_revert".
+ +
+Ltac2 @ external admit : unit -> unit := "rocq-runtime.plugins.ltac2" "tac_admit".
+ +
+Ltac2 @ external fix_ : ident -> int -> unit := "rocq-runtime.plugins.ltac2" "tac_fix".
+Ltac2 @ external cofix_ : ident -> unit := "rocq-runtime.plugins.ltac2" "tac_cofix".
+ +
+Ltac2 @ external clear : ident list -> unit := "rocq-runtime.plugins.ltac2" "tac_clear".
+Ltac2 @ external keep : ident list -> unit := "rocq-runtime.plugins.ltac2" "tac_keep".
+ +
+Ltac2 @ external clearbody : ident list -> unit := "rocq-runtime.plugins.ltac2" "tac_clearbody".
+ +
+Ltac2 @ external exact_no_check : constr -> unit := "rocq-runtime.plugins.ltac2" "tac_exactnocheck".
+Ltac2 @ external vm_cast_no_check : constr -> unit := "rocq-runtime.plugins.ltac2" "tac_vmcastnocheck".
+Ltac2 @ external native_cast_no_check : constr -> unit := "rocq-runtime.plugins.ltac2" "tac_nativecastnocheck".
+ +
+Ltac2 @ external inversion : inversion_kind -> destruction_arg -> intro_pattern option -> ident list option -> unit := "rocq-runtime.plugins.ltac2" "tac_inversion".
+ +
+
+ +
+coretactics +
+
+ +
+Ltac2 @ external move : ident -> move_location -> unit := "rocq-runtime.plugins.ltac2" "tac_move".
+ +
+Ltac2 @ external intro : ident option -> move_location option -> unit := "rocq-runtime.plugins.ltac2" "tac_intro".
+ +
+Ltac2 @ external specialize : constr_with_bindings -> intro_pattern option -> unit := "rocq-runtime.plugins.ltac2" "tac_specialize".
+ +
+
+ +
+extratactics +
+
+ +
+Ltac2 @ external discriminate : evar_flag -> destruction_arg option -> unit := "rocq-runtime.plugins.ltac2" "tac_discriminate".
+Ltac2 @ external injection : evar_flag -> intro_pattern list option -> destruction_arg option -> unit := "rocq-runtime.plugins.ltac2" "tac_injection".
+ +
+Ltac2 @ external absurd : constr -> unit := "rocq-runtime.plugins.ltac2" "tac_absurd".
+Ltac2 @ external contradiction : constr_with_bindings option -> unit := "rocq-runtime.plugins.ltac2" "tac_contradiction".
+ +
+Ltac2 @ external autorewrite : bool -> (unit -> unit) option -> ident list -> clause -> unit := "rocq-runtime.plugins.ltac2" "tac_autorewrite".
+ +
+Ltac2 @ external subst : ident list -> unit := "rocq-runtime.plugins.ltac2" "tac_subst".
+Ltac2 @ external subst_all : unit -> unit := "rocq-runtime.plugins.ltac2" "tac_substall".
+ +
+
+ +
+auto +
+
+ +
+Ltac2 Type debug := [ Off | Info | Debug ].
+ +
+Ltac2 Type strategy := [ BFS | DFS ].
+ +
+Ltac2 @ external trivial : debug -> reference list -> ident list option -> unit := "rocq-runtime.plugins.ltac2" "tac_trivial".
+ +
+Ltac2 @ external auto : debug -> int option -> reference list -> ident list option -> unit := "rocq-runtime.plugins.ltac2" "tac_auto".
+ +
+Ltac2 @ external eauto : debug -> int option -> reference list -> ident list option -> unit := "rocq-runtime.plugins.ltac2" "tac_eauto".
+ +
+Ltac2 @ external typeclasses_eauto : strategy option -> int option -> ident list option -> unit := "rocq-runtime.plugins.ltac2" "tac_typeclasses_eauto".
+ +
+Ltac2 @ external resolve_tc : constr -> unit := "rocq-runtime.plugins.ltac2" "tac_resolve_tc".
+
+ +
+Resolve the existential variables appearing in the constr + whose types are typeclasses. + Fail if any of them cannot be resolved. + Does not focus. +
+
+ +
+Ltac2 @ external unify : constr -> constr -> unit := "rocq-runtime.plugins.ltac2" "tac_unify".
+ +
+Ltac2 @ external congruence : int option -> constr list option -> unit :=
+  "rocq-runtime.plugins.ltac2" "congruence".
+Ltac2 @ external simple_congruence : int option -> constr list option -> unit :=
+  "rocq-runtime.plugins.ltac2" "simple_congruence".
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.String.html b/master/corelib/Ltac2.String.html new file mode 100644 index 0000000000..59f812a3fb --- /dev/null +++ b/master/corelib/Ltac2.String.html @@ -0,0 +1,101 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.String

+ +
+ +
+Require Import Ltac2.Init.
+ +
+Ltac2 Type t := string.
+ +
+Ltac2 @external make : int -> char -> string := "rocq-runtime.plugins.ltac2" "string_make".
+Ltac2 @external length : string -> int := "rocq-runtime.plugins.ltac2" "string_length".
+Ltac2 @external get : string -> int -> char := "rocq-runtime.plugins.ltac2" "string_get".
+Ltac2 @external set : string -> int -> char -> unit := "rocq-runtime.plugins.ltac2" "string_set".
+Ltac2 @external concat : string -> string list -> string := "rocq-runtime.plugins.ltac2" "string_concat".
+Ltac2 @external app : string -> string -> string := "rocq-runtime.plugins.ltac2" "string_app".
+Ltac2 @external sub : string -> int -> int -> string := "rocq-runtime.plugins.ltac2" "string_sub".
+Ltac2 @external equal : string -> string -> bool := "rocq-runtime.plugins.ltac2" "string_equal".
+Ltac2 @external compare : string -> string -> int := "rocq-runtime.plugins.ltac2" "string_compare".
+ +
+Ltac2 is_empty s := match s with "" => true | _ => false end.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.TransparentState.html b/master/corelib/Ltac2.TransparentState.html new file mode 100644 index 0000000000..00a3e870da --- /dev/null +++ b/master/corelib/Ltac2.TransparentState.html @@ -0,0 +1,124 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.TransparentState

+ +
+ +
+Require Import Ltac2.Init.
+ +
+
+ +
+Abstract type representing a transparency state. +
+
+Ltac2 Type t.
+ +
+
+ +
+empty is the empty transparency state (all constants are opaque). +
+
+Ltac2 @ external empty : t :=
+  "rocq-runtime.plugins.ltac2" "empty_transparent_state".
+ +
+
+ +
+full is the full transparency state (all constants are transparent). +
+
+Ltac2 @ external full : t :=
+  "rocq-runtime.plugins.ltac2" "full_transparent_state".
+ +
+
+ +
+current () gives the transparency state of the goal, which is influenced + by, e.g., the Strategy command, or the with_strategy Ltac tactic. +
+
+Ltac2 @ external current : unit -> t :=
+  "rocq-runtime.plugins.ltac2" "current_transparent_state".
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Uint63.html b/master/corelib/Ltac2.Uint63.html new file mode 100644 index 0000000000..01ffdcc7ef --- /dev/null +++ b/master/corelib/Ltac2.Uint63.html @@ -0,0 +1,99 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Uint63

+ +
+ +
+Require Import Ltac2.Init.
+ +
+Ltac2 Type t := uint63.
+ +
+Ltac2 @ external equal : t -> t -> bool := "rocq-runtime.plugins.ltac2" "uint63_equal".
+ +
+Ltac2 @external compare : t -> t -> int := "rocq-runtime.plugins.ltac2" "uint63_compare".
+ +
+Ltac2 @external of_int : int -> t := "rocq-runtime.plugins.ltac2" "uint63_of_int".
+ +
+Ltac2 @external print : t -> message := "rocq-runtime.plugins.ltac2" "uint63_print".
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/Ltac2.Unification.html b/master/corelib/Ltac2.Unification.html new file mode 100644 index 0000000000..6f6770e10a --- /dev/null +++ b/master/corelib/Ltac2.Unification.html @@ -0,0 +1,117 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+
+ +
+ + + +
+ +

Library Ltac2.Unification

+ +
+ +
+Require Import Ltac2.Init.
+Require Ltac2.TransparentState.
+ +
+
+ +
+unify ts c1 c2 unifies c1 and c2 (using Evarconv unification), which + may have the effect of instantiating evars. If the c1 and c2 cannot be + unified, an Internal exception is raised. +
+
+Ltac2 @ external unify : TransparentState.t -> constr -> constr -> unit :=
+  "rocq-runtime.plugins.ltac2" "evarconv_unify".
+ +
+
+ +
+unify_with_full_ts is like unify TransparentState.full. +
+
+Ltac2 unify_with_full_ts : constr -> constr -> unit := fun c1 c2 =>
+  unify TransparentState.full c1 c2.
+ +
+
+ +
+unify_with_current_ts is like unify (TransparentState.current ()). +
+
+Ltac2 unify_with_current_ts : constr -> constr -> unit := fun c1 c2 =>
+  unify (TransparentState.current ()) c1 c2.
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/coqdoc.css b/master/corelib/coqdoc.css new file mode 100644 index 0000000000..48096e555a --- /dev/null +++ b/master/corelib/coqdoc.css @@ -0,0 +1,338 @@ +body { padding: 0px 0px; + margin: 0px 0px; + background-color: white } + +#page { display: block; + padding: 0px; + margin: 0px; + padding-bottom: 10px; } + +#header { display: block; + position: relative; + padding: 0; + margin: 0; + vertical-align: middle; + border-bottom-style: solid; + border-width: thin } + +#header h1 { padding: 0; + margin: 0;} + + +/* Contents */ + +#main{ display: block; + padding: 10px; + font-family: sans-serif; + font-size: 100%; + line-height: 100% } + +#main h1 { line-height: 95% } /* allow for multi-line headers */ + +#main a.idref:visited {color : #416DFF; text-decoration : none; } +#main a.idref:link {color : #416DFF; text-decoration : none; } +#main a.idref:hover {text-decoration : none; } +#main a.idref:active {text-decoration : none; } + +#main a.modref:visited {color : #416DFF; text-decoration : none; } +#main a.modref:link {color : #416DFF; text-decoration : none; } +#main a.modref:hover {text-decoration : none; } +#main a.modref:active {text-decoration : none; } + +#main .keyword { color : #cf1d1d } +#main { color: black } + +.section { background-color: rgb(60%,60%,100%); + padding-top: 13px; + padding-bottom: 13px; + padding-left: 3px; + margin-top: 5px; + margin-bottom: 5px; + font-size : 175% } + +h2.section { background-color: rgb(80%,80%,100%); + padding-left: 3px; + padding-top: 12px; + padding-bottom: 10px; + font-size : 130% } + +h3.section { background-color: rgb(90%,90%,100%); + padding-left: 3px; + padding-top: 7px; + padding-bottom: 7px; + font-size : 115% } + +h4.section { +/* + background-color: rgb(80%,80%,80%); + max-width: 20em; + padding-left: 5px; + padding-top: 5px; + padding-bottom: 5px; +*/ + background-color: white; + padding-left: 0px; + padding-top: 0px; + padding-bottom: 0px; + font-size : 100%; + font-weight : bold; + text-decoration : underline; + } + +#main .doc { margin: 0px; + font-family: sans-serif; + font-size: 100%; + line-height: 125%; + max-width: 40em; + color: black; + padding: 10px; + background-color: #90bdff } + +.inlinecode { + display: inline; +/* font-size: 125%; */ + color: #666666; + font-family: monospace } + +.doc .inlinecode { + display: inline; + font-size: 120%; + color: rgb(30%,30%,70%); + font-family: monospace } + +.doc .inlinecode .id { + color: rgb(30%,30%,70%); +} + +.inlinecodenm { + display: inline; + color: #444444; +} + +.doc .code { + display: inline; + font-size: 120%; + color: rgb(30%,30%,70%); + font-family: monospace } + +.comment { + display: inline; + font-family: monospace; + color: rgb(50%,50%,80%); +} + +.code { + display: block; +/* padding-left: 15px; */ + font-size: 110%; + font-family: monospace; + } + +table.infrule { + border: 0px; + margin-left: 50px; + margin-top: 10px; + margin-bottom: 10px; +} + +td.infrule { + font-family: monospace; + text-align: center; +/* color: rgb(35%,35%,70%); */ + padding: 0px; + line-height: 100%; +} + +tr.infrulemiddle hr { + margin: 1px 0 1px 0; +} + +.infrulenamecol { + color: rgb(60%,60%,60%); + font-size: 80%; + padding-left: 1em; + padding-bottom: 0.1em +} + +/* Pied de page */ + +#footer { font-size: 65%; + font-family: sans-serif; } + +/* Identifiers: ) */ + +.id { display: inline; } + +.id[title="constructor"] { + color: rgb(60%,0%,0%); +} + +.id[title="var"] { + color: rgb(40%,0%,40%); +} + +.id[title="variable"] { + color: rgb(40%,0%,40%); +} + +.id[title="definition"] { + color: rgb(0%,40%,0%); +} + +.id[title="abbreviation"] { + color: rgb(0%,40%,0%); +} + +.id[title="lemma"] { + color: rgb(0%,40%,0%); +} + +.id[title="instance"] { + color: rgb(0%,40%,0%); +} + +.id[title="projection"] { + color: rgb(0%,40%,0%); +} + +.id[title="method"] { + color: rgb(0%,40%,0%); +} + +.id[title="inductive"] { + color: rgb(0%,0%,80%); +} + +.id[title="record"] { + color: rgb(0%,0%,80%); +} + +.id[title="class"] { + color: rgb(0%,0%,80%); +} + +.id[title="keyword"] { + color : #cf1d1d; +/* color: black; */ +} + +/* Deprecated rules using the 'type' attribute of (not xhtml valid) */ + +.id[type="constructor"] { + color: rgb(60%,0%,0%); +} + +.id[type="var"] { + color: rgb(40%,0%,40%); +} + +.id[type="variable"] { + color: rgb(40%,0%,40%); +} + +.id[title="binder"] { + color: rgb(40%,0%,40%); +} + +.id[type="definition"] { + color: rgb(0%,40%,0%); +} + +.id[type="abbreviation"] { + color: rgb(0%,40%,0%); +} + +.id[type="lemma"] { + color: rgb(0%,40%,0%); +} + +.id[type="instance"] { + color: rgb(0%,40%,0%); +} + +.id[type="projection"] { + color: rgb(0%,40%,0%); +} + +.id[type="method"] { + color: rgb(0%,40%,0%); +} + +.id[type="inductive"] { + color: rgb(0%,0%,80%); +} + +.id[type="record"] { + color: rgb(0%,0%,80%); +} + +.id[type="class"] { + color: rgb(0%,0%,80%); +} + +.id[type="keyword"] { + color : #cf1d1d; +/* color: black; */ +} + +.inlinecode .id { + color: rgb(0%,0%,0%); +} + + +/* TOC */ + +#toc h2 { + padding: 10px; + background-color: rgb(60%,60%,100%); +} + +#toc li { + padding-bottom: 8px; +} + +/* Index */ + +#index { + margin: 0; + padding: 0; + width: 100%; +} + +#index #frontispiece { + margin: 1em auto; + padding: 1em; + width: 60%; +} + +.booktitle { font-size : 140% } +.authors { font-size : 90%; + line-height: 115%; } +.moreauthors { font-size : 60% } + +#index #entrance { + text-align: center; +} + +#index #entrance .spacer { + margin: 0 30px 0 30px; +} + +#index #footer { + position: absolute; + bottom: 0; +} + +.paragraph { + height: 0.75em; +} + +ul.doclist { + margin-top: 0em; + margin-bottom: 0em; +} + +.code :target { + border: 2px solid #D4D4D4; + background-color: #e5eecc; +} diff --git a/master/corelib/genindex.html b/master/corelib/genindex.html new file mode 100644 index 0000000000..605e47c73c --- /dev/null +++ b/master/corelib/genindex.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index.html b/master/corelib/index.html new file mode 100644 index 0000000000..efb45fb328 --- /dev/null +++ b/master/corelib/index.html @@ -0,0 +1,265 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + +

The Core Library

+ +

Here is a short description of the core library, which is +distributed with the system. +It provides a set of modules directly available +through the Require Import command.

+ +

The core library is composed of the following subdirectories:

+ +
+
Init: + The prelude (automatically loaded when starting Coq) +
+
+ Ltac + Notations + Datatypes + Logic + Byte + Nat + Decimal + Hexadecimal + Number + Peano + Specif + Sumbool + Tactics + Tauto + Wf + (Prelude) +
+ +
Binary numbers: + Basic definitions of binary arithmetic +
+
+ BinNums + PosDef + NatDef + IntDef +
+ +
Cyclic: + 63-bits-based cyclic arithmetic +
+
+ CarryType + PrimInt63 + Uint63Axioms + Sint63Axioms +
+ +
Floats: + Floating-point arithmetic +
+
+ FloatClass + PrimFloat + SpecFloat + FloatOps + FloatAxioms +
+ +
Relations: + Relations (definitions) +
+
+ Relation_Definitions +
+ +
Classes: +
+
+ Init + RelationClasses + Morphisms + Morphisms_Prop + Equivalence + CRelationClasses + CMorphisms + SetoidTactics +
+ +
Setoids: +
+
+ Setoid +
+ +
Lists: + Polymorphic lists +
+
+ ListDef +
+ +
Program: + Support for dependently-typed programming +
+
+ Basics + Wf + Tactics + Utils +
+ +
SSReflect: + Base libraries for the SSReflect proof language and the + small scale reflection formalization technique +
+
+ ssrmatching + ssrclasses + ssreflect + ssrbool + ssrfun +
+ +
Ltac2: + The Ltac2 tactic programming language +
+
+ Ltac2 + Array + Bool + Char + Constant + Constr + Constructor + Control + Env + Evar + Float + FMap + FSet + Fresh + Ident + Ind + Init + Int + Lazy + List + Ltac1 + Message + Meta + Notations + Option + Pattern + Printf + Proj + Pstring + RedFlags + Ref + Std + String + TransparentState + Uint63 + Unification +
+ +
Compat: + Compatibility wrappers for previous versions of Coq +
+
+ Coq818 + Coq819 + Coq820 + Coq818 + Coq819 +
+ +
Array: + Persistent native arrays +
+
+ PrimArray + ArrayAxioms +
+ +
Primitive strings + Native string type +
+
+ PrimString + PrimStringAxioms +
+
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_abbreviation_*.html b/master/corelib/index_abbreviation_*.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_abbreviation_*.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_abbreviation_A.html b/master/corelib/index_abbreviation_A.html new file mode 100644 index 0000000000..c649965812 --- /dev/null +++ b/master/corelib/index_abbreviation_A.html @@ -0,0 +1,563 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

A (abbreviation)

+a [in Corelib.ssr.ssrbool]
+Acc_iter_2 [in Corelib.Init.Wf]
+Acc_iter [in Corelib.Init.Wf]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_abbreviation_B.html b/master/corelib/index_abbreviation_B.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_abbreviation_B.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_abbreviation_C.html b/master/corelib/index_abbreviation_C.html new file mode 100644 index 0000000000..9b9e4986e1 --- /dev/null +++ b/master/corelib/index_abbreviation_C.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

C (abbreviation)

+char63_compare [in Corelib.Strings.PrimStringAxioms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_abbreviation_D.html b/master/corelib/index_abbreviation_D.html new file mode 100644 index 0000000000..e18e332262 --- /dev/null +++ b/master/corelib/index_abbreviation_D.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

D (abbreviation)

+dec [in Corelib.Program.Utils]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_abbreviation_E.html b/master/corelib/index_abbreviation_E.html new file mode 100644 index 0000000000..3f0beab058 --- /dev/null +++ b/master/corelib/index_abbreviation_E.html @@ -0,0 +1,563 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

E (abbreviation)

+ecast [in Corelib.ssr.ssrfun]
+emin [in Corelib.Floats.FloatOps]
+erefl [in Corelib.ssr.ssrfun]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_abbreviation_F.html b/master/corelib/index_abbreviation_F.html new file mode 100644 index 0000000000..cad1098287 --- /dev/null +++ b/master/corelib/index_abbreviation_F.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

F (abbreviation)

+fstT [in Corelib.Init.Datatypes]
+

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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

I (abbreviation)

+id [in Corelib.ssr.ssrfun]
+identity [in Corelib.Init.Datatypes]
+identity_rect_r [in Corelib.Init.Datatypes]
+identity_rec_r [in Corelib.Init.Datatypes]
+identity_ind_r [in Corelib.Init.Datatypes]
+identity_congr [in Corelib.Init.Datatypes]
+identity_trans [in Corelib.Init.Datatypes]
+identity_sym [in Corelib.Init.Datatypes]
+identity_rect [in Corelib.Init.Datatypes]
+identity_rec [in Corelib.Init.Datatypes]
+identity_ind [in Corelib.Init.Datatypes]
+identity_refl [in Corelib.Init.Datatypes]
+int [in Corelib.Init.Hexadecimal]
+int [in Corelib.Init.Decimal]
+int [in Corelib.Init.Number]
+internal_int_dec_bl [in Corelib.Init.Hexadecimal]
+internal_int_dec_lb [in Corelib.Init.Hexadecimal]
+internal_int_dec_bl [in Corelib.Init.Decimal]
+internal_int_dec_lb [in Corelib.Init.Decimal]
+internal_int_dec_bl [in Corelib.Init.Number]
+internal_int_dec_lb [in Corelib.Init.Number]
+int_beq [in Corelib.Init.Hexadecimal]
+int_eq_dec [in Corelib.Init.Hexadecimal]
+int_beq [in Corelib.Init.Decimal]
+int_eq_dec [in Corelib.Init.Decimal]
+int_beq [in Corelib.Init.Number]
+int_eq_dec [in Corelib.Init.Number]
+in_unkey [in Corelib.ssr.ssrbool]
+in_bounds [in Corelib.Array.ArrayAxioms]
+in_right [in Corelib.Program.Utils]
+in_left [in Corelib.Program.Utils]
+

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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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+ + + diff --git a/master/corelib/index_abbreviation_M.html b/master/corelib/index_abbreviation_M.html new file mode 100644 index 0000000000..f05c0baf15 --- /dev/null +++ b/master/corelib/index_abbreviation_M.html @@ -0,0 +1,567 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

M (abbreviation)

+max [in Corelib.Init.Peano]
+min [in Corelib.Init.Peano]
+minus [in Corelib.Init.Peano]
+mono2W_in [in Corelib.ssr.ssrbool]
+mult [in Corelib.Init.Peano]
+mult_succ_r_reverse [in Corelib.Init.Peano]
+mult_0_r_reverse [in Corelib.Init.Peano]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_abbreviation_N.html b/master/corelib/index_abbreviation_N.html new file mode 100644 index 0000000000..8ab24c4e15 --- /dev/null +++ b/master/corelib/index_abbreviation_N.html @@ -0,0 +1,564 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

N (abbreviation)

+NonPropType.Exports.nonPropType [in Corelib.ssr.ssreflect]
+NonPropType.Exports.notProp [in Corelib.ssr.ssreflect]
+nosimpl [in Corelib.ssr.ssreflect]
+not_identity_sym [in Corelib.Init.Datatypes]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_abbreviation_O.html b/master/corelib/index_abbreviation_O.html new file mode 100644 index 0000000000..bcc3d83d2b --- /dev/null +++ b/master/corelib/index_abbreviation_O.html @@ -0,0 +1,566 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

O (abbreviation)

+oapp [in Corelib.ssr.ssrfun]
+obind [in Corelib.ssr.ssrfun]
+odflt [in Corelib.ssr.ssrfun]
+of_nat [in Corelib.Strings.PrimStringAxioms]
+olift [in Corelib.ssr.ssrfun]
+omap [in Corelib.ssr.ssrfun]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_abbreviation_P.html b/master/corelib/index_abbreviation_P.html new file mode 100644 index 0000000000..e10fe057af --- /dev/null +++ b/master/corelib/index_abbreviation_P.html @@ -0,0 +1,573 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

P (abbreviation)

+pairT [in Corelib.Init.Datatypes]
+ph [in Corelib.ssr.ssrbool]
+ph [in Corelib.ssr.ssrbool]
+plus [in Corelib.Init.Peano]
+plus_succ_r_reverse [in Corelib.Init.Peano]
+plus_0_r_reverse [in Corelib.Init.Peano]
+pred [in Corelib.Init.Peano]
+predicate [in Corelib.Classes.RelationClasses]
+pred_of_simpl [in Corelib.ssr.ssrbool]
+prodT [in Corelib.Init.Datatypes]
+prodT_ind [in Corelib.Init.Datatypes]
+prodT_rec [in Corelib.Init.Datatypes]
+prodT_rect [in Corelib.Init.Datatypes]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_abbreviation_Q.html b/master/corelib/index_abbreviation_Q.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_abbreviation_Q.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_abbreviation_R.html b/master/corelib/index_abbreviation_R.html new file mode 100644 index 0000000000..ad75aa66ef --- /dev/null +++ b/master/corelib/index_abbreviation_R.html @@ -0,0 +1,567 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

R (abbreviation)

+reflect [in Corelib.ssr.ssrbool]
+ReflectF [in Corelib.ssr.ssrbool]
+ReflectT [in Corelib.ssr.ssrbool]
+refl_id [in Corelib.Init.Datatypes]
+refl_equal [in Corelib.Init.Logic]
+RocqGenericDependentIf [in Corelib.ssr.ssreflect]
+RocqGenericIf [in Corelib.ssr.ssreflect]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_abbreviation_S.html b/master/corelib/index_abbreviation_S.html new file mode 100644 index 0000000000..82b79b8799 --- /dev/null +++ b/master/corelib/index_abbreviation_S.html @@ -0,0 +1,572 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

S (abbreviation)

+sixteen [in Corelib.Init.Nat]
+sndT [in Corelib.Init.Datatypes]
+some [in Corelib.ssr.ssrfun]
+SsrMatchingSyntax.LHS [in Corelib.ssrmatching.ssrmatching]
+SsrMatchingSyntax.RHS [in Corelib.ssrmatching.ssrmatching]
+sval [in Corelib.ssr.ssrfun]
+sym_not_id [in Corelib.Init.Datatypes]
+sym_id [in Corelib.Init.Datatypes]
+sym_not_equal [in Corelib.Init.Logic]
+sym_equal [in Corelib.Init.Logic]
+sym_not_eq [in Corelib.Init.Logic]
+sym_eq [in Corelib.Init.Logic]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_abbreviation_T.html b/master/corelib/index_abbreviation_T.html new file mode 100644 index 0000000000..ff99d48762 --- /dev/null +++ b/master/corelib/index_abbreviation_T.html @@ -0,0 +1,565 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

T (abbreviation)

+ten [in Corelib.Init.Nat]
+to_nat [in Corelib.Strings.PrimStringAxioms]
+trans_id [in Corelib.Init.Datatypes]
+trans_equal [in Corelib.Init.Logic]
+trans_eq [in Corelib.Init.Logic]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_abbreviation_U.html b/master/corelib/index_abbreviation_U.html new file mode 100644 index 0000000000..0951ba4bd0 --- /dev/null +++ b/master/corelib/index_abbreviation_U.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

U (abbreviation)

+unkeyed [in Corelib.ssr.ssreflect]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_abbreviation_V.html b/master/corelib/index_abbreviation_V.html new file mode 100644 index 0000000000..687e1ac27c --- /dev/null +++ b/master/corelib/index_abbreviation_V.html @@ -0,0 +1,562 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

V (abbreviation)

+valid_binary [in Corelib.Floats.FloatAxioms]
+void [in Corelib.ssr.ssrfun]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_abbreviation_W.html b/master/corelib/index_abbreviation_W.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_abbreviation_W.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_abbreviation_X.html b/master/corelib/index_abbreviation_X.html new file mode 100644 index 0000000000..65e9b05830 --- /dev/null +++ b/master/corelib/index_abbreviation_X.html @@ -0,0 +1,569 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

X (abbreviation)

+xpredC [in Corelib.ssr.ssrbool]
+xpredD [in Corelib.ssr.ssrbool]
+xpredI [in Corelib.ssr.ssrbool]
+xpredT [in Corelib.ssr.ssrbool]
+xpredU [in Corelib.ssr.ssrbool]
+xpred0 [in Corelib.ssr.ssrbool]
+xpreim [in Corelib.ssr.ssrbool]
+xrelpre [in Corelib.ssr.ssrbool]
+xrelU [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_abbreviation_Y.html b/master/corelib/index_abbreviation_Y.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_abbreviation_Y.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_abbreviation_Z.html b/master/corelib/index_abbreviation_Z.html new file mode 100644 index 0000000000..69ffbf5fca --- /dev/null +++ b/master/corelib/index_abbreviation_Z.html @@ -0,0 +1,562 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

Z (abbreviation)

+zero [in Corelib.Init.Hexadecimal]
+zero [in Corelib.Init.Decimal]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_abbreviation__.html b/master/corelib/index_abbreviation__.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_abbreviation__.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_axiom_*.html b/master/corelib/index_axiom_*.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_axiom_*.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_axiom_A.html b/master/corelib/index_axiom_A.html new file mode 100644 index 0000000000..43d434d962 --- /dev/null +++ b/master/corelib/index_axiom_A.html @@ -0,0 +1,576 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

A (axiom)

+abs [in Corelib.Floats.PrimFloat]
+abs_spec [in Corelib.Floats.FloatAxioms]
+add [in Corelib.Floats.PrimFloat]
+add [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+addc [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+addcarryc [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+addcarryc_def_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+addc_def_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+addmuldiv [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+addmuldiv_def_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+add_spec [in Corelib.Floats.FloatAxioms]
+add_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+array [in Corelib.Array.PrimArray]
+array_ext [in Corelib.Array.ArrayAxioms]
+asr [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+asr_spec [in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_axiom_B.html b/master/corelib/index_axiom_B.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_axiom_B.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_axiom_C.html b/master/corelib/index_axiom_C.html new file mode 100644 index 0000000000..6a0cce8a24 --- /dev/null +++ b/master/corelib/index_axiom_C.html @@ -0,0 +1,573 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

C (axiom)

+cat [in Corelib.Strings.PrimString]
+cat_spec [in Corelib.Strings.PrimStringAxioms]
+classify [in Corelib.Floats.PrimFloat]
+classify_spec [in Corelib.Floats.FloatAxioms]
+compare [in Corelib.Strings.PrimString]
+compare [in Corelib.Floats.PrimFloat]
+compare [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+compares [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+compare_spec [in Corelib.Floats.FloatAxioms]
+compare_def_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+compare_spec [in Corelib.Strings.PrimStringAxioms]
+compare_spec [in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+copy [in Corelib.Array.PrimArray]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_axiom_D.html b/master/corelib/index_axiom_D.html new file mode 100644 index 0000000000..f175860c82 --- /dev/null +++ b/master/corelib/index_axiom_D.html @@ -0,0 +1,572 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

D (axiom)

+default [in Corelib.Array.PrimArray]
+default_set [in Corelib.Array.ArrayAxioms]
+div [in Corelib.Floats.PrimFloat]
+div [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+diveucl [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+diveucl_21_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+diveucl_def_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+diveucl_21 [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+divs [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+div_spec [in Corelib.Floats.FloatAxioms]
+div_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+div_spec [in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_axiom_E.html b/master/corelib/index_axiom_E.html new file mode 100644 index 0000000000..afa0d49661 --- /dev/null +++ b/master/corelib/index_axiom_E.html @@ -0,0 +1,565 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

E (axiom)

+eqb [in Corelib.Floats.PrimFloat]
+eqb [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+eqb_spec [in Corelib.Floats.FloatAxioms]
+eqb_refl [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+eqb_correct [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_axiom_F.html b/master/corelib/index_axiom_F.html new file mode 100644 index 0000000000..abe3a8520c --- /dev/null +++ b/master/corelib/index_axiom_F.html @@ -0,0 +1,563 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

F (axiom)

+float [in Corelib.Floats.PrimFloat]
+frshiftexp [in Corelib.Floats.PrimFloat]
+frshiftexp_spec [in Corelib.Floats.FloatAxioms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_axiom_G.html b/master/corelib/index_axiom_G.html new file mode 100644 index 0000000000..bfb5e44ca1 --- /dev/null +++ b/master/corelib/index_axiom_G.html @@ -0,0 +1,568 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

G (axiom)

+get [in Corelib.Strings.PrimString]
+get [in Corelib.Array.PrimArray]
+get_copy [in Corelib.Array.ArrayAxioms]
+get_make [in Corelib.Array.ArrayAxioms]
+get_set_other [in Corelib.Array.ArrayAxioms]
+get_set_same [in Corelib.Array.ArrayAxioms]
+get_out_of_bounds [in Corelib.Array.ArrayAxioms]
+get_spec [in Corelib.Strings.PrimStringAxioms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_axiom_H.html b/master/corelib/index_axiom_H.html new file mode 100644 index 0000000000..e56a86e1bd --- /dev/null +++ b/master/corelib/index_axiom_H.html @@ -0,0 +1,562 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

H (axiom)

+head0 [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+head0_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_axiom_I.html b/master/corelib/index_axiom_I.html new file mode 100644 index 0000000000..ff0bd4441e --- /dev/null +++ b/master/corelib/index_axiom_I.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

I (axiom)

+int [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_axiom_J.html b/master/corelib/index_axiom_J.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_axiom_J.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_axiom_K.html b/master/corelib/index_axiom_K.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_axiom_K.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_axiom_L.html b/master/corelib/index_axiom_L.html new file mode 100644 index 0000000000..e0027c2ccf --- /dev/null +++ b/master/corelib/index_axiom_L.html @@ -0,0 +1,1075 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

L (axiom)

+land [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+land_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+ldshiftexp [in Corelib.Floats.PrimFloat]
+ldshiftexp_spec [in Corelib.Floats.FloatAxioms]
+leb [in Corelib.Floats.PrimFloat]
+leb [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+leb_spec [in Corelib.Floats.FloatAxioms]
+leb_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+leb_length [in Corelib.Array.ArrayAxioms]
+leb_spec [in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+Leibniz.eqb [in Corelib.Floats.PrimFloat]
+Leibniz.eqb_spec [in Corelib.Floats.FloatAxioms]
+length [in Corelib.Strings.PrimString]
+length [in Corelib.Array.PrimArray]
+length_copy [in Corelib.Array.ArrayAxioms]
+length_set [in Corelib.Array.ArrayAxioms]
+length_make [in Corelib.Array.ArrayAxioms]
+length_spec [in Corelib.Strings.PrimStringAxioms]
+lesb [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+lor [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+lor_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+lsl [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+lsl_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+lsr [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+lsr_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+ltb [in Corelib.Floats.PrimFloat]
+ltb [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+ltb_spec [in Corelib.Floats.FloatAxioms]
+ltb_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+ltb_spec [in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+ltsb [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+lxor [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+lxor_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_axiom_M.html b/master/corelib/index_axiom_M.html new file mode 100644 index 0000000000..96dc14d0e0 --- /dev/null +++ b/master/corelib/index_axiom_M.html @@ -0,0 +1,575 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

M (axiom)

+make [in Corelib.Strings.PrimString]
+make [in Corelib.Array.PrimArray]
+make_spec [in Corelib.Strings.PrimStringAxioms]
+max_length [in Corelib.Strings.PrimString]
+max_length [in Corelib.Array.PrimArray]
+mod [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+mods [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+mod_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+mod_spec [in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+mul [in Corelib.Floats.PrimFloat]
+mul [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+mulc [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+mulc_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+mul_spec [in Corelib.Floats.FloatAxioms]
+mul_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_axiom_N.html b/master/corelib/index_axiom_N.html new file mode 100644 index 0000000000..5ca063c023 --- /dev/null +++ b/master/corelib/index_axiom_N.html @@ -0,0 +1,566 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

N (axiom)

+next_down_spec [in Corelib.Floats.FloatAxioms]
+next_up_spec [in Corelib.Floats.FloatAxioms]
+next_down [in Corelib.Floats.PrimFloat]
+next_up [in Corelib.Floats.PrimFloat]
+normfr_mantissa_spec [in Corelib.Floats.FloatAxioms]
+normfr_mantissa [in Corelib.Floats.PrimFloat]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_axiom_O.html b/master/corelib/index_axiom_O.html new file mode 100644 index 0000000000..1fa7b5d801 --- /dev/null +++ b/master/corelib/index_axiom_O.html @@ -0,0 +1,566 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

O (axiom)

+of_uint63_spec [in Corelib.Floats.FloatAxioms]
+of_to_Z [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+of_to_list [in Corelib.Strings.PrimStringAxioms]
+of_uint63 [in Corelib.Floats.PrimFloat]
+opp [in Corelib.Floats.PrimFloat]
+opp_spec [in Corelib.Floats.FloatAxioms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_axiom_P.html b/master/corelib/index_axiom_P.html new file mode 100644 index 0000000000..fa70147139 --- /dev/null +++ b/master/corelib/index_axiom_P.html @@ -0,0 +1,563 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

P (axiom)

+PredSortOfSimplSignature.coerce [in Corelib.ssr.ssrbool]
+Prim2SF_SF2Prim [in Corelib.Floats.FloatAxioms]
+Prim2SF_valid [in Corelib.Floats.FloatAxioms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_axiom_Q.html b/master/corelib/index_axiom_Q.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_axiom_Q.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_axiom_R.html b/master/corelib/index_axiom_R.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_axiom_R.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_axiom_S.html b/master/corelib/index_axiom_S.html new file mode 100644 index 0000000000..f234316055 --- /dev/null +++ b/master/corelib/index_axiom_S.html @@ -0,0 +1,575 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

S (axiom)

+set [in Corelib.Array.PrimArray]
+SF2Prim_Prim2SF [in Corelib.Floats.FloatAxioms]
+sqrt [in Corelib.Floats.PrimFloat]
+sqrt_spec [in Corelib.Floats.FloatAxioms]
+string [in Corelib.Strings.PrimString]
+sub [in Corelib.Strings.PrimString]
+sub [in Corelib.Floats.PrimFloat]
+sub [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+subc [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+subcarryc [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+subcarryc_def_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+subc_def_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+sub_spec [in Corelib.Floats.FloatAxioms]
+sub_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+sub_spec [in Corelib.Strings.PrimStringAxioms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_axiom_T.html b/master/corelib/index_axiom_T.html new file mode 100644 index 0000000000..8077959603 --- /dev/null +++ b/master/corelib/index_axiom_T.html @@ -0,0 +1,564 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

T (axiom)

+tail0 [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+tail0_spec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+to_list_char63_valid [in Corelib.Strings.PrimStringAxioms]
+to_list_length [in Corelib.Strings.PrimStringAxioms]
+

+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

U (axiom)

+UNDER_REL.under_rel_done [in Corelib.ssr.ssrunder]
+UNDER_REL.over_rel_done [in Corelib.ssr.ssrunder]
+UNDER_REL.over_rel [in Corelib.ssr.ssrunder]
+UNDER_REL.Over_rel [in Corelib.ssr.ssrunder]
+UNDER_REL.Under_relE [in Corelib.ssr.ssrunder]
+UNDER_REL.Under_rel_from_rel [in Corelib.ssr.ssrunder]
+UNDER_REL.Under_rel [in Corelib.ssr.ssrunder]
+

+ +
+ +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
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Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
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Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_*.html b/master/corelib/index_constructor_*.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_constructor_*.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_A.html b/master/corelib/index_constructor_A.html new file mode 100644 index 0000000000..c5edf70c61 --- /dev/null +++ b/master/corelib/index_constructor_A.html @@ -0,0 +1,570 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

A (constructor)

+Acc_intro [in Corelib.Init.Wf]
+AltFalse [in Corelib.ssr.ssrbool]
+AltTrue [in Corelib.ssr.ssrbool]
+And3 [in Corelib.ssr.ssrbool]
+And4 [in Corelib.ssr.ssrbool]
+And5 [in Corelib.ssr.ssrbool]
+antisymmetry [in Corelib.Classes.RelationClasses]
+antisymmetry [in Corelib.Classes.CRelationClasses]
+asymmetry [in Corelib.Classes.RelationClasses]
+asymmetry [in Corelib.Classes.CRelationClasses]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_B.html b/master/corelib/index_constructor_B.html new file mode 100644 index 0000000000..48fe61ecf6 --- /dev/null +++ b/master/corelib/index_constructor_B.html @@ -0,0 +1,563 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

B (constructor)

+Bijective [in Corelib.ssr.ssrfun]
+BoolSpecF [in Corelib.Init.Datatypes]
+BoolSpecT [in Corelib.Init.Datatypes]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_C.html b/master/corelib/index_constructor_C.html new file mode 100644 index 0000000000..9ded65167d --- /dev/null +++ b/master/corelib/index_constructor_C.html @@ -0,0 +1,570 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

C (constructor)

+CompEq [in Corelib.Init.Datatypes]
+CompEqT [in Corelib.Init.Datatypes]
+CompGt [in Corelib.Init.Datatypes]
+CompGtT [in Corelib.Init.Datatypes]
+CompLt [in Corelib.Init.Datatypes]
+CompLtT [in Corelib.Init.Datatypes]
+conj [in Corelib.Init.Logic]
+cons [in Corelib.Init.Datatypes]
+C0 [in Corelib.Numbers.Cyclic.Int63.CarryType]
+C1 [in Corelib.Numbers.Cyclic.Int63.CarryType]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_D.html b/master/corelib/index_constructor_D.html new file mode 100644 index 0000000000..833f6dd6ba --- /dev/null +++ b/master/corelib/index_constructor_D.html @@ -0,0 +1,1076 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

D (constructor)

+Da [in Corelib.Init.Hexadecimal]
+Db [in Corelib.Init.Hexadecimal]
+Dc [in Corelib.Init.Hexadecimal]
+Dd [in Corelib.Init.Hexadecimal]
+De [in Corelib.Init.Hexadecimal]
+Decimal [in Corelib.Init.Decimal]
+Decimal [in Corelib.Init.Number]
+DecimalExp [in Corelib.Init.Decimal]
+DefaultPredKey [in Corelib.ssr.ssrbool]
+Df [in Corelib.Init.Hexadecimal]
+did_normalization [in Corelib.Classes.CMorphisms]
+did_normalization [in Corelib.Classes.Morphisms]
+do_subrelation [in Corelib.Classes.CMorphisms]
+do_subrelation [in Corelib.Classes.Morphisms]
+D0 [in Corelib.Init.Hexadecimal]
+D0 [in Corelib.Init.Decimal]
+D1 [in Corelib.Init.Hexadecimal]
+D1 [in Corelib.Init.Decimal]
+D2 [in Corelib.Init.Hexadecimal]
+D2 [in Corelib.Init.Decimal]
+D3 [in Corelib.Init.Hexadecimal]
+D3 [in Corelib.Init.Decimal]
+D4 [in Corelib.Init.Hexadecimal]
+D4 [in Corelib.Init.Decimal]
+D5 [in Corelib.Init.Hexadecimal]
+D5 [in Corelib.Init.Decimal]
+D6 [in Corelib.Init.Hexadecimal]
+D6 [in Corelib.Init.Decimal]
+D7 [in Corelib.Init.Hexadecimal]
+D7 [in Corelib.Init.Decimal]
+D8 [in Corelib.Init.Hexadecimal]
+D8 [in Corelib.Init.Decimal]
+D9 [in Corelib.Init.Hexadecimal]
+D9 [in Corelib.Init.Decimal]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_E.html b/master/corelib/index_constructor_E.html new file mode 100644 index 0000000000..959b6b178f --- /dev/null +++ b/master/corelib/index_constructor_E.html @@ -0,0 +1,568 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

E (constructor)

+Eq [in Corelib.Init.Datatypes]
+eq_refl [in Corelib.Init.Logic]
+exist [in Corelib.Init.Specif]
+existT [in Corelib.Init.Specif]
+existT2 [in Corelib.Init.Specif]
+exist2 [in Corelib.Init.Specif]
+ex_intro2 [in Corelib.Init.Logic]
+ex_intro [in Corelib.Init.Logic]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_F.html b/master/corelib/index_constructor_F.html new file mode 100644 index 0000000000..c9b7fb3dfa --- /dev/null +++ b/master/corelib/index_constructor_F.html @@ -0,0 +1,567 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

F (constructor)

+false [in Corelib.Init.Datatypes]
+FEq [in Corelib.Floats.PrimFloat]
+FGt [in Corelib.Floats.PrimFloat]
+FLt [in Corelib.Floats.PrimFloat]
+FNotComparable [in Corelib.Floats.PrimFloat]
+Forall_cons [in Corelib.Lists.ListDef]
+Forall_nil [in Corelib.Lists.ListDef]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_G.html b/master/corelib/index_constructor_G.html new file mode 100644 index 0000000000..ef0eaa0e15 --- /dev/null +++ b/master/corelib/index_constructor_G.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

G (constructor)

+Gt [in Corelib.Init.Datatypes]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_H.html b/master/corelib/index_constructor_H.html new file mode 100644 index 0000000000..380fd6ec82 --- /dev/null +++ b/master/corelib/index_constructor_H.html @@ -0,0 +1,563 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

H (constructor)

+Hexadecimal [in Corelib.Init.Hexadecimal]
+Hexadecimal [in Corelib.Init.Number]
+HexadecimalExp [in Corelib.Init.Hexadecimal]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_I.html b/master/corelib/index_constructor_I.html new file mode 100644 index 0000000000..45d2939dde --- /dev/null +++ b/master/corelib/index_constructor_I.html @@ -0,0 +1,576 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

I (constructor)

+I [in Corelib.Init.Logic]
+IfSpecFalse [in Corelib.ssr.ssrbool]
+IfSpecTrue [in Corelib.ssr.ssrbool]
+Implies [in Corelib.ssr.ssrbool]
+inhabits [in Corelib.Init.Logic]
+inl [in Corelib.Init.Datatypes]
+inleft [in Corelib.Init.Specif]
+inr [in Corelib.Init.Datatypes]
+inright [in Corelib.Init.Specif]
+IntDecimal [in Corelib.Init.Number]
+IntHexadecimal [in Corelib.Init.Number]
+irreflexivity [in Corelib.Classes.RelationClasses]
+irreflexivity [in Corelib.Classes.CRelationClasses]
+is_subrelation [in Corelib.Classes.RelationClasses]
+is_eq_true [in Corelib.Init.Datatypes]
+is_subrelation [in Corelib.Classes.CRelationClasses]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_J.html b/master/corelib/index_constructor_J.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_constructor_J.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_K.html b/master/corelib/index_constructor_K.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_constructor_K.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_L.html b/master/corelib/index_constructor_L.html new file mode 100644 index 0000000000..01b16a8539 --- /dev/null +++ b/master/corelib/index_constructor_L.html @@ -0,0 +1,566 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

L (constructor)

+left [in Corelib.Init.Specif]
+le_S [in Corelib.Init.Peano]
+le_n [in Corelib.Init.Peano]
+loc_Inexact [in Corelib.Floats.SpecFloat]
+loc_Exact [in Corelib.Floats.SpecFloat]
+Lt [in Corelib.Init.Datatypes]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_M.html b/master/corelib/index_constructor_M.html new file mode 100644 index 0000000000..60a1ef2288 --- /dev/null +++ b/master/corelib/index_constructor_M.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

M (constructor)

+Mem [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_N.html b/master/corelib/index_constructor_N.html new file mode 100644 index 0000000000..917b7a4fc1 --- /dev/null +++ b/master/corelib/index_constructor_N.html @@ -0,0 +1,576 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

N (constructor)

+NaN [in Corelib.Floats.FloatClass]
+Neg [in Corelib.Init.Hexadecimal]
+Neg [in Corelib.Init.Decimal]
+Neg [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+nil [in Corelib.Init.Datatypes]
+Nil [in Corelib.Init.Hexadecimal]
+Nil [in Corelib.Init.Decimal]
+NInf [in Corelib.Floats.FloatClass]
+NNormal [in Corelib.Floats.FloatClass]
+None [in Corelib.Init.Datatypes]
+normalizes [in Corelib.Classes.CMorphisms]
+normalizes [in Corelib.Classes.Morphisms]
+Npos [in Corelib.Numbers.BinNums]
+NSubn [in Corelib.Floats.FloatClass]
+NZero [in Corelib.Floats.FloatClass]
+N0 [in Corelib.Numbers.BinNums]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_O.html b/master/corelib/index_constructor_O.html new file mode 100644 index 0000000000..0da2bb8079 --- /dev/null +++ b/master/corelib/index_constructor_O.html @@ -0,0 +1,570 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

O (constructor)

+O [in Corelib.Init.Datatypes]
+or_intror [in Corelib.Init.Logic]
+or_introl [in Corelib.Init.Logic]
+Or31 [in Corelib.ssr.ssrbool]
+Or32 [in Corelib.ssr.ssrbool]
+Or33 [in Corelib.ssr.ssrbool]
+Or41 [in Corelib.ssr.ssrbool]
+Or42 [in Corelib.ssr.ssrbool]
+Or43 [in Corelib.ssr.ssrbool]
+Or44 [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_P.html b/master/corelib/index_constructor_P.html new file mode 100644 index 0000000000..9b20b169f9 --- /dev/null +++ b/master/corelib/index_constructor_P.html @@ -0,0 +1,579 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

P (constructor)

+pair [in Corelib.Init.Datatypes]
+partial_order_equivalence [in Corelib.Classes.RelationClasses]
+partial_order_equivalence [in Corelib.Classes.CRelationClasses]
+Phant [in Corelib.ssr.ssreflect]
+Phantom [in Corelib.ssr.ssreflect]
+PInf [in Corelib.Floats.FloatClass]
+PNormal [in Corelib.Floats.FloatClass]
+Pos [in Corelib.Init.Hexadecimal]
+Pos [in Corelib.Init.Decimal]
+Pos [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+Pos.IsNeg [in Corelib.BinNums.PosDef]
+Pos.IsNul [in Corelib.BinNums.PosDef]
+Pos.IsPos [in Corelib.BinNums.PosDef]
+proper_proxy [in Corelib.Classes.CMorphisms]
+proper_prf [in Corelib.Classes.CMorphisms]
+proper_proxy [in Corelib.Classes.Morphisms]
+proper_prf [in Corelib.Classes.Morphisms]
+PSubn [in Corelib.Floats.FloatClass]
+PZero [in Corelib.Floats.FloatClass]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_Q.html b/master/corelib/index_constructor_Q.html new file mode 100644 index 0000000000..62675fb12e --- /dev/null +++ b/master/corelib/index_constructor_Q.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

Q (constructor)

+Qualifier [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_R.html b/master/corelib/index_constructor_R.html new file mode 100644 index 0000000000..134edbb070 --- /dev/null +++ b/master/corelib/index_constructor_R.html @@ -0,0 +1,567 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

R (constructor)

+ReflectF [in Corelib.Init.Datatypes]
+ReflectT [in Corelib.Init.Datatypes]
+reflexive_proxy [in Corelib.Classes.Morphisms]
+reflexivity [in Corelib.Classes.RelationClasses]
+reflexivity [in Corelib.ssr.ssrclasses]
+reflexivity [in Corelib.Classes.CRelationClasses]
+right [in Corelib.Init.Specif]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_S.html b/master/corelib/index_constructor_S.html new file mode 100644 index 0000000000..c0690730e2 --- /dev/null +++ b/master/corelib/index_constructor_S.html @@ -0,0 +1,569 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

S (constructor)

+S [in Corelib.Init.Datatypes]
+SimplFun [in Corelib.ssr.ssrfun]
+Some [in Corelib.Init.Datatypes]
+symmetry [in Corelib.Classes.RelationClasses]
+symmetry [in Corelib.Classes.CRelationClasses]
+S754_finite [in Corelib.Floats.SpecFloat]
+S754_nan [in Corelib.Floats.SpecFloat]
+S754_infinity [in Corelib.Floats.SpecFloat]
+S754_zero [in Corelib.Floats.SpecFloat]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_T.html b/master/corelib/index_constructor_T.html new file mode 100644 index 0000000000..078adf6e6a --- /dev/null +++ b/master/corelib/index_constructor_T.html @@ -0,0 +1,568 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

T (constructor)

+tactic_view [in Corelib.ssr.ssreflect]
+Tcons [in Corelib.Classes.RelationClasses]
+TheCanonical.Put [in Corelib.ssr.ssreflect]
+Tnil [in Corelib.Classes.RelationClasses]
+transitivity [in Corelib.Classes.RelationClasses]
+transitivity [in Corelib.Classes.CRelationClasses]
+true [in Corelib.Init.Datatypes]
+tt [in Corelib.Init.Datatypes]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_U.html b/master/corelib/index_constructor_U.html new file mode 100644 index 0000000000..3ba0351d3e --- /dev/null +++ b/master/corelib/index_constructor_U.html @@ -0,0 +1,563 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

U (constructor)

+UIntDecimal [in Corelib.Init.Number]
+UIntHexadecimal [in Corelib.Init.Number]
+unconvertible [in Corelib.Classes.Init]
+

+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

V (constructor)

+vm_compute [in Corelib.ssr.ssreflect]
+

+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

X (constructor)

+xaa [in Corelib.Init.Byte]
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+x99 [in Corelib.Init.Byte]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_Y.html b/master/corelib/index_constructor_Y.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_constructor_Y.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor_Z.html b/master/corelib/index_constructor_Z.html new file mode 100644 index 0000000000..0865efea25 --- /dev/null +++ b/master/corelib/index_constructor_Z.html @@ -0,0 +1,563 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

Z (constructor)

+Zneg [in Corelib.Numbers.BinNums]
+Zpos [in Corelib.Numbers.BinNums]
+Z0 [in Corelib.Numbers.BinNums]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_constructor__.html b/master/corelib/index_constructor__.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_constructor__.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_*.html b/master/corelib/index_definition_*.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_definition_*.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_A.html b/master/corelib/index_definition_A.html new file mode 100644 index 0000000000..e204d58b08 --- /dev/null +++ b/master/corelib/index_definition_A.html @@ -0,0 +1,1096 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

A (definition)

+abs [in Corelib.Init.Hexadecimal]
+abs [in Corelib.Init.Decimal]
+abstract [in Corelib.ssr.ssreflect]
+abstract_key [in Corelib.ssr.ssreflect]
+abstract_lock [in Corelib.ssr.ssreflect]
+Acc_intro_generator [in Corelib.Init.Wf]
+Acc_inv_dep [in Corelib.Init.Wf]
+Acc_sind [in Corelib.Init.Wf]
+Acc_rec [in Corelib.Init.Wf]
+Acc_ind [in Corelib.Init.Wf]
+Acc_rect [in Corelib.Init.Wf]
+add [in Corelib.Init.Nat]
+addb [in Corelib.ssr.ssrbool]
+addcarry [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+addcarryc_def [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+addc_def [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+addmuldiv_def [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+all [in Corelib.Init.Logic]
+all_equal_to [in Corelib.ssr.ssrfun]
+all_pair [in Corelib.ssr.ssrfun]
+andb [in Corelib.Init.Datatypes]
+and_sind [in Corelib.Init.Logic]
+and_rec [in Corelib.Init.Logic]
+and_ind [in Corelib.Init.Logic]
+and_rect [in Corelib.Init.Logic]
+and3_sind [in Corelib.ssr.ssrbool]
+and3_rec [in Corelib.ssr.ssrbool]
+and3_ind [in Corelib.ssr.ssrbool]
+and3_rect [in Corelib.ssr.ssrbool]
+and4_sind [in Corelib.ssr.ssrbool]
+and4_rec [in Corelib.ssr.ssrbool]
+and4_ind [in Corelib.ssr.ssrbool]
+and4_rect [in Corelib.ssr.ssrbool]
+and5_sind [in Corelib.ssr.ssrbool]
+and5_rec [in Corelib.ssr.ssrbool]
+and5_ind [in Corelib.ssr.ssrbool]
+and5_rect [in Corelib.ssr.ssrbool]
+antisymmetric [in Corelib.ssr.ssrbool]
+antisymmetric [in Corelib.Relations.Relation_Definitions]
+app [in Corelib.Init.Datatypes]
+app [in Corelib.Init.Hexadecimal]
+app [in Corelib.Init.Decimal]
+ApplicativePred [in Corelib.ssr.ssrbool]
+applicative_pred_applicative [in Corelib.ssr.ssrbool]
+applicative_pred_of_simpl [in Corelib.ssr.ssrbool]
+applicative_pred [in Corelib.ssr.ssrbool]
+apply [in Corelib.Program.Basics]
+app_int [in Corelib.Init.Hexadecimal]
+app_int [in Corelib.Init.Decimal]
+argumentType [in Corelib.ssr.ssreflect]
+arrow [in Corelib.Program.Basics]
+arrow [in Corelib.Classes.CRelationClasses]
+arrows [in Corelib.Classes.RelationClasses]
+associative [in Corelib.ssr.ssrfun]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_B.html b/master/corelib/index_definition_B.html new file mode 100644 index 0000000000..9ad7d8e7fe --- /dev/null +++ b/master/corelib/index_definition_B.html @@ -0,0 +1,586 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

B (definition)

+bijective_on [in Corelib.ssr.ssrbool]
+bijective_in [in Corelib.ssr.ssrbool]
+binary_normalize [in Corelib.Floats.SpecFloat]
+binary_round [in Corelib.Floats.SpecFloat]
+binary_round_aux [in Corelib.Floats.SpecFloat]
+binary_relation [in Corelib.Classes.RelationClasses]
+binary_operation [in Corelib.Classes.RelationClasses]
+bit [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+bitwise [in Corelib.Init.Nat]
+boolfunPredType [in Corelib.ssr.ssrbool]
+BoolSpec_sind [in Corelib.Init.Datatypes]
+BoolSpec_ind [in Corelib.Init.Datatypes]
+bool_sind [in Corelib.Init.Datatypes]
+bool_rec [in Corelib.Init.Datatypes]
+bool_ind [in Corelib.Init.Datatypes]
+bool_rect [in Corelib.Init.Datatypes]
+bool_of_sumbool [in Corelib.Init.Sumbool]
+bool_eq_ind [in Corelib.Init.Sumbool]
+bool_eq_rec [in Corelib.Init.Sumbool]
+bounded [in Corelib.Floats.SpecFloat]
+Build_Setoid_Theory [in Corelib.Setoids.Setoid]
+byte_of_byte [in Corelib.Init.Byte]
+byte_sind [in Corelib.Init.Byte]
+byte_rec [in Corelib.Init.Byte]
+byte_ind [in Corelib.Init.Byte]
+byte_rect [in Corelib.Init.Byte]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_C.html b/master/corelib/index_definition_C.html new file mode 100644 index 0000000000..1c9f4b2a51 --- /dev/null +++ b/master/corelib/index_definition_C.html @@ -0,0 +1,1086 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

C (definition)

+cancel [in Corelib.ssr.ssrfun]
+canonical_mantissa [in Corelib.Floats.SpecFloat]
+catcomp [in Corelib.ssr.ssrfun]
+char63 [in Corelib.Strings.PrimString]
+Char63Notations.parse [in Corelib.Strings.PrimString]
+Char63Notations.print [in Corelib.Strings.PrimString]
+char63_valid [in Corelib.Strings.PrimStringAxioms]
+check_applicative_mem_pred [in Corelib.ssr.ssrbool]
+classically [in Corelib.ssr.ssrbool]
+clone_pred [in Corelib.ssr.ssrbool]
+collective_pred_of_simpl [in Corelib.ssr.ssrbool]
+collective_pred [in Corelib.ssr.ssrbool]
+commut [in Corelib.Relations.Relation_Definitions]
+commutative [in Corelib.ssr.ssrfun]
+comp [in Corelib.ssr.ssrfun]
+compare [in Corelib.Init.Nat]
+CompareSpecT_sind [in Corelib.Init.Datatypes]
+CompareSpecT_rec [in Corelib.Init.Datatypes]
+CompareSpecT_ind [in Corelib.Init.Datatypes]
+CompareSpecT_rect [in Corelib.Init.Datatypes]
+CompareSpec_sind [in Corelib.Init.Datatypes]
+CompareSpec_ind [in Corelib.Init.Datatypes]
+compare_def [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+comparison_sind [in Corelib.Init.Datatypes]
+comparison_rec [in Corelib.Init.Datatypes]
+comparison_ind [in Corelib.Init.Datatypes]
+comparison_rect [in Corelib.Init.Datatypes]
+complement [in Corelib.Classes.RelationClasses]
+complement [in Corelib.Classes.CRelationClasses]
+complement_proper [in Corelib.Classes.Morphisms]
+CompOpp [in Corelib.Init.Datatypes]
+compose [in Corelib.Program.Basics]
+CompSpec [in Corelib.Init.Datatypes]
+CompSpecT [in Corelib.Init.Datatypes]
+cond_Zopp [in Corelib.Floats.SpecFloat]
+congr1 [in Corelib.ssr.ssrfun]
+congr2 [in Corelib.ssr.ssrfun]
+const [in Corelib.Program.Basics]
+contraNN [in Corelib.ssr.ssrbool]
+contraNT [in Corelib.ssr.ssrbool]
+contraTN [in Corelib.ssr.ssrbool]
+contraTT [in Corelib.ssr.ssrbool]
+crelation [in Corelib.Classes.CRelationClasses]
+curry [in Corelib.Init.Datatypes]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_D.html b/master/corelib/index_definition_D.html new file mode 100644 index 0000000000..fcf5b42bd4 --- /dev/null +++ b/master/corelib/index_definition_D.html @@ -0,0 +1,582 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

D (definition)

+decidable [in Corelib.ssr.ssrbool]
+decimal_eq_dec [in Corelib.Init.Decimal]
+decP [in Corelib.ssr.ssrbool]
+DefaultKeying.default_keyed_qualifier [in Corelib.ssr.ssrbool]
+DefaultKeying.default_keyed_pred [in Corelib.ssr.ssrbool]
+default_relation [in Corelib.Classes.SetoidTactics]
+del_tail_int [in Corelib.Init.Hexadecimal]
+del_tail [in Corelib.Init.Hexadecimal]
+del_head_int [in Corelib.Init.Hexadecimal]
+del_head [in Corelib.Init.Hexadecimal]
+del_tail_int [in Corelib.Init.Decimal]
+del_tail [in Corelib.Init.Decimal]
+del_head_int [in Corelib.Init.Decimal]
+del_head [in Corelib.Init.Decimal]
+dependentReturnType [in Corelib.ssr.ssreflect]
+digits [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+digits2_pos [in Corelib.Floats.SpecFloat]
+div [in Corelib.Init.Nat]
+diveucl_def [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+divmod [in Corelib.Init.Nat]
+div2 [in Corelib.Init.Nat]
+double [in Corelib.Init.Nat]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_E.html b/master/corelib/index_definition_E.html new file mode 100644 index 0000000000..ead30e73d0 --- /dev/null +++ b/master/corelib/index_definition_E.html @@ -0,0 +1,1219 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

E (definition)

+emax [in Corelib.Floats.FloatOps]
+emin [in Corelib.Floats.SpecFloat]
+Empty_set_sind [in Corelib.Init.Datatypes]
+Empty_set_rec [in Corelib.Init.Datatypes]
+Empty_set_ind [in Corelib.Init.Datatypes]
+Empty_set_rect [in Corelib.Init.Datatypes]
+eqb [in Corelib.Init.Nat]
+eqfun [in Corelib.ssr.ssrfun]
+eqrel [in Corelib.ssr.ssrfun]
+equiv [in Corelib.Relations.Relation_Definitions]
+equiv [in Corelib.Classes.Equivalence]
+equivalence_rewrite_relation [in Corelib.Classes.RelationClasses]
+equivalence_rel [in Corelib.ssr.ssrbool]
+eq_true_sind [in Corelib.Init.Datatypes]
+eq_true_rec [in Corelib.Init.Datatypes]
+eq_true_ind [in Corelib.Init.Datatypes]
+eq_true_rect [in Corelib.Init.Datatypes]
+eq_mem [in Corelib.ssr.ssrbool]
+eq_sig2_nondep [in Corelib.Init.Specif]
+eq_sig2_hprop_iff [in Corelib.Init.Specif]
+eq_sig2_ind_uncurried [in Corelib.Init.Specif]
+eq_sig2_rec_uncurried [in Corelib.Init.Specif]
+eq_sig2_rect_uncurried [in Corelib.Init.Specif]
+eq_sig2_rect_exist2 [in Corelib.Init.Specif]
+eq_sig2_rect_exist2_r [in Corelib.Init.Specif]
+eq_sig2_rect_exist2_l [in Corelib.Init.Specif]
+eq_sig2_ind [in Corelib.Init.Specif]
+eq_sig2_rec [in Corelib.Init.Specif]
+eq_sig2_rect [in Corelib.Init.Specif]
+eq_sig2_uncurried_iff [in Corelib.Init.Specif]
+eq_sig2_hprop [in Corelib.Init.Specif]
+eq_exist2_r [in Corelib.Init.Specif]
+eq_exist2_l [in Corelib.Init.Specif]
+eq_sig2 [in Corelib.Init.Specif]
+eq_sig2_uncurried [in Corelib.Init.Specif]
+eq_exist2_uncurried [in Corelib.Init.Specif]
+eq_sigT2_nondep [in Corelib.Init.Specif]
+eq_sigT2_hprop_iff [in Corelib.Init.Specif]
+eq_sigT2_ind_uncurried [in Corelib.Init.Specif]
+eq_sigT2_rec_uncurried [in Corelib.Init.Specif]
+eq_sigT2_rect_uncurried [in Corelib.Init.Specif]
+eq_sigT2_rect_existT2 [in Corelib.Init.Specif]
+eq_sigT2_rect_existT2_r [in Corelib.Init.Specif]
+eq_sigT2_rect_existT2_l [in Corelib.Init.Specif]
+eq_sigT2_ind [in Corelib.Init.Specif]
+eq_sigT2_rec [in Corelib.Init.Specif]
+eq_sigT2_rect [in Corelib.Init.Specif]
+eq_sigT2_uncurried_iff [in Corelib.Init.Specif]
+eq_sigT2_hprop [in Corelib.Init.Specif]
+eq_existT2_r [in Corelib.Init.Specif]
+eq_existT2_l [in Corelib.Init.Specif]
+eq_sigT2 [in Corelib.Init.Specif]
+eq_sigT2_uncurried [in Corelib.Init.Specif]
+eq_existT2_uncurried [in Corelib.Init.Specif]
+eq_sig_hprop_iff [in Corelib.Init.Specif]
+eq_sig_uncurried_iff [in Corelib.Init.Specif]
+eq_sig_hprop [in Corelib.Init.Specif]
+eq_sig_ind_uncurried [in Corelib.Init.Specif]
+eq_sig_rec_uncurried [in Corelib.Init.Specif]
+eq_sig_rect_uncurried [in Corelib.Init.Specif]
+eq_sig_rect_exist [in Corelib.Init.Specif]
+eq_sig_rect_exist_r [in Corelib.Init.Specif]
+eq_sig_rect_exist_l [in Corelib.Init.Specif]
+eq_sig_ind [in Corelib.Init.Specif]
+eq_sig_rec [in Corelib.Init.Specif]
+eq_sig_rect [in Corelib.Init.Specif]
+eq_exist_r [in Corelib.Init.Specif]
+eq_exist_l [in Corelib.Init.Specif]
+eq_sig [in Corelib.Init.Specif]
+eq_sig_uncurried [in Corelib.Init.Specif]
+eq_exist_uncurried [in Corelib.Init.Specif]
+eq_sigT_nondep [in Corelib.Init.Specif]
+eq_sigT_hprop_iff [in Corelib.Init.Specif]
+eq_sigT_ind_uncurried [in Corelib.Init.Specif]
+eq_sigT_rec_uncurried [in Corelib.Init.Specif]
+eq_sigT_rect_uncurried [in Corelib.Init.Specif]
+eq_sigT_rect_existT [in Corelib.Init.Specif]
+eq_sigT_rect_existT_r [in Corelib.Init.Specif]
+eq_sigT_rect_existT_l [in Corelib.Init.Specif]
+eq_sigT_ind [in Corelib.Init.Specif]
+eq_sigT_rec [in Corelib.Init.Specif]
+eq_sigT_rect [in Corelib.Init.Specif]
+eq_sigT_uncurried_iff [in Corelib.Init.Specif]
+eq_sigT_hprop [in Corelib.Init.Specif]
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+eq_existT_uncurried [in Corelib.Init.Specif]
+eq_add_S [in Corelib.Init.Peano]
+eq_S [in Corelib.Init.Peano]
+eq_ex2_nondep [in Corelib.Init.Logic]
+eq_ex2_hprop_iff [in Corelib.Init.Logic]
+eq_ex2_ind_uncurried [in Corelib.Init.Logic]
+eq_ex2_rec_uncurried [in Corelib.Init.Logic]
+eq_ex2_rect_uncurried [in Corelib.Init.Logic]
+eq_ex2_rect_ex_intro2 [in Corelib.Init.Logic]
+eq_ex2_rect_ex_intro2_r [in Corelib.Init.Logic]
+eq_ex2_rect_ex_intro2_l [in Corelib.Init.Logic]
+eq_ex2_ind [in Corelib.Init.Logic]
+eq_ex2_rec [in Corelib.Init.Logic]
+eq_ex2_rect [in Corelib.Init.Logic]
+eq_ex2_eta [in Corelib.Init.Logic]
+eq_ex2_uncurried_iff [in Corelib.Init.Logic]
+eq_ex_intro2_hprop [in Corelib.Init.Logic]
+eq_ex_intro2_hprop_nondep [in Corelib.Init.Logic]
+eq_ex2_hprop [in Corelib.Init.Logic]
+eq_ex_intro2_r [in Corelib.Init.Logic]
+eq_ex_intro2_l [in Corelib.Init.Logic]
+eq_ex_intro2 [in Corelib.Init.Logic]
+eq_ex2 [in Corelib.Init.Logic]
+eq_ex2_uncurried [in Corelib.Init.Logic]
+eq_ex_intro2_uncurried [in Corelib.Init.Logic]
+eq_ex_hprop_iff [in Corelib.Init.Logic]
+eq_ex_uncurried_iff [in Corelib.Init.Logic]
+eq_ex_intro_hprop [in Corelib.Init.Logic]
+eq_ex_hprop [in Corelib.Init.Logic]
+eq_ex_ind_uncurried [in Corelib.Init.Logic]
+eq_ex_rec_uncurried [in Corelib.Init.Logic]
+eq_ex_rect_uncurried [in Corelib.Init.Logic]
+eq_ex_rect_ex_intro [in Corelib.Init.Logic]
+eq_ex_rect_ex_intro_r [in Corelib.Init.Logic]
+eq_ex_rect_ex_intro_l [in Corelib.Init.Logic]
+eq_ex_ind [in Corelib.Init.Logic]
+eq_ex_rec [in Corelib.Init.Logic]
+eq_ex_rect [in Corelib.Init.Logic]
+eq_ex_eta [in Corelib.Init.Logic]
+eq_ex_intro_r [in Corelib.Init.Logic]
+eq_ex_intro_l [in Corelib.Init.Logic]
+eq_ex [in Corelib.Init.Logic]
+eq_ex_intro [in Corelib.Init.Logic]
+eq_ex_uncurried [in Corelib.Init.Logic]
+eq_ex_intro_uncurried [in Corelib.Init.Logic]
+eq_rect_r [in Corelib.Init.Logic]
+eq_rec_r [in Corelib.Init.Logic]
+eq_ind_r [in Corelib.Init.Logic]
+eq_sind_r [in Corelib.Init.Logic]
+eq_sind [in Corelib.Init.Logic]
+eq_rec [in Corelib.Init.Logic]
+eq_ind [in Corelib.Init.Logic]
+eq_rect [in Corelib.Init.Logic]
+error [in Corelib.Init.Specif]
+esym [in Corelib.ssr.ssrfun]
+etrans [in Corelib.ssr.ssrfun]
+even [in Corelib.Init.Nat]
+Exc [in Corelib.Init.Specif]
+except [in Corelib.Init.Specif]
+expose_mem_pred [in Corelib.ssr.ssrbool]
+expose_simpl_pred [in Corelib.ssr.ssrbool]
+external_view_sind [in Corelib.ssr.ssreflect]
+external_view_rec [in Corelib.ssr.ssreflect]
+external_view_ind [in Corelib.ssr.ssreflect]
+external_view_rect [in Corelib.ssr.ssreflect]
+ex_of_sigT [in Corelib.Init.Specif]
+ex_of_sig [in Corelib.Init.Specif]
+ex_proj3_eq [in Corelib.Init.Logic]
+ex_proj2_of_ex2_eq [in Corelib.Init.Logic]
+ex_proj1_of_ex2_eq [in Corelib.Init.Logic]
+ex_of_ex2_eq [in Corelib.Init.Logic]
+ex_proj2_eq [in Corelib.Init.Logic]
+ex_proj1_eq [in Corelib.Init.Logic]
+ex_rec [in Corelib.Init.Logic]
+ex_rect [in Corelib.Init.Logic]
+ex_eta [in Corelib.Init.Logic]
+ex_proj3 [in Corelib.Init.Logic]
+ex_of_ex2 [in Corelib.Init.Logic]
+ex_proj2 [in Corelib.Init.Logic]
+ex_proj1 [in Corelib.Init.Logic]
+ex_sind [in Corelib.Init.Logic]
+ex_ind [in Corelib.Init.Logic]
+ex2_of_sigT2 [in Corelib.Init.Specif]
+ex2_of_sig2 [in Corelib.Init.Specif]
+ex2_rec [in Corelib.Init.Logic]
+ex2_rect [in Corelib.Init.Logic]
+ex2_eta [in Corelib.Init.Logic]
+ex2_sind [in Corelib.Init.Logic]
+ex2_ind [in Corelib.Init.Logic]
+

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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_F.html b/master/corelib/index_definition_F.html new file mode 100644 index 0000000000..f983adeb16 --- /dev/null +++ b/master/corelib/index_definition_F.html @@ -0,0 +1,1081 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

F (definition)

+false_predicate [in Corelib.Classes.RelationClasses]
+False_sind [in Corelib.Init.Logic]
+False_rec [in Corelib.Init.Logic]
+False_ind [in Corelib.Init.Logic]
+False_rect [in Corelib.Init.Logic]
+fexp [in Corelib.Floats.SpecFloat]
+firstn [in Corelib.Lists.ListDef]
+Fix [in Corelib.Init.Wf]
+Fix_sub [in Corelib.Program.Wf]
+Fix_F_sub [in Corelib.Program.Wf]
+fix_proto [in Corelib.Program.Tactics]
+Fix_F_2 [in Corelib.Init.Wf]
+Fix_F [in Corelib.Init.Wf]
+flatten_cmp_opt [in Corelib.Floats.FloatAxioms]
+flip [in Corelib.Program.Basics]
+flip [in Corelib.Classes.CRelationClasses]
+flip_Transitive [in Corelib.Classes.RelationClasses]
+flip_Asymmetric [in Corelib.Classes.RelationClasses]
+flip_Symmetric [in Corelib.Classes.RelationClasses]
+flip_Irreflexive [in Corelib.Classes.RelationClasses]
+flip_proper [in Corelib.Classes.CMorphisms]
+flip_proper [in Corelib.Classes.Morphisms]
+flip_Transitive [in Corelib.Classes.CRelationClasses]
+flip_Asymmetric [in Corelib.Classes.CRelationClasses]
+flip_Symmetric [in Corelib.Classes.CRelationClasses]
+flip_Irreflexive [in Corelib.Classes.CRelationClasses]
+forall_relation [in Corelib.Classes.CMorphisms]
+forall_def [in Corelib.Classes.CMorphisms]
+forall_relation [in Corelib.Classes.Morphisms]
+forall_def [in Corelib.Classes.Morphisms]
+Forall_sind [in Corelib.Lists.ListDef]
+Forall_ind [in Corelib.Lists.ListDef]
+fst [in Corelib.Init.Datatypes]
+fun_of_simpl [in Corelib.ssr.ssrfun]
+f_equal2_mult [in Corelib.Init.Peano]
+f_equal2_nat [in Corelib.Init.Peano]
+f_equal2_plus [in Corelib.Init.Peano]
+f_equal_pred [in Corelib.Init.Peano]
+f_equal_nat [in Corelib.Init.Peano]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_G.html b/master/corelib/index_definition_G.html new file mode 100644 index 0000000000..532085355d --- /dev/null +++ b/master/corelib/index_definition_G.html @@ -0,0 +1,566 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

G (definition)

+gcd [in Corelib.Init.Nat]
+ge [in Corelib.Init.Peano]
+gen_st [in Corelib.Setoids.Setoid]
+get_digit [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+get_sign [in Corelib.Floats.PrimFloat]
+gt [in Corelib.Init.Peano]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_H.html b/master/corelib/index_definition_H.html new file mode 100644 index 0000000000..fe022f0d3d --- /dev/null +++ b/master/corelib/index_definition_H.html @@ -0,0 +1,564 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

H (definition)

+has_quality [in Corelib.ssr.ssrbool]
+hexadecimal_eq_dec [in Corelib.Init.Hexadecimal]
+homomorphism_2 [in Corelib.ssr.ssrfun]
+homomorphism_1 [in Corelib.ssr.ssrfun]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_I.html b/master/corelib/index_definition_I.html new file mode 100644 index 0000000000..ca749f14e8 --- /dev/null +++ b/master/corelib/index_definition_I.html @@ -0,0 +1,1082 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

I (definition)

+id [in Corelib.Init.Datatypes]
+ID [in Corelib.Init.Datatypes]
+idempotent [in Corelib.ssr.ssrfun]
+idfun [in Corelib.ssr.ssrfun]
+idProp [in Corelib.Init.Datatypes]
+IDProp [in Corelib.Init.Datatypes]
+id_int [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+iff [in Corelib.Init.Logic]
+iffT [in Corelib.Classes.CRelationClasses]
+if_expr [in Corelib.ssr.ssrbool]
+impl [in Corelib.Program.Basics]
+implb [in Corelib.Init.Datatypes]
+inclusion [in Corelib.Relations.Relation_Definitions]
+inE [in Corelib.ssr.ssrbool]
+infinity [in Corelib.Floats.PrimFloat]
+inhabited_sind [in Corelib.Init.Logic]
+inhabited_ind [in Corelib.Init.Logic]
+injective [in Corelib.ssr.ssrfun]
+inPhantom [in Corelib.ssr.ssrbool]
+interchange [in Corelib.ssr.ssrfun]
+int_of_int [in Corelib.Init.Decimal]
+int_of_int [in Corelib.Init.Number]
+involutive [in Corelib.ssr.ssrfun]
+in_mem [in Corelib.ssr.ssrbool]
+irreflexive [in Corelib.ssr.ssrbool]
+isSome [in Corelib.ssr.ssrbool]
+IsSucc [in Corelib.Init.Peano]
+isT [in Corelib.ssr.ssrbool]
+is_true [in Corelib.Init.Datatypes]
+is_inleft [in Corelib.ssr.ssrbool]
+is_left [in Corelib.ssr.ssrbool]
+is_inl [in Corelib.ssr.ssrbool]
+is_even [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+is_zero [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+is_finite [in Corelib.Floats.PrimFloat]
+is_infinity [in Corelib.Floats.PrimFloat]
+is_zero [in Corelib.Floats.PrimFloat]
+is_nan [in Corelib.Floats.PrimFloat]
+iter [in Corelib.Init.Nat]
+iter_pos [in Corelib.Floats.SpecFloat]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_J.html b/master/corelib/index_definition_J.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_definition_J.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_K.html b/master/corelib/index_definition_K.html new file mode 100644 index 0000000000..ebef5aefce --- /dev/null +++ b/master/corelib/index_definition_K.html @@ -0,0 +1,565 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

K (definition)

+KeyedPred [in Corelib.ssr.ssrbool]
+KeyedQualifier [in Corelib.ssr.ssrbool]
+keyed_qualifier_keyed [in Corelib.ssr.ssrbool]
+keyed_mem_simpl [in Corelib.ssr.ssrbool]
+keyed_mem [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_L.html b/master/corelib/index_definition_L.html new file mode 100644 index 0000000000..9a457c8d00 --- /dev/null +++ b/master/corelib/index_definition_L.html @@ -0,0 +1,1081 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

L (definition)

+land [in Corelib.Init.Nat]
+ldiff [in Corelib.Init.Nat]
+leb [in Corelib.Init.Nat]
+left_transitive [in Corelib.ssr.ssrbool]
+left_loop [in Corelib.ssr.ssrfun]
+left_commutative [in Corelib.ssr.ssrfun]
+left_id [in Corelib.ssr.ssrfun]
+left_distributive [in Corelib.ssr.ssrfun]
+left_zero [in Corelib.ssr.ssrfun]
+left_injective [in Corelib.ssr.ssrfun]
+left_inverse [in Corelib.ssr.ssrfun]
+length [in Corelib.Init.Datatypes]
+le_sind [in Corelib.Init.Peano]
+le_ind [in Corelib.Init.Peano]
+list_sind [in Corelib.Init.Datatypes]
+list_rec [in Corelib.Init.Datatypes]
+list_ind [in Corelib.Init.Datatypes]
+list_rect [in Corelib.Init.Datatypes]
+list_compare [in Corelib.Lists.ListDef]
+Little.double [in Corelib.Init.Hexadecimal]
+Little.double [in Corelib.Init.Decimal]
+Little.succ [in Corelib.Init.Hexadecimal]
+Little.succ [in Corelib.Init.Decimal]
+Little.succ_double [in Corelib.Init.Hexadecimal]
+Little.succ_double [in Corelib.Init.Decimal]
+location_sind [in Corelib.Floats.SpecFloat]
+location_rec [in Corelib.Floats.SpecFloat]
+location_ind [in Corelib.Floats.SpecFloat]
+location_rect [in Corelib.Floats.SpecFloat]
+locked [in Corelib.ssr.ssreflect]
+locked_with_unlockable [in Corelib.ssr.ssreflect]
+locked_with [in Corelib.ssr.ssreflect]
+loc_of_shr_record [in Corelib.Floats.SpecFloat]
+log2 [in Corelib.Init.Nat]
+log2_iter [in Corelib.Init.Nat]
+lor [in Corelib.Init.Nat]
+lt [in Corelib.Init.Peano]
+ltb [in Corelib.Init.Nat]
+lxor [in Corelib.Init.Nat]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_M.html b/master/corelib/index_definition_M.html new file mode 100644 index 0000000000..592d0b5b84 --- /dev/null +++ b/master/corelib/index_definition_M.html @@ -0,0 +1,575 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

M (definition)

+map [in Corelib.Lists.ListDef]
+max [in Corelib.Init.Nat]
+max_int [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+mem [in Corelib.ssr.ssrbool]
+memE [in Corelib.ssr.ssrbool]
+memPredType [in Corelib.ssr.ssrbool]
+min [in Corelib.Init.Nat]
+min_int [in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+modulo [in Corelib.Init.Nat]
+monomorphism_2 [in Corelib.ssr.ssrfun]
+monomorphism_1 [in Corelib.ssr.ssrfun]
+morphism_2 [in Corelib.ssr.ssrfun]
+morphism_1 [in Corelib.ssr.ssrfun]
+MR [in Corelib.Program.Wf]
+mul [in Corelib.Init.Nat]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_N.html b/master/corelib/index_definition_N.html new file mode 100644 index 0000000000..f4758bbee4 --- /dev/null +++ b/master/corelib/index_definition_N.html @@ -0,0 +1,1090 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

N (definition)

+nan [in Corelib.Floats.PrimFloat]
+nary_congruence_statement [in Corelib.ssr.ssreflect]
+nat_sind [in Corelib.Init.Datatypes]
+nat_rec [in Corelib.Init.Datatypes]
+nat_ind [in Corelib.Init.Datatypes]
+nat_rect [in Corelib.Init.Datatypes]
+nb_digits [in Corelib.Init.Hexadecimal]
+nb_digits [in Corelib.Init.Decimal]
+negb [in Corelib.Init.Datatypes]
+neg_zero [in Corelib.Floats.PrimFloat]
+neg_infinity [in Corelib.Floats.PrimFloat]
+nesym [in Corelib.ssr.ssrfun]
+new_location [in Corelib.Floats.SpecFloat]
+new_location_odd [in Corelib.Floats.SpecFloat]
+new_location_even [in Corelib.Floats.SpecFloat]
+NonPropType.call [in Corelib.ssr.ssreflect]
+NonPropType.check [in Corelib.ssr.ssreflect]
+NonPropType.maybeProp [in Corelib.ssr.ssreflect]
+NonPropType.test_negative [in Corelib.ssr.ssreflect]
+NonPropType.test_Prop [in Corelib.ssr.ssreflect]
+norm [in Corelib.Init.Hexadecimal]
+norm [in Corelib.Init.Decimal]
+not [in Corelib.Init.Logic]
+notF [in Corelib.ssr.ssrbool]
+notT [in Corelib.Init.Logic]
+nth [in Corelib.Lists.ListDef]
+number_eq_dec [in Corelib.Init.Number]
+nzhead [in Corelib.Init.Hexadecimal]
+nzhead [in Corelib.Init.Decimal]
+nztail [in Corelib.Init.Hexadecimal]
+nztail [in Corelib.Init.Decimal]
+nztail_int [in Corelib.Init.Hexadecimal]
+nztail_int [in Corelib.Init.Decimal]
+N_sind [in Corelib.Numbers.BinNums]
+N_rec [in Corelib.Numbers.BinNums]
+N_ind [in Corelib.Numbers.BinNums]
+N_rect [in Corelib.Numbers.BinNums]
+N.compare [in Corelib.BinNums.NatDef]
+N.double [in Corelib.BinNums.NatDef]
+N.land [in Corelib.BinNums.NatDef]
+N.ldiff [in Corelib.BinNums.NatDef]
+N.leb [in Corelib.BinNums.NatDef]
+N.lor [in Corelib.BinNums.NatDef]
+N.lxor [in Corelib.BinNums.NatDef]
+N.pos_div_eucl [in Corelib.BinNums.NatDef]
+N.sub [in Corelib.BinNums.NatDef]
+N.succ_pos [in Corelib.BinNums.NatDef]
+N.succ_double [in Corelib.BinNums.NatDef]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_O.html b/master/corelib/index_definition_O.html new file mode 100644 index 0000000000..5940462909 --- /dev/null +++ b/master/corelib/index_definition_O.html @@ -0,0 +1,1081 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

O (definition)

+ocancel [in Corelib.ssr.ssrfun]
+odd [in Corelib.Init.Nat]
+of_bits [in Corelib.Init.Byte]
+of_num_int [in Corelib.Init.Nat]
+of_hex_int [in Corelib.Init.Nat]
+of_int [in Corelib.Init.Nat]
+of_num_uint [in Corelib.Init.Nat]
+of_hex_uint [in Corelib.Init.Nat]
+of_hex_uint_acc [in Corelib.Init.Nat]
+of_uint [in Corelib.Init.Nat]
+of_uint_acc [in Corelib.Init.Nat]
+of_void [in Corelib.ssr.ssrfun]
+of_Z [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+of_pos [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+of_pos_rec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+of_list [in Corelib.Strings.PrimStringAxioms]
+one [in Corelib.Init.Nat]
+one [in Corelib.Floats.PrimFloat]
+onPhantom [in Corelib.ssr.ssrbool]
+opp [in Corelib.Init.Hexadecimal]
+opp [in Corelib.Init.Decimal]
+option_map [in Corelib.Init.Datatypes]
+option_sind [in Corelib.Init.Datatypes]
+option_rec [in Corelib.Init.Datatypes]
+option_ind [in Corelib.Init.Datatypes]
+option_rect [in Corelib.Init.Datatypes]
+Option.apply [in Corelib.ssr.ssrfun]
+Option.bind [in Corelib.ssr.ssrfun]
+Option.default [in Corelib.ssr.ssrfun]
+Option.lift [in Corelib.ssr.ssrfun]
+Option.map [in Corelib.ssr.ssrfun]
+orb [in Corelib.Init.Datatypes]
+or_sind [in Corelib.Init.Logic]
+or_ind [in Corelib.Init.Logic]
+or3_sind [in Corelib.ssr.ssrbool]
+or3_ind [in Corelib.ssr.ssrbool]
+or4_sind [in Corelib.ssr.ssrbool]
+or4_ind [in Corelib.ssr.ssrbool]
+over [in Corelib.ssr.ssreflect]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_P.html b/master/corelib/index_definition_P.html new file mode 100644 index 0000000000..fa13734d46 --- /dev/null +++ b/master/corelib/index_definition_P.html @@ -0,0 +1,1154 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

P (definition)

+pair_of_and [in Corelib.ssr.ssrfun]
+parser [in Corelib.Floats.PrimFloat]
+parser [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+pcancel [in Corelib.ssr.ssrfun]
+pcomp [in Corelib.ssr.ssrfun]
+pequiv [in Corelib.Classes.Equivalence]
+phant_id [in Corelib.ssr.ssrfun]
+pointwise_lifting [in Corelib.Classes.RelationClasses]
+pointwise_extension [in Corelib.Classes.RelationClasses]
+pointwise_relation [in Corelib.Classes.CMorphisms]
+pointwise_relation [in Corelib.Classes.Morphisms]
+positive_sind [in Corelib.Numbers.BinNums]
+positive_rec [in Corelib.Numbers.BinNums]
+positive_ind [in Corelib.Numbers.BinNums]
+positive_rect [in Corelib.Numbers.BinNums]
+Pos.add [in Corelib.BinNums.PosDef]
+Pos.add_carry [in Corelib.BinNums.PosDef]
+Pos.compare [in Corelib.BinNums.PosDef]
+Pos.compare_cont [in Corelib.BinNums.PosDef]
+Pos.div2 [in Corelib.BinNums.PosDef]
+Pos.div2_up [in Corelib.BinNums.PosDef]
+Pos.double_pred_mask [in Corelib.BinNums.PosDef]
+Pos.double_mask [in Corelib.BinNums.PosDef]
+Pos.eqb [in Corelib.BinNums.PosDef]
+Pos.iter [in Corelib.BinNums.PosDef]
+Pos.iter_op [in Corelib.BinNums.PosDef]
+Pos.land [in Corelib.BinNums.PosDef]
+Pos.ldiff [in Corelib.BinNums.PosDef]
+Pos.leb [in Corelib.BinNums.PosDef]
+Pos.lor [in Corelib.BinNums.PosDef]
+Pos.lxor [in Corelib.BinNums.PosDef]
+Pos.mask_sind [in Corelib.BinNums.PosDef]
+Pos.mask_rec [in Corelib.BinNums.PosDef]
+Pos.mask_ind [in Corelib.BinNums.PosDef]
+Pos.mask_rect [in Corelib.BinNums.PosDef]
+Pos.mul [in Corelib.BinNums.PosDef]
+Pos.Ndouble [in Corelib.BinNums.PosDef]
+Pos.Nsucc_double [in Corelib.BinNums.PosDef]
+Pos.of_succ_nat [in Corelib.BinNums.PosDef]
+Pos.pred_N [in Corelib.BinNums.PosDef]
+Pos.pred_double [in Corelib.BinNums.PosDef]
+Pos.sqrt [in Corelib.BinNums.PosDef]
+Pos.sqrtrem [in Corelib.BinNums.PosDef]
+Pos.sqrtrem_step [in Corelib.BinNums.PosDef]
+Pos.sub [in Corelib.BinNums.PosDef]
+Pos.sub_mask_carry [in Corelib.BinNums.PosDef]
+Pos.sub_mask [in Corelib.BinNums.PosDef]
+Pos.succ [in Corelib.BinNums.PosDef]
+Pos.succ_double_mask [in Corelib.BinNums.PosDef]
+Pos.to_nat [in Corelib.BinNums.PosDef]
+pow [in Corelib.Init.Nat]
+prec [in Corelib.Floats.FloatOps]
+pred [in Corelib.Init.Nat]
+pred [in Corelib.ssr.ssrbool]
+predArgType [in Corelib.ssr.ssrbool]
+predC [in Corelib.ssr.ssrbool]
+predD [in Corelib.ssr.ssrbool]
+predI [in Corelib.ssr.ssrbool]
+predicate_union [in Corelib.Classes.RelationClasses]
+predicate_intersection [in Corelib.Classes.RelationClasses]
+predicate_implication [in Corelib.Classes.RelationClasses]
+predicate_equivalence [in Corelib.Classes.RelationClasses]
+predicate_exists [in Corelib.Classes.RelationClasses]
+predicate_all [in Corelib.Classes.RelationClasses]
+PredOfSimpl.coerce [in Corelib.ssr.ssrbool]
+predPredType [in Corelib.ssr.ssrbool]
+predT [in Corelib.ssr.ssrbool]
+predU [in Corelib.ssr.ssrbool]
+pred_oapp [in Corelib.ssr.ssrbool]
+pred_of_mem [in Corelib.ssr.ssrbool]
+pred_of_argType [in Corelib.ssr.ssrbool]
+pred0 [in Corelib.ssr.ssrbool]
+preim [in Corelib.ssr.ssrbool]
+pre_symmetric [in Corelib.ssr.ssrbool]
+Prim2SF [in Corelib.Floats.FloatOps]
+printer [in Corelib.Floats.PrimFloat]
+printer [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+prod_sind [in Corelib.Init.Datatypes]
+prod_rec [in Corelib.Init.Datatypes]
+prod_ind [in Corelib.Init.Datatypes]
+prod_rect [in Corelib.Init.Datatypes]
+prod_of_sigT [in Corelib.Init.Specif]
+projT1 [in Corelib.Init.Specif]
+projT1_of_sigT2_eq [in Corelib.Init.Specif]
+projT1_eq [in Corelib.Init.Specif]
+projT2 [in Corelib.Init.Specif]
+projT2_of_sigT2_eq [in Corelib.Init.Specif]
+projT2_eq [in Corelib.Init.Specif]
+projT3 [in Corelib.Init.Specif]
+projT3_eq [in Corelib.Init.Specif]
+proj1_sig_of_sig2_eq [in Corelib.Init.Specif]
+proj1_sig_eq [in Corelib.Init.Specif]
+proj1_sig [in Corelib.Init.Specif]
+proj2_sig_of_sig2_eq [in Corelib.Init.Specif]
+proj2_sig_eq [in Corelib.Init.Specif]
+proj2_sig [in Corelib.Init.Specif]
+proj3_sig_eq [in Corelib.Init.Specif]
+proj3_sig [in Corelib.Init.Specif]
+proper_flip_proper [in Corelib.Classes.CMorphisms]
+proper_flip_proper [in Corelib.Classes.Morphisms]
+prop_on2 [in Corelib.ssr.ssrbool]
+prop_on1 [in Corelib.ssr.ssrbool]
+prop_in3 [in Corelib.ssr.ssrbool]
+prop_in21 [in Corelib.ssr.ssrbool]
+prop_in12 [in Corelib.ssr.ssrbool]
+prop_in111 [in Corelib.ssr.ssrbool]
+prop_in2 [in Corelib.ssr.ssrbool]
+prop_in11 [in Corelib.ssr.ssrbool]
+prop_in1 [in Corelib.ssr.ssrbool]
+prop_for [in Corelib.ssr.ssrbool]
+protect_term [in Corelib.ssr.ssreflect]
+PStringNotations.id_string [in Corelib.Strings.PrimString]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_Q.html b/master/corelib/index_definition_Q.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_definition_Q.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_R.html b/master/corelib/index_definition_R.html new file mode 100644 index 0000000000..c70cb40392 --- /dev/null +++ b/master/corelib/index_definition_R.html @@ -0,0 +1,1084 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

R (definition)

+reflect_sind [in Corelib.Init.Datatypes]
+reflect_rec [in Corelib.Init.Datatypes]
+reflect_ind [in Corelib.Init.Datatypes]
+reflect_rect [in Corelib.Init.Datatypes]
+reflexive [in Corelib.ssr.ssrbool]
+reflexive [in Corelib.Relations.Relation_Definitions]
+rel [in Corelib.ssr.ssrbool]
+relation [in Corelib.Relations.Relation_Definitions]
+relation_disjunction [in Corelib.Classes.RelationClasses]
+relation_conjunction [in Corelib.Classes.RelationClasses]
+relation_equivalence [in Corelib.Classes.RelationClasses]
+relation_disjunction [in Corelib.Classes.CRelationClasses]
+relation_conjunction [in Corelib.Classes.CRelationClasses]
+relation_equivalence [in Corelib.Classes.CRelationClasses]
+relpre [in Corelib.ssr.ssrbool]
+relU [in Corelib.ssr.ssrbool]
+rel_of_simpl [in Corelib.ssr.ssrbool]
+repeat [in Corelib.Lists.ListDef]
+respectful [in Corelib.Classes.CMorphisms]
+respectful [in Corelib.Classes.Morphisms]
+respectful_hetero [in Corelib.Classes.CMorphisms]
+respectful_hetero [in Corelib.Classes.Morphisms]
+respecting [in Corelib.Classes.Equivalence]
+returnType [in Corelib.ssr.ssreflect]
+rev [in Corelib.Init.Hexadecimal]
+rev [in Corelib.Init.Decimal]
+revapp [in Corelib.Init.Hexadecimal]
+revapp [in Corelib.Init.Decimal]
+ReverseCoercionSource [in Corelib.Init.Prelude]
+ReverseCoercionTarget [in Corelib.Init.Prelude]
+reverse_coercion [in Corelib.Init.Prelude]
+rev_left_loop [in Corelib.ssr.ssrfun]
+rev_right_loop [in Corelib.ssr.ssrfun]
+right_transitive [in Corelib.ssr.ssrbool]
+right_distributive [in Corelib.ssr.ssrfun]
+right_zero [in Corelib.ssr.ssrfun]
+right_loop [in Corelib.ssr.ssrfun]
+right_commutative [in Corelib.ssr.ssrfun]
+right_id [in Corelib.ssr.ssrfun]
+right_injective [in Corelib.ssr.ssrfun]
+right_inverse [in Corelib.ssr.ssrfun]
+round_nearest_even [in Corelib.Floats.SpecFloat]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_S.html b/master/corelib/index_definition_S.html new file mode 100644 index 0000000000..24116afe92 --- /dev/null +++ b/master/corelib/index_definition_S.html @@ -0,0 +1,1164 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

S (definition)

+same_relation [in Corelib.Relations.Relation_Definitions]
+self_inverse [in Corelib.ssr.ssrfun]
+seq [in Corelib.Lists.ListDef]
+Seq_trans [in Corelib.Setoids.Setoid]
+Seq_sym [in Corelib.Setoids.Setoid]
+Seq_refl [in Corelib.Setoids.Setoid]
+Setoid_Theory [in Corelib.Setoids.Setoid]
+set_digit [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+SFabs [in Corelib.Floats.SpecFloat]
+SFadd [in Corelib.Floats.SpecFloat]
+SFclassify [in Corelib.Floats.SpecFloat]
+SFcompare [in Corelib.Floats.SpecFloat]
+SFdiv [in Corelib.Floats.SpecFloat]
+SFdiv_core_binary [in Corelib.Floats.SpecFloat]
+SFeqb [in Corelib.Floats.SpecFloat]
+SFfrexp [in Corelib.Floats.SpecFloat]
+SFldexp [in Corelib.Floats.SpecFloat]
+SFleb [in Corelib.Floats.SpecFloat]
+SFltb [in Corelib.Floats.SpecFloat]
+SFmax_float [in Corelib.Floats.SpecFloat]
+SFmul [in Corelib.Floats.SpecFloat]
+SFnormfr_mantissa [in Corelib.Floats.SpecFloat]
+SFone [in Corelib.Floats.SpecFloat]
+SFopp [in Corelib.Floats.SpecFloat]
+SFpred [in Corelib.Floats.SpecFloat]
+SFpred_pos [in Corelib.Floats.SpecFloat]
+SFsqrt [in Corelib.Floats.SpecFloat]
+SFsqrt_core_binary [in Corelib.Floats.SpecFloat]
+SFsub [in Corelib.Floats.SpecFloat]
+SFsucc [in Corelib.Floats.SpecFloat]
+SFulp [in Corelib.Floats.SpecFloat]
+SF2Prim [in Corelib.Floats.FloatOps]
+SF64add [in Corelib.Floats.FloatAxioms]
+SF64classify [in Corelib.Floats.FloatAxioms]
+SF64div [in Corelib.Floats.FloatAxioms]
+SF64mul [in Corelib.Floats.FloatAxioms]
+SF64pred [in Corelib.Floats.FloatAxioms]
+SF64sqrt [in Corelib.Floats.FloatAxioms]
+SF64sub [in Corelib.Floats.FloatAxioms]
+SF64succ [in Corelib.Floats.FloatAxioms]
+shift [in Corelib.Floats.FloatOps]
+shiftl [in Corelib.Init.Nat]
+shiftr [in Corelib.Init.Nat]
+shl_align [in Corelib.Floats.SpecFloat]
+shr [in Corelib.Floats.SpecFloat]
+shr_fexp [in Corelib.Floats.SpecFloat]
+shr_record_of_loc [in Corelib.Floats.SpecFloat]
+shr_1 [in Corelib.Floats.SpecFloat]
+signed_int_eq_dec [in Corelib.Init.Hexadecimal]
+signed_int_eq_dec [in Corelib.Init.Decimal]
+signed_int_eq_dec [in Corelib.Init.Number]
+sigT_of_sigT2_eq [in Corelib.Init.Specif]
+sigT_of_prod [in Corelib.Init.Specif]
+sigT_eta [in Corelib.Init.Specif]
+sigT_of_sig [in Corelib.Init.Specif]
+sigT_of_sigT2 [in Corelib.Init.Specif]
+sigT_sind [in Corelib.Init.Specif]
+sigT_rec [in Corelib.Init.Specif]
+sigT_ind [in Corelib.Init.Specif]
+sigT_rect [in Corelib.Init.Specif]
+sigT2_eta [in Corelib.Init.Specif]
+sigT2_of_sig2 [in Corelib.Init.Specif]
+sigT2_sind [in Corelib.Init.Specif]
+sigT2_rec [in Corelib.Init.Specif]
+sigT2_ind [in Corelib.Init.Specif]
+sigT2_rect [in Corelib.Init.Specif]
+sig_of_sig2_eq [in Corelib.Init.Specif]
+sig_eta [in Corelib.Init.Specif]
+sig_of_sigT [in Corelib.Init.Specif]
+sig_of_sig2 [in Corelib.Init.Specif]
+sig_sind [in Corelib.Init.Specif]
+sig_rec [in Corelib.Init.Specif]
+sig_ind [in Corelib.Init.Specif]
+sig_rect [in Corelib.Init.Specif]
+sig_of_sig2 [in Corelib.ssr.ssrfun]
+sig2_eta [in Corelib.Init.Specif]
+sig2_of_sigT2 [in Corelib.Init.Specif]
+sig2_sind [in Corelib.Init.Specif]
+sig2_rec [in Corelib.Init.Specif]
+sig2_ind [in Corelib.Init.Specif]
+sig2_rect [in Corelib.Init.Specif]
+SimplFunDelta [in Corelib.ssr.ssrfun]
+SimplPred [in Corelib.ssr.ssrbool]
+simplPredType [in Corelib.ssr.ssrbool]
+SimplRel [in Corelib.ssr.ssrbool]
+simpl_of_mem [in Corelib.ssr.ssrbool]
+simpl_rel [in Corelib.ssr.ssrbool]
+simpl_pred [in Corelib.ssr.ssrbool]
+size [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+skipn [in Corelib.Lists.ListDef]
+snd [in Corelib.Init.Datatypes]
+sqrt [in Corelib.Init.Nat]
+sqrt_iter [in Corelib.Init.Nat]
+square [in Corelib.Init.Nat]
+ssr_converse [in Corelib.ssr.ssreflect]
+sub [in Corelib.Init.Nat]
+subcarryc_def [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+subc_def [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+subpred [in Corelib.ssr.ssrbool]
+subrel [in Corelib.ssr.ssrbool]
+subrelation [in Corelib.Init.Logic]
+sub_mem [in Corelib.ssr.ssrbool]
+succ [in Corelib.Init.Nat]
+sumbool_sind [in Corelib.Init.Specif]
+sumbool_rec [in Corelib.Init.Specif]
+sumbool_ind [in Corelib.Init.Specif]
+sumbool_rect [in Corelib.Init.Specif]
+sumbool_not [in Corelib.Init.Sumbool]
+sumbool_or [in Corelib.Init.Sumbool]
+sumbool_and [in Corelib.Init.Sumbool]
+sumbool_of_bool [in Corelib.Init.Sumbool]
+sumor_sind [in Corelib.Init.Specif]
+sumor_rec [in Corelib.Init.Specif]
+sumor_ind [in Corelib.Init.Specif]
+sumor_rect [in Corelib.Init.Specif]
+sum_sind [in Corelib.Init.Datatypes]
+sum_rec [in Corelib.Init.Datatypes]
+sum_ind [in Corelib.Init.Datatypes]
+sum_rect [in Corelib.Init.Datatypes]
+symmetric [in Corelib.ssr.ssrbool]
+symmetric [in Corelib.Relations.Relation_Definitions]
+s2val [in Corelib.ssr.ssrfun]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_T.html b/master/corelib/index_definition_T.html new file mode 100644 index 0000000000..7facb9577a --- /dev/null +++ b/master/corelib/index_definition_T.html @@ -0,0 +1,1087 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

T (definition)

+t [in Corelib.Init.Nat]
+tag [in Corelib.ssr.ssrfun]
+Tagged [in Corelib.ssr.ssrfun]
+tagged [in Corelib.ssr.ssrfun]
+Tagged2 [in Corelib.ssr.ssrfun]
+tagged2 [in Corelib.ssr.ssrfun]
+tagged2' [in Corelib.ssr.ssrfun]
+tag_of_sig [in Corelib.ssr.ssrfun]
+tag_of_tag2 [in Corelib.ssr.ssrfun]
+tag2 [in Corelib.ssr.ssrfun]
+tail_mul [in Corelib.Init.Nat]
+tail_addmul [in Corelib.Init.Nat]
+tail_add [in Corelib.Init.Nat]
+ternary_operation [in Corelib.Classes.RelationClasses]
+testbit [in Corelib.Init.Nat]
+TheCanonical.get [in Corelib.ssr.ssreflect]
+TheCanonical.get_by [in Corelib.ssr.ssreflect]
+Tlist_sind [in Corelib.Classes.RelationClasses]
+Tlist_rec [in Corelib.Classes.RelationClasses]
+Tlist_ind [in Corelib.Classes.RelationClasses]
+Tlist_rect [in Corelib.Classes.RelationClasses]
+total [in Corelib.ssr.ssrbool]
+to_bits [in Corelib.Init.Byte]
+to_num_int [in Corelib.Init.Nat]
+to_hex_int [in Corelib.Init.Nat]
+to_int [in Corelib.Init.Nat]
+to_num_hex_uint [in Corelib.Init.Nat]
+to_num_uint [in Corelib.Init.Nat]
+to_hex_uint [in Corelib.Init.Nat]
+to_little_hex_uint [in Corelib.Init.Nat]
+to_uint [in Corelib.Init.Nat]
+to_little_uint [in Corelib.Init.Nat]
+to_Z [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+to_Z_rec [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+to_list [in Corelib.Strings.PrimStringAxioms]
+to_Z [in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+transitive [in Corelib.ssr.ssrbool]
+transitive [in Corelib.Relations.Relation_Definitions]
+true_predicate [in Corelib.Classes.RelationClasses]
+True_sind [in Corelib.Init.Logic]
+True_rec [in Corelib.Init.Logic]
+True_ind [in Corelib.Init.Logic]
+True_rect [in Corelib.Init.Logic]
+two [in Corelib.Init.Nat]
+two [in Corelib.Floats.PrimFloat]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_U.html b/master/corelib/index_definition_U.html new file mode 100644 index 0000000000..28eda16a3b --- /dev/null +++ b/master/corelib/index_definition_U.html @@ -0,0 +1,589 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

U (definition)

+uint_eq_dec [in Corelib.Init.Hexadecimal]
+uint_sind [in Corelib.Init.Hexadecimal]
+uint_rec [in Corelib.Init.Hexadecimal]
+uint_ind [in Corelib.Init.Hexadecimal]
+uint_rect [in Corelib.Init.Hexadecimal]
+uint_of_uint [in Corelib.Init.Decimal]
+uint_eq_dec [in Corelib.Init.Decimal]
+uint_sind [in Corelib.Init.Decimal]
+uint_rec [in Corelib.Init.Decimal]
+uint_ind [in Corelib.Init.Decimal]
+uint_rect [in Corelib.Init.Decimal]
+uint_of_uint [in Corelib.Init.Number]
+uint_eq_dec [in Corelib.Init.Number]
+ulp [in Corelib.Floats.FloatOps]
+unary_predicate [in Corelib.Classes.RelationClasses]
+unary_operation [in Corelib.Classes.RelationClasses]
+uncurry [in Corelib.Init.Datatypes]
+UnderE [in Corelib.ssr.ssreflect]
+Under_rel.Over_rel [in Corelib.ssr.ssrunder]
+Under_rel.Under_rel [in Corelib.ssr.ssrunder]
+unique [in Corelib.Init.Logic]
+uniqueness [in Corelib.Init.Logic]
+unit_sind [in Corelib.Init.Datatypes]
+unit_rec [in Corelib.Init.Datatypes]
+unit_ind [in Corelib.Init.Datatypes]
+unit_rect [in Corelib.Init.Datatypes]
+unless [in Corelib.ssr.ssrbool]
+unorm [in Corelib.Init.Hexadecimal]
+unorm [in Corelib.Init.Decimal]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_V.html b/master/corelib/index_definition_V.html new file mode 100644 index 0000000000..9d1c384c18 --- /dev/null +++ b/master/corelib/index_definition_V.html @@ -0,0 +1,562 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

V (definition)

+valid_binary [in Corelib.Floats.SpecFloat]
+value [in Corelib.Init.Specif]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_W.html b/master/corelib/index_definition_W.html new file mode 100644 index 0000000000..eed7a50184 --- /dev/null +++ b/master/corelib/index_definition_W.html @@ -0,0 +1,563 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

W (definition)

+wB [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+well_founded [in Corelib.Init.Wf]
+wrap [in Corelib.ssr.ssrfun]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_X.html b/master/corelib/index_definition_X.html new file mode 100644 index 0000000000..55f8d741ba --- /dev/null +++ b/master/corelib/index_definition_X.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

X (definition)

+xorb [in Corelib.Init.Datatypes]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_Y.html b/master/corelib/index_definition_Y.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_definition_Y.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition_Z.html b/master/corelib/index_definition_Z.html new file mode 100644 index 0000000000..882eed64dc --- /dev/null +++ b/master/corelib/index_definition_Z.html @@ -0,0 +1,1090 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

Z (definition)

+Zdigits2 [in Corelib.Floats.SpecFloat]
+zero [in Corelib.Init.Nat]
+zero [in Corelib.Floats.PrimFloat]
+Z_sind [in Corelib.Numbers.BinNums]
+Z_rec [in Corelib.Numbers.BinNums]
+Z_ind [in Corelib.Numbers.BinNums]
+Z_rect [in Corelib.Numbers.BinNums]
+Z.add [in Corelib.BinNums.IntDef]
+Z.compare [in Corelib.BinNums.IntDef]
+Z.div [in Corelib.BinNums.IntDef]
+Z.div_eucl [in Corelib.BinNums.IntDef]
+Z.div2 [in Corelib.BinNums.IntDef]
+Z.double [in Corelib.BinNums.IntDef]
+Z.eqb [in Corelib.BinNums.IntDef]
+Z.even [in Corelib.BinNums.IntDef]
+Z.frexp [in Corelib.Floats.FloatOps]
+Z.ge [in Corelib.BinNums.IntDef]
+Z.gt [in Corelib.BinNums.IntDef]
+Z.land [in Corelib.BinNums.IntDef]
+Z.ldexp [in Corelib.Floats.FloatOps]
+Z.le [in Corelib.BinNums.IntDef]
+Z.leb [in Corelib.BinNums.IntDef]
+Z.lor [in Corelib.BinNums.IntDef]
+Z.lt [in Corelib.BinNums.IntDef]
+Z.ltb [in Corelib.BinNums.IntDef]
+Z.lxor [in Corelib.BinNums.IntDef]
+Z.max [in Corelib.BinNums.IntDef]
+Z.min [in Corelib.BinNums.IntDef]
+Z.modulo [in Corelib.BinNums.IntDef]
+Z.mul [in Corelib.BinNums.IntDef]
+Z.of_N [in Corelib.BinNums.IntDef]
+Z.of_nat [in Corelib.BinNums.IntDef]
+Z.opp [in Corelib.BinNums.IntDef]
+Z.pos_div_eucl [in Corelib.BinNums.IntDef]
+Z.pos_sub [in Corelib.BinNums.IntDef]
+Z.pow [in Corelib.BinNums.IntDef]
+Z.pow_pos [in Corelib.BinNums.IntDef]
+Z.pred_double [in Corelib.BinNums.IntDef]
+Z.quot [in Corelib.BinNums.IntDef]
+Z.quotrem [in Corelib.BinNums.IntDef]
+Z.rem [in Corelib.BinNums.IntDef]
+Z.shiftl [in Corelib.BinNums.IntDef]
+Z.shiftr [in Corelib.BinNums.IntDef]
+Z.sqrtrem [in Corelib.BinNums.IntDef]
+Z.sub [in Corelib.BinNums.IntDef]
+Z.succ_double [in Corelib.BinNums.IntDef]
+Z.to_pos [in Corelib.BinNums.IntDef]
+Z.to_nat [in Corelib.BinNums.IntDef]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_definition__.html b/master/corelib/index_definition__.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_definition__.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_*.html b/master/corelib/index_global_*.html new file mode 100644 index 0000000000..698596524e --- /dev/null +++ b/master/corelib/index_global_*.html @@ -0,0 +1,1280 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

other

+if _ as _ return _ then _ else _ (boolean_if_scope) [notation, in Corelib.ssr.ssreflect]
+if _ then _ else _ (boolean_if_scope) [notation, in Corelib.ssr.ssreflect]
+if _ return _ then _ else _ (boolean_if_scope) [notation, in Corelib.ssr.ssreflect]
+_ && _ (bool_scope) [notation, in Corelib.Init.Datatypes]
+_ || _ (bool_scope) [notation, in Corelib.Init.Datatypes]
+_ \is an _ (bool_scope) [notation, in Corelib.ssr.ssrbool]
+_ \is a _ (bool_scope) [notation, in Corelib.ssr.ssrbool]
+_ \is _ (bool_scope) [notation, in Corelib.ssr.ssrbool]
+_ \in _ (bool_scope) [notation, in Corelib.ssr.ssrbool]
+_ \isn't an _ (bool_scope) [notation, in Corelib.ssr.ssrbool]
+_ \isn't a _ (bool_scope) [notation, in Corelib.ssr.ssrbool]
+_ \isn't _ (bool_scope) [notation, in Corelib.ssr.ssrbool]
+_ \is an _ (bool_scope) [notation, in Corelib.ssr.ssrbool]
+_ \is an _ (bool_scope) [notation, in Corelib.ssr.ssrbool]
+_ \is a _ (bool_scope) [notation, in Corelib.ssr.ssrbool]
+_ \is a _ (bool_scope) [notation, in Corelib.ssr.ssrbool]
+_ \is _ (bool_scope) [notation, in Corelib.ssr.ssrbool]
+_ \is _ (bool_scope) [notation, in Corelib.ssr.ssrbool]
+_ \notin _ (bool_scope) [notation, in Corelib.ssr.ssrbool]
+_ \in _ (bool_scope) [notation, in Corelib.ssr.ssrbool]
+_ \in _ (bool_scope) [notation, in Corelib.ssr.ssrbool]
+[ ==> _ => _ ] (bool_scope) [notation, in Corelib.ssr.ssrbool]
+[ ==> _ , _ , .. , _ => _ ] (bool_scope) [notation, in Corelib.ssr.ssrbool]
+[ || _ , _ , .. , _ | _ ] (bool_scope) [notation, in Corelib.ssr.ssrbool]
+[ || _ | _ ] (bool_scope) [notation, in Corelib.ssr.ssrbool]
+[ && _ , _ , .. , _ & _ ] (bool_scope) [notation, in Corelib.ssr.ssrbool]
+[ && _ & _ ] (bool_scope) [notation, in Corelib.ssr.ssrbool]
+_ (+) _ (bool_scope) [notation, in Corelib.ssr.ssrbool]
+_ ==> _ (bool_scope) [notation, in Corelib.ssr.ssrbool]
+~~ _ (bool_scope) [notation, in Corelib.ssr.ssrbool]
+( _ , _ , .. , _ ) (core_scope) [notation, in Corelib.Init.Datatypes]
+_ =~= _ (equiv_scope) [notation, in Corelib.Classes.Equivalence]
+_ =/= _ (equiv_scope) [notation, in Corelib.Classes.Equivalence]
+_ === _ (equiv_scope) [notation, in Corelib.Classes.Equivalence]
+[ qualify an _ : _ | _ ] (form_scope) [notation, in Corelib.ssr.ssrbool]
+[ qualify an _ | _ ] (form_scope) [notation, in Corelib.ssr.ssrbool]
+[ qualify a _ : _ | _ ] (form_scope) [notation, in Corelib.ssr.ssrbool]
+[ qualify a _ | _ ] (form_scope) [notation, in Corelib.ssr.ssrbool]
+[ qualify _ : _ | _ ] (form_scope) [notation, in Corelib.ssr.ssrbool]
+[ qualify _ | _ ] (form_scope) [notation, in Corelib.ssr.ssrbool]
+[ predType of _ ] (form_scope) [notation, in Corelib.ssr.ssrbool]
+[ unlockable fun _ ] (form_scope) [notation, in Corelib.ssr.ssreflect]
+[ unlockable of _ ] (form_scope) [notation, in Corelib.ssr.ssreflect]
+=^~ _ (form_scope) [notation, in Corelib.ssr.ssreflect]
+[ the _ of _ ] (form_scope) [notation, in Corelib.ssr.ssreflect]
+[ the _ of _ by _ ] (form_scope) [notation, in Corelib.ssr.ssreflect]
+[ the _ of _ ] (form_scope) [notation, in Corelib.ssr.ssreflect]
+[ the _ of _ by _ ] (form_scope) [notation, in Corelib.ssr.ssreflect]
+[ rel _ _ in _ ] (function_scope) [notation, in Corelib.ssr.ssrbool]
+[ rel _ _ in _ | _ ] (function_scope) [notation, in Corelib.ssr.ssrbool]
+[ rel _ _ in _ & _ ] (function_scope) [notation, in Corelib.ssr.ssrbool]
+[ rel _ _ in _ & _ | _ ] (function_scope) [notation, in Corelib.ssr.ssrbool]
+[ pred _ in _ | _ & _ ] (function_scope) [notation, in Corelib.ssr.ssrbool]
+[ pred _ in _ | _ ] (function_scope) [notation, in Corelib.ssr.ssrbool]
+[ pred _ in _ ] (function_scope) [notation, in Corelib.ssr.ssrbool]
+[ preim _ of _ ] (function_scope) [notation, in Corelib.ssr.ssrbool]
+[ predC _ ] (function_scope) [notation, in Corelib.ssr.ssrbool]
+[ predD _ & _ ] (function_scope) [notation, in Corelib.ssr.ssrbool]
+[ predU _ & _ ] (function_scope) [notation, in Corelib.ssr.ssrbool]
+[ predI _ & _ ] (function_scope) [notation, in Corelib.ssr.ssrbool]
+[ mem _ ] (function_scope) [notation, in Corelib.ssr.ssrbool]
+[ in _ ] (function_scope) [notation, in Corelib.ssr.ssrbool]
+[ rel _ _ : _ | _ ] (function_scope) [notation, in Corelib.ssr.ssrbool]
+[ rel _ _ | _ ] (function_scope) [notation, in Corelib.ssr.ssrbool]
+[ pred _ : _ | _ & _ ] (function_scope) [notation, in Corelib.ssr.ssrbool]
+[ pred _ : _ | _ ] (function_scope) [notation, in Corelib.ssr.ssrbool]
+[ pred _ | _ & _ ] (function_scope) [notation, in Corelib.ssr.ssrbool]
+[ pred _ | _ ] (function_scope) [notation, in Corelib.ssr.ssrbool]
+[ pred : _ | _ ] (function_scope) [notation, in Corelib.ssr.ssrbool]
+@ sval (function_scope) [notation, in Corelib.ssr.ssrfun]
+@ id _ (function_scope) [notation, in Corelib.ssr.ssrfun]
+fun => _ (function_scope) [notation, in Corelib.ssr.ssrfun]
+[ eta _ ] (function_scope) [notation, in Corelib.ssr.ssrfun]
+_ \; _ (function_scope) [notation, in Corelib.ssr.ssrfun]
+_ \o _ (function_scope) [notation, in Corelib.ssr.ssrfun]
+[ fun ( _ : _ ) ( _ : _ ) => _ ] (function_scope) [notation, in Corelib.ssr.ssrfun]
+[ fun _ ( _ : _ ) => _ ] (function_scope) [notation, in Corelib.ssr.ssrfun]
+[ fun ( _ : _ ) _ => _ ] (function_scope) [notation, in Corelib.ssr.ssrfun]
+[ fun _ _ : _ => _ ] (function_scope) [notation, in Corelib.ssr.ssrfun]
+[ fun _ : _ => _ ] (function_scope) [notation, in Corelib.ssr.ssrfun]
+[ fun _ _ => _ ] (function_scope) [notation, in Corelib.ssr.ssrfun]
+[ fun _ => _ ] (function_scope) [notation, in Corelib.ssr.ssrfun]
+[ fun : _ => _ ] (function_scope) [notation, in Corelib.ssr.ssrfun]
+@^~ _ (function_scope) [notation, in Corelib.ssr.ssrfun]
+_ ^~ _ (function_scope) [notation, in Corelib.ssr.ssrfun]
+if _ as _ return _ then _ else _ (general_if_scope) [notation, in Corelib.ssr.ssreflect]
+if _ return _ then _ else _ (general_if_scope) [notation, in Corelib.ssr.ssreflect]
+if _ then _ else _ (general_if_scope) [notation, in Corelib.ssr.ssreflect]
+_ ++ _ (list_scope) [notation, in Corelib.Init.Datatypes]
+_ :: _ (list_scope) [notation, in Corelib.Init.Datatypes]
+_ mod _ (nat_scope) [notation, in Corelib.Init.Nat]
+_ / _ (nat_scope) [notation, in Corelib.Init.Nat]
+_ ^ _ (nat_scope) [notation, in Corelib.Init.Nat]
+_ ?= _ (nat_scope) [notation, in Corelib.Init.Nat]
+_ <? _ (nat_scope) [notation, in Corelib.Init.Nat]
+_ <=? _ (nat_scope) [notation, in Corelib.Init.Nat]
+_ =? _ (nat_scope) [notation, in Corelib.Init.Nat]
+_ - _ (nat_scope) [notation, in Corelib.Init.Nat]
+_ * _ (nat_scope) [notation, in Corelib.Init.Nat]
+_ + _ (nat_scope) [notation, in Corelib.Init.Nat]
+_ < _ <= _ (nat_scope) [notation, in Corelib.Init.Peano]
+_ < _ < _ (nat_scope) [notation, in Corelib.Init.Peano]
+_ <= _ < _ (nat_scope) [notation, in Corelib.Init.Peano]
+_ <= _ <= _ (nat_scope) [notation, in Corelib.Init.Peano]
+_ > _ (nat_scope) [notation, in Corelib.Init.Peano]
+_ >= _ (nat_scope) [notation, in Corelib.Init.Peano]
+_ < _ (nat_scope) [notation, in Corelib.Init.Peano]
+_ <= _ (nat_scope) [notation, in Corelib.Init.Peano]
+_ - _ (nat_scope) [notation, in Corelib.Init.Peano]
+_ * _ (nat_scope) [notation, in Corelib.Init.Peano]
+_ + _ (nat_scope) [notation, in Corelib.Init.Peano]
+_ .2 (pair_scope) [notation, in Corelib.ssr.ssrfun]
+_ .1 (pair_scope) [notation, in Corelib.ssr.ssrfun]
+3 (positive_scope) [notation, in Corelib.BinNums.PosDef]
+2 (positive_scope) [notation, in Corelib.BinNums.PosDef]
+1 (positive_scope) [notation, in Corelib.BinNums.PosDef]
+_ ~ 0 (positive_scope) [notation, in Corelib.BinNums.PosDef]
+_ ~ 1 (positive_scope) [notation, in Corelib.BinNums.PosDef]
+∙⊥∙ (predicate_scope) [notation, in Corelib.Classes.RelationClasses]
+∙⊤∙ (predicate_scope) [notation, in Corelib.Classes.RelationClasses]
+_ \∙/ _ (predicate_scope) [notation, in Corelib.Classes.RelationClasses]
+_ /∙\ _ (predicate_scope) [notation, in Corelib.Classes.RelationClasses]
+_ -∙> _ (predicate_scope) [notation, in Corelib.Classes.RelationClasses]
+_ <∙> _ (predicate_scope) [notation, in Corelib.Classes.RelationClasses]
+_ ∘ _ (program_scope) [notation, in Corelib.Program.Basics]
+` _ (program_scope) [notation, in Corelib.Program.Utils]
+! (program_scope) [notation, in Corelib.Program.Utils]
+_ (* _ *) (ssr_scope) [notation, in Corelib.ssr.ssreflect]
+<hidden _ > (ssr_scope) [notation, in Corelib.ssr.ssreflect]
+_ * _ (type_scope) [notation, in Corelib.Init.Datatypes]
+_ + _ (type_scope) [notation, in Corelib.Init.Datatypes]
+{ on _ , bijective _ } (type_scope) [notation, in Corelib.ssr.ssrbool]
+{ in _ , bijective _ } (type_scope) [notation, in Corelib.ssr.ssrbool]
+{ on _ , _ & _ } (type_scope) [notation, in Corelib.ssr.ssrbool]
+{ on _ & , _ } (type_scope) [notation, in Corelib.ssr.ssrbool]
+{ on _ , _ } (type_scope) [notation, in Corelib.ssr.ssrbool]
+{ in _ & & , _ } (type_scope) [notation, in Corelib.ssr.ssrbool]
+{ in _ & _ & , _ } (type_scope) [notation, in Corelib.ssr.ssrbool]
+{ in _ & & _ , _ } (type_scope) [notation, in Corelib.ssr.ssrbool]
+{ in _ & _ & _ , _ } (type_scope) [notation, in Corelib.ssr.ssrbool]
+{ in _ & , _ } (type_scope) [notation, in Corelib.ssr.ssrbool]
+{ in _ & _ , _ } (type_scope) [notation, in Corelib.ssr.ssrbool]
+{ in _ , _ } (type_scope) [notation, in Corelib.ssr.ssrbool]
+{ for _ , _ } (type_scope) [notation, in Corelib.ssr.ssrbool]
+{ subset _ <= _ } (type_scope) [notation, in Corelib.ssr.ssrbool]
+_ =i _ (type_scope) [notation, in Corelib.ssr.ssrbool]
+{ : _ } (type_scope) [notation, in Corelib.ssr.ssrbool]
+{ pred _ } (type_scope) [notation, in Corelib.ssr.ssrbool]
+[ \/ _ , _ , _ | _ ] (type_scope) [notation, in Corelib.ssr.ssrbool]
+[ \/ _ , _ | _ ] (type_scope) [notation, in Corelib.ssr.ssrbool]
+[ \/ _ | _ ] (type_scope) [notation, in Corelib.ssr.ssrbool]
+[ /\ _ , _ , _ , _ & _ ] (type_scope) [notation, in Corelib.ssr.ssrbool]
+[ /\ _ , _ , _ & _ ] (type_scope) [notation, in Corelib.ssr.ssrbool]
+[ /\ _ , _ & _ ] (type_scope) [notation, in Corelib.ssr.ssrbool]
+[ /\ _ & _ ] (type_scope) [notation, in Corelib.ssr.ssrbool]
+\unless _ , _ (type_scope) [notation, in Corelib.ssr.ssrbool]
+{ type of _ for _ } (type_scope) [notation, in Corelib.ssr.ssreflect]
+_ + { _ } (type_scope) [notation, in Corelib.Init.Specif]
+{ _ } + { _ } (type_scope) [notation, in Corelib.Init.Specif]
+{ ' _ : _ & _ & _ } (type_scope) [notation, in Corelib.Init.Specif]
+{ ' _ : _ & _ } (type_scope) [notation, in Corelib.Init.Specif]
+{ ' _ & _ & _ } (type_scope) [notation, in Corelib.Init.Specif]
+{ ' _ & _ } (type_scope) [notation, in Corelib.Init.Specif]
+{ ' _ : _ | _ & _ } (type_scope) [notation, in Corelib.Init.Specif]
+{ ' _ : _ | _ } (type_scope) [notation, in Corelib.Init.Specif]
+{ ' _ | _ & _ } (type_scope) [notation, in Corelib.Init.Specif]
+{ ' _ | _ } (type_scope) [notation, in Corelib.Init.Specif]
+{ _ : _ & _ & _ } (type_scope) [notation, in Corelib.Init.Specif]
+{ _ : _ & _ } (type_scope) [notation, in Corelib.Init.Specif]
+{ _ & _ & _ } (type_scope) [notation, in Corelib.Init.Specif]
+{ _ & _ } (type_scope) [notation, in Corelib.Init.Specif]
+{ _ : _ | _ & _ } (type_scope) [notation, in Corelib.Init.Specif]
+{ _ : _ | _ } (type_scope) [notation, in Corelib.Init.Specif]
+{ _ | _ & _ } (type_scope) [notation, in Corelib.Init.Specif]
+{ _ | _ } (type_scope) [notation, in Corelib.Init.Specif]
+{ mono _ : _ _ /~ _ } (type_scope) [notation, in Corelib.ssr.ssrfun]
+{ mono _ : _ _ / _ } (type_scope) [notation, in Corelib.ssr.ssrfun]
+{ mono _ : _ _ / _ >-> _ } (type_scope) [notation, in Corelib.ssr.ssrfun]
+{ mono _ : _ / _ } (type_scope) [notation, in Corelib.ssr.ssrfun]
+{ mono _ : _ / _ >-> _ } (type_scope) [notation, in Corelib.ssr.ssrfun]
+{ homo _ : _ _ /~ _ } (type_scope) [notation, in Corelib.ssr.ssrfun]
+{ homo _ : _ _ / _ } (type_scope) [notation, in Corelib.ssr.ssrfun]
+{ homo _ : _ _ / _ >-> _ } (type_scope) [notation, in Corelib.ssr.ssrfun]
+{ homo _ : _ / _ } (type_scope) [notation, in Corelib.ssr.ssrfun]
+{ homo _ : _ / _ >-> _ } (type_scope) [notation, in Corelib.ssr.ssrfun]
+{ morph _ : _ _ / _ } (type_scope) [notation, in Corelib.ssr.ssrfun]
+{ morph _ : _ _ / _ >-> _ } (type_scope) [notation, in Corelib.ssr.ssrfun]
+{ morph _ : _ / _ } (type_scope) [notation, in Corelib.ssr.ssrfun]
+{ morph _ : _ / _ >-> _ } (type_scope) [notation, in Corelib.ssr.ssrfun]
+_ =2 _ :> _ (type_scope) [notation, in Corelib.ssr.ssrfun]
+_ =2 _ (type_scope) [notation, in Corelib.ssr.ssrfun]
+_ =1 _ :> _ (type_scope) [notation, in Corelib.ssr.ssrfun]
+_ =1 _ (type_scope) [notation, in Corelib.ssr.ssrfun]
+exists ! _ .. _ , _ (type_scope) [notation, in Corelib.Init.Logic]
+_ <> _ (type_scope) [notation, in Corelib.Init.Logic]
+_ <> _ :> _ (type_scope) [notation, in Corelib.Init.Logic]
+_ = _ (type_scope) [notation, in Corelib.Init.Logic]
+_ = _ :> _ (type_scope) [notation, in Corelib.Init.Logic]
+exists2 ' _ : _ , _ & _ (type_scope) [notation, in Corelib.Init.Logic]
+exists2 ' _ , _ & _ (type_scope) [notation, in Corelib.Init.Logic]
+exists2 _ : _ , _ & _ (type_scope) [notation, in Corelib.Init.Logic]
+exists2 _ , _ & _ (type_scope) [notation, in Corelib.Init.Logic]
+exists _ .. _ , _ (type_scope) [notation, in Corelib.Init.Logic]
+_ <-> _ (type_scope) [notation, in Corelib.Init.Logic]
+_ \/ _ (type_scope) [notation, in Corelib.Init.Logic]
+_ /\ _ (type_scope) [notation, in Corelib.Init.Logic]
+~ _ (type_scope) [notation, in Corelib.Init.Logic]
+_ -> _ (type_scope) [notation, in Corelib.Init.Logic]
+{ ( _ , _ ) : _ | _ } (type_scope) [notation, in Corelib.Program.Utils]
+_ <= _ < _ (Z_scope) [notation, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+_ < _ (Z_scope) [notation, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+_ <= _ (Z_scope) [notation, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+_ ^ _ (Z_scope) [notation, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+_ * _ (Z_scope) [notation, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+_ - _ (Z_scope) [notation, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+_ + _ (Z_scope) [notation, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+2 (Z_scope) [notation, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+1 (Z_scope) [notation, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+0 (Z_scope) [notation, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+_ < _ (Z_scope) [notation, in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+_ <= _ (Z_scope) [notation, in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+_ ^ _ (Z_scope) [notation, in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+2 (Z_scope) [notation, in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+_ :: _ [notation, in Corelib.Classes.RelationClasses]
+_ .3 [notation, in Corelib.Init.Specif]
+0 [notation, in Corelib.BinNums.IntDef]
+0 [notation, in Corelib.Init.Byte]
+0 [notation, in Corelib.Init.Nat]
+0 [notation, in Corelib.Init.Peano]
+1 [notation, in Corelib.BinNums.IntDef]
+1 [notation, in Corelib.Init.Byte]
+1 [notation, in Corelib.Init.Nat]
+2 [notation, in Corelib.BinNums.IntDef]
+2 [notation, in Corelib.Init.Nat]
+[ elaborate _ ] [notation, in Corelib.ssr.ssreflect]
+{ all3 _ } [notation, in Corelib.ssr.ssrbool]
+{ all2 _ } [notation, in Corelib.ssr.ssrbool]
+{ all1 _ } [notation, in Corelib.ssr.ssrbool]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_A.html b/master/corelib/index_global_A.html new file mode 100644 index 0000000000..79675d8724 --- /dev/null +++ b/master/corelib/index_global_A.html @@ -0,0 +1,1245 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

A

+a [abbreviation, in Corelib.ssr.ssrbool]
+abs [definition, in Corelib.Init.Hexadecimal]
+abs [definition, in Corelib.Init.Decimal]
+abs [axiom, in Corelib.Floats.PrimFloat]
+abstract [definition, in Corelib.ssr.ssreflect]
+abstract_context [lemma, in Corelib.ssr.ssreflect]
+abstract_key [definition, in Corelib.ssr.ssreflect]
+abstract_lock [definition, in Corelib.ssr.ssreflect]
+absurd [lemma, in Corelib.Init.Logic]
+absurd_set [lemma, in Corelib.Init.Specif]
+abs_spec [axiom, in Corelib.Floats.FloatAxioms]
+Acc [inductive, in Corelib.Init.Wf]
+Acc_rel_morphism [instance, in Corelib.Classes.Morphisms_Prop]
+Acc_pt_morphism [instance, in Corelib.Classes.Morphisms_Prop]
+Acc_intro_generator [definition, in Corelib.Init.Wf]
+Acc_generator.R [variable, in Corelib.Init.Wf]
+Acc_generator.A [variable, in Corelib.Init.Wf]
+Acc_generator [section, in Corelib.Init.Wf]
+Acc_iter_2 [abbreviation, in Corelib.Init.Wf]
+Acc_iter [abbreviation, in Corelib.Init.Wf]
+Acc_inv_dep [definition, in Corelib.Init.Wf]
+Acc_inv [lemma, in Corelib.Init.Wf]
+Acc_sind [definition, in Corelib.Init.Wf]
+Acc_rec [definition, in Corelib.Init.Wf]
+Acc_ind [definition, in Corelib.Init.Wf]
+Acc_rect [definition, in Corelib.Init.Wf]
+Acc_intro [constructor, in Corelib.Init.Wf]
+add [definition, in Corelib.Init.Nat]
+add [axiom, in Corelib.Floats.PrimFloat]
+add [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+addb [definition, in Corelib.ssr.ssrbool]
+addbA [lemma, in Corelib.ssr.ssrbool]
+addbAC [lemma, in Corelib.ssr.ssrbool]
+addbACA [lemma, in Corelib.ssr.ssrbool]
+addbb [lemma, in Corelib.ssr.ssrbool]
+addbC [lemma, in Corelib.ssr.ssrbool]
+addbCA [lemma, in Corelib.ssr.ssrbool]
+addbF [lemma, in Corelib.ssr.ssrbool]
+addbI [lemma, in Corelib.ssr.ssrbool]
+addbK [lemma, in Corelib.ssr.ssrbool]
+addbN [lemma, in Corelib.ssr.ssrbool]
+addbP [lemma, in Corelib.ssr.ssrbool]
+addbT [lemma, in Corelib.ssr.ssrbool]
+addc [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+addcarry [definition, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+addcarryc [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+addcarryc_def_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+addcarryc_def [definition, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+addc_def_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+addc_def [definition, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+addFb [lemma, in Corelib.ssr.ssrbool]
+addIb [lemma, in Corelib.ssr.ssrbool]
+addKb [lemma, in Corelib.ssr.ssrbool]
+addmuldiv [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+addmuldiv_def_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+addmuldiv_def [definition, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+addNb [lemma, in Corelib.ssr.ssrbool]
+addTb [lemma, in Corelib.ssr.ssrbool]
+add_spec [axiom, in Corelib.Floats.FloatAxioms]
+add_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+all [definition, in Corelib.Init.Logic]
+AllAnd [section, in Corelib.ssr.ssrbool]
+AllAnd.P1 [variable, in Corelib.ssr.ssrbool]
+AllAnd.P2 [variable, in Corelib.ssr.ssrbool]
+AllAnd.P3 [variable, in Corelib.ssr.ssrbool]
+AllAnd.P4 [variable, in Corelib.ssr.ssrbool]
+AllAnd.P5 [variable, in Corelib.ssr.ssrbool]
+AllAnd.T [variable, in Corelib.ssr.ssrbool]
+all_sig2_cond [lemma, in Corelib.ssr.ssrbool]
+all_sig_cond [lemma, in Corelib.ssr.ssrbool]
+all_sig_cond_dep [lemma, in Corelib.ssr.ssrbool]
+all_tag_cond [lemma, in Corelib.ssr.ssrbool]
+all_tag_cond_dep [lemma, in Corelib.ssr.ssrbool]
+all_and5 [lemma, in Corelib.ssr.ssrbool]
+all_and4 [lemma, in Corelib.ssr.ssrbool]
+all_and3 [lemma, in Corelib.ssr.ssrbool]
+all_and2 [lemma, in Corelib.ssr.ssrbool]
+all_sig2 [lemma, in Corelib.ssr.ssrfun]
+all_sig [lemma, in Corelib.ssr.ssrfun]
+all_tag2 [lemma, in Corelib.ssr.ssrfun]
+all_tag [lemma, in Corelib.ssr.ssrfun]
+all_equal_to [definition, in Corelib.ssr.ssrfun]
+all_pair [definition, in Corelib.ssr.ssrfun]
+all_flip_impl_morphism [instance, in Corelib.Classes.Morphisms_Prop]
+all_impl_morphism [instance, in Corelib.Classes.Morphisms_Prop]
+all_iff_morphism [instance, in Corelib.Classes.Morphisms_Prop]
+AltFalse [constructor, in Corelib.ssr.ssrbool]
+altP [lemma, in Corelib.ssr.ssrbool]
+AltTrue [constructor, in Corelib.ssr.ssrbool]
+alt_spec [inductive, in Corelib.ssr.ssrbool]
+and [inductive, in Corelib.Init.Logic]
+andb [definition, in Corelib.Init.Datatypes]
+andbA [lemma, in Corelib.ssr.ssrbool]
+andbAC [lemma, in Corelib.ssr.ssrbool]
+andbACA [lemma, in Corelib.ssr.ssrbool]
+andbb [lemma, in Corelib.ssr.ssrbool]
+andbC [lemma, in Corelib.ssr.ssrbool]
+andbCA [lemma, in Corelib.ssr.ssrbool]
+andbF [lemma, in Corelib.ssr.ssrbool]
+andbK [lemma, in Corelib.ssr.ssrbool]
+andbN [lemma, in Corelib.ssr.ssrbool]
+andbT [lemma, in Corelib.ssr.ssrbool]
+andb_true_intro [lemma, in Corelib.Init.Datatypes]
+andb_prop [lemma, in Corelib.Init.Datatypes]
+andb_addr [lemma, in Corelib.ssr.ssrbool]
+andb_addl [lemma, in Corelib.ssr.ssrbool]
+andb_id2r [lemma, in Corelib.ssr.ssrbool]
+andb_id2l [lemma, in Corelib.ssr.ssrbool]
+andb_idr [lemma, in Corelib.ssr.ssrbool]
+andb_idl [lemma, in Corelib.ssr.ssrbool]
+andb_orr [lemma, in Corelib.ssr.ssrbool]
+andb_orl [lemma, in Corelib.ssr.ssrbool]
+andFb [lemma, in Corelib.ssr.ssrbool]
+andKb [lemma, in Corelib.ssr.ssrbool]
+andNb [lemma, in Corelib.ssr.ssrbool]
+andP [lemma, in Corelib.ssr.ssrbool]
+andPP [lemma, in Corelib.ssr.ssrbool]
+andTb [lemma, in Corelib.ssr.ssrbool]
+and_assoc [lemma, in Corelib.Init.Logic]
+and_comm [lemma, in Corelib.Init.Logic]
+and_cancel_r [lemma, in Corelib.Init.Logic]
+and_cancel_l [lemma, in Corelib.Init.Logic]
+and_iff_compat_r [lemma, in Corelib.Init.Logic]
+and_iff_compat_l [lemma, in Corelib.Init.Logic]
+and_sind [definition, in Corelib.Init.Logic]
+and_rec [definition, in Corelib.Init.Logic]
+and_ind [definition, in Corelib.Init.Logic]
+and_rect [definition, in Corelib.Init.Logic]
+and_iff_morphism [instance, in Corelib.Classes.Morphisms_Prop]
+and_impl_morphism [instance, in Corelib.Classes.Morphisms_Prop]
+And3 [constructor, in Corelib.ssr.ssrbool]
+and3 [inductive, in Corelib.ssr.ssrbool]
+and3P [lemma, in Corelib.ssr.ssrbool]
+and3_sind [definition, in Corelib.ssr.ssrbool]
+and3_rec [definition, in Corelib.ssr.ssrbool]
+and3_ind [definition, in Corelib.ssr.ssrbool]
+and3_rect [definition, in Corelib.ssr.ssrbool]
+And4 [constructor, in Corelib.ssr.ssrbool]
+and4 [inductive, in Corelib.ssr.ssrbool]
+and4P [lemma, in Corelib.ssr.ssrbool]
+and4_sind [definition, in Corelib.ssr.ssrbool]
+and4_rec [definition, in Corelib.ssr.ssrbool]
+and4_ind [definition, in Corelib.ssr.ssrbool]
+and4_rect [definition, in Corelib.ssr.ssrbool]
+And5 [constructor, in Corelib.ssr.ssrbool]
+and5 [inductive, in Corelib.ssr.ssrbool]
+and5P [lemma, in Corelib.ssr.ssrbool]
+and5_sind [definition, in Corelib.ssr.ssrbool]
+and5_rec [definition, in Corelib.ssr.ssrbool]
+and5_ind [definition, in Corelib.ssr.ssrbool]
+and5_rect [definition, in Corelib.ssr.ssrbool]
+Antisymmetric [record, in Corelib.Classes.RelationClasses]
+Antisymmetric [inductive, in Corelib.Classes.RelationClasses]
+antisymmetric [definition, in Corelib.ssr.ssrbool]
+Antisymmetric [record, in Corelib.Classes.CRelationClasses]
+Antisymmetric [inductive, in Corelib.Classes.CRelationClasses]
+antisymmetric [definition, in Corelib.Relations.Relation_Definitions]
+antisymmetry [projection, in Corelib.Classes.RelationClasses]
+antisymmetry [constructor, in Corelib.Classes.RelationClasses]
+antisymmetry [projection, in Corelib.Classes.CRelationClasses]
+antisymmetry [constructor, in Corelib.Classes.CRelationClasses]
+app [definition, in Corelib.Init.Datatypes]
+app [definition, in Corelib.Init.Hexadecimal]
+app [definition, in Corelib.Init.Decimal]
+ApplicativePred [definition, in Corelib.ssr.ssrbool]
+applicative_mem_pred_value [projection, in Corelib.ssr.ssrbool]
+applicative_mem_pred [record, in Corelib.ssr.ssrbool]
+applicative_pred_applicative [definition, in Corelib.ssr.ssrbool]
+applicative_pred_value [projection, in Corelib.ssr.ssrbool]
+applicative_pred_of_simpl [definition, in Corelib.ssr.ssrbool]
+applicative_pred [definition, in Corelib.ssr.ssrbool]
+apply [definition, in Corelib.Program.Basics]
+ApplyIff [section, in Corelib.ssr.ssreflect]
+ApplyIff.eqPQ [variable, in Corelib.ssr.ssreflect]
+ApplyIff.P [variable, in Corelib.ssr.ssreflect]
+ApplyIff.Q [variable, in Corelib.ssr.ssreflect]
+apply_subrelation [inductive, in Corelib.Classes.CMorphisms]
+apply_subrelation [inductive, in Corelib.Classes.Morphisms]
+appP [lemma, in Corelib.ssr.ssrbool]
+app_predE [lemma, in Corelib.ssr.ssrbool]
+app_int [definition, in Corelib.Init.Hexadecimal]
+app_int [definition, in Corelib.Init.Decimal]
+argumentType [definition, in Corelib.ssr.ssreflect]
+array [axiom, in Corelib.Array.PrimArray]
+Array [library]
+ArrayAxioms [library]
+array_ext [axiom, in Corelib.Array.ArrayAxioms]
+arrow [definition, in Corelib.Program.Basics]
+arrow [definition, in Corelib.Classes.CRelationClasses]
+arrows [definition, in Corelib.Classes.RelationClasses]
+arrow_Transitive [instance, in Corelib.Classes.CRelationClasses]
+arrow_Reflexive [instance, in Corelib.Classes.CRelationClasses]
+asr [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+asr_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+associative [definition, in Corelib.ssr.ssrfun]
+Asymmetric [record, in Corelib.Classes.RelationClasses]
+Asymmetric [inductive, in Corelib.Classes.RelationClasses]
+Asymmetric [record, in Corelib.Classes.CRelationClasses]
+Asymmetric [inductive, in Corelib.Classes.CRelationClasses]
+asymmetry [projection, in Corelib.Classes.RelationClasses]
+asymmetry [constructor, in Corelib.Classes.RelationClasses]
+asymmetry [projection, in Corelib.Classes.CRelationClasses]
+asymmetry [constructor, in Corelib.Classes.CRelationClasses]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_B.html b/master/corelib/index_global_B.html new file mode 100644 index 0000000000..a0d862dbe0 --- /dev/null +++ b/master/corelib/index_global_B.html @@ -0,0 +1,1113 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

B

+Basics [library]
+Bijections [section, in Corelib.ssr.ssrfun]
+BijectionsTheory [section, in Corelib.ssr.ssrfun]
+BijectionsTheory.A [variable, in Corelib.ssr.ssrfun]
+BijectionsTheory.B [variable, in Corelib.ssr.ssrfun]
+BijectionsTheory.C [variable, in Corelib.ssr.ssrfun]
+BijectionsTheory.f [variable, in Corelib.ssr.ssrfun]
+BijectionsTheory.h [variable, in Corelib.ssr.ssrfun]
+Bijections.A [variable, in Corelib.ssr.ssrfun]
+Bijections.B [variable, in Corelib.ssr.ssrfun]
+Bijections.bijf [variable, in Corelib.ssr.ssrfun]
+Bijections.f [variable, in Corelib.ssr.ssrfun]
+Bijective [constructor, in Corelib.ssr.ssrfun]
+bijective [inductive, in Corelib.ssr.ssrfun]
+bijective_on [definition, in Corelib.ssr.ssrbool]
+bijective_in [definition, in Corelib.ssr.ssrbool]
+bij_can_bij [lemma, in Corelib.ssr.ssrfun]
+bij_comp [lemma, in Corelib.ssr.ssrfun]
+bij_can_eq [lemma, in Corelib.ssr.ssrfun]
+bij_can_sym [lemma, in Corelib.ssr.ssrfun]
+bij_inj [lemma, in Corelib.ssr.ssrfun]
+Binary [section, in Corelib.Classes.RelationClasses]
+Binary [section, in Corelib.Classes.CRelationClasses]
+binary_normalize [definition, in Corelib.Floats.SpecFloat]
+binary_round [definition, in Corelib.Floats.SpecFloat]
+binary_round_aux [definition, in Corelib.Floats.SpecFloat]
+binary_relation [definition, in Corelib.Classes.RelationClasses]
+binary_operation [definition, in Corelib.Classes.RelationClasses]
+Binary.A [variable, in Corelib.Classes.RelationClasses]
+Binary.A [variable, in Corelib.Classes.CRelationClasses]
+Binder [module, in Ltac2.Constr]
+bind_unless [lemma, in Corelib.ssr.ssrbool]
+BinNums [library]
+bit [definition, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+bitwise [definition, in Corelib.Init.Nat]
+bool [inductive, in Corelib.Init.Datatypes]
+Bool [library]
+boolfunPredType [definition, in Corelib.ssr.ssrbool]
+BoolIf [section, in Corelib.ssr.ssrbool]
+BoolIf.A [variable, in Corelib.ssr.ssrbool]
+BoolIf.b [variable, in Corelib.ssr.ssrbool]
+BoolIf.B [variable, in Corelib.ssr.ssrbool]
+BoolIf.f [variable, in Corelib.ssr.ssrbool]
+BoolIf.vF [variable, in Corelib.ssr.ssrbool]
+BoolIf.vT [variable, in Corelib.ssr.ssrbool]
+BoolIf.x [variable, in Corelib.ssr.ssrbool]
+BoolNotations [module, in Ltac2.Bool]
+boolP [lemma, in Corelib.ssr.ssrbool]
+BoolSpec [inductive, in Corelib.Init.Datatypes]
+BoolSpecF [constructor, in Corelib.Init.Datatypes]
+BoolSpecT [constructor, in Corelib.Init.Datatypes]
+BoolSpec_sind [definition, in Corelib.Init.Datatypes]
+BoolSpec_ind [definition, in Corelib.Init.Datatypes]
+bool_sind [definition, in Corelib.Init.Datatypes]
+bool_rec [definition, in Corelib.Init.Datatypes]
+bool_ind [definition, in Corelib.Init.Datatypes]
+bool_rect [definition, in Corelib.Init.Datatypes]
+bool_choice [lemma, in Corelib.Init.Specif]
+bool_of_sumbool [definition, in Corelib.Init.Sumbool]
+bool_eq_ind [definition, in Corelib.Init.Sumbool]
+bool_eq_rec [definition, in Corelib.Init.Sumbool]
+bounded [definition, in Corelib.Floats.SpecFloat]
+Build_Setoid_Theory [definition, in Corelib.Setoids.Setoid]
+byte [inductive, in Corelib.Init.Byte]
+Byte [library]
+ByteSyntaxNotations [module, in Corelib.Init.Byte]
+byte_of_byte [definition, in Corelib.Init.Byte]
+byte_sind [definition, in Corelib.Init.Byte]
+byte_rec [definition, in Corelib.Init.Byte]
+byte_ind [definition, in Corelib.Init.Byte]
+byte_rect [definition, in Corelib.Init.Byte]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_C.html b/master/corelib/index_global_C.html new file mode 100644 index 0000000000..e0793600d9 --- /dev/null +++ b/master/corelib/index_global_C.html @@ -0,0 +1,1225 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

C

+cancel [definition, in Corelib.ssr.ssrfun]
+CancelOn [section, in Corelib.ssr.ssrbool]
+CancelOn.aD [variable, in Corelib.ssr.ssrbool]
+CancelOn.aT [variable, in Corelib.ssr.ssrbool]
+CancelOn.f [variable, in Corelib.ssr.ssrbool]
+CancelOn.g [variable, in Corelib.ssr.ssrbool]
+CancelOn.rD [variable, in Corelib.ssr.ssrbool]
+CancelOn.rT [variable, in Corelib.ssr.ssrbool]
+canLR [lemma, in Corelib.ssr.ssrfun]
+canLR_on [lemma, in Corelib.ssr.ssrbool]
+canLR_in [lemma, in Corelib.ssr.ssrbool]
+canonical_mantissa [definition, in Corelib.Floats.SpecFloat]
+canRL [lemma, in Corelib.ssr.ssrfun]
+canRL_on [lemma, in Corelib.ssr.ssrbool]
+canRL_in [lemma, in Corelib.ssr.ssrbool]
+can_mono_in [lemma, in Corelib.ssr.ssrbool]
+can_mono [lemma, in Corelib.ssr.ssrbool]
+can_in_comp [lemma, in Corelib.ssr.ssrbool]
+can_in_pcan [lemma, in Corelib.ssr.ssrbool]
+can_in_inj [lemma, in Corelib.ssr.ssrbool]
+can_comp [lemma, in Corelib.ssr.ssrfun]
+can_inj [lemma, in Corelib.ssr.ssrfun]
+can_pcan [lemma, in Corelib.ssr.ssrfun]
+carry [inductive, in Corelib.Numbers.Cyclic.Int63.CarryType]
+CarryType [library]
+Cast [module, in Ltac2.Constr]
+cat [axiom, in Corelib.Strings.PrimString]
+catcomp [definition, in Corelib.ssr.ssrfun]
+cat_spec [axiom, in Corelib.Strings.PrimStringAxioms]
+Char [library]
+char63 [definition, in Corelib.Strings.PrimString]
+Char63Notations [module, in Corelib.Strings.PrimString]
+Char63Notations.parse [definition, in Corelib.Strings.PrimString]
+Char63Notations.print [definition, in Corelib.Strings.PrimString]
+char63_wrap [projection, in Corelib.Strings.PrimString]
+char63_wrapper [record, in Corelib.Strings.PrimString]
+char63_compare [abbreviation, in Corelib.Strings.PrimStringAxioms]
+char63_valid [definition, in Corelib.Strings.PrimStringAxioms]
+check_applicative_mem_pred [definition, in Corelib.ssr.ssrbool]
+Choice [lemma, in Corelib.Init.Specif]
+Choice_lemmas.R2 [variable, in Corelib.Init.Specif]
+Choice_lemmas.R1 [variable, in Corelib.Init.Specif]
+Choice_lemmas.R' [variable, in Corelib.Init.Specif]
+Choice_lemmas.R [variable, in Corelib.Init.Specif]
+Choice_lemmas.S' [variable, in Corelib.Init.Specif]
+Choice_lemmas.S [variable, in Corelib.Init.Specif]
+Choice_lemmas [section, in Corelib.Init.Specif]
+Choice2 [lemma, in Corelib.Init.Specif]
+classically [definition, in Corelib.ssr.ssrbool]
+classicP [lemma, in Corelib.ssr.ssrbool]
+classicW [lemma, in Corelib.ssr.ssrbool]
+classic_ex [lemma, in Corelib.ssr.ssrbool]
+classic_sigW [lemma, in Corelib.ssr.ssrbool]
+classic_imply [lemma, in Corelib.ssr.ssrbool]
+classic_pick [lemma, in Corelib.ssr.ssrbool]
+classic_EM [lemma, in Corelib.ssr.ssrbool]
+classic_bind [lemma, in Corelib.ssr.ssrbool]
+classify [axiom, in Corelib.Floats.PrimFloat]
+classify_spec [axiom, in Corelib.Floats.FloatAxioms]
+clone_pred [definition, in Corelib.ssr.ssrbool]
+CMorphisms [library]
+collective_pred_of_simpl [definition, in Corelib.ssr.ssrbool]
+collective_pred [definition, in Corelib.ssr.ssrbool]
+commut [definition, in Corelib.Relations.Relation_Definitions]
+commutative [definition, in Corelib.ssr.ssrfun]
+comp [definition, in Corelib.ssr.ssrfun]
+compA [lemma, in Corelib.ssr.ssrfun]
+compare [definition, in Corelib.Init.Nat]
+compare [axiom, in Corelib.Strings.PrimString]
+Compare [section, in Corelib.Lists.ListDef]
+compare [axiom, in Corelib.Floats.PrimFloat]
+compare [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+compares [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+CompareSpec [inductive, in Corelib.Init.Datatypes]
+CompareSpecT [inductive, in Corelib.Init.Datatypes]
+CompareSpecT_sind [definition, in Corelib.Init.Datatypes]
+CompareSpecT_rec [definition, in Corelib.Init.Datatypes]
+CompareSpecT_ind [definition, in Corelib.Init.Datatypes]
+CompareSpecT_rect [definition, in Corelib.Init.Datatypes]
+CompareSpec_sind [definition, in Corelib.Init.Datatypes]
+CompareSpec_ind [definition, in Corelib.Init.Datatypes]
+CompareSpec2Type [lemma, in Corelib.Init.Datatypes]
+compare_spec [axiom, in Corelib.Floats.FloatAxioms]
+compare_def_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+compare_def [definition, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+compare_spec [axiom, in Corelib.Strings.PrimStringAxioms]
+compare_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+Compare.A [variable, in Corelib.Lists.ListDef]
+Compare.cmp [variable, in Corelib.Lists.ListDef]
+comparison [inductive, in Corelib.Init.Datatypes]
+comparison_eq_stable [lemma, in Corelib.Init.Datatypes]
+comparison_sind [definition, in Corelib.Init.Datatypes]
+comparison_rec [definition, in Corelib.Init.Datatypes]
+comparison_ind [definition, in Corelib.Init.Datatypes]
+comparison_rect [definition, in Corelib.Init.Datatypes]
+compat_Reflexive [instance, in Corelib.ssr.ssrsetoid]
+CompEq [constructor, in Corelib.Init.Datatypes]
+CompEqT [constructor, in Corelib.Init.Datatypes]
+CompGt [constructor, in Corelib.Init.Datatypes]
+CompGtT [constructor, in Corelib.Init.Datatypes]
+complement [definition, in Corelib.Classes.RelationClasses]
+complement [definition, in Corelib.Classes.CRelationClasses]
+complement_Symmetric [lemma, in Corelib.Classes.RelationClasses]
+complement_Irreflexive [lemma, in Corelib.Classes.RelationClasses]
+complement_inverse [lemma, in Corelib.Classes.RelationClasses]
+complement_proper [definition, in Corelib.Classes.Morphisms]
+complement_Symmetric [lemma, in Corelib.Classes.CRelationClasses]
+complement_Irreflexive [lemma, in Corelib.Classes.CRelationClasses]
+complement_inverse [lemma, in Corelib.Classes.CRelationClasses]
+CompLt [constructor, in Corelib.Init.Datatypes]
+CompLtT [constructor, in Corelib.Init.Datatypes]
+CompOpp [definition, in Corelib.Init.Datatypes]
+CompOpp_iff [lemma, in Corelib.Init.Datatypes]
+CompOpp_inj [lemma, in Corelib.Init.Datatypes]
+CompOpp_involutive [lemma, in Corelib.Init.Datatypes]
+compose [definition, in Corelib.Program.Basics]
+compose_proper [instance, in Corelib.Classes.CMorphisms]
+compose_proper [instance, in Corelib.Classes.Morphisms]
+Composition [section, in Corelib.ssr.ssrfun]
+Composition.A [variable, in Corelib.ssr.ssrfun]
+Composition.B [variable, in Corelib.ssr.ssrfun]
+Composition.C [variable, in Corelib.ssr.ssrfun]
+CompSpec [definition, in Corelib.Init.Datatypes]
+CompSpecT [definition, in Corelib.Init.Datatypes]
+CompSpec2Type [lemma, in Corelib.Init.Datatypes]
+cond_Zopp [definition, in Corelib.Floats.SpecFloat]
+congr1 [definition, in Corelib.ssr.ssrfun]
+congr2 [definition, in Corelib.ssr.ssrfun]
+conj [constructor, in Corelib.Init.Logic]
+Conjunction [section, in Corelib.Init.Logic]
+Conjunction.A [variable, in Corelib.Init.Logic]
+Conjunction.B [variable, in Corelib.Init.Logic]
+connectives [section, in Corelib.Init.Sumbool]
+connectives.A [variable, in Corelib.Init.Sumbool]
+connectives.B [variable, in Corelib.Init.Sumbool]
+connectives.C [variable, in Corelib.Init.Sumbool]
+connectives.D [variable, in Corelib.Init.Sumbool]
+connectives.H1 [variable, in Corelib.Init.Sumbool]
+connectives.H2 [variable, in Corelib.Init.Sumbool]
+cons [constructor, in Corelib.Init.Datatypes]
+const [definition, in Corelib.Program.Basics]
+Constant [library]
+Constr [library]
+Constructor [library]
+contra [lemma, in Corelib.ssr.ssrbool]
+contraFF [lemma, in Corelib.ssr.ssrbool]
+contraFN [lemma, in Corelib.ssr.ssrbool]
+contraFnot [lemma, in Corelib.ssr.ssrbool]
+contraFT [lemma, in Corelib.ssr.ssrbool]
+contraL [lemma, in Corelib.ssr.ssrbool]
+contraLR [lemma, in Corelib.ssr.ssrbool]
+contraNF [lemma, in Corelib.ssr.ssrbool]
+contraNN [definition, in Corelib.ssr.ssrbool]
+contraNnot [lemma, in Corelib.ssr.ssrbool]
+contraNT [definition, in Corelib.ssr.ssrbool]
+contraPF [lemma, in Corelib.ssr.ssrbool]
+contraPN [lemma, in Corelib.ssr.ssrbool]
+contraPnot [lemma, in Corelib.ssr.ssrbool]
+contraPT [lemma, in Corelib.ssr.ssrbool]
+contraR [lemma, in Corelib.ssr.ssrbool]
+contraT [lemma, in Corelib.ssr.ssrbool]
+contraTF [lemma, in Corelib.ssr.ssrbool]
+contraTN [definition, in Corelib.ssr.ssrbool]
+contraTnot [lemma, in Corelib.ssr.ssrbool]
+contraTT [definition, in Corelib.ssr.ssrbool]
+contra_notF [lemma, in Corelib.ssr.ssrbool]
+contra_notN [lemma, in Corelib.ssr.ssrbool]
+contra_notT [lemma, in Corelib.ssr.ssrbool]
+contra_not [lemma, in Corelib.ssr.ssrbool]
+Control [library]
+copy [axiom, in Corelib.Array.PrimArray]
+Coq818 [library]
+Coq818 [library]
+Coq819 [library]
+Coq819 [library]
+Coq820 [library]
+crelation [definition, in Corelib.Classes.CRelationClasses]
+CRelationClasses [library]
+curry [definition, in Corelib.Init.Datatypes]
+Cutting [section, in Corelib.Lists.ListDef]
+Cutting.A [variable, in Corelib.Lists.ListDef]
+C0 [constructor, in Corelib.Numbers.Cyclic.Int63.CarryType]
+C1 [constructor, in Corelib.Numbers.Cyclic.Int63.CarryType]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_D.html b/master/corelib/index_global_D.html new file mode 100644 index 0000000000..aa451e0a34 --- /dev/null +++ b/master/corelib/index_global_D.html @@ -0,0 +1,1138 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

D

+Da [constructor, in Corelib.Init.Hexadecimal]
+Datatypes [library]
+Db [constructor, in Corelib.Init.Hexadecimal]
+Dc [constructor, in Corelib.Init.Hexadecimal]
+Dd [constructor, in Corelib.Init.Hexadecimal]
+De [constructor, in Corelib.Init.Hexadecimal]
+dec [abbreviation, in Corelib.Program.Utils]
+decidable [definition, in Corelib.ssr.ssrbool]
+decide_right [lemma, in Corelib.Init.Tactics]
+decide_left [lemma, in Corelib.Init.Tactics]
+Decimal [constructor, in Corelib.Init.Decimal]
+decimal [inductive, in Corelib.Init.Decimal]
+Decimal [constructor, in Corelib.Init.Number]
+Decimal [library]
+DecimalExp [constructor, in Corelib.Init.Decimal]
+decimal_eq_dec [definition, in Corelib.Init.Decimal]
+DeclarePredSortOfSimpl [module, in Corelib.ssr.ssrbool]
+decP [definition, in Corelib.ssr.ssrbool]
+decPcases [lemma, in Corelib.ssr.ssrbool]
+default [axiom, in Corelib.Array.PrimArray]
+DefaultKeying [module, in Corelib.ssr.ssrbool]
+DefaultKeying.default_keyed_qualifier [definition, in Corelib.ssr.ssrbool]
+DefaultKeying.default_keyed_pred [definition, in Corelib.ssr.ssrbool]
+DefaultPredKey [constructor, in Corelib.ssr.ssrbool]
+DefaultRelation [record, in Corelib.Classes.SetoidTactics]
+default_relation [definition, in Corelib.Classes.SetoidTactics]
+default_set [axiom, in Corelib.Array.ArrayAxioms]
+Defs [section, in Corelib.Classes.RelationClasses]
+Defs [section, in Corelib.ssr.ssrclasses]
+Defs [section, in Corelib.Classes.CRelationClasses]
+Defs.A [variable, in Corelib.Classes.RelationClasses]
+Defs.A [variable, in Corelib.ssr.ssrclasses]
+Defs.A [variable, in Corelib.Classes.CRelationClasses]
+Defs.complement [section, in Corelib.Classes.RelationClasses]
+Defs.complement [section, in Corelib.Classes.CRelationClasses]
+Defs.flip [section, in Corelib.Classes.RelationClasses]
+Defs.flip [section, in Corelib.Classes.CRelationClasses]
+Defs.Leibniz [section, in Corelib.Classes.RelationClasses]
+Defs.Leibniz [section, in Corelib.Classes.CRelationClasses]
+Defs.LeibnizNot [section, in Corelib.Classes.RelationClasses]
+del_tail_int [definition, in Corelib.Init.Hexadecimal]
+del_tail [definition, in Corelib.Init.Hexadecimal]
+del_head_int [definition, in Corelib.Init.Hexadecimal]
+del_head [definition, in Corelib.Init.Hexadecimal]
+del_tail_int [definition, in Corelib.Init.Decimal]
+del_tail [definition, in Corelib.Init.Decimal]
+del_head_int [definition, in Corelib.Init.Decimal]
+del_head [definition, in Corelib.Init.Decimal]
+dependentReturnType [definition, in Corelib.ssr.ssreflect]
+dependent_choice [lemma, in Corelib.Init.Specif]
+Dependent_choice_lemmas.R [variable, in Corelib.Init.Specif]
+Dependent_choice_lemmas.X [variable, in Corelib.Init.Specif]
+Dependent_choice_lemmas [section, in Corelib.Init.Specif]
+Derive [library]
+Df [constructor, in Corelib.Init.Hexadecimal]
+did_normalization [constructor, in Corelib.Classes.CMorphisms]
+did_normalization [constructor, in Corelib.Classes.Morphisms]
+digits [definition, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+digits2_pos [definition, in Corelib.Floats.SpecFloat]
+div [definition, in Corelib.Init.Nat]
+div [axiom, in Corelib.Floats.PrimFloat]
+div [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+diveucl [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+diveucl_21_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+diveucl_def_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+diveucl_def [definition, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+diveucl_21 [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+divmod [definition, in Corelib.Init.Nat]
+divs [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+div_spec [axiom, in Corelib.Floats.FloatAxioms]
+div_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+div_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+div2 [definition, in Corelib.Init.Nat]
+double [definition, in Corelib.Init.Nat]
+do_subrelation [constructor, in Corelib.Classes.CMorphisms]
+do_subrelation [constructor, in Corelib.Classes.Morphisms]
+D0 [constructor, in Corelib.Init.Hexadecimal]
+D0 [constructor, in Corelib.Init.Decimal]
+D1 [constructor, in Corelib.Init.Hexadecimal]
+D1 [constructor, in Corelib.Init.Decimal]
+D2 [constructor, in Corelib.Init.Hexadecimal]
+D2 [constructor, in Corelib.Init.Decimal]
+D3 [constructor, in Corelib.Init.Hexadecimal]
+D3 [constructor, in Corelib.Init.Decimal]
+D4 [constructor, in Corelib.Init.Hexadecimal]
+D4 [constructor, in Corelib.Init.Decimal]
+D5 [constructor, in Corelib.Init.Hexadecimal]
+D5 [constructor, in Corelib.Init.Decimal]
+D6 [constructor, in Corelib.Init.Hexadecimal]
+D6 [constructor, in Corelib.Init.Decimal]
+D7 [constructor, in Corelib.Init.Hexadecimal]
+D7 [constructor, in Corelib.Init.Decimal]
+D8 [constructor, in Corelib.Init.Hexadecimal]
+D8 [constructor, in Corelib.Init.Decimal]
+D9 [constructor, in Corelib.Init.Hexadecimal]
+D9 [constructor, in Corelib.Init.Decimal]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_E.html b/master/corelib/index_global_E.html new file mode 100644 index 0000000000..9456f4e4dc --- /dev/null +++ b/master/corelib/index_global_E.html @@ -0,0 +1,1386 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

E

+ecast [abbreviation, in Corelib.ssr.ssrfun]
+elimF [lemma, in Corelib.ssr.ssrbool]
+elimFn [lemma, in Corelib.ssr.ssrbool]
+elimN [lemma, in Corelib.ssr.ssrbool]
+elimNf [lemma, in Corelib.ssr.ssrbool]
+elimNTF [lemma, in Corelib.ssr.ssrbool]
+elimT [lemma, in Corelib.ssr.ssrbool]
+elimTF [lemma, in Corelib.ssr.ssrbool]
+elimTFn [lemma, in Corelib.ssr.ssrbool]
+elimTn [lemma, in Corelib.ssr.ssrbool]
+Elts [section, in Corelib.Lists.ListDef]
+Elts.A [variable, in Corelib.Lists.ListDef]
+emax [definition, in Corelib.Floats.FloatOps]
+emin [definition, in Corelib.Floats.SpecFloat]
+emin [abbreviation, in Corelib.Floats.FloatOps]
+Empty_set_sind [definition, in Corelib.Init.Datatypes]
+Empty_set_rec [definition, in Corelib.Init.Datatypes]
+Empty_set_ind [definition, in Corelib.Init.Datatypes]
+Empty_set_rect [definition, in Corelib.Init.Datatypes]
+Empty_set [inductive, in Corelib.Init.Datatypes]
+Env [library]
+Eq [constructor, in Corelib.Init.Datatypes]
+eq [inductive, in Corelib.Init.Logic]
+eqb [definition, in Corelib.Init.Nat]
+eqb [axiom, in Corelib.Floats.PrimFloat]
+eqb [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+eqbLR [lemma, in Corelib.ssr.ssrbool]
+eqbRL [lemma, in Corelib.ssr.ssrbool]
+eqb_spec [axiom, in Corelib.Floats.FloatAxioms]
+eqb_refl [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+eqb_correct [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+eqfun [definition, in Corelib.ssr.ssrfun]
+EqNotations [module, in Corelib.Init.Logic]
+rew dependent <- [ _ ] _ in _ [notation, in Corelib.Init.Logic]
+rew dependent -> [ _ ] _ in _ [notation, in Corelib.Init.Logic]
+rew dependent [ _ ] _ in _ [notation, in Corelib.Init.Logic]
+rew dependent <- [ fun _ _ => _ ] _ in _ [notation, in Corelib.Init.Logic]
+rew dependent -> [ fun _ _ => _ ] _ in _ [notation, in Corelib.Init.Logic]
+rew dependent [ fun _ _ => _ ] _ in _ [notation, in Corelib.Init.Logic]
+rew dependent <- _ in _ [notation, in Corelib.Init.Logic]
+rew dependent -> _ in _ [notation, in Corelib.Init.Logic]
+rew dependent _ in _ [notation, in Corelib.Init.Logic]
+rew -> [ _ ] _ in _ [notation, in Corelib.Init.Logic]
+rew -> _ in _ [notation, in Corelib.Init.Logic]
+rew <- [ _ ] _ in _ [notation, in Corelib.Init.Logic]
+rew <- _ in _ [notation, in Corelib.Init.Logic]
+rew [ _ ] _ in _ [notation, in Corelib.Init.Logic]
+rew _ in _ [notation, in Corelib.Init.Logic]
+eqrel [definition, in Corelib.ssr.ssrfun]
+equality_dep.y [variable, in Corelib.Init.Logic]
+equality_dep.x [variable, in Corelib.Init.Logic]
+equality_dep.f [variable, in Corelib.Init.Logic]
+equality_dep.B [variable, in Corelib.Init.Logic]
+equality_dep.A [variable, in Corelib.Init.Logic]
+equality_dep [section, in Corelib.Init.Logic]
+equiv [definition, in Corelib.Relations.Relation_Definitions]
+equiv [definition, in Corelib.Classes.Equivalence]
+Equivalence [record, in Corelib.Classes.RelationClasses]
+Equivalence [record, in Corelib.Classes.CRelationClasses]
+Equivalence [section, in Corelib.Init.Logic]
+equivalence [record, in Corelib.Relations.Relation_Definitions]
+Equivalence [library]
+equivalence_default [instance, in Corelib.Classes.SetoidTactics]
+equivalence_rewrite_relation [definition, in Corelib.Classes.RelationClasses]
+Equivalence_PreOrder [instance, in Corelib.Classes.RelationClasses]
+Equivalence_PER [instance, in Corelib.Classes.RelationClasses]
+Equivalence_Transitive [projection, in Corelib.Classes.RelationClasses]
+Equivalence_Symmetric [projection, in Corelib.Classes.RelationClasses]
+Equivalence_Reflexive [projection, in Corelib.Classes.RelationClasses]
+equivalence_relP_in [lemma, in Corelib.ssr.ssrbool]
+equivalence_relP [lemma, in Corelib.ssr.ssrbool]
+equivalence_rel [definition, in Corelib.ssr.ssrbool]
+equivalence_rewrite_crelation [instance, in Corelib.Classes.CRelationClasses]
+Equivalence_PER [instance, in Corelib.Classes.CRelationClasses]
+Equivalence_Transitive [projection, in Corelib.Classes.CRelationClasses]
+Equivalence_Symmetric [projection, in Corelib.Classes.CRelationClasses]
+Equivalence_Reflexive [projection, in Corelib.Classes.CRelationClasses]
+equivP [lemma, in Corelib.ssr.ssrbool]
+equivPif [lemma, in Corelib.ssr.ssrbool]
+equivPifn [lemma, in Corelib.ssr.ssrbool]
+equiv_sym [projection, in Corelib.Relations.Relation_Definitions]
+equiv_trans [projection, in Corelib.Relations.Relation_Definitions]
+equiv_refl [projection, in Corelib.Relations.Relation_Definitions]
+equiv_transitive [instance, in Corelib.Classes.Equivalence]
+equiv_symmetric [instance, in Corelib.Classes.Equivalence]
+equiv_reflexive [instance, in Corelib.Classes.Equivalence]
+eq_equivalence [instance, in Corelib.Classes.RelationClasses]
+eq_Transitive [instance, in Corelib.Classes.RelationClasses]
+eq_Symmetric [instance, in Corelib.Classes.RelationClasses]
+eq_Reflexive [instance, in Corelib.Classes.RelationClasses]
+eq_true_rect_r [lemma, in Corelib.Init.Datatypes]
+eq_true_rec_r [lemma, in Corelib.Init.Datatypes]
+eq_true_ind_r [lemma, in Corelib.Init.Datatypes]
+eq_true_sind [definition, in Corelib.Init.Datatypes]
+eq_true_rec [definition, in Corelib.Init.Datatypes]
+eq_true_ind [definition, in Corelib.Init.Datatypes]
+eq_true_rect [definition, in Corelib.Init.Datatypes]
+eq_true [inductive, in Corelib.Init.Datatypes]
+eq_Reflexive [instance, in Corelib.ssr.ssrclasses]
+eq_mem [definition, in Corelib.ssr.ssrbool]
+eq_subrelation [lemma, in Corelib.Classes.CMorphisms]
+eq_proper_proxy [lemma, in Corelib.Classes.CMorphisms]
+eq_Fix_F_sub [lemma, in Corelib.Program.Wf]
+eq_sig2_nondep [definition, in Corelib.Init.Specif]
+eq_sig2_hprop_iff [definition, in Corelib.Init.Specif]
+eq_sig2_ind_uncurried [definition, in Corelib.Init.Specif]
+eq_sig2_rec_uncurried [definition, in Corelib.Init.Specif]
+eq_sig2_rect_uncurried [definition, in Corelib.Init.Specif]
+eq_sig2_rect_exist2 [definition, in Corelib.Init.Specif]
+eq_sig2_rect_exist2_r [definition, in Corelib.Init.Specif]
+eq_sig2_rect_exist2_l [definition, in Corelib.Init.Specif]
+eq_sig2_ind [definition, in Corelib.Init.Specif]
+eq_sig2_rec [definition, in Corelib.Init.Specif]
+eq_sig2_rect [definition, in Corelib.Init.Specif]
+eq_sig2_uncurried_iff [definition, in Corelib.Init.Specif]
+eq_sig2_hprop [definition, in Corelib.Init.Specif]
+eq_exist2_r [definition, in Corelib.Init.Specif]
+eq_exist2_l [definition, in Corelib.Init.Specif]
+eq_sig2 [definition, in Corelib.Init.Specif]
+eq_exist2_curried [lemma, in Corelib.Init.Specif]
+eq_sig2_uncurried [definition, in Corelib.Init.Specif]
+eq_exist2_uncurried [definition, in Corelib.Init.Specif]
+eq_sigT2_nondep [definition, in Corelib.Init.Specif]
+eq_sigT2_hprop_iff [definition, in Corelib.Init.Specif]
+eq_sigT2_ind_uncurried [definition, in Corelib.Init.Specif]
+eq_sigT2_rec_uncurried [definition, in Corelib.Init.Specif]
+eq_sigT2_rect_uncurried [definition, in Corelib.Init.Specif]
+eq_sigT2_rect_existT2 [definition, in Corelib.Init.Specif]
+eq_sigT2_rect_existT2_r [definition, in Corelib.Init.Specif]
+eq_sigT2_rect_existT2_l [definition, in Corelib.Init.Specif]
+eq_sigT2_ind [definition, in Corelib.Init.Specif]
+eq_sigT2_rec [definition, in Corelib.Init.Specif]
+eq_sigT2_rect [definition, in Corelib.Init.Specif]
+eq_sigT2_uncurried_iff [definition, in Corelib.Init.Specif]
+eq_sigT2_hprop [definition, in Corelib.Init.Specif]
+eq_existT2_r [definition, in Corelib.Init.Specif]
+eq_existT2_l [definition, in Corelib.Init.Specif]
+eq_sigT2 [definition, in Corelib.Init.Specif]
+eq_existT2_curried [lemma, in Corelib.Init.Specif]
+eq_sigT2_uncurried [definition, in Corelib.Init.Specif]
+eq_existT2_uncurried [definition, in Corelib.Init.Specif]
+eq_sig_hprop_iff [definition, in Corelib.Init.Specif]
+eq_sig_uncurried_iff [definition, in Corelib.Init.Specif]
+eq_sig_hprop [definition, in Corelib.Init.Specif]
+eq_sig_ind_uncurried [definition, in Corelib.Init.Specif]
+eq_sig_rec_uncurried [definition, in Corelib.Init.Specif]
+eq_sig_rect_uncurried [definition, in Corelib.Init.Specif]
+eq_sig_rect_exist [definition, in Corelib.Init.Specif]
+eq_sig_rect_exist_r [definition, in Corelib.Init.Specif]
+eq_sig_rect_exist_l [definition, in Corelib.Init.Specif]
+eq_sig_ind [definition, in Corelib.Init.Specif]
+eq_sig_rec [definition, in Corelib.Init.Specif]
+eq_sig_rect [definition, in Corelib.Init.Specif]
+eq_exist_r [definition, in Corelib.Init.Specif]
+eq_exist_l [definition, in Corelib.Init.Specif]
+eq_sig [definition, in Corelib.Init.Specif]
+eq_exist_curried [lemma, in Corelib.Init.Specif]
+eq_sig_uncurried [definition, in Corelib.Init.Specif]
+eq_exist_uncurried [definition, in Corelib.Init.Specif]
+eq_sigT_nondep [definition, in Corelib.Init.Specif]
+eq_sigT_hprop_iff [definition, in Corelib.Init.Specif]
+eq_sigT_ind_uncurried [definition, in Corelib.Init.Specif]
+eq_sigT_rec_uncurried [definition, in Corelib.Init.Specif]
+eq_sigT_rect_uncurried [definition, in Corelib.Init.Specif]
+eq_sigT_rect_existT [definition, in Corelib.Init.Specif]
+eq_sigT_rect_existT_r [definition, in Corelib.Init.Specif]
+eq_sigT_rect_existT_l [definition, in Corelib.Init.Specif]
+eq_sigT_ind [definition, in Corelib.Init.Specif]
+eq_sigT_rec [definition, in Corelib.Init.Specif]
+eq_sigT_rect [definition, in Corelib.Init.Specif]
+eq_sigT_uncurried_iff [definition, in Corelib.Init.Specif]
+eq_sigT_hprop [definition, in Corelib.Init.Specif]
+eq_existT_r [definition, in Corelib.Init.Specif]
+eq_existT_l [definition, in Corelib.Init.Specif]
+eq_sigT [definition, in Corelib.Init.Specif]
+eq_existT_curried_congr [lemma, in Corelib.Init.Specif]
+eq_existT_curried_trans [lemma, in Corelib.Init.Specif]
+eq_existT_curried_map [lemma, in Corelib.Init.Specif]
+eq_existT_curried [lemma, in Corelib.Init.Specif]
+eq_sigT_uncurried [definition, in Corelib.Init.Specif]
+eq_existT_uncurried [definition, in Corelib.Init.Specif]
+eq_add_S [definition, in Corelib.Init.Peano]
+eq_S [definition, in Corelib.Init.Peano]
+eq_bij [lemma, in Corelib.ssr.ssrfun]
+eq_can [lemma, in Corelib.ssr.ssrfun]
+eq_inj [lemma, in Corelib.ssr.ssrfun]
+eq_comp [lemma, in Corelib.ssr.ssrfun]
+eq_pars [instance, in Corelib.Classes.Morphisms]
+eq_subrelation [lemma, in Corelib.Classes.Morphisms]
+eq_rewrite_relation [lemma, in Corelib.Classes.Morphisms]
+eq_proper_proxy [lemma, in Corelib.Classes.Morphisms]
+eq_equivalence [instance, in Corelib.Classes.CRelationClasses]
+eq_Transitive [instance, in Corelib.Classes.CRelationClasses]
+eq_Symmetric [instance, in Corelib.Classes.CRelationClasses]
+eq_Reflexive [instance, in Corelib.Classes.CRelationClasses]
+eq_ex2_nondep [definition, in Corelib.Init.Logic]
+eq_ex2_hprop_iff [definition, in Corelib.Init.Logic]
+eq_ex2_ind_uncurried [definition, in Corelib.Init.Logic]
+eq_ex2_rec_uncurried [definition, in Corelib.Init.Logic]
+eq_ex2_rect_uncurried [definition, in Corelib.Init.Logic]
+eq_ex2_rect_ex_intro2 [definition, in Corelib.Init.Logic]
+eq_ex2_rect_ex_intro2_r [definition, in Corelib.Init.Logic]
+eq_ex2_rect_ex_intro2_l [definition, in Corelib.Init.Logic]
+eq_ex2_ind [definition, in Corelib.Init.Logic]
+eq_ex2_rec [definition, in Corelib.Init.Logic]
+eq_ex2_rect [definition, in Corelib.Init.Logic]
+eq_ex2_eta [definition, in Corelib.Init.Logic]
+eq_ex2_uncurried_iff [definition, in Corelib.Init.Logic]
+eq_ex_intro2_hprop [definition, in Corelib.Init.Logic]
+eq_ex_intro2_hprop_nondep [definition, in Corelib.Init.Logic]
+eq_ex2_hprop [definition, in Corelib.Init.Logic]
+eq_ex_intro2_r [definition, in Corelib.Init.Logic]
+eq_ex_intro2_l [definition, in Corelib.Init.Logic]
+eq_ex_intro2 [definition, in Corelib.Init.Logic]
+eq_ex2 [definition, in Corelib.Init.Logic]
+eq_ex2_uncurried [definition, in Corelib.Init.Logic]
+eq_ex_intro2_uncurried [definition, in Corelib.Init.Logic]
+eq_ex_hprop_iff [definition, in Corelib.Init.Logic]
+eq_ex_uncurried_iff [definition, in Corelib.Init.Logic]
+eq_ex_intro_hprop [definition, in Corelib.Init.Logic]
+eq_ex_hprop [definition, in Corelib.Init.Logic]
+eq_ex_ind_uncurried [definition, in Corelib.Init.Logic]
+eq_ex_rec_uncurried [definition, in Corelib.Init.Logic]
+eq_ex_rect_uncurried [definition, in Corelib.Init.Logic]
+eq_ex_rect_ex_intro [definition, in Corelib.Init.Logic]
+eq_ex_rect_ex_intro_r [definition, in Corelib.Init.Logic]
+eq_ex_rect_ex_intro_l [definition, in Corelib.Init.Logic]
+eq_ex_ind [definition, in Corelib.Init.Logic]
+eq_ex_rec [definition, in Corelib.Init.Logic]
+eq_ex_rect [definition, in Corelib.Init.Logic]
+eq_ex_eta [definition, in Corelib.Init.Logic]
+eq_ex_intro_r [definition, in Corelib.Init.Logic]
+eq_ex_intro_l [definition, in Corelib.Init.Logic]
+eq_ex [definition, in Corelib.Init.Logic]
+eq_ex_intro [definition, in Corelib.Init.Logic]
+eq_ex_uncurried [definition, in Corelib.Init.Logic]
+eq_ex_intro_uncurried [definition, in Corelib.Init.Logic]
+eq_stepl [lemma, in Corelib.Init.Logic]
+eq_trans_rew_distr [lemma, in Corelib.Init.Logic]
+eq_trans_sym_distr [lemma, in Corelib.Init.Logic]
+eq_sym_map_distr [lemma, in Corelib.Init.Logic]
+eq_trans_map_distr [lemma, in Corelib.Init.Logic]
+eq_refl_map_distr [lemma, in Corelib.Init.Logic]
+eq_id_comm_r [lemma, in Corelib.Init.Logic]
+eq_id_comm_l [lemma, in Corelib.Init.Logic]
+eq_trans_map [lemma, in Corelib.Init.Logic]
+eq_trans_assoc [lemma, in Corelib.Init.Logic]
+eq_trans_sym_inv_r [lemma, in Corelib.Init.Logic]
+eq_trans_sym_inv_l [lemma, in Corelib.Init.Logic]
+eq_sym_involutive [lemma, in Corelib.Init.Logic]
+eq_trans_refl_r [lemma, in Corelib.Init.Logic]
+eq_trans_refl_l [lemma, in Corelib.Init.Logic]
+eq_rect_r [definition, in Corelib.Init.Logic]
+eq_rec_r [definition, in Corelib.Init.Logic]
+eq_ind_r [definition, in Corelib.Init.Logic]
+eq_sind_r [definition, in Corelib.Init.Logic]
+eq_trans_r [lemma, in Corelib.Init.Logic]
+eq_trans [lemma, in Corelib.Init.Logic]
+eq_sym [lemma, in Corelib.Init.Logic]
+eq_sind [definition, in Corelib.Init.Logic]
+eq_rec [definition, in Corelib.Init.Logic]
+eq_ind [definition, in Corelib.Init.Logic]
+eq_rect [definition, in Corelib.Init.Logic]
+eq_refl [constructor, in Corelib.Init.Logic]
+erefl [abbreviation, in Corelib.ssr.ssrfun]
+error [definition, in Corelib.Init.Specif]
+esym [definition, in Corelib.ssr.ssrfun]
+esymK [lemma, in Corelib.ssr.ssrfun]
+etrans [definition, in Corelib.ssr.ssrfun]
+etrans_id [lemma, in Corelib.ssr.ssrfun]
+Evar [library]
+even [definition, in Corelib.Init.Nat]
+ex [section, in Corelib.Init.Logic]
+ex [inductive, in Corelib.Init.Logic]
+Exc [definition, in Corelib.Init.Specif]
+Exc [section, in Corelib.Init.Specif]
+except [definition, in Corelib.Init.Specif]
+Exc.A [variable, in Corelib.Init.Specif]
+exist [constructor, in Corelib.Init.Specif]
+exists_to_inhabited_sig [lemma, in Corelib.Init.Specif]
+Exists_Forall.One_predicate.P [variable, in Corelib.Lists.ListDef]
+Exists_Forall.One_predicate [section, in Corelib.Lists.ListDef]
+Exists_Forall.A [variable, in Corelib.Lists.ListDef]
+Exists_Forall [section, in Corelib.Lists.ListDef]
+exists_inhabited [lemma, in Corelib.Init.Logic]
+existT [constructor, in Corelib.Init.Specif]
+existT2 [constructor, in Corelib.Init.Specif]
+exist2 [constructor, in Corelib.Init.Specif]
+expose_mem_pred [definition, in Corelib.ssr.ssrbool]
+expose_simpl_pred [definition, in Corelib.ssr.ssrbool]
+ExtensionalEquality [section, in Corelib.ssr.ssrfun]
+ExtensionalEquality.A [variable, in Corelib.ssr.ssrfun]
+ExtensionalEquality.B [variable, in Corelib.ssr.ssrfun]
+ExtensionalEquality.C [variable, in Corelib.ssr.ssrfun]
+external_view_sind [definition, in Corelib.ssr.ssreflect]
+external_view_rec [definition, in Corelib.ssr.ssreflect]
+external_view_ind [definition, in Corelib.ssr.ssreflect]
+external_view_rect [definition, in Corelib.ssr.ssreflect]
+external_view [inductive, in Corelib.ssr.ssreflect]
+Extraction [library]
+ExtrHaskellBasic [library]
+ExtrOcamlBasic [library]
+ex_of_sigT [definition, in Corelib.Init.Specif]
+ex_of_sig [definition, in Corelib.Init.Specif]
+ex_proj3_eq [definition, in Corelib.Init.Logic]
+ex_proj2_of_ex2_eq [definition, in Corelib.Init.Logic]
+ex_proj1_of_ex2_eq [definition, in Corelib.Init.Logic]
+ex_of_ex2_eq [definition, in Corelib.Init.Logic]
+ex_proj2_eq [definition, in Corelib.Init.Logic]
+ex_proj1_eq [definition, in Corelib.Init.Logic]
+ex_rec [definition, in Corelib.Init.Logic]
+ex_rect [definition, in Corelib.Init.Logic]
+ex_Prop.P [variable, in Corelib.Init.Logic]
+ex_Prop.A [variable, in Corelib.Init.Logic]
+ex_Prop [section, in Corelib.Init.Logic]
+ex_eta [definition, in Corelib.Init.Logic]
+ex_proj3 [definition, in Corelib.Init.Logic]
+ex_of_ex2 [definition, in Corelib.Init.Logic]
+ex_intro2 [constructor, in Corelib.Init.Logic]
+ex_proj2 [definition, in Corelib.Init.Logic]
+ex_proj1 [definition, in Corelib.Init.Logic]
+ex_sind [definition, in Corelib.Init.Logic]
+ex_ind [definition, in Corelib.Init.Logic]
+ex_intro [constructor, in Corelib.Init.Logic]
+ex_flip_impl_morphism [instance, in Corelib.Classes.Morphisms_Prop]
+ex_impl_morphism [instance, in Corelib.Classes.Morphisms_Prop]
+ex_iff_morphism [instance, in Corelib.Classes.Morphisms_Prop]
+ex2 [section, in Corelib.Init.Logic]
+ex2 [inductive, in Corelib.Init.Logic]
+ex2_of_sigT2 [definition, in Corelib.Init.Specif]
+ex2_of_sig2 [definition, in Corelib.Init.Specif]
+ex2_rec [definition, in Corelib.Init.Logic]
+ex2_rect [definition, in Corelib.Init.Logic]
+ex2_Prop.Q [variable, in Corelib.Init.Logic]
+ex2_Prop.P [variable, in Corelib.Init.Logic]
+ex2_Prop.A [variable, in Corelib.Init.Logic]
+ex2_Prop [section, in Corelib.Init.Logic]
+ex2_eta [definition, in Corelib.Init.Logic]
+ex2_Projections.Q [variable, in Corelib.Init.Logic]
+ex2_Projections.P [variable, in Corelib.Init.Logic]
+ex2_Projections.A [variable, in Corelib.Init.Logic]
+ex2_Projections [section, in Corelib.Init.Logic]
+ex2_sind [definition, in Corelib.Init.Logic]
+ex2_ind [definition, in Corelib.Init.Logic]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_F.html b/master/corelib/index_global_F.html new file mode 100644 index 0000000000..48122c2777 --- /dev/null +++ b/master/corelib/index_global_F.html @@ -0,0 +1,1173 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

F

+false [constructor, in Corelib.Init.Datatypes]
+False [inductive, in Corelib.Init.Logic]
+false_predicate [definition, in Corelib.Classes.RelationClasses]
+False_sind [definition, in Corelib.Init.Logic]
+False_rec [definition, in Corelib.Init.Logic]
+False_ind [definition, in Corelib.Init.Logic]
+False_rect [definition, in Corelib.Init.Logic]
+FEq [constructor, in Corelib.Floats.PrimFloat]
+fexp [definition, in Corelib.Floats.SpecFloat]
+FGt [constructor, in Corelib.Floats.PrimFloat]
+firstn [definition, in Corelib.Lists.ListDef]
+Fix [definition, in Corelib.Init.Wf]
+Fix_sub_rect [lemma, in Corelib.Program.Wf]
+Fix_rects.equiv_lowers [variable, in Corelib.Program.Wf]
+Fix_F_sub_rect [lemma, in Corelib.Program.Wf]
+Fix_rects.f [variable, in Corelib.Program.Wf]
+Fix_rects.Rwf [variable, in Corelib.Program.Wf]
+Fix_rects.R [variable, in Corelib.Program.Wf]
+Fix_rects.P [variable, in Corelib.Program.Wf]
+Fix_rects.A [variable, in Corelib.Program.Wf]
+Fix_rects [section, in Corelib.Program.Wf]
+fix_sub_eq [lemma, in Corelib.Program.Wf]
+Fix_eq [lemma, in Corelib.Program.Wf]
+Fix_F_inv [lemma, in Corelib.Program.Wf]
+Fix_F_eq [lemma, in Corelib.Program.Wf]
+Fix_sub [definition, in Corelib.Program.Wf]
+Fix_F_sub [definition, in Corelib.Program.Wf]
+fix_proto [definition, in Corelib.Program.Tactics]
+Fix_F_2 [definition, in Corelib.Init.Wf]
+Fix_eq [lemma, in Corelib.Init.Wf]
+Fix_F_inv [lemma, in Corelib.Init.Wf]
+Fix_F_eq [lemma, in Corelib.Init.Wf]
+Fix_F [definition, in Corelib.Init.Wf]
+flatten_cmp_opt [definition, in Corelib.Floats.FloatAxioms]
+flip [definition, in Corelib.Program.Basics]
+flip [definition, in Corelib.Classes.CRelationClasses]
+flip_Equivalence [lemma, in Corelib.Classes.RelationClasses]
+flip_PER [lemma, in Corelib.Classes.RelationClasses]
+flip_StrictOrder [lemma, in Corelib.Classes.RelationClasses]
+flip_PreOrder [lemma, in Corelib.Classes.RelationClasses]
+flip_Antisymmetric [lemma, in Corelib.Classes.RelationClasses]
+flip_Transitive [definition, in Corelib.Classes.RelationClasses]
+flip_Asymmetric [definition, in Corelib.Classes.RelationClasses]
+flip_Symmetric [definition, in Corelib.Classes.RelationClasses]
+flip_Irreflexive [definition, in Corelib.Classes.RelationClasses]
+flip_Reflexive [lemma, in Corelib.Classes.RelationClasses]
+flip_arrow [lemma, in Corelib.Classes.CMorphisms]
+flip_atom [lemma, in Corelib.Classes.CMorphisms]
+flip_respectful [lemma, in Corelib.Classes.CMorphisms]
+flip_proper [definition, in Corelib.Classes.CMorphisms]
+flip_arrow [lemma, in Corelib.Classes.Morphisms]
+flip_atom [lemma, in Corelib.Classes.Morphisms]
+flip_pars [instance, in Corelib.Classes.Morphisms]
+flip_respectful [lemma, in Corelib.Classes.Morphisms]
+flip_proper [definition, in Corelib.Classes.Morphisms]
+flip_Equivalence [lemma, in Corelib.Classes.CRelationClasses]
+flip_PER [lemma, in Corelib.Classes.CRelationClasses]
+flip_StrictOrder [lemma, in Corelib.Classes.CRelationClasses]
+flip_PreOrder [lemma, in Corelib.Classes.CRelationClasses]
+flip_Antisymmetric [lemma, in Corelib.Classes.CRelationClasses]
+flip_Transitive [definition, in Corelib.Classes.CRelationClasses]
+flip_Asymmetric [definition, in Corelib.Classes.CRelationClasses]
+flip_Symmetric [definition, in Corelib.Classes.CRelationClasses]
+flip_Irreflexive [definition, in Corelib.Classes.CRelationClasses]
+flip_Reflexive [lemma, in Corelib.Classes.CRelationClasses]
+flip1 [lemma, in Corelib.Classes.CMorphisms]
+flip1 [lemma, in Corelib.Classes.Morphisms]
+flip2 [lemma, in Corelib.Classes.CMorphisms]
+flip2 [lemma, in Corelib.Classes.Morphisms]
+float [axiom, in Corelib.Floats.PrimFloat]
+Float [library]
+FloatAxioms [library]
+FloatClass [library]
+FloatOps [section, in Corelib.Floats.SpecFloat]
+FloatOps [library]
+FloatOps.emax [variable, in Corelib.Floats.SpecFloat]
+FloatOps.Iter [section, in Corelib.Floats.SpecFloat]
+FloatOps.Iter.A [variable, in Corelib.Floats.SpecFloat]
+FloatOps.Iter.f [variable, in Corelib.Floats.SpecFloat]
+FloatOps.prec [variable, in Corelib.Floats.SpecFloat]
+FloatOps.Rounding [section, in Corelib.Floats.SpecFloat]
+FloatOps.ValidBinary [section, in Corelib.Floats.SpecFloat]
+FloatOps.Zdigits2 [section, in Corelib.Floats.SpecFloat]
+float_class [inductive, in Corelib.Floats.FloatClass]
+float_wrap [projection, in Corelib.Floats.PrimFloat]
+float_wrapper [record, in Corelib.Floats.PrimFloat]
+float_comparison [inductive, in Corelib.Floats.PrimFloat]
+FLt [constructor, in Corelib.Floats.PrimFloat]
+FMap [library]
+FNotComparable [constructor, in Corelib.Floats.PrimFloat]
+Forall [inductive, in Corelib.Lists.ListDef]
+forall_subrelation [lemma, in Corelib.Classes.CMorphisms]
+forall_relation [definition, in Corelib.Classes.CMorphisms]
+forall_def [definition, in Corelib.Classes.CMorphisms]
+forall_subrelation [lemma, in Corelib.Classes.Morphisms]
+forall_relation [definition, in Corelib.Classes.Morphisms]
+forall_def [definition, in Corelib.Classes.Morphisms]
+Forall_sind [definition, in Corelib.Lists.ListDef]
+Forall_ind [definition, in Corelib.Lists.ListDef]
+Forall_cons [constructor, in Corelib.Lists.ListDef]
+Forall_nil [constructor, in Corelib.Lists.ListDef]
+forall_exists_coincide_unique_domain [lemma, in Corelib.Init.Logic]
+forall_exists_unique_domain_coincide [lemma, in Corelib.Init.Logic]
+forE [lemma, in Corelib.ssr.ssrbool]
+Format [module, in Ltac2.Message]
+Free [module, in Ltac2.Fresh]
+frefl [lemma, in Corelib.ssr.ssrfun]
+Fresh [library]
+frshiftexp [axiom, in Corelib.Floats.PrimFloat]
+frshiftexp_spec [axiom, in Corelib.Floats.FloatAxioms]
+FSet [library]
+fst [definition, in Corelib.Init.Datatypes]
+fstT [abbreviation, in Corelib.Init.Datatypes]
+fsym [lemma, in Corelib.ssr.ssrfun]
+ftrans [lemma, in Corelib.ssr.ssrfun]
+fun_if [lemma, in Corelib.ssr.ssrbool]
+fun_of_simpl [definition, in Corelib.ssr.ssrfun]
+F_unfold [lemma, in Corelib.Program.Wf]
+f_equal2_mult [definition, in Corelib.Init.Peano]
+f_equal2_nat [definition, in Corelib.Init.Peano]
+f_equal2_plus [definition, in Corelib.Init.Peano]
+f_equal_pred [definition, in Corelib.Init.Peano]
+f_equal_nat [definition, in Corelib.Init.Peano]
+f_equal_compose [lemma, in Corelib.Init.Logic]
+f_equal5 [lemma, in Corelib.Init.Logic]
+f_equal4 [lemma, in Corelib.Init.Logic]
+f_equal3 [lemma, in Corelib.Init.Logic]
+f_equal2 [lemma, in Corelib.Init.Logic]
+f_equal_dep2 [lemma, in Corelib.Init.Logic]
+f_equal_dep [lemma, in Corelib.Init.Logic]
+f_equal [lemma, in Corelib.Init.Logic]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_G.html b/master/corelib/index_global_G.html new file mode 100644 index 0000000000..6997665859 --- /dev/null +++ b/master/corelib/index_global_G.html @@ -0,0 +1,582 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

G

+gcd [definition, in Corelib.Init.Nat]
+ge [definition, in Corelib.Init.Peano]
+gen [lemma, in Corelib.Init.Logic]
+GenericInstances [section, in Corelib.Classes.CMorphisms]
+GenericInstances [section, in Corelib.Classes.Morphisms]
+GenericInstances.A [variable, in Corelib.Classes.Morphisms]
+GenericInstances.B [variable, in Corelib.Classes.Morphisms]
+GenericInstances.C [variable, in Corelib.Classes.Morphisms]
+GenericInstances.U [variable, in Corelib.Classes.Morphisms]
+gen_st [definition, in Corelib.Setoids.Setoid]
+get [axiom, in Corelib.Strings.PrimString]
+get [axiom, in Corelib.Array.PrimArray]
+get_digit [definition, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+get_copy [axiom, in Corelib.Array.ArrayAxioms]
+get_make [axiom, in Corelib.Array.ArrayAxioms]
+get_set_other [axiom, in Corelib.Array.ArrayAxioms]
+get_set_same [axiom, in Corelib.Array.ArrayAxioms]
+get_out_of_bounds [axiom, in Corelib.Array.ArrayAxioms]
+get_spec [axiom, in Corelib.Strings.PrimStringAxioms]
+get_sign [definition, in Corelib.Floats.PrimFloat]
+Gt [constructor, in Corelib.Init.Datatypes]
+gt [definition, in Corelib.Init.Peano]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_H.html b/master/corelib/index_global_H.html new file mode 100644 index 0000000000..410e929318 --- /dev/null +++ b/master/corelib/index_global_H.html @@ -0,0 +1,588 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

H

+has_quality [definition, in Corelib.ssr.ssrbool]
+head0 [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+head0_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+Hexadecimal [constructor, in Corelib.Init.Hexadecimal]
+hexadecimal [inductive, in Corelib.Init.Hexadecimal]
+Hexadecimal [constructor, in Corelib.Init.Number]
+Hexadecimal [library]
+HexadecimalExp [constructor, in Corelib.Init.Hexadecimal]
+hexadecimal_eq_dec [definition, in Corelib.Init.Hexadecimal]
+homoLR [lemma, in Corelib.ssr.ssrbool]
+homoLR_in [lemma, in Corelib.ssr.ssrbool]
+HomoMonoMorphismFlip [section, in Corelib.ssr.ssrbool]
+HomoMonoMorphismFlip.aD [variable, in Corelib.ssr.ssrbool]
+HomoMonoMorphismFlip.aD' [variable, in Corelib.ssr.ssrbool]
+HomoMonoMorphismFlip.aR [variable, in Corelib.ssr.ssrbool]
+HomoMonoMorphismFlip.aT [variable, in Corelib.ssr.ssrbool]
+HomoMonoMorphismFlip.f [variable, in Corelib.ssr.ssrbool]
+HomoMonoMorphismFlip.rR [variable, in Corelib.ssr.ssrbool]
+HomoMonoMorphismFlip.rT [variable, in Corelib.ssr.ssrbool]
+homomorphism_2 [definition, in Corelib.ssr.ssrfun]
+homomorphism_1 [definition, in Corelib.ssr.ssrfun]
+homoRL [lemma, in Corelib.ssr.ssrbool]
+homoRL_in [lemma, in Corelib.ssr.ssrbool]
+homo_sym_in11 [lemma, in Corelib.ssr.ssrbool]
+homo_sym_in [lemma, in Corelib.ssr.ssrbool]
+homo_sym [lemma, in Corelib.ssr.ssrbool]
+homo_mono_in [lemma, in Corelib.ssr.ssrbool]
+homo_mono [lemma, in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_I.html b/master/corelib/index_global_I.html new file mode 100644 index 0000000000..cb2b498eb2 --- /dev/null +++ b/master/corelib/index_global_I.html @@ -0,0 +1,1310 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

I

+I [constructor, in Corelib.Init.Logic]
+id [definition, in Corelib.Init.Datatypes]
+ID [definition, in Corelib.Init.Datatypes]
+id [abbreviation, in Corelib.ssr.ssrfun]
+idempotent [definition, in Corelib.ssr.ssrfun]
+Ident [library]
+identity [abbreviation, in Corelib.Init.Datatypes]
+identity_rect_r [abbreviation, in Corelib.Init.Datatypes]
+identity_rec_r [abbreviation, in Corelib.Init.Datatypes]
+identity_ind_r [abbreviation, in Corelib.Init.Datatypes]
+identity_congr [abbreviation, in Corelib.Init.Datatypes]
+identity_trans [abbreviation, in Corelib.Init.Datatypes]
+identity_sym [abbreviation, in Corelib.Init.Datatypes]
+identity_rect [abbreviation, in Corelib.Init.Datatypes]
+identity_rec [abbreviation, in Corelib.Init.Datatypes]
+identity_ind [abbreviation, in Corelib.Init.Datatypes]
+identity_refl [abbreviation, in Corelib.Init.Datatypes]
+idfun [definition, in Corelib.ssr.ssrfun]
+idP [lemma, in Corelib.ssr.ssrbool]
+idPn [lemma, in Corelib.ssr.ssrbool]
+idProp [definition, in Corelib.Init.Datatypes]
+IDProp [definition, in Corelib.Init.Datatypes]
+id_int [definition, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+ifE [lemma, in Corelib.ssr.ssrbool]
+ifF [lemma, in Corelib.ssr.ssrbool]
+iff [definition, in Corelib.Init.Logic]
+iffLR [lemma, in Corelib.ssr.ssreflect]
+iffLRn [lemma, in Corelib.ssr.ssreflect]
+iffP [lemma, in Corelib.ssr.ssrbool]
+iffRL [lemma, in Corelib.ssr.ssreflect]
+iffRLn [lemma, in Corelib.ssr.ssreflect]
+iffT [definition, in Corelib.Classes.CRelationClasses]
+iffT_flip_arrow_subrelation [instance, in Corelib.Classes.CMorphisms]
+iffT_arrow_subrelation [instance, in Corelib.Classes.CMorphisms]
+iffT_Transitive [instance, in Corelib.Classes.CRelationClasses]
+iffT_Symmetric [instance, in Corelib.Classes.CRelationClasses]
+iffT_Reflexive [instance, in Corelib.Classes.CRelationClasses]
+iff_equivalence [instance, in Corelib.Classes.RelationClasses]
+iff_Transitive [instance, in Corelib.Classes.RelationClasses]
+iff_Symmetric [instance, in Corelib.Classes.RelationClasses]
+iff_Reflexive [instance, in Corelib.Classes.RelationClasses]
+iff_rewrite_relation [instance, in Corelib.Classes.RelationClasses]
+iff_Reflexive [instance, in Corelib.ssr.ssrclasses]
+iff_flip_impl_subrelation [instance, in Corelib.Classes.CMorphisms]
+iff_impl_subrelation [instance, in Corelib.Classes.CMorphisms]
+iff_pars [instance, in Corelib.Classes.Morphisms]
+iff_flip_impl_subrelation [instance, in Corelib.Classes.Morphisms]
+iff_impl_subrelation [instance, in Corelib.Classes.Morphisms]
+iff_equivalence [instance, in Corelib.Classes.CRelationClasses]
+iff_Transitive [instance, in Corelib.Classes.CRelationClasses]
+iff_Symmetric [instance, in Corelib.Classes.CRelationClasses]
+iff_Reflexive [instance, in Corelib.Classes.CRelationClasses]
+iff_stepl [lemma, in Corelib.Init.Logic]
+iff_to_and [lemma, in Corelib.Init.Logic]
+iff_and [lemma, in Corelib.Init.Logic]
+iff_sym [lemma, in Corelib.Init.Logic]
+iff_trans [lemma, in Corelib.Init.Logic]
+iff_refl [lemma, in Corelib.Init.Logic]
+iff_iff_iff_impl_morphism [instance, in Corelib.Classes.Morphisms_Prop]
+ifN [lemma, in Corelib.ssr.ssrbool]
+IfNotations [module, in Corelib.Init.Notations]
+if _ is _ then _ else _ [notation, in Corelib.Init.Notations]
+ifP [lemma, in Corelib.ssr.ssrbool]
+ifPn [lemma, in Corelib.ssr.ssrbool]
+IfSpecFalse [constructor, in Corelib.ssr.ssrbool]
+IfSpecTrue [constructor, in Corelib.ssr.ssrbool]
+ifT [lemma, in Corelib.ssr.ssrbool]
+if_expr [definition, in Corelib.ssr.ssrbool]
+if_arg [lemma, in Corelib.ssr.ssrbool]
+if_neg [lemma, in Corelib.ssr.ssrbool]
+if_same [lemma, in Corelib.ssr.ssrbool]
+if_spec [inductive, in Corelib.ssr.ssrbool]
+impl [definition, in Corelib.Program.Basics]
+implb [definition, in Corelib.Init.Datatypes]
+Implies [constructor, in Corelib.ssr.ssrbool]
+implies [inductive, in Corelib.ssr.ssrbool]
+impliesP [lemma, in Corelib.ssr.ssrbool]
+impliesPn [lemma, in Corelib.ssr.ssrbool]
+implybb [lemma, in Corelib.ssr.ssrbool]
+implybE [lemma, in Corelib.ssr.ssrbool]
+implybF [lemma, in Corelib.ssr.ssrbool]
+implybN [lemma, in Corelib.ssr.ssrbool]
+implybNN [lemma, in Corelib.ssr.ssrbool]
+implybT [lemma, in Corelib.ssr.ssrbool]
+implyb_id2l [lemma, in Corelib.ssr.ssrbool]
+implyb_idr [lemma, in Corelib.ssr.ssrbool]
+implyb_idl [lemma, in Corelib.ssr.ssrbool]
+implyFb [lemma, in Corelib.ssr.ssrbool]
+implyNb [lemma, in Corelib.ssr.ssrbool]
+implyP [lemma, in Corelib.ssr.ssrbool]
+implyPP [lemma, in Corelib.ssr.ssrbool]
+implyTb [lemma, in Corelib.ssr.ssrbool]
+impl_Transitive [instance, in Corelib.Classes.RelationClasses]
+impl_Reflexive [instance, in Corelib.Classes.RelationClasses]
+impl_rewrite_relation [instance, in Corelib.Classes.RelationClasses]
+impl_pars [instance, in Corelib.Classes.Morphisms]
+impl_Transitive [instance, in Corelib.Classes.CRelationClasses]
+impl_Reflexive [instance, in Corelib.Classes.CRelationClasses]
+imp_iff_compat_r [lemma, in Corelib.Init.Logic]
+imp_iff_compat_l [lemma, in Corelib.Init.Logic]
+inclusion [definition, in Corelib.Relations.Relation_Definitions]
+Ind [library]
+inE [definition, in Corelib.ssr.ssrbool]
+infinity [definition, in Corelib.Floats.PrimFloat]
+inhabited [inductive, in Corelib.Init.Logic]
+inhabited_sig_to_exists [lemma, in Corelib.Init.Specif]
+inhabited_covariant [lemma, in Corelib.Init.Logic]
+inhabited_sind [definition, in Corelib.Init.Logic]
+inhabited_ind [definition, in Corelib.Init.Logic]
+inhabits [constructor, in Corelib.Init.Logic]
+Init [library]
+Init [library]
+Injections [section, in Corelib.ssr.ssrfun]
+InjectionsTheory [section, in Corelib.ssr.ssrfun]
+InjectionsTheory.A [variable, in Corelib.ssr.ssrfun]
+InjectionsTheory.B [variable, in Corelib.ssr.ssrfun]
+InjectionsTheory.C [variable, in Corelib.ssr.ssrfun]
+InjectionsTheory.f [variable, in Corelib.ssr.ssrfun]
+InjectionsTheory.g [variable, in Corelib.ssr.ssrfun]
+InjectionsTheory.h [variable, in Corelib.ssr.ssrfun]
+Injections.aT [variable, in Corelib.ssr.ssrfun]
+Injections.f [variable, in Corelib.ssr.ssrfun]
+Injections.rT [variable, in Corelib.ssr.ssrfun]
+injective [definition, in Corelib.ssr.ssrfun]
+injective_projections [lemma, in Corelib.Init.Datatypes]
+inj_can_sym_in [lemma, in Corelib.ssr.ssrbool]
+inj_can_sym_on [lemma, in Corelib.ssr.ssrbool]
+inj_can_sym_in_on [lemma, in Corelib.ssr.ssrbool]
+inj_can_sym_in_on.g [variable, in Corelib.ssr.ssrbool]
+inj_can_sym_in_on.f [variable, in Corelib.ssr.ssrbool]
+inj_can_sym_in_on.rD [variable, in Corelib.ssr.ssrbool]
+inj_can_sym_in_on.aD [variable, in Corelib.ssr.ssrbool]
+inj_can_sym_in_on.rT [variable, in Corelib.ssr.ssrbool]
+inj_can_sym_in_on.aT [variable, in Corelib.ssr.ssrbool]
+inj_can_sym_in_on [section, in Corelib.ssr.ssrbool]
+inj_can_eq [lemma, in Corelib.ssr.ssrfun]
+inj_compr [lemma, in Corelib.ssr.ssrfun]
+inj_comp [lemma, in Corelib.ssr.ssrfun]
+inj_can_sym [lemma, in Corelib.ssr.ssrfun]
+inj_id [lemma, in Corelib.ssr.ssrfun]
+inl [constructor, in Corelib.Init.Datatypes]
+inleft [constructor, in Corelib.Init.Specif]
+inPhantom [definition, in Corelib.ssr.ssrbool]
+inr [constructor, in Corelib.Init.Datatypes]
+inright [constructor, in Corelib.Init.Specif]
+inst [lemma, in Corelib.Init.Logic]
+int [abbreviation, in Corelib.Init.Hexadecimal]
+int [abbreviation, in Corelib.Init.Decimal]
+int [abbreviation, in Corelib.Init.Number]
+int [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+Int [library]
+IntDecimal [constructor, in Corelib.Init.Number]
+IntDef [library]
+interchange [definition, in Corelib.ssr.ssrfun]
+internal_int_dec_bl [abbreviation, in Corelib.Init.Hexadecimal]
+internal_int_dec_lb [abbreviation, in Corelib.Init.Hexadecimal]
+internal_int_dec_bl [abbreviation, in Corelib.Init.Decimal]
+internal_int_dec_lb [abbreviation, in Corelib.Init.Decimal]
+internal_int_dec_bl [abbreviation, in Corelib.Init.Number]
+internal_int_dec_lb [abbreviation, in Corelib.Init.Number]
+IntHexadecimal [constructor, in Corelib.Init.Number]
+introF [lemma, in Corelib.ssr.ssrbool]
+introFn [lemma, in Corelib.ssr.ssrbool]
+introN [lemma, in Corelib.ssr.ssrbool]
+introNf [lemma, in Corelib.ssr.ssrbool]
+introNTF [lemma, in Corelib.ssr.ssrbool]
+introP [lemma, in Corelib.ssr.ssrbool]
+introT [lemma, in Corelib.ssr.ssrbool]
+introTF [lemma, in Corelib.ssr.ssrbool]
+introTFn [lemma, in Corelib.ssr.ssrbool]
+introTn [lemma, in Corelib.ssr.ssrbool]
+inT_bij [lemma, in Corelib.ssr.ssrbool]
+int_beq [abbreviation, in Corelib.Init.Hexadecimal]
+int_eq_dec [abbreviation, in Corelib.Init.Hexadecimal]
+int_of_int [definition, in Corelib.Init.Decimal]
+int_beq [abbreviation, in Corelib.Init.Decimal]
+int_eq_dec [abbreviation, in Corelib.Init.Decimal]
+int_of_int [definition, in Corelib.Init.Number]
+int_beq [abbreviation, in Corelib.Init.Number]
+int_eq_dec [abbreviation, in Corelib.Init.Number]
+int_wrap [projection, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+int_wrapper [record, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+Int63NotationsInternalA [module, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+inverse_impl_rewrite_relation [instance, in Corelib.Classes.RelationClasses]
+Involutions [section, in Corelib.ssr.ssrfun]
+Involutions.A [variable, in Corelib.ssr.ssrfun]
+Involutions.f [variable, in Corelib.ssr.ssrfun]
+Involutions.Hf [variable, in Corelib.ssr.ssrfun]
+involutive [definition, in Corelib.ssr.ssrfun]
+inv_bij [lemma, in Corelib.ssr.ssrfun]
+inv_inj [lemma, in Corelib.ssr.ssrfun]
+inW_bij [lemma, in Corelib.ssr.ssrbool]
+in_onS_can [lemma, in Corelib.ssr.ssrbool]
+in_onW_can [lemma, in Corelib.ssr.ssrbool]
+in_sig.P3 [variable, in Corelib.ssr.ssrbool]
+in_sig.P2 [variable, in Corelib.ssr.ssrbool]
+in_sig.P1 [variable, in Corelib.ssr.ssrbool]
+in_sig.D3 [variable, in Corelib.ssr.ssrbool]
+in_sig.D2 [variable, in Corelib.ssr.ssrbool]
+in_sig.D1 [variable, in Corelib.ssr.ssrbool]
+in_sig.T3 [variable, in Corelib.ssr.ssrbool]
+in_sig.T2 [variable, in Corelib.ssr.ssrbool]
+in_sig.T1 [variable, in Corelib.ssr.ssrbool]
+in_sig [section, in Corelib.ssr.ssrbool]
+in_inj_comp [lemma, in Corelib.ssr.ssrbool]
+in_on2S [lemma, in Corelib.ssr.ssrbool]
+in_on1lS [lemma, in Corelib.ssr.ssrbool]
+in_on1S [lemma, in Corelib.ssr.ssrbool]
+in_on2W [lemma, in Corelib.ssr.ssrbool]
+in_on1lW [lemma, in Corelib.ssr.ssrbool]
+in_on1W [lemma, in Corelib.ssr.ssrbool]
+in_on2P [lemma, in Corelib.ssr.ssrbool]
+in_on1lP [lemma, in Corelib.ssr.ssrbool]
+in_on1P [lemma, in Corelib.ssr.ssrbool]
+in_unkey [abbreviation, in Corelib.ssr.ssrbool]
+in_simpl [lemma, in Corelib.ssr.ssrbool]
+in_collective [lemma, in Corelib.ssr.ssrbool]
+in_applicative [lemma, in Corelib.ssr.ssrbool]
+in_mem [definition, in Corelib.ssr.ssrbool]
+in_bounds [abbreviation, in Corelib.Array.ArrayAxioms]
+in_right [abbreviation, in Corelib.Program.Utils]
+in_left [abbreviation, in Corelib.Program.Utils]
+in1T [lemma, in Corelib.ssr.ssrbool]
+in1W [lemma, in Corelib.ssr.ssrbool]
+in1_sig [lemma, in Corelib.ssr.ssrbool]
+in2T [lemma, in Corelib.ssr.ssrbool]
+in2W [lemma, in Corelib.ssr.ssrbool]
+in2_sig [lemma, in Corelib.ssr.ssrbool]
+in3T [lemma, in Corelib.ssr.ssrbool]
+in3W [lemma, in Corelib.ssr.ssrbool]
+in3_sig [lemma, in Corelib.ssr.ssrbool]
+ipat [module, in Corelib.ssr.ssreflect]
+[ ! _ ] (ssripat_scope) [notation, in Corelib.ssr.ssreflect]
+[ 1 ! _ ] (ssripat_scope) [notation, in Corelib.ssr.ssreflect]
+[ dup ] (ssripat_scope) [notation, in Corelib.ssr.ssreflect]
+[ swap ] (ssripat_scope) [notation, in Corelib.ssr.ssreflect]
+[ apply ] (ssripat_scope) [notation, in Corelib.ssr.ssreflect]
+Irreflexive [record, in Corelib.Classes.RelationClasses]
+Irreflexive [inductive, in Corelib.Classes.RelationClasses]
+irreflexive [definition, in Corelib.ssr.ssrbool]
+Irreflexive [record, in Corelib.Classes.CRelationClasses]
+Irreflexive [inductive, in Corelib.Classes.CRelationClasses]
+irreflexivity [projection, in Corelib.Classes.RelationClasses]
+irreflexivity [constructor, in Corelib.Classes.RelationClasses]
+irreflexivity [projection, in Corelib.Classes.CRelationClasses]
+irreflexivity [constructor, in Corelib.Classes.CRelationClasses]
+isSome [definition, in Corelib.ssr.ssrbool]
+IsSucc [definition, in Corelib.Init.Peano]
+isT [definition, in Corelib.ssr.ssrbool]
+is_subrelation [projection, in Corelib.Classes.RelationClasses]
+is_subrelation [constructor, in Corelib.Classes.RelationClasses]
+is_true [definition, in Corelib.Init.Datatypes]
+is_eq_true [constructor, in Corelib.Init.Datatypes]
+is_inleft [definition, in Corelib.ssr.ssrbool]
+is_left [definition, in Corelib.ssr.ssrbool]
+is_inl [definition, in Corelib.ssr.ssrbool]
+is_true_locked_true [lemma, in Corelib.ssr.ssrbool]
+is_true_true [lemma, in Corelib.ssr.ssrbool]
+is_even [definition, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+is_zero [definition, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+is_subrelation [projection, in Corelib.Classes.CRelationClasses]
+is_subrelation [constructor, in Corelib.Classes.CRelationClasses]
+is_finite [definition, in Corelib.Floats.PrimFloat]
+is_infinity [definition, in Corelib.Floats.PrimFloat]
+is_zero [definition, in Corelib.Floats.PrimFloat]
+is_nan [definition, in Corelib.Floats.PrimFloat]
+iter [definition, in Corelib.Init.Nat]
+iter_pos [definition, in Corelib.Floats.SpecFloat]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_J.html b/master/corelib/index_global_J.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_global_J.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_K.html b/master/corelib/index_global_K.html new file mode 100644 index 0000000000..02ce204441 --- /dev/null +++ b/master/corelib/index_global_K.html @@ -0,0 +1,580 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

K

+KeyedPred [definition, in Corelib.ssr.ssrbool]
+KeyedQualifier [definition, in Corelib.ssr.ssrbool]
+KeyedQualifier [section, in Corelib.ssr.ssrbool]
+KeyedQualifier.k [variable, in Corelib.ssr.ssrbool]
+KeyedQualifier.k_q [variable, in Corelib.ssr.ssrbool]
+KeyedQualifier.n [variable, in Corelib.ssr.ssrbool]
+KeyedQualifier.q [variable, in Corelib.ssr.ssrbool]
+KeyedQualifier.T [variable, in Corelib.ssr.ssrbool]
+keyed_qualifier_keyed [definition, in Corelib.ssr.ssrbool]
+keyed_qualifier_suproof [lemma, in Corelib.ssr.ssrbool]
+keyed_qualifier [record, in Corelib.ssr.ssrbool]
+keyed_mem_simpl [definition, in Corelib.ssr.ssrbool]
+keyed_mem [definition, in Corelib.ssr.ssrbool]
+keyed_predE [lemma, in Corelib.ssr.ssrbool]
+keyed_pred [record, in Corelib.ssr.ssrbool]
+KeyPred [section, in Corelib.ssr.ssrbool]
+KeyPred.k [variable, in Corelib.ssr.ssrbool]
+KeyPred.k_p [variable, in Corelib.ssr.ssrbool]
+KeyPred.p [variable, in Corelib.ssr.ssrbool]
+KeyPred.T [variable, in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_L.html b/master/corelib/index_global_L.html new file mode 100644 index 0000000000..c9e9f565a8 --- /dev/null +++ b/master/corelib/index_global_L.html @@ -0,0 +1,1187 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

L

+land [definition, in Corelib.Init.Nat]
+land [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+land_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+Lazy [library]
+ldiff [definition, in Corelib.Init.Nat]
+ldshiftexp [axiom, in Corelib.Floats.PrimFloat]
+ldshiftexp_spec [axiom, in Corelib.Floats.FloatAxioms]
+le [inductive, in Corelib.Init.Peano]
+leb [definition, in Corelib.Init.Nat]
+leb [axiom, in Corelib.Floats.PrimFloat]
+leb [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+leb_spec [axiom, in Corelib.Floats.FloatAxioms]
+leb_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+leb_length [axiom, in Corelib.Array.ArrayAxioms]
+leb_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+left [constructor, in Corelib.Init.Specif]
+left_transitive [definition, in Corelib.ssr.ssrbool]
+left_loop [definition, in Corelib.ssr.ssrfun]
+left_commutative [definition, in Corelib.ssr.ssrfun]
+left_id [definition, in Corelib.ssr.ssrfun]
+left_distributive [definition, in Corelib.ssr.ssrfun]
+left_zero [definition, in Corelib.ssr.ssrfun]
+left_injective [definition, in Corelib.ssr.ssrfun]
+left_inverse [definition, in Corelib.ssr.ssrfun]
+Leibniz [module, in Corelib.Floats.FloatAxioms]
+Leibniz [module, in Corelib.Floats.PrimFloat]
+Leibniz.eqb [axiom, in Corelib.Floats.PrimFloat]
+Leibniz.eqb_spec [axiom, in Corelib.Floats.FloatAxioms]
+length [definition, in Corelib.Init.Datatypes]
+length [axiom, in Corelib.Strings.PrimString]
+length [axiom, in Corelib.Array.PrimArray]
+length_copy [axiom, in Corelib.Array.ArrayAxioms]
+length_set [axiom, in Corelib.Array.ArrayAxioms]
+length_make [axiom, in Corelib.Array.ArrayAxioms]
+length_spec [axiom, in Corelib.Strings.PrimStringAxioms]
+lesb [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+le_n_S [lemma, in Corelib.Init.Peano]
+le_0_n [lemma, in Corelib.Init.Peano]
+le_S_n [lemma, in Corelib.Init.Peano]
+le_pred [lemma, in Corelib.Init.Peano]
+le_sind [definition, in Corelib.Init.Peano]
+le_ind [definition, in Corelib.Init.Peano]
+le_S [constructor, in Corelib.Init.Peano]
+le_n [constructor, in Corelib.Init.Peano]
+list [inductive, in Corelib.Init.Datatypes]
+List [library]
+ListDef [library]
+list_sind [definition, in Corelib.Init.Datatypes]
+list_rec [definition, in Corelib.Init.Datatypes]
+list_ind [definition, in Corelib.Init.Datatypes]
+list_rect [definition, in Corelib.Init.Datatypes]
+list_compare [definition, in Corelib.Lists.ListDef]
+Little [module, in Corelib.Init.Hexadecimal]
+Little [module, in Corelib.Init.Decimal]
+Little.double [definition, in Corelib.Init.Hexadecimal]
+Little.double [definition, in Corelib.Init.Decimal]
+Little.succ [definition, in Corelib.Init.Hexadecimal]
+Little.succ [definition, in Corelib.Init.Decimal]
+Little.succ_double [definition, in Corelib.Init.Hexadecimal]
+Little.succ_double [definition, in Corelib.Init.Decimal]
+LocalGlobal [section, in Corelib.ssr.ssrbool]
+LocalGlobal.allQ1 [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.allQ1l [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.allQ2 [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.d1 [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.D1 [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.d1' [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.d2 [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.D2 [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.d2' [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.d3 [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.D3 [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.d3' [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.f [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.f' [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.g [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.h [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.P1 [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.P2 [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.P3 [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.Q1 [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.Q1l [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.Q2 [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.sub1 [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.sub2 [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.sub3 [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.T1 [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.T2 [variable, in Corelib.ssr.ssrbool]
+LocalGlobal.T3 [variable, in Corelib.ssr.ssrbool]
+LocalProperties [section, in Corelib.ssr.ssrbool]
+LocalProperties.d1 [variable, in Corelib.ssr.ssrbool]
+LocalProperties.d2 [variable, in Corelib.ssr.ssrbool]
+LocalProperties.d3 [variable, in Corelib.ssr.ssrbool]
+LocalProperties.f [variable, in Corelib.ssr.ssrbool]
+LocalProperties.T1 [variable, in Corelib.ssr.ssrbool]
+LocalProperties.T2 [variable, in Corelib.ssr.ssrbool]
+LocalProperties.T3 [variable, in Corelib.ssr.ssrbool]
+location [inductive, in Corelib.Floats.SpecFloat]
+location_sind [definition, in Corelib.Floats.SpecFloat]
+location_rec [definition, in Corelib.Floats.SpecFloat]
+location_ind [definition, in Corelib.Floats.SpecFloat]
+location_rect [definition, in Corelib.Floats.SpecFloat]
+lock [lemma, in Corelib.ssr.ssreflect]
+locked [definition, in Corelib.ssr.ssreflect]
+locked_with_unlockable [definition, in Corelib.ssr.ssreflect]
+locked_withE [lemma, in Corelib.ssr.ssreflect]
+locked_with [definition, in Corelib.ssr.ssreflect]
+loc_of_shr_record [definition, in Corelib.Floats.SpecFloat]
+loc_Inexact [constructor, in Corelib.Floats.SpecFloat]
+loc_Exact [constructor, in Corelib.Floats.SpecFloat]
+Logic [library]
+Logic_lemmas.equality.z [variable, in Corelib.Init.Logic]
+Logic_lemmas.equality.y [variable, in Corelib.Init.Logic]
+Logic_lemmas.equality.x [variable, in Corelib.Init.Logic]
+Logic_lemmas.equality.f [variable, in Corelib.Init.Logic]
+Logic_lemmas.equality.B [variable, in Corelib.Init.Logic]
+Logic_lemmas.equality.A [variable, in Corelib.Init.Logic]
+Logic_lemmas.equality [section, in Corelib.Init.Logic]
+Logic_lemmas [section, in Corelib.Init.Logic]
+log2 [definition, in Corelib.Init.Nat]
+log2_iter [definition, in Corelib.Init.Nat]
+lor [definition, in Corelib.Init.Nat]
+lor [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+lor_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+lsl [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+lsl_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+lsr [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+lsr_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+Lt [constructor, in Corelib.Init.Datatypes]
+lt [definition, in Corelib.Init.Peano]
+Ltac [library]
+Ltac1 [library]
+Ltac2 [module, in Ltac2.Compat.Coq818]
+Ltac2 [library]
+Ltac2.Array [module, in Ltac2.Compat.Coq818]
+ltb [definition, in Corelib.Init.Nat]
+ltb [axiom, in Corelib.Floats.PrimFloat]
+ltb [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+ltb_spec [axiom, in Corelib.Floats.FloatAxioms]
+ltb_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+ltb_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+ltsb [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+lxor [definition, in Corelib.Init.Nat]
+lxor [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+lxor_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_M.html b/master/corelib/index_global_M.html new file mode 100644 index 0000000000..2f0c2f8e02 --- /dev/null +++ b/master/corelib/index_global_M.html @@ -0,0 +1,1151 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

M

+make [axiom, in Corelib.Strings.PrimString]
+make [axiom, in Corelib.Array.PrimArray]
+make_spec [axiom, in Corelib.Strings.PrimStringAxioms]
+manifest_mem_pred [record, in Corelib.ssr.ssrbool]
+manifest_simpl_pred [record, in Corelib.ssr.ssrbool]
+map [definition, in Corelib.Lists.ListDef]
+Map [section, in Corelib.Lists.ListDef]
+map_subst_map [lemma, in Corelib.Init.Logic]
+map_subst [lemma, in Corelib.Init.Logic]
+Map.A [variable, in Corelib.Lists.ListDef]
+Map.B [variable, in Corelib.Lists.ListDef]
+Map.f [variable, in Corelib.Lists.ListDef]
+master_key [lemma, in Corelib.ssr.ssreflect]
+max [definition, in Corelib.Init.Nat]
+max [abbreviation, in Corelib.Init.Peano]
+max_r [lemma, in Corelib.Init.Peano]
+max_l [lemma, in Corelib.Init.Peano]
+max_length [axiom, in Corelib.Strings.PrimString]
+max_int [definition, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+max_length [axiom, in Corelib.Array.PrimArray]
+measure_wf [lemma, in Corelib.Program.Wf]
+Measure_well_founded.m [variable, in Corelib.Program.Wf]
+Measure_well_founded.wf [variable, in Corelib.Program.Wf]
+Measure_well_founded.R [variable, in Corelib.Program.Wf]
+Measure_well_founded.M [variable, in Corelib.Program.Wf]
+Measure_well_founded.T [variable, in Corelib.Program.Wf]
+Measure_well_founded [section, in Corelib.Program.Wf]
+mem [definition, in Corelib.ssr.ssrbool]
+Mem [constructor, in Corelib.ssr.ssrbool]
+memE [definition, in Corelib.ssr.ssrbool]
+memPredType [definition, in Corelib.ssr.ssrbool]
+mem_mem [lemma, in Corelib.ssr.ssrbool]
+mem_simpl [lemma, in Corelib.ssr.ssrbool]
+mem_topred [lemma, in Corelib.ssr.ssrbool]
+mem_pred_value [projection, in Corelib.ssr.ssrbool]
+mem_pred [inductive, in Corelib.ssr.ssrbool]
+Message [library]
+Meta [library]
+min [definition, in Corelib.Init.Nat]
+min [abbreviation, in Corelib.Init.Peano]
+minus [abbreviation, in Corelib.Init.Peano]
+min_r [lemma, in Corelib.Init.Peano]
+min_l [lemma, in Corelib.Init.Peano]
+min_int [definition, in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+mod [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+mods [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+modulo [definition, in Corelib.Init.Nat]
+mod_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+mod_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+MonoHomoMorphismTheory [section, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.mem_g [variable, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.fgK [variable, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.rR [variable, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.aR [variable, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.rP [variable, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.aP [variable, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.rD [variable, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.aD [variable, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.g [variable, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.f [variable, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.rT [variable, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.aT [variable, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in [section, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory.aP [variable, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory.aR [variable, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory.aT [variable, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory.f [variable, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory.fgK [variable, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory.g [variable, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory.rP [variable, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory.rR [variable, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory.rT [variable, in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory.sT [variable, in Corelib.ssr.ssrbool]
+monoLR [lemma, in Corelib.ssr.ssrbool]
+monoLR_in [lemma, in Corelib.ssr.ssrbool]
+monomorphism_2 [definition, in Corelib.ssr.ssrfun]
+monomorphism_1 [definition, in Corelib.ssr.ssrfun]
+monoRL [lemma, in Corelib.ssr.ssrbool]
+monoRL_in [lemma, in Corelib.ssr.ssrbool]
+monoW [lemma, in Corelib.ssr.ssrbool]
+monoW_in [lemma, in Corelib.ssr.ssrbool]
+mono_sym_in11 [lemma, in Corelib.ssr.ssrbool]
+mono_sym_in [lemma, in Corelib.ssr.ssrbool]
+mono_sym [lemma, in Corelib.ssr.ssrbool]
+mono1W_in [lemma, in Corelib.ssr.ssrbool]
+mono2W [lemma, in Corelib.ssr.ssrbool]
+mono2W_in [abbreviation, in Corelib.ssr.ssrbool]
+Morphism [section, in Corelib.ssr.ssrfun]
+Morphisms [library]
+Morphisms_Prop [library]
+morphism_2 [definition, in Corelib.ssr.ssrfun]
+morphism_1 [definition, in Corelib.ssr.ssrfun]
+Morphism.aT [variable, in Corelib.ssr.ssrfun]
+Morphism.f [variable, in Corelib.ssr.ssrfun]
+Morphism.rT [variable, in Corelib.ssr.ssrfun]
+Morphism.sT [variable, in Corelib.ssr.ssrfun]
+MR [definition, in Corelib.Program.Wf]
+mul [definition, in Corelib.Init.Nat]
+mul [axiom, in Corelib.Floats.PrimFloat]
+mul [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+mulc [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+mulc_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+mult [abbreviation, in Corelib.Init.Peano]
+mult_succ_r_reverse [abbreviation, in Corelib.Init.Peano]
+mult_0_r_reverse [abbreviation, in Corelib.Init.Peano]
+mult_n_Sm [lemma, in Corelib.Init.Peano]
+mult_n_O [lemma, in Corelib.Init.Peano]
+mul_spec [axiom, in Corelib.Floats.FloatAxioms]
+mul_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_N.html b/master/corelib/index_global_N.html new file mode 100644 index 0000000000..371617cd43 --- /dev/null +++ b/master/corelib/index_global_N.html @@ -0,0 +1,1182 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

N

+N [inductive, in Corelib.Numbers.BinNums]
+N [module, in Corelib.BinNums.NatDef]
+NaN [constructor, in Corelib.Floats.FloatClass]
+nan [definition, in Corelib.Floats.PrimFloat]
+nandP [lemma, in Corelib.ssr.ssrbool]
+nary_congruence [lemma, in Corelib.ssr.ssreflect]
+nary_congruence_statement [definition, in Corelib.ssr.ssreflect]
+nat [inductive, in Corelib.Init.Datatypes]
+Nat [library]
+NatDef [library]
+NatSeq [section, in Corelib.Lists.ListDef]
+nat_sind [definition, in Corelib.Init.Datatypes]
+nat_rec [definition, in Corelib.Init.Datatypes]
+nat_ind [definition, in Corelib.Init.Datatypes]
+nat_rect [definition, in Corelib.Init.Datatypes]
+nat_rect_plus [lemma, in Corelib.Init.Peano]
+nat_rect_succ_r [lemma, in Corelib.Init.Peano]
+nat_double_ind [lemma, in Corelib.Init.Peano]
+nat_case [lemma, in Corelib.Init.Peano]
+nb_digits [definition, in Corelib.Init.Hexadecimal]
+nb_digits [definition, in Corelib.Init.Decimal]
+Neg [constructor, in Corelib.Init.Hexadecimal]
+Neg [constructor, in Corelib.Init.Decimal]
+Neg [constructor, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+negb [definition, in Corelib.Init.Datatypes]
+negbF [lemma, in Corelib.ssr.ssrbool]
+negbFE [lemma, in Corelib.ssr.ssrbool]
+negbK [lemma, in Corelib.ssr.ssrbool]
+negbLR [lemma, in Corelib.ssr.ssrbool]
+negbNE [lemma, in Corelib.ssr.ssrbool]
+negbRL [lemma, in Corelib.ssr.ssrbool]
+negbT [lemma, in Corelib.ssr.ssrbool]
+negbTE [lemma, in Corelib.ssr.ssrbool]
+negb_imply [lemma, in Corelib.ssr.ssrbool]
+negb_or [lemma, in Corelib.ssr.ssrbool]
+negb_and [lemma, in Corelib.ssr.ssrbool]
+negb_inj [lemma, in Corelib.ssr.ssrbool]
+negP [lemma, in Corelib.ssr.ssrbool]
+negPf [lemma, in Corelib.ssr.ssrbool]
+negPn [lemma, in Corelib.ssr.ssrbool]
+negPP [lemma, in Corelib.ssr.ssrbool]
+neg_false [lemma, in Corelib.Init.Logic]
+neg_zero [definition, in Corelib.Floats.PrimFloat]
+neg_infinity [definition, in Corelib.Floats.PrimFloat]
+neq_Symmetric [instance, in Corelib.Classes.RelationClasses]
+nesym [definition, in Corelib.ssr.ssrfun]
+new_location [definition, in Corelib.Floats.SpecFloat]
+new_location_odd [definition, in Corelib.Floats.SpecFloat]
+new_location_even [definition, in Corelib.Floats.SpecFloat]
+next_down_spec [axiom, in Corelib.Floats.FloatAxioms]
+next_up_spec [axiom, in Corelib.Floats.FloatAxioms]
+next_down [axiom, in Corelib.Floats.PrimFloat]
+next_up [axiom, in Corelib.Floats.PrimFloat]
+nil [constructor, in Corelib.Init.Datatypes]
+Nil [constructor, in Corelib.Init.Hexadecimal]
+Nil [constructor, in Corelib.Init.Decimal]
+NInf [constructor, in Corelib.Floats.FloatClass]
+NNormal [constructor, in Corelib.Floats.FloatClass]
+None [constructor, in Corelib.Init.Datatypes]
+NonPropType [module, in Corelib.ssr.ssreflect]
+NonPropType.call [definition, in Corelib.ssr.ssreflect]
+NonPropType.callee [projection, in Corelib.ssr.ssreflect]
+NonPropType.call_of [record, in Corelib.ssr.ssreflect]
+NonPropType.check [definition, in Corelib.ssr.ssreflect]
+NonPropType.condition [projection, in Corelib.ssr.ssreflect]
+NonPropType.Exports [module, in Corelib.ssr.ssreflect]
+NonPropType.Exports.nonPropType [abbreviation, in Corelib.ssr.ssreflect]
+NonPropType.Exports.notProp [abbreviation, in Corelib.ssr.ssreflect]
+NonPropType.frame [projection, in Corelib.ssr.ssreflect]
+NonPropType.maybeProp [definition, in Corelib.ssr.ssreflect]
+NonPropType.result [projection, in Corelib.ssr.ssreflect]
+NonPropType.test [projection, in Corelib.ssr.ssreflect]
+NonPropType.test_negative [definition, in Corelib.ssr.ssreflect]
+NonPropType.test_Prop [definition, in Corelib.ssr.ssreflect]
+NonPropType.test_of [record, in Corelib.ssr.ssreflect]
+NonPropType.type [record, in Corelib.ssr.ssreflect]
+norm [definition, in Corelib.Init.Hexadecimal]
+norm [definition, in Corelib.Init.Decimal]
+normalization_done [inductive, in Corelib.Classes.CMorphisms]
+normalization_done [inductive, in Corelib.Classes.Morphisms]
+Normalize [section, in Corelib.Classes.CMorphisms]
+Normalize [section, in Corelib.Classes.Morphisms]
+normalizes [projection, in Corelib.Classes.CMorphisms]
+Normalizes [record, in Corelib.Classes.CMorphisms]
+normalizes [constructor, in Corelib.Classes.CMorphisms]
+Normalizes [inductive, in Corelib.Classes.CMorphisms]
+normalizes [projection, in Corelib.Classes.Morphisms]
+Normalizes [record, in Corelib.Classes.Morphisms]
+normalizes [constructor, in Corelib.Classes.Morphisms]
+Normalizes [inductive, in Corelib.Classes.Morphisms]
+Normalize.A [variable, in Corelib.Classes.CMorphisms]
+Normalize.A [variable, in Corelib.Classes.Morphisms]
+normfr_mantissa_spec [axiom, in Corelib.Floats.FloatAxioms]
+normfr_mantissa [axiom, in Corelib.Floats.PrimFloat]
+norP [lemma, in Corelib.ssr.ssrbool]
+nosimpl [abbreviation, in Corelib.ssr.ssreflect]
+not [definition, in Corelib.Init.Logic]
+Notations [module, in Ltac2.RedFlags]
+Notations [module, in Ltac2.Lazy]
+Notations [library]
+Notations [library]
+notF [definition, in Corelib.ssr.ssrbool]
+notT [definition, in Corelib.Init.Logic]
+not_identity_sym [abbreviation, in Corelib.Init.Datatypes]
+not_false_is_true [lemma, in Corelib.ssr.ssrbool]
+not_eq_S [lemma, in Corelib.Init.Peano]
+not_eq_sym [lemma, in Corelib.Init.Logic]
+not_iff_compat [lemma, in Corelib.Init.Logic]
+not_iff_morphism [instance, in Corelib.Classes.Morphisms_Prop]
+not_impl_morphism [instance, in Corelib.Classes.Morphisms_Prop]
+Npos [constructor, in Corelib.Numbers.BinNums]
+NSubn [constructor, in Corelib.Floats.FloatClass]
+nth [definition, in Corelib.Lists.ListDef]
+number [inductive, in Corelib.Init.Number]
+Number [library]
+number_eq_dec [definition, in Corelib.Init.Number]
+NZero [constructor, in Corelib.Floats.FloatClass]
+nzhead [definition, in Corelib.Init.Hexadecimal]
+nzhead [definition, in Corelib.Init.Decimal]
+nztail [definition, in Corelib.Init.Hexadecimal]
+nztail [definition, in Corelib.Init.Decimal]
+nztail_int [definition, in Corelib.Init.Hexadecimal]
+nztail_int [definition, in Corelib.Init.Decimal]
+N_sind [definition, in Corelib.Numbers.BinNums]
+N_rec [definition, in Corelib.Numbers.BinNums]
+N_ind [definition, in Corelib.Numbers.BinNums]
+N_rect [definition, in Corelib.Numbers.BinNums]
+n_Sn [lemma, in Corelib.Init.Peano]
+N.compare [definition, in Corelib.BinNums.NatDef]
+N.double [definition, in Corelib.BinNums.NatDef]
+N.land [definition, in Corelib.BinNums.NatDef]
+N.ldiff [definition, in Corelib.BinNums.NatDef]
+N.leb [definition, in Corelib.BinNums.NatDef]
+N.lor [definition, in Corelib.BinNums.NatDef]
+N.lxor [definition, in Corelib.BinNums.NatDef]
+N.pos_div_eucl [definition, in Corelib.BinNums.NatDef]
+N.sub [definition, in Corelib.BinNums.NatDef]
+N.succ_pos [definition, in Corelib.BinNums.NatDef]
+N.succ_double [definition, in Corelib.BinNums.NatDef]
+N0 [constructor, in Corelib.Numbers.BinNums]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_O.html b/master/corelib/index_global_O.html new file mode 100644 index 0000000000..dbcad89065 --- /dev/null +++ b/master/corelib/index_global_O.html @@ -0,0 +1,1195 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

O

+O [constructor, in Corelib.Init.Datatypes]
+oapp [abbreviation, in Corelib.ssr.ssrfun]
+oappEmap [lemma, in Corelib.ssr.ssrfun]
+oapp_comp_f [lemma, in Corelib.ssr.ssrfun]
+oapp_comp [lemma, in Corelib.ssr.ssrfun]
+obind [abbreviation, in Corelib.ssr.ssrfun]
+obindEapp [lemma, in Corelib.ssr.ssrfun]
+ocancel [definition, in Corelib.ssr.ssrfun]
+ocan_in_comp [lemma, in Corelib.ssr.ssrbool]
+ocan_comp [lemma, in Corelib.ssr.ssrfun]
+odd [definition, in Corelib.Init.Nat]
+odflt [abbreviation, in Corelib.ssr.ssrfun]
+of_bits_to_bits [lemma, in Corelib.Init.Byte]
+of_bits [definition, in Corelib.Init.Byte]
+of_uint63_spec [axiom, in Corelib.Floats.FloatAxioms]
+of_num_int [definition, in Corelib.Init.Nat]
+of_hex_int [definition, in Corelib.Init.Nat]
+of_int [definition, in Corelib.Init.Nat]
+of_num_uint [definition, in Corelib.Init.Nat]
+of_hex_uint [definition, in Corelib.Init.Nat]
+of_hex_uint_acc [definition, in Corelib.Init.Nat]
+of_uint [definition, in Corelib.Init.Nat]
+of_uint_acc [definition, in Corelib.Init.Nat]
+of_voidK [lemma, in Corelib.ssr.ssrfun]
+of_void [definition, in Corelib.ssr.ssrfun]
+of_to_Z [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+of_Z [definition, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+of_pos [definition, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+of_pos_rec [definition, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+of_to_list [axiom, in Corelib.Strings.PrimStringAxioms]
+of_list [definition, in Corelib.Strings.PrimStringAxioms]
+of_nat [abbreviation, in Corelib.Strings.PrimStringAxioms]
+of_uint63 [axiom, in Corelib.Floats.PrimFloat]
+olift [abbreviation, in Corelib.ssr.ssrfun]
+olift_comp [lemma, in Corelib.ssr.ssrfun]
+omap [abbreviation, in Corelib.ssr.ssrfun]
+omapEapp [lemma, in Corelib.ssr.ssrfun]
+omapEbind [lemma, in Corelib.ssr.ssrfun]
+omap_comp [lemma, in Corelib.ssr.ssrfun]
+one [definition, in Corelib.Init.Nat]
+one [definition, in Corelib.Floats.PrimFloat]
+onPhantom [definition, in Corelib.ssr.ssrbool]
+onS_can_in [lemma, in Corelib.ssr.ssrbool]
+onS_can [lemma, in Corelib.ssr.ssrbool]
+onT_bij [lemma, in Corelib.ssr.ssrbool]
+onW_can_in [lemma, in Corelib.ssr.ssrbool]
+onW_can [lemma, in Corelib.ssr.ssrbool]
+onW_bij [lemma, in Corelib.ssr.ssrbool]
+on_can_inj [lemma, in Corelib.ssr.ssrbool]
+on1lS [lemma, in Corelib.ssr.ssrbool]
+on1lS_in [lemma, in Corelib.ssr.ssrbool]
+on1lT [lemma, in Corelib.ssr.ssrbool]
+on1lW [lemma, in Corelib.ssr.ssrbool]
+on1lW_in [lemma, in Corelib.ssr.ssrbool]
+on1S [lemma, in Corelib.ssr.ssrbool]
+on1S_in [lemma, in Corelib.ssr.ssrbool]
+on1T [lemma, in Corelib.ssr.ssrbool]
+on1W [lemma, in Corelib.ssr.ssrbool]
+on1W_in [lemma, in Corelib.ssr.ssrbool]
+on2S [lemma, in Corelib.ssr.ssrbool]
+on2S_in [lemma, in Corelib.ssr.ssrbool]
+on2T [lemma, in Corelib.ssr.ssrbool]
+on2W [lemma, in Corelib.ssr.ssrbool]
+on2W_in [lemma, in Corelib.ssr.ssrbool]
+OperationProperties [section, in Corelib.ssr.ssrfun]
+OperationProperties.R [variable, in Corelib.ssr.ssrfun]
+OperationProperties.S [variable, in Corelib.ssr.ssrfun]
+OperationProperties.SopSisS [section, in Corelib.ssr.ssrfun]
+OperationProperties.SopSisT [section, in Corelib.ssr.ssrfun]
+OperationProperties.SopTisR [section, in Corelib.ssr.ssrfun]
+OperationProperties.SopTisS [section, in Corelib.ssr.ssrfun]
+OperationProperties.SopTisT [section, in Corelib.ssr.ssrfun]
+OperationProperties.T [variable, in Corelib.ssr.ssrfun]
+opp [definition, in Corelib.Init.Hexadecimal]
+opp [definition, in Corelib.Init.Decimal]
+opp [axiom, in Corelib.Floats.PrimFloat]
+opp_spec [axiom, in Corelib.Floats.FloatAxioms]
+option [inductive, in Corelib.Init.Datatypes]
+Option [module, in Corelib.ssr.ssrfun]
+Option [library]
+OptionTheory [section, in Corelib.ssr.ssrfun]
+OptionTheory.aT [variable, in Corelib.ssr.ssrfun]
+OptionTheory.f [variable, in Corelib.ssr.ssrfun]
+OptionTheory.g [variable, in Corelib.ssr.ssrfun]
+OptionTheory.rT [variable, in Corelib.ssr.ssrfun]
+OptionTheory.sT [variable, in Corelib.ssr.ssrfun]
+option_map [definition, in Corelib.Init.Datatypes]
+option_sind [definition, in Corelib.Init.Datatypes]
+option_rec [definition, in Corelib.Init.Datatypes]
+option_ind [definition, in Corelib.Init.Datatypes]
+option_rect [definition, in Corelib.Init.Datatypes]
+Option.apply [definition, in Corelib.ssr.ssrfun]
+Option.bind [definition, in Corelib.ssr.ssrfun]
+Option.default [definition, in Corelib.ssr.ssrfun]
+Option.lift [definition, in Corelib.ssr.ssrfun]
+Option.map [definition, in Corelib.ssr.ssrfun]
+or [inductive, in Corelib.Init.Logic]
+orb [definition, in Corelib.Init.Datatypes]
+orbA [lemma, in Corelib.ssr.ssrbool]
+orbAC [lemma, in Corelib.ssr.ssrbool]
+orbACA [lemma, in Corelib.ssr.ssrbool]
+orbb [lemma, in Corelib.ssr.ssrbool]
+orbC [lemma, in Corelib.ssr.ssrbool]
+orbCA [lemma, in Corelib.ssr.ssrbool]
+orbF [lemma, in Corelib.ssr.ssrbool]
+orbK [lemma, in Corelib.ssr.ssrbool]
+orbN [lemma, in Corelib.ssr.ssrbool]
+orbT [lemma, in Corelib.ssr.ssrbool]
+orb_id2r [lemma, in Corelib.ssr.ssrbool]
+orb_id2l [lemma, in Corelib.ssr.ssrbool]
+orb_idr [lemma, in Corelib.ssr.ssrbool]
+orb_idl [lemma, in Corelib.ssr.ssrbool]
+orb_andr [lemma, in Corelib.ssr.ssrbool]
+orb_andl [lemma, in Corelib.ssr.ssrbool]
+order [record, in Corelib.Relations.Relation_Definitions]
+ord_antisym [projection, in Corelib.Relations.Relation_Definitions]
+ord_trans [projection, in Corelib.Relations.Relation_Definitions]
+ord_refl [projection, in Corelib.Relations.Relation_Definitions]
+orFb [lemma, in Corelib.ssr.ssrbool]
+orKb [lemma, in Corelib.ssr.ssrbool]
+orNb [lemma, in Corelib.ssr.ssrbool]
+orP [lemma, in Corelib.ssr.ssrbool]
+orPP [lemma, in Corelib.ssr.ssrbool]
+orTb [lemma, in Corelib.ssr.ssrbool]
+or_assoc [lemma, in Corelib.Init.Logic]
+or_comm [lemma, in Corelib.Init.Logic]
+or_cancel_r [lemma, in Corelib.Init.Logic]
+or_cancel_l [lemma, in Corelib.Init.Logic]
+or_iff_compat_r [lemma, in Corelib.Init.Logic]
+or_iff_compat_l [lemma, in Corelib.Init.Logic]
+or_sind [definition, in Corelib.Init.Logic]
+or_ind [definition, in Corelib.Init.Logic]
+or_intror [constructor, in Corelib.Init.Logic]
+or_introl [constructor, in Corelib.Init.Logic]
+or_iff_morphism [instance, in Corelib.Classes.Morphisms_Prop]
+or_impl_morphism [instance, in Corelib.Classes.Morphisms_Prop]
+or3 [inductive, in Corelib.ssr.ssrbool]
+or3P [lemma, in Corelib.ssr.ssrbool]
+or3_sind [definition, in Corelib.ssr.ssrbool]
+or3_ind [definition, in Corelib.ssr.ssrbool]
+Or31 [constructor, in Corelib.ssr.ssrbool]
+Or32 [constructor, in Corelib.ssr.ssrbool]
+Or33 [constructor, in Corelib.ssr.ssrbool]
+or4 [inductive, in Corelib.ssr.ssrbool]
+or4P [lemma, in Corelib.ssr.ssrbool]
+or4_sind [definition, in Corelib.ssr.ssrbool]
+or4_ind [definition, in Corelib.ssr.ssrbool]
+Or41 [constructor, in Corelib.ssr.ssrbool]
+Or42 [constructor, in Corelib.ssr.ssrbool]
+Or43 [constructor, in Corelib.ssr.ssrbool]
+Or44 [constructor, in Corelib.ssr.ssrbool]
+over [definition, in Corelib.ssr.ssreflect]
+O_S [lemma, in Corelib.Init.Peano]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_P.html b/master/corelib/index_global_P.html new file mode 100644 index 0000000000..00d3b18411 --- /dev/null +++ b/master/corelib/index_global_P.html @@ -0,0 +1,1365 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

P

+pair [constructor, in Corelib.Init.Datatypes]
+pairT [abbreviation, in Corelib.Init.Datatypes]
+pair_equal_spec [lemma, in Corelib.Init.Datatypes]
+pair_andP [lemma, in Corelib.ssr.ssrbool]
+pair_of_and [definition, in Corelib.ssr.ssrfun]
+Params [record, in Corelib.Classes.CMorphisms]
+Params [record, in Corelib.Classes.Morphisms]
+PArrayNotations [module, in Corelib.Array.PrimArray]
+_ .[ _ <- _ ] [notation, in Corelib.Array.PrimArray]
+_ .[ _ ] [notation, in Corelib.Array.PrimArray]
+parser [definition, in Corelib.Floats.PrimFloat]
+parser [definition, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+PartialApplication [record, in Corelib.Classes.CMorphisms]
+PartialApplication [record, in Corelib.Classes.Morphisms]
+PartialOrder [record, in Corelib.Classes.RelationClasses]
+PartialOrder [inductive, in Corelib.Classes.RelationClasses]
+PartialOrder [record, in Corelib.Classes.CRelationClasses]
+PartialOrder [inductive, in Corelib.Classes.CRelationClasses]
+PartialOrder_inverse [lemma, in Corelib.Classes.RelationClasses]
+PartialOrder_StrictOrder [lemma, in Corelib.Classes.CMorphisms]
+PartialOrder_proper_type [instance, in Corelib.Classes.CMorphisms]
+PartialOrder_StrictOrder [lemma, in Corelib.Classes.Morphisms]
+PartialOrder_proper [instance, in Corelib.Classes.Morphisms]
+PartialOrder_inverse [lemma, in Corelib.Classes.CRelationClasses]
+partial_order_antisym [instance, in Corelib.Classes.RelationClasses]
+partial_order_equivalence [projection, in Corelib.Classes.RelationClasses]
+partial_order_equivalence [constructor, in Corelib.Classes.RelationClasses]
+partial_order_antisym [instance, in Corelib.Classes.CRelationClasses]
+partial_order_equivalence [projection, in Corelib.Classes.CRelationClasses]
+partial_order_equivalence [constructor, in Corelib.Classes.CRelationClasses]
+Pattern [library]
+pcancel [definition, in Corelib.ssr.ssrfun]
+pcan_in_comp [lemma, in Corelib.ssr.ssrbool]
+pcan_in_inj [lemma, in Corelib.ssr.ssrbool]
+pcan_pcomp [lemma, in Corelib.ssr.ssrfun]
+pcan_inj [lemma, in Corelib.ssr.ssrfun]
+pcomp [definition, in Corelib.ssr.ssrfun]
+Peano [library]
+pequiv [definition, in Corelib.Classes.Equivalence]
+PER [record, in Corelib.Classes.RelationClasses]
+PER [record, in Corelib.Classes.CRelationClasses]
+PER [record, in Corelib.Relations.Relation_Definitions]
+PER_Transitive [projection, in Corelib.Classes.RelationClasses]
+PER_Symmetric [projection, in Corelib.Classes.RelationClasses]
+PER_type_morphism [instance, in Corelib.Classes.CMorphisms]
+per_partial_app_type_morphism [instance, in Corelib.Classes.CMorphisms]
+PER_morphism [instance, in Corelib.Classes.Morphisms]
+per_partial_app_morphism [instance, in Corelib.Classes.Morphisms]
+PER_Transitive [projection, in Corelib.Classes.CRelationClasses]
+PER_Symmetric [projection, in Corelib.Classes.CRelationClasses]
+per_trans [projection, in Corelib.Relations.Relation_Definitions]
+per_sym [projection, in Corelib.Relations.Relation_Definitions]
+ph [abbreviation, in Corelib.ssr.ssrbool]
+ph [abbreviation, in Corelib.ssr.ssrbool]
+Phant [constructor, in Corelib.ssr.ssreflect]
+phant [inductive, in Corelib.ssr.ssreflect]
+Phantom [constructor, in Corelib.ssr.ssreflect]
+phantom [inductive, in Corelib.ssr.ssreflect]
+phant_id [definition, in Corelib.ssr.ssrfun]
+PInf [constructor, in Corelib.Floats.FloatClass]
+plus [abbreviation, in Corelib.Init.Peano]
+plus_succ_r_reverse [abbreviation, in Corelib.Init.Peano]
+plus_0_r_reverse [abbreviation, in Corelib.Init.Peano]
+plus_Sn_m [lemma, in Corelib.Init.Peano]
+plus_n_Sm [lemma, in Corelib.Init.Peano]
+plus_O_n [lemma, in Corelib.Init.Peano]
+plus_n_O [lemma, in Corelib.Init.Peano]
+PNormal [constructor, in Corelib.Floats.FloatClass]
+pointwise_lifting [definition, in Corelib.Classes.RelationClasses]
+pointwise_extension [definition, in Corelib.Classes.RelationClasses]
+pointwise_subrelation [instance, in Corelib.Classes.CMorphisms]
+pointwise_pointwise [lemma, in Corelib.Classes.CMorphisms]
+pointwise_relation [definition, in Corelib.Classes.CMorphisms]
+pointwise_subrelation [instance, in Corelib.Classes.Morphisms]
+pointwise_pointwise [lemma, in Corelib.Classes.Morphisms]
+pointwise_relation [definition, in Corelib.Classes.Morphisms]
+pointwise_equivalence [instance, in Corelib.Classes.Equivalence]
+pointwise_transitive [instance, in Corelib.Classes.Equivalence]
+pointwise_symmetric [instance, in Corelib.Classes.Equivalence]
+pointwise_reflexive [instance, in Corelib.Classes.Equivalence]
+Pos [constructor, in Corelib.Init.Hexadecimal]
+Pos [constructor, in Corelib.Init.Decimal]
+Pos [module, in Corelib.BinNums.PosDef]
+Pos [constructor, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+PosDef [library]
+positive [inductive, in Corelib.Numbers.BinNums]
+positive_sind [definition, in Corelib.Numbers.BinNums]
+positive_rec [definition, in Corelib.Numbers.BinNums]
+positive_ind [definition, in Corelib.Numbers.BinNums]
+positive_rect [definition, in Corelib.Numbers.BinNums]
+pos_neg_int63 [inductive, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+Pos.add [definition, in Corelib.BinNums.PosDef]
+Pos.add_carry [definition, in Corelib.BinNums.PosDef]
+Pos.compare [definition, in Corelib.BinNums.PosDef]
+Pos.compare_cont [definition, in Corelib.BinNums.PosDef]
+Pos.div2 [definition, in Corelib.BinNums.PosDef]
+Pos.div2_up [definition, in Corelib.BinNums.PosDef]
+Pos.double_pred_mask [definition, in Corelib.BinNums.PosDef]
+Pos.double_mask [definition, in Corelib.BinNums.PosDef]
+Pos.eqb [definition, in Corelib.BinNums.PosDef]
+Pos.IsNeg [constructor, in Corelib.BinNums.PosDef]
+Pos.IsNul [constructor, in Corelib.BinNums.PosDef]
+Pos.IsPos [constructor, in Corelib.BinNums.PosDef]
+Pos.iter [definition, in Corelib.BinNums.PosDef]
+Pos.iter_op [definition, in Corelib.BinNums.PosDef]
+Pos.land [definition, in Corelib.BinNums.PosDef]
+Pos.ldiff [definition, in Corelib.BinNums.PosDef]
+Pos.leb [definition, in Corelib.BinNums.PosDef]
+Pos.lor [definition, in Corelib.BinNums.PosDef]
+Pos.lxor [definition, in Corelib.BinNums.PosDef]
+Pos.mask [inductive, in Corelib.BinNums.PosDef]
+Pos.mask_sind [definition, in Corelib.BinNums.PosDef]
+Pos.mask_rec [definition, in Corelib.BinNums.PosDef]
+Pos.mask_ind [definition, in Corelib.BinNums.PosDef]
+Pos.mask_rect [definition, in Corelib.BinNums.PosDef]
+Pos.mul [definition, in Corelib.BinNums.PosDef]
+Pos.Ndouble [definition, in Corelib.BinNums.PosDef]
+Pos.Nsucc_double [definition, in Corelib.BinNums.PosDef]
+Pos.of_succ_nat [definition, in Corelib.BinNums.PosDef]
+Pos.pred_N [definition, in Corelib.BinNums.PosDef]
+Pos.pred_double [definition, in Corelib.BinNums.PosDef]
+Pos.sqrt [definition, in Corelib.BinNums.PosDef]
+Pos.sqrtrem [definition, in Corelib.BinNums.PosDef]
+Pos.sqrtrem_step [definition, in Corelib.BinNums.PosDef]
+Pos.sub [definition, in Corelib.BinNums.PosDef]
+Pos.sub_mask_carry [definition, in Corelib.BinNums.PosDef]
+Pos.sub_mask [definition, in Corelib.BinNums.PosDef]
+Pos.succ [definition, in Corelib.BinNums.PosDef]
+Pos.succ_double_mask [definition, in Corelib.BinNums.PosDef]
+Pos.to_nat [definition, in Corelib.BinNums.PosDef]
+pow [definition, in Corelib.Init.Nat]
+prec [definition, in Corelib.Floats.FloatOps]
+pred [definition, in Corelib.Init.Nat]
+pred [definition, in Corelib.ssr.ssrbool]
+pred [abbreviation, in Corelib.Init.Peano]
+predArgType [definition, in Corelib.ssr.ssrbool]
+predC [definition, in Corelib.ssr.ssrbool]
+predD [definition, in Corelib.ssr.ssrbool]
+predI [definition, in Corelib.ssr.ssrbool]
+predicate [abbreviation, in Corelib.Classes.RelationClasses]
+PredicateSimplification [section, in Corelib.ssr.ssrbool]
+PredicateSimplification.T [variable, in Corelib.ssr.ssrbool]
+predicate_implication_preorder [instance, in Corelib.Classes.RelationClasses]
+predicate_equivalence_equivalence [instance, in Corelib.Classes.RelationClasses]
+predicate_union [definition, in Corelib.Classes.RelationClasses]
+predicate_intersection [definition, in Corelib.Classes.RelationClasses]
+predicate_implication [definition, in Corelib.Classes.RelationClasses]
+predicate_equivalence [definition, in Corelib.Classes.RelationClasses]
+predicate_exists [definition, in Corelib.Classes.RelationClasses]
+predicate_all [definition, in Corelib.Classes.RelationClasses]
+PredOfSimpl [module, in Corelib.ssr.ssrbool]
+PredOfSimpl.coerce [definition, in Corelib.ssr.ssrbool]
+predPredType [definition, in Corelib.ssr.ssrbool]
+PredSortOfSimplCoercion [module, in Corelib.ssr.ssrbool]
+PredSortOfSimplSignature [module, in Corelib.ssr.ssrbool]
+PredSortOfSimplSignature.coerce [axiom, in Corelib.ssr.ssrbool]
+predT [definition, in Corelib.ssr.ssrbool]
+predType [record, in Corelib.ssr.ssrbool]
+predU [definition, in Corelib.ssr.ssrbool]
+pred_oapp [definition, in Corelib.ssr.ssrbool]
+pred_key [inductive, in Corelib.ssr.ssrbool]
+pred_of_mem [definition, in Corelib.ssr.ssrbool]
+pred_of_argType [definition, in Corelib.ssr.ssrbool]
+pred_of_simpl [abbreviation, in Corelib.ssr.ssrbool]
+pred_sort [projection, in Corelib.ssr.ssrbool]
+pred_Sn [lemma, in Corelib.Init.Peano]
+pred0 [definition, in Corelib.ssr.ssrbool]
+preim [definition, in Corelib.ssr.ssrbool]
+Prelude [library]
+PreOrder [record, in Corelib.Classes.RelationClasses]
+PreOrder [record, in Corelib.Classes.CRelationClasses]
+preorder [record, in Corelib.Relations.Relation_Definitions]
+PreOrder_Transitive [projection, in Corelib.Classes.RelationClasses]
+PreOrder_Reflexive [projection, in Corelib.Classes.RelationClasses]
+PreOrder_Transitive [projection, in Corelib.Classes.CRelationClasses]
+PreOrder_Reflexive [projection, in Corelib.Classes.CRelationClasses]
+preord_trans [projection, in Corelib.Relations.Relation_Definitions]
+preord_refl [projection, in Corelib.Relations.Relation_Definitions]
+Pretype [module, in Ltac2.Constr]
+Pretype.Flags [module, in Ltac2.Constr]
+pre_symmetric [definition, in Corelib.ssr.ssrbool]
+PrimArray [library]
+PrimFloat [library]
+PrimFloatNotations [module, in Corelib.Floats.PrimFloat]
+PrimFloatNotationsInternalA [module, in Corelib.Floats.PrimFloat]
+PrimFloatNotationsInternalB [module, in Corelib.Floats.PrimFloat]
+_ / _ (float_scope) [notation, in Corelib.Floats.PrimFloat]
+_ - _ (float_scope) [notation, in Corelib.Floats.PrimFloat]
+_ + _ (float_scope) [notation, in Corelib.Floats.PrimFloat]
+_ * _ (float_scope) [notation, in Corelib.Floats.PrimFloat]
+_ ?= _ (float_scope) [notation, in Corelib.Floats.PrimFloat]
+_ <=? _ (float_scope) [notation, in Corelib.Floats.PrimFloat]
+_ <? _ (float_scope) [notation, in Corelib.Floats.PrimFloat]
+_ =? _ (float_scope) [notation, in Corelib.Floats.PrimFloat]
+- _ (float_scope) [notation, in Corelib.Floats.PrimFloat]
+PrimInt63 [library]
+PrimInt63Notations [module, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+PrimString [library]
+PrimStringAxioms [library]
+Prim2SF [definition, in Corelib.Floats.FloatOps]
+Prim2SF_inj [lemma, in Corelib.Floats.FloatAxioms]
+Prim2SF_SF2Prim [axiom, in Corelib.Floats.FloatAxioms]
+Prim2SF_valid [axiom, in Corelib.Floats.FloatAxioms]
+printer [definition, in Corelib.Floats.PrimFloat]
+printer [definition, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+Printf [library]
+prod [inductive, in Corelib.Init.Datatypes]
+ProdSigT [section, in Corelib.Init.Specif]
+ProdSigT.A [variable, in Corelib.Init.Specif]
+ProdSigT.B [variable, in Corelib.Init.Specif]
+prodT [abbreviation, in Corelib.Init.Datatypes]
+prodT_ind [abbreviation, in Corelib.Init.Datatypes]
+prodT_rec [abbreviation, in Corelib.Init.Datatypes]
+prodT_rect [abbreviation, in Corelib.Init.Datatypes]
+prod_sind [definition, in Corelib.Init.Datatypes]
+prod_rec [definition, in Corelib.Init.Datatypes]
+prod_ind [definition, in Corelib.Init.Datatypes]
+prod_rect [definition, in Corelib.Init.Datatypes]
+prod_sigT_prod [lemma, in Corelib.Init.Specif]
+prod_of_sigT [definition, in Corelib.Init.Specif]
+Proj [library]
+projections [section, in Corelib.Init.Datatypes]
+Projections [section, in Corelib.Init.Specif]
+Projections [section, in Corelib.Init.Logic]
+projections.A [variable, in Corelib.Init.Datatypes]
+Projections.A [variable, in Corelib.Init.Specif]
+Projections.A [variable, in Corelib.Init.Logic]
+projections.B [variable, in Corelib.Init.Datatypes]
+Projections.P [variable, in Corelib.Init.Specif]
+Projections.P [variable, in Corelib.Init.Logic]
+Projections2 [section, in Corelib.Init.Specif]
+Projections2.A [variable, in Corelib.Init.Specif]
+Projections2.P [variable, in Corelib.Init.Specif]
+Projections2.Q [variable, in Corelib.Init.Specif]
+projT1 [definition, in Corelib.Init.Specif]
+projT1_of_sigT2_eq [definition, in Corelib.Init.Specif]
+projT1_eq [definition, in Corelib.Init.Specif]
+projT2 [definition, in Corelib.Init.Specif]
+projT2_of_sigT2_eq [definition, in Corelib.Init.Specif]
+projT2_eq [definition, in Corelib.Init.Specif]
+projT3 [definition, in Corelib.Init.Specif]
+projT3_eq [definition, in Corelib.Init.Specif]
+proj1 [lemma, in Corelib.Init.Logic]
+proj1_sig_of_sig2_eq [definition, in Corelib.Init.Specif]
+proj1_sig_eq [definition, in Corelib.Init.Specif]
+proj1_sig [definition, in Corelib.Init.Specif]
+proj2 [lemma, in Corelib.Init.Logic]
+proj2_sig_of_sig2_eq [definition, in Corelib.Init.Specif]
+proj2_sig_eq [definition, in Corelib.Init.Specif]
+proj2_sig [definition, in Corelib.Init.Specif]
+proj3_sig_eq [definition, in Corelib.Init.Specif]
+proj3_sig [definition, in Corelib.Init.Specif]
+Proper [record, in Corelib.Classes.CMorphisms]
+Proper [inductive, in Corelib.Classes.CMorphisms]
+Proper [section, in Corelib.Classes.CMorphisms]
+Proper [record, in Corelib.Classes.Morphisms]
+Proper [inductive, in Corelib.Classes.Morphisms]
+Proper [section, in Corelib.Classes.Morphisms]
+ProperNotations [module, in Corelib.Classes.CMorphisms]
+ProperNotations [module, in Corelib.Classes.Morphisms]
+_ --> _ (signatureT_scope) [notation, in Corelib.Classes.CMorphisms]
+_ ==> _ (signatureT_scope) [notation, in Corelib.Classes.CMorphisms]
+_ ++> _ (signatureT_scope) [notation, in Corelib.Classes.CMorphisms]
+_ --> _ (signature_scope) [notation, in Corelib.Classes.Morphisms]
+_ ==> _ (signature_scope) [notation, in Corelib.Classes.Morphisms]
+_ ++> _ (signature_scope) [notation, in Corelib.Classes.Morphisms]
+ProperProxy [record, in Corelib.Classes.CMorphisms]
+ProperProxy [inductive, in Corelib.Classes.CMorphisms]
+ProperProxy [record, in Corelib.Classes.Morphisms]
+ProperProxy [inductive, in Corelib.Classes.Morphisms]
+proper_sym_arrow_iffT_2 [lemma, in Corelib.Classes.CMorphisms]
+proper_sym_impl_iff_2 [lemma, in Corelib.Classes.CMorphisms]
+proper_sym_arrow_iffT [lemma, in Corelib.Classes.CMorphisms]
+proper_sym_impl_iff [lemma, in Corelib.Classes.CMorphisms]
+proper_sym_flip_2 [lemma, in Corelib.Classes.CMorphisms]
+proper_sym_flip [lemma, in Corelib.Classes.CMorphisms]
+proper_normalizes_proper [lemma, in Corelib.Classes.CMorphisms]
+proper_proper [instance, in Corelib.Classes.CMorphisms]
+proper_eq [lemma, in Corelib.Classes.CMorphisms]
+proper_flip_proper [definition, in Corelib.Classes.CMorphisms]
+proper_subrelation_proper_arrow [instance, in Corelib.Classes.CMorphisms]
+proper_proper_proxy [lemma, in Corelib.Classes.CMorphisms]
+proper_proxy [projection, in Corelib.Classes.CMorphisms]
+proper_proxy [constructor, in Corelib.Classes.CMorphisms]
+proper_prf [projection, in Corelib.Classes.CMorphisms]
+proper_prf [constructor, in Corelib.Classes.CMorphisms]
+proper_sym_impl_iff_2 [lemma, in Corelib.Classes.Morphisms]
+proper_sym_impl_iff [lemma, in Corelib.Classes.Morphisms]
+proper_sym_flip_2 [lemma, in Corelib.Classes.Morphisms]
+proper_sym_flip [lemma, in Corelib.Classes.Morphisms]
+proper_normalizes_proper [lemma, in Corelib.Classes.Morphisms]
+proper_proper [instance, in Corelib.Classes.Morphisms]
+proper_eq [lemma, in Corelib.Classes.Morphisms]
+proper_flip_proper [definition, in Corelib.Classes.Morphisms]
+proper_subrelation_proper [instance, in Corelib.Classes.Morphisms]
+proper_proper_proxy [lemma, in Corelib.Classes.Morphisms]
+proper_proxy [projection, in Corelib.Classes.Morphisms]
+proper_proxy [constructor, in Corelib.Classes.Morphisms]
+proper_prf [projection, in Corelib.Classes.Morphisms]
+proper_prf [constructor, in Corelib.Classes.Morphisms]
+Proper.A [variable, in Corelib.Classes.CMorphisms]
+Proper.A [variable, in Corelib.Classes.Morphisms]
+Proper.B [variable, in Corelib.Classes.Morphisms]
+Proper.U [variable, in Corelib.Classes.Morphisms]
+prop_on2 [definition, in Corelib.ssr.ssrbool]
+prop_on1 [definition, in Corelib.ssr.ssrbool]
+prop_in3 [definition, in Corelib.ssr.ssrbool]
+prop_in21 [definition, in Corelib.ssr.ssrbool]
+prop_in12 [definition, in Corelib.ssr.ssrbool]
+prop_in111 [definition, in Corelib.ssr.ssrbool]
+prop_in2 [definition, in Corelib.ssr.ssrbool]
+prop_in11 [definition, in Corelib.ssr.ssrbool]
+prop_in1 [definition, in Corelib.ssr.ssrbool]
+prop_for [definition, in Corelib.ssr.ssrbool]
+prop_congr [lemma, in Corelib.ssr.ssrbool]
+protect_term [definition, in Corelib.ssr.ssreflect]
+Pstring [library]
+PStringNotations [module, in Corelib.Strings.PrimString]
+PStringNotations.id_string [definition, in Corelib.Strings.PrimString]
+PStringNotations.string_wrap [projection, in Corelib.Strings.PrimString]
+PStringNotations.string_wrapper [record, in Corelib.Strings.PrimString]
+PSubn [constructor, in Corelib.Floats.FloatClass]
+PZero [constructor, in Corelib.Floats.FloatClass]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_Q.html b/master/corelib/index_global_Q.html new file mode 100644 index 0000000000..88f65138a0 --- /dev/null +++ b/master/corelib/index_global_Q.html @@ -0,0 +1,563 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

Q

+qualifE [lemma, in Corelib.ssr.ssrbool]
+Qualifier [constructor, in Corelib.ssr.ssrbool]
+qualifier [inductive, in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_R.html b/master/corelib/index_global_R.html new file mode 100644 index 0000000000..b67cd50687 --- /dev/null +++ b/master/corelib/index_global_R.html @@ -0,0 +1,1211 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

R

+RedFlags [library]
+Ref [library]
+reflect [inductive, in Corelib.Init.Datatypes]
+Reflect [section, in Corelib.ssr.ssrbool]
+reflect [abbreviation, in Corelib.ssr.ssrbool]
+ReflectCombinators [section, in Corelib.ssr.ssrbool]
+ReflectCombinators.p [variable, in Corelib.ssr.ssrbool]
+ReflectCombinators.P [variable, in Corelib.ssr.ssrbool]
+ReflectCombinators.q [variable, in Corelib.ssr.ssrbool]
+ReflectCombinators.Q [variable, in Corelib.ssr.ssrbool]
+ReflectCombinators.rP [variable, in Corelib.ssr.ssrbool]
+ReflectCombinators.rQ [variable, in Corelib.ssr.ssrbool]
+ReflectConnectives [section, in Corelib.ssr.ssrbool]
+ReflectConnectives.b1 [variable, in Corelib.ssr.ssrbool]
+ReflectConnectives.b2 [variable, in Corelib.ssr.ssrbool]
+ReflectConnectives.b3 [variable, in Corelib.ssr.ssrbool]
+ReflectConnectives.b4 [variable, in Corelib.ssr.ssrbool]
+ReflectConnectives.b5 [variable, in Corelib.ssr.ssrbool]
+ReflectCore [section, in Corelib.ssr.ssrbool]
+ReflectCore.b [variable, in Corelib.ssr.ssrbool]
+ReflectCore.c [variable, in Corelib.ssr.ssrbool]
+ReflectCore.Hb [variable, in Corelib.ssr.ssrbool]
+ReflectCore.P [variable, in Corelib.ssr.ssrbool]
+ReflectCore.Q [variable, in Corelib.ssr.ssrbool]
+ReflectF [constructor, in Corelib.Init.Datatypes]
+ReflectF [abbreviation, in Corelib.ssr.ssrbool]
+ReflectNegCore [section, in Corelib.ssr.ssrbool]
+ReflectNegCore.b [variable, in Corelib.ssr.ssrbool]
+ReflectNegCore.c [variable, in Corelib.ssr.ssrbool]
+ReflectNegCore.Hb [variable, in Corelib.ssr.ssrbool]
+ReflectNegCore.P [variable, in Corelib.ssr.ssrbool]
+ReflectNegCore.Q [variable, in Corelib.ssr.ssrbool]
+ReflectT [constructor, in Corelib.Init.Datatypes]
+ReflectT [abbreviation, in Corelib.ssr.ssrbool]
+reflect_sind [definition, in Corelib.Init.Datatypes]
+reflect_rec [definition, in Corelib.Init.Datatypes]
+reflect_ind [definition, in Corelib.Init.Datatypes]
+reflect_rect [definition, in Corelib.Init.Datatypes]
+Reflect.b [variable, in Corelib.ssr.ssrbool]
+Reflect.b' [variable, in Corelib.ssr.ssrbool]
+Reflect.c [variable, in Corelib.ssr.ssrbool]
+Reflect.P [variable, in Corelib.ssr.ssrbool]
+Reflect.Pb [variable, in Corelib.ssr.ssrbool]
+Reflect.Pb' [variable, in Corelib.ssr.ssrbool]
+Reflect.Q [variable, in Corelib.ssr.ssrbool]
+Reflexive [record, in Corelib.Classes.RelationClasses]
+Reflexive [inductive, in Corelib.Classes.RelationClasses]
+Reflexive [record, in Corelib.ssr.ssrclasses]
+Reflexive [inductive, in Corelib.ssr.ssrclasses]
+reflexive [definition, in Corelib.ssr.ssrbool]
+Reflexive [record, in Corelib.Classes.CRelationClasses]
+Reflexive [inductive, in Corelib.Classes.CRelationClasses]
+reflexive [definition, in Corelib.Relations.Relation_Definitions]
+ReflexiveProxy [record, in Corelib.Classes.Morphisms]
+ReflexiveProxy [inductive, in Corelib.Classes.Morphisms]
+reflexive_proper [lemma, in Corelib.Classes.CMorphisms]
+Reflexive_partial_app_morphism [lemma, in Corelib.Classes.CMorphisms]
+reflexive_eq_dom_reflexive [instance, in Corelib.Classes.CMorphisms]
+reflexive_proper_proxy [lemma, in Corelib.Classes.CMorphisms]
+Reflexive_partial_app_morphism [lemma, in Corelib.Classes.Morphisms]
+reflexive_eq_dom_reflexive [instance, in Corelib.Classes.Morphisms]
+reflexive_reflexive_proxy [lemma, in Corelib.Classes.Morphisms]
+reflexive_proper_proxy [lemma, in Corelib.Classes.Morphisms]
+reflexive_proper [lemma, in Corelib.Classes.Morphisms]
+reflexive_proxy [projection, in Corelib.Classes.Morphisms]
+reflexive_proxy [constructor, in Corelib.Classes.Morphisms]
+reflexivity [projection, in Corelib.Classes.RelationClasses]
+reflexivity [constructor, in Corelib.Classes.RelationClasses]
+reflexivity [projection, in Corelib.ssr.ssrclasses]
+reflexivity [constructor, in Corelib.ssr.ssrclasses]
+reflexivity [projection, in Corelib.Classes.CRelationClasses]
+reflexivity [constructor, in Corelib.Classes.CRelationClasses]
+refl_id [abbreviation, in Corelib.Init.Datatypes]
+refl_equal [abbreviation, in Corelib.Init.Logic]
+registered_applicative_pred [record, in Corelib.ssr.ssrbool]
+rel [definition, in Corelib.ssr.ssrbool]
+relation [definition, in Corelib.Relations.Relation_Definitions]
+RelationClasses [library]
+RelationProperties [section, in Corelib.ssr.ssrbool]
+RelationProperties.PER [section, in Corelib.ssr.ssrbool]
+RelationProperties.PER.symR [variable, in Corelib.ssr.ssrbool]
+RelationProperties.PER.trR [variable, in Corelib.ssr.ssrbool]
+RelationProperties.R [variable, in Corelib.ssr.ssrbool]
+RelationProperties.T [variable, in Corelib.ssr.ssrbool]
+Relations [section, in Corelib.Classes.CMorphisms]
+Relations [section, in Corelib.Classes.Morphisms]
+Relations.A [variable, in Corelib.Classes.CMorphisms]
+Relations.A [variable, in Corelib.Classes.Morphisms]
+Relations.B [variable, in Corelib.Classes.Morphisms]
+Relations.P [variable, in Corelib.Classes.Morphisms]
+Relations.U [variable, in Corelib.Classes.Morphisms]
+relation_implication_preorder [instance, in Corelib.Classes.RelationClasses]
+relation_equivalence_equivalence [instance, in Corelib.Classes.RelationClasses]
+relation_disjunction [definition, in Corelib.Classes.RelationClasses]
+relation_conjunction [definition, in Corelib.Classes.RelationClasses]
+relation_equivalence_rewrite_relation [instance, in Corelib.Classes.RelationClasses]
+relation_equivalence [definition, in Corelib.Classes.RelationClasses]
+relation_implication_preorder [instance, in Corelib.Classes.CRelationClasses]
+relation_equivalence_equivalence [instance, in Corelib.Classes.CRelationClasses]
+relation_disjunction [definition, in Corelib.Classes.CRelationClasses]
+relation_conjunction [definition, in Corelib.Classes.CRelationClasses]
+relation_equivalence [definition, in Corelib.Classes.CRelationClasses]
+Relation_Definition.Relations_of_Relations [section, in Corelib.Relations.Relation_Definitions]
+Relation_Definition.Sets_of_Relations [section, in Corelib.Relations.Relation_Definitions]
+Relation_Definition.General_Properties_of_Relations [section, in Corelib.Relations.Relation_Definitions]
+Relation_Definition.R [variable, in Corelib.Relations.Relation_Definitions]
+Relation_Definition.A [variable, in Corelib.Relations.Relation_Definitions]
+Relation_Definition [section, in Corelib.Relations.Relation_Definitions]
+Relation_Definitions [library]
+relpre [definition, in Corelib.ssr.ssrbool]
+relU [definition, in Corelib.ssr.ssrbool]
+rel_of_simpl [definition, in Corelib.ssr.ssrbool]
+repeat [definition, in Corelib.Lists.ListDef]
+Repeat [section, in Corelib.Lists.ListDef]
+Repeat.A [variable, in Corelib.Lists.ListDef]
+respectful [definition, in Corelib.Classes.CMorphisms]
+respectful [definition, in Corelib.Classes.Morphisms]
+respectful_morphism [instance, in Corelib.Classes.CMorphisms]
+respectful_per [instance, in Corelib.Classes.CMorphisms]
+respectful_hetero [definition, in Corelib.Classes.CMorphisms]
+respectful_morphism [instance, in Corelib.Classes.Morphisms]
+respectful_per [instance, in Corelib.Classes.Morphisms]
+respectful_hetero [definition, in Corelib.Classes.Morphisms]
+respecting [definition, in Corelib.Classes.Equivalence]
+Respecting [section, in Corelib.Classes.Equivalence]
+respecting_equiv [instance, in Corelib.Classes.Equivalence]
+returnType [definition, in Corelib.ssr.ssreflect]
+rev [definition, in Corelib.Init.Hexadecimal]
+rev [definition, in Corelib.Init.Decimal]
+revapp [definition, in Corelib.Init.Hexadecimal]
+revapp [definition, in Corelib.Init.Decimal]
+ReverseCoercionSource [definition, in Corelib.Init.Prelude]
+ReverseCoercionTarget [definition, in Corelib.Init.Prelude]
+reverse_coercion [definition, in Corelib.Init.Prelude]
+rev_trans [lemma, in Corelib.ssr.ssrbool]
+rev_left_loop [definition, in Corelib.ssr.ssrfun]
+rev_right_loop [definition, in Corelib.ssr.ssrfun]
+RewriteRelation [record, in Corelib.Classes.RelationClasses]
+RewriteRelation [record, in Corelib.Classes.CRelationClasses]
+rewrite_relation_eq_dom [lemma, in Corelib.Classes.Morphisms]
+rewrite_relation_pointwise [lemma, in Corelib.Classes.Morphisms]
+rew_pair [lemma, in Corelib.Init.Datatypes]
+rew_sig2 [lemma, in Corelib.Init.Specif]
+rew_sigT2 [lemma, in Corelib.Init.Specif]
+rew_sig [lemma, in Corelib.Init.Specif]
+rew_sigT [lemma, in Corelib.Init.Specif]
+rew_ex2 [lemma, in Corelib.Init.Logic]
+rew_ex [lemma, in Corelib.Init.Logic]
+rew_const [lemma, in Corelib.Init.Logic]
+rew_compose [lemma, in Corelib.Init.Logic]
+rew_swap [lemma, in Corelib.Init.Logic]
+rew_map [lemma, in Corelib.Init.Logic]
+rew_opp_l [lemma, in Corelib.Init.Logic]
+rew_opp_r [lemma, in Corelib.Init.Logic]
+right [constructor, in Corelib.Init.Specif]
+right_transitive [definition, in Corelib.ssr.ssrbool]
+right_distributive [definition, in Corelib.ssr.ssrfun]
+right_zero [definition, in Corelib.ssr.ssrfun]
+right_loop [definition, in Corelib.ssr.ssrfun]
+right_commutative [definition, in Corelib.ssr.ssrfun]
+right_id [definition, in Corelib.ssr.ssrfun]
+right_injective [definition, in Corelib.ssr.ssrfun]
+right_inverse [definition, in Corelib.ssr.ssrfun]
+RocqGenericDependentIf [abbreviation, in Corelib.ssr.ssreflect]
+RocqGenericIf [abbreviation, in Corelib.ssr.ssreflect]
+round_nearest_even [definition, in Corelib.Floats.SpecFloat]
+rrefl [lemma, in Corelib.ssr.ssrfun]
+rwP [lemma, in Corelib.ssr.ssrbool]
+rwP2 [lemma, in Corelib.ssr.ssrbool]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_S.html b/master/corelib/index_global_S.html new file mode 100644 index 0000000000..3432496bc9 --- /dev/null +++ b/master/corelib/index_global_S.html @@ -0,0 +1,1324 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

S

+S [constructor, in Corelib.Init.Datatypes]
+sameP [lemma, in Corelib.ssr.ssrbool]
+same_relation [definition, in Corelib.Relations.Relation_Definitions]
+self_inverse [definition, in Corelib.ssr.ssrfun]
+seq [definition, in Corelib.Lists.ListDef]
+Seq_trans [definition, in Corelib.Setoids.Setoid]
+Seq_sym [definition, in Corelib.Setoids.Setoid]
+Seq_refl [definition, in Corelib.Setoids.Setoid]
+set [axiom, in Corelib.Array.PrimArray]
+Setoid [library]
+SetoidTactics [library]
+Setoid_Theory [definition, in Corelib.Setoids.Setoid]
+set_digit [definition, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+SFabs [definition, in Corelib.Floats.SpecFloat]
+SFadd [definition, in Corelib.Floats.SpecFloat]
+SFclassify [definition, in Corelib.Floats.SpecFloat]
+SFcompare [definition, in Corelib.Floats.SpecFloat]
+SFdiv [definition, in Corelib.Floats.SpecFloat]
+SFdiv_core_binary [definition, in Corelib.Floats.SpecFloat]
+SFeqb [definition, in Corelib.Floats.SpecFloat]
+SFfrexp [definition, in Corelib.Floats.SpecFloat]
+SFldexp [definition, in Corelib.Floats.SpecFloat]
+SFleb [definition, in Corelib.Floats.SpecFloat]
+SFltb [definition, in Corelib.Floats.SpecFloat]
+SFmax_float [definition, in Corelib.Floats.SpecFloat]
+SFmul [definition, in Corelib.Floats.SpecFloat]
+SFnormfr_mantissa [definition, in Corelib.Floats.SpecFloat]
+SFone [definition, in Corelib.Floats.SpecFloat]
+SFopp [definition, in Corelib.Floats.SpecFloat]
+SFpred [definition, in Corelib.Floats.SpecFloat]
+SFpred_pos [definition, in Corelib.Floats.SpecFloat]
+SFsqrt [definition, in Corelib.Floats.SpecFloat]
+SFsqrt_core_binary [definition, in Corelib.Floats.SpecFloat]
+SFsub [definition, in Corelib.Floats.SpecFloat]
+SFsucc [definition, in Corelib.Floats.SpecFloat]
+SFulp [definition, in Corelib.Floats.SpecFloat]
+SF2Prim [definition, in Corelib.Floats.FloatOps]
+SF2Prim_inj [lemma, in Corelib.Floats.FloatAxioms]
+SF2Prim_Prim2SF [axiom, in Corelib.Floats.FloatAxioms]
+SF64add [definition, in Corelib.Floats.FloatAxioms]
+SF64classify [definition, in Corelib.Floats.FloatAxioms]
+SF64div [definition, in Corelib.Floats.FloatAxioms]
+SF64mul [definition, in Corelib.Floats.FloatAxioms]
+SF64pred [definition, in Corelib.Floats.FloatAxioms]
+SF64sqrt [definition, in Corelib.Floats.FloatAxioms]
+SF64sub [definition, in Corelib.Floats.FloatAxioms]
+SF64succ [definition, in Corelib.Floats.FloatAxioms]
+shift [definition, in Corelib.Floats.FloatOps]
+shiftl [definition, in Corelib.Init.Nat]
+shiftr [definition, in Corelib.Init.Nat]
+shl_align [definition, in Corelib.Floats.SpecFloat]
+shr [definition, in Corelib.Floats.SpecFloat]
+shr_fexp [definition, in Corelib.Floats.SpecFloat]
+shr_record_of_loc [definition, in Corelib.Floats.SpecFloat]
+shr_1 [definition, in Corelib.Floats.SpecFloat]
+shr_s [projection, in Corelib.Floats.SpecFloat]
+shr_r [projection, in Corelib.Floats.SpecFloat]
+shr_m [projection, in Corelib.Floats.SpecFloat]
+shr_record [record, in Corelib.Floats.SpecFloat]
+sig [section, in Corelib.Init.Specif]
+sig [inductive, in Corelib.Init.Specif]
+Sig [section, in Corelib.ssr.ssrfun]
+signed_int_eq_dec [definition, in Corelib.Init.Hexadecimal]
+signed_int [inductive, in Corelib.Init.Hexadecimal]
+signed_int_eq_dec [definition, in Corelib.Init.Decimal]
+signed_int [inductive, in Corelib.Init.Decimal]
+signed_int_eq_dec [definition, in Corelib.Init.Number]
+signed_int [inductive, in Corelib.Init.Number]
+sigT [section, in Corelib.Init.Specif]
+sigT [inductive, in Corelib.Init.Specif]
+SigTNotations [module, in Corelib.Init.Specif]
+_ .2 [notation, in Corelib.Init.Specif]
+_ .1 [notation, in Corelib.Init.Specif]
+( _ ; _ ) [notation, in Corelib.Init.Specif]
+sigT_of_sigT2_eq [definition, in Corelib.Init.Specif]
+sigT_prod_sigT [lemma, in Corelib.Init.Specif]
+sigT_of_prod [definition, in Corelib.Init.Specif]
+sigT_eta [definition, in Corelib.Init.Specif]
+sigT_of_sig [definition, in Corelib.Init.Specif]
+sigT_of_sigT2 [definition, in Corelib.Init.Specif]
+sigT_sind [definition, in Corelib.Init.Specif]
+sigT_rec [definition, in Corelib.Init.Specif]
+sigT_ind [definition, in Corelib.Init.Specif]
+sigT_rect [definition, in Corelib.Init.Specif]
+(= _ ; _ ) [notation, in Corelib.Init.Specif]
+sigT2 [section, in Corelib.Init.Specif]
+sigT2 [inductive, in Corelib.Init.Specif]
+sigT2_eta [definition, in Corelib.Init.Specif]
+sigT2_of_sig2 [definition, in Corelib.Init.Specif]
+sigT2_sind [definition, in Corelib.Init.Specif]
+sigT2_rec [definition, in Corelib.Init.Specif]
+sigT2_ind [definition, in Corelib.Init.Specif]
+sigT2_rect [definition, in Corelib.Init.Specif]
+sig_of_sig2_eq [definition, in Corelib.Init.Specif]
+sig_eta [definition, in Corelib.Init.Specif]
+sig_of_sigT [definition, in Corelib.Init.Specif]
+sig_of_sig2 [definition, in Corelib.Init.Specif]
+sig_sind [definition, in Corelib.Init.Specif]
+sig_rec [definition, in Corelib.Init.Specif]
+sig_ind [definition, in Corelib.Init.Specif]
+sig_rect [definition, in Corelib.Init.Specif]
+sig_of_sig2 [definition, in Corelib.ssr.ssrfun]
+Sig.P [variable, in Corelib.ssr.ssrfun]
+Sig.Q [variable, in Corelib.ssr.ssrfun]
+Sig.T [variable, in Corelib.ssr.ssrfun]
+sig2 [section, in Corelib.Init.Specif]
+sig2 [inductive, in Corelib.Init.Specif]
+sig2_eta [definition, in Corelib.Init.Specif]
+sig2_of_sigT2 [definition, in Corelib.Init.Specif]
+sig2_sind [definition, in Corelib.Init.Specif]
+sig2_rec [definition, in Corelib.Init.Specif]
+sig2_ind [definition, in Corelib.Init.Specif]
+sig2_rect [definition, in Corelib.Init.Specif]
+SimplFun [section, in Corelib.ssr.ssrfun]
+SimplFun [constructor, in Corelib.ssr.ssrfun]
+SimplFunDelta [definition, in Corelib.ssr.ssrfun]
+SimplFun.aT [variable, in Corelib.ssr.ssrfun]
+SimplFun.rT [variable, in Corelib.ssr.ssrfun]
+SimplPred [definition, in Corelib.ssr.ssrbool]
+simplPredType [definition, in Corelib.ssr.ssrbool]
+SimplRel [definition, in Corelib.ssr.ssrbool]
+simpl_predE [lemma, in Corelib.ssr.ssrbool]
+simpl_pred_value [projection, in Corelib.ssr.ssrbool]
+simpl_of_mem [definition, in Corelib.ssr.ssrbool]
+simpl_rel [definition, in Corelib.ssr.ssrbool]
+simpl_pred [definition, in Corelib.ssr.ssrbool]
+simpl_fun [inductive, in Corelib.ssr.ssrfun]
+Sint63Axioms [library]
+sixteen [abbreviation, in Corelib.Init.Nat]
+size [definition, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+skipn [definition, in Corelib.Lists.ListDef]
+snd [definition, in Corelib.Init.Datatypes]
+sndT [abbreviation, in Corelib.Init.Datatypes]
+Some [constructor, in Corelib.Init.Datatypes]
+some [abbreviation, in Corelib.ssr.ssrfun]
+Some_inj [lemma, in Corelib.ssr.ssrfun]
+SpecFloat [library]
+Specif [library]
+spec_float [inductive, in Corelib.Floats.SpecFloat]
+sqrt [definition, in Corelib.Init.Nat]
+sqrt [axiom, in Corelib.Floats.PrimFloat]
+sqrt_spec [axiom, in Corelib.Floats.FloatAxioms]
+sqrt_iter [definition, in Corelib.Init.Nat]
+square [definition, in Corelib.Init.Nat]
+ssrbool [library]
+ssrclasses [library]
+ssreflect [library]
+ssrfun [library]
+ssrmatching [library]
+SsrMatchingSyntax [module, in Corelib.ssrmatching.ssrmatching]
+SsrMatchingSyntax.LHS [abbreviation, in Corelib.ssrmatching.ssrmatching]
+SsrMatchingSyntax.RHS [abbreviation, in Corelib.ssrmatching.ssrmatching]
+( _ in _ ) (ssrpatternscope) [notation, in Corelib.ssrmatching.ssrmatching]
+ssrsetoid [library]
+SsrSyntax [module, in Corelib.ssr.ssreflect]
+ssrunder [library]
+ssr_congr_arrow [lemma, in Corelib.ssr.ssreflect]
+ssr_have_upoly [lemma, in Corelib.ssr.ssreflect]
+ssr_have [lemma, in Corelib.ssr.ssreflect]
+ssr_converse [definition, in Corelib.ssr.ssreflect]
+Std [library]
+StrictOrder [record, in Corelib.Classes.RelationClasses]
+StrictOrder [record, in Corelib.Classes.CRelationClasses]
+StrictOrder_Asymmetric [instance, in Corelib.Classes.RelationClasses]
+StrictOrder_Transitive [projection, in Corelib.Classes.RelationClasses]
+StrictOrder_Irreflexive [projection, in Corelib.Classes.RelationClasses]
+StrictOrder_PartialOrder [lemma, in Corelib.Classes.CMorphisms]
+StrictOrder_PreOrder [lemma, in Corelib.Classes.CMorphisms]
+StrictOrder_PartialOrder [lemma, in Corelib.Classes.Morphisms]
+StrictOrder_PreOrder [lemma, in Corelib.Classes.Morphisms]
+StrictOrder_Asymmetric [instance, in Corelib.Classes.CRelationClasses]
+StrictOrder_Transitive [projection, in Corelib.Classes.CRelationClasses]
+StrictOrder_Irreflexive [projection, in Corelib.Classes.CRelationClasses]
+string [axiom, in Corelib.Strings.PrimString]
+String [library]
+sub [definition, in Corelib.Init.Nat]
+sub [axiom, in Corelib.Strings.PrimString]
+sub [axiom, in Corelib.Floats.PrimFloat]
+sub [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+subc [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+subcarryc [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+subcarryc_def_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+subcarryc_def [definition, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+subc_def_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+subc_def [definition, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+subon_bij [lemma, in Corelib.ssr.ssrbool]
+subon1 [lemma, in Corelib.ssr.ssrbool]
+subon1l [lemma, in Corelib.ssr.ssrbool]
+subon2 [lemma, in Corelib.ssr.ssrbool]
+subpred [definition, in Corelib.ssr.ssrbool]
+subrel [definition, in Corelib.ssr.ssrbool]
+subrelation [record, in Corelib.Classes.RelationClasses]
+subrelation [inductive, in Corelib.Classes.RelationClasses]
+subrelation [record, in Corelib.Classes.CRelationClasses]
+subrelation [inductive, in Corelib.Classes.CRelationClasses]
+subrelation [definition, in Corelib.Init.Logic]
+subrelation_partial_order [instance, in Corelib.Classes.RelationClasses]
+subrelation_symmetric [lemma, in Corelib.Classes.RelationClasses]
+subrelation_proper [lemma, in Corelib.Classes.CMorphisms]
+subrelation_refl [lemma, in Corelib.Classes.CMorphisms]
+subrelation_respectful [lemma, in Corelib.Classes.CMorphisms]
+subrelation_id_proper [instance, in Corelib.Classes.CMorphisms]
+subrelation_proper [lemma, in Corelib.Classes.Morphisms]
+subrelation_refl [lemma, in Corelib.Classes.Morphisms]
+subrelation_respectful [lemma, in Corelib.Classes.Morphisms]
+subrelation_id_proper [instance, in Corelib.Classes.Morphisms]
+subrelation_symmetric [lemma, in Corelib.Classes.CRelationClasses]
+subrelUl [lemma, in Corelib.ssr.ssrbool]
+subrelUr [lemma, in Corelib.ssr.ssrbool]
+Subset_projections2.Q [variable, in Corelib.Init.Specif]
+Subset_projections2.P [variable, in Corelib.Init.Specif]
+Subset_projections2.A [variable, in Corelib.Init.Specif]
+Subset_projections2 [section, in Corelib.Init.Specif]
+Subset_projections.P [variable, in Corelib.Init.Specif]
+Subset_projections.A [variable, in Corelib.Init.Specif]
+Subset_projections [section, in Corelib.Init.Specif]
+sub_spec [axiom, in Corelib.Floats.FloatAxioms]
+sub_in21 [lemma, in Corelib.ssr.ssrbool]
+sub_in12 [lemma, in Corelib.ssr.ssrbool]
+sub_in3 [lemma, in Corelib.ssr.ssrbool]
+sub_in2 [lemma, in Corelib.ssr.ssrbool]
+sub_in_bij [lemma, in Corelib.ssr.ssrbool]
+sub_in111 [lemma, in Corelib.ssr.ssrbool]
+sub_in11 [lemma, in Corelib.ssr.ssrbool]
+sub_in1 [lemma, in Corelib.ssr.ssrbool]
+sub_refl [lemma, in Corelib.ssr.ssrbool]
+sub_mem [definition, in Corelib.ssr.ssrbool]
+sub_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+sub_spec [axiom, in Corelib.Strings.PrimStringAxioms]
+succ [definition, in Corelib.Init.Nat]
+sum [inductive, in Corelib.Init.Datatypes]
+sumbool [inductive, in Corelib.Init.Specif]
+Sumbool [library]
+sumboolP [lemma, in Corelib.ssr.ssrbool]
+sumbool_sind [definition, in Corelib.Init.Specif]
+sumbool_rec [definition, in Corelib.Init.Specif]
+sumbool_ind [definition, in Corelib.Init.Specif]
+sumbool_rect [definition, in Corelib.Init.Specif]
+sumbool_not [definition, in Corelib.Init.Sumbool]
+sumbool_or [definition, in Corelib.Init.Sumbool]
+sumbool_and [definition, in Corelib.Init.Sumbool]
+sumbool_of_bool [definition, in Corelib.Init.Sumbool]
+sumor [inductive, in Corelib.Init.Specif]
+sumor_sind [definition, in Corelib.Init.Specif]
+sumor_rec [definition, in Corelib.Init.Specif]
+sumor_ind [definition, in Corelib.Init.Specif]
+sumor_rect [definition, in Corelib.Init.Specif]
+sum_sind [definition, in Corelib.Init.Datatypes]
+sum_rec [definition, in Corelib.Init.Datatypes]
+sum_ind [definition, in Corelib.Init.Datatypes]
+sum_rect [definition, in Corelib.Init.Datatypes]
+surjective_pairing [lemma, in Corelib.Init.Datatypes]
+sval [abbreviation, in Corelib.ssr.ssrfun]
+svalP [lemma, in Corelib.ssr.ssrfun]
+Symmetric [record, in Corelib.Classes.RelationClasses]
+Symmetric [inductive, in Corelib.Classes.RelationClasses]
+symmetric [definition, in Corelib.ssr.ssrbool]
+Symmetric [record, in Corelib.Classes.CRelationClasses]
+Symmetric [inductive, in Corelib.Classes.CRelationClasses]
+symmetric [definition, in Corelib.Relations.Relation_Definitions]
+symmetric_from_pre [lemma, in Corelib.ssr.ssrbool]
+symmetric_equiv_flip [lemma, in Corelib.Classes.CMorphisms]
+symmetric_equiv_flip [lemma, in Corelib.Classes.Morphisms]
+symmetry [projection, in Corelib.Classes.RelationClasses]
+symmetry [constructor, in Corelib.Classes.RelationClasses]
+symmetry [projection, in Corelib.Classes.CRelationClasses]
+symmetry [constructor, in Corelib.Classes.CRelationClasses]
+sym_not_id [abbreviation, in Corelib.Init.Datatypes]
+sym_id [abbreviation, in Corelib.Init.Datatypes]
+sym_right_transitive [lemma, in Corelib.ssr.ssrbool]
+sym_left_transitive [lemma, in Corelib.ssr.ssrbool]
+sym_not_equal [abbreviation, in Corelib.Init.Logic]
+sym_equal [abbreviation, in Corelib.Init.Logic]
+sym_not_eq [abbreviation, in Corelib.Init.Logic]
+sym_eq [abbreviation, in Corelib.Init.Logic]
+s2val [definition, in Corelib.ssr.ssrfun]
+s2valP [lemma, in Corelib.ssr.ssrfun]
+s2valP' [lemma, in Corelib.ssr.ssrfun]
+S754_finite [constructor, in Corelib.Floats.SpecFloat]
+S754_nan [constructor, in Corelib.Floats.SpecFloat]
+S754_infinity [constructor, in Corelib.Floats.SpecFloat]
+S754_zero [constructor, in Corelib.Floats.SpecFloat]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_T.html b/master/corelib/index_global_T.html new file mode 100644 index 0000000000..580bde376b --- /dev/null +++ b/master/corelib/index_global_T.html @@ -0,0 +1,1139 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

T

+t [definition, in Corelib.Init.Nat]
+Tactics [library]
+Tactics [library]
+tactic_view [constructor, in Corelib.ssr.ssreflect]
+tag [definition, in Corelib.ssr.ssrfun]
+Tag [section, in Corelib.ssr.ssrfun]
+Tagged [definition, in Corelib.ssr.ssrfun]
+tagged [definition, in Corelib.ssr.ssrfun]
+Tagged2 [definition, in Corelib.ssr.ssrfun]
+tagged2 [definition, in Corelib.ssr.ssrfun]
+tagged2' [definition, in Corelib.ssr.ssrfun]
+Tags [module, in Ltac2.FSet]
+tag_of_sig [definition, in Corelib.ssr.ssrfun]
+tag_of_tag2 [definition, in Corelib.ssr.ssrfun]
+Tag.i [variable, in Corelib.ssr.ssrfun]
+Tag.I [variable, in Corelib.ssr.ssrfun]
+Tag.T_ [variable, in Corelib.ssr.ssrfun]
+Tag.U_ [variable, in Corelib.ssr.ssrfun]
+tag2 [definition, in Corelib.ssr.ssrfun]
+tail_mul [definition, in Corelib.Init.Nat]
+tail_addmul [definition, in Corelib.Init.Nat]
+tail_add [definition, in Corelib.Init.Nat]
+tail0 [axiom, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+tail0_spec [axiom, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+Tauto [library]
+Tcons [constructor, in Corelib.Classes.RelationClasses]
+ten [abbreviation, in Corelib.Init.Nat]
+ternary_operation [definition, in Corelib.Classes.RelationClasses]
+testbit [definition, in Corelib.Init.Nat]
+TheCanonical [module, in Corelib.ssr.ssreflect]
+TheCanonical.get [definition, in Corelib.ssr.ssreflect]
+TheCanonical.get_by [definition, in Corelib.ssr.ssreflect]
+TheCanonical.Put [constructor, in Corelib.ssr.ssreflect]
+TheCanonical.put [inductive, in Corelib.ssr.ssreflect]
+Tlist [inductive, in Corelib.Classes.RelationClasses]
+Tlist_sind [definition, in Corelib.Classes.RelationClasses]
+Tlist_rec [definition, in Corelib.Classes.RelationClasses]
+Tlist_ind [definition, in Corelib.Classes.RelationClasses]
+Tlist_rect [definition, in Corelib.Classes.RelationClasses]
+Tnil [constructor, in Corelib.Classes.RelationClasses]
+topred [projection, in Corelib.ssr.ssrbool]
+topredE [lemma, in Corelib.ssr.ssrbool]
+total [definition, in Corelib.ssr.ssrbool]
+to_bits_of_bits [lemma, in Corelib.Init.Byte]
+to_bits [definition, in Corelib.Init.Byte]
+to_num_int [definition, in Corelib.Init.Nat]
+to_hex_int [definition, in Corelib.Init.Nat]
+to_int [definition, in Corelib.Init.Nat]
+to_num_hex_uint [definition, in Corelib.Init.Nat]
+to_num_uint [definition, in Corelib.Init.Nat]
+to_hex_uint [definition, in Corelib.Init.Nat]
+to_little_hex_uint [definition, in Corelib.Init.Nat]
+to_uint [definition, in Corelib.Init.Nat]
+to_little_uint [definition, in Corelib.Init.Nat]
+to_Z [definition, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+to_Z_rec [definition, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+to_list_char63_valid [axiom, in Corelib.Strings.PrimStringAxioms]
+to_list_length [axiom, in Corelib.Strings.PrimStringAxioms]
+to_list [definition, in Corelib.Strings.PrimStringAxioms]
+to_nat [abbreviation, in Corelib.Strings.PrimStringAxioms]
+to_Z [definition, in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+Transitive [record, in Corelib.Classes.RelationClasses]
+Transitive [inductive, in Corelib.Classes.RelationClasses]
+transitive [definition, in Corelib.ssr.ssrbool]
+Transitive [record, in Corelib.Classes.CRelationClasses]
+Transitive [inductive, in Corelib.Classes.CRelationClasses]
+transitive [definition, in Corelib.Relations.Relation_Definitions]
+transitivity [projection, in Corelib.Classes.RelationClasses]
+transitivity [constructor, in Corelib.Classes.RelationClasses]
+transitivity [projection, in Corelib.Classes.CRelationClasses]
+transitivity [constructor, in Corelib.Classes.CRelationClasses]
+TransparentState [library]
+trans_id [abbreviation, in Corelib.Init.Datatypes]
+trans_co_eq_inv_arrow_morphism [instance, in Corelib.Classes.CMorphisms]
+trans_sym_contra_arrow_morphism [instance, in Corelib.Classes.CMorphisms]
+trans_sym_co_inv_impl_type_morphism [instance, in Corelib.Classes.CMorphisms]
+trans_co_impl_type_morphism [instance, in Corelib.Classes.CMorphisms]
+trans_contra_inv_impl_type_morphism [instance, in Corelib.Classes.CMorphisms]
+trans_contra_co_type_morphism [instance, in Corelib.Classes.CMorphisms]
+trans_co_eq_inv_impl_morphism [instance, in Corelib.Classes.Morphisms]
+trans_sym_contra_impl_morphism [instance, in Corelib.Classes.Morphisms]
+trans_sym_co_inv_impl_morphism [instance, in Corelib.Classes.Morphisms]
+trans_co_impl_morphism [instance, in Corelib.Classes.Morphisms]
+trans_contra_inv_impl_morphism [instance, in Corelib.Classes.Morphisms]
+trans_contra_co_morphism [instance, in Corelib.Classes.Morphisms]
+trans_equal [abbreviation, in Corelib.Init.Logic]
+trans_eq [abbreviation, in Corelib.Init.Logic]
+true [constructor, in Corelib.Init.Datatypes]
+True [inductive, in Corelib.Init.Logic]
+true_predicate [definition, in Corelib.Classes.RelationClasses]
+True_sind [definition, in Corelib.Init.Logic]
+True_rec [definition, in Corelib.Init.Logic]
+True_ind [definition, in Corelib.Init.Logic]
+True_rect [definition, in Corelib.Init.Logic]
+tt [constructor, in Corelib.Init.Datatypes]
+two [definition, in Corelib.Init.Nat]
+two [definition, in Corelib.Floats.PrimFloat]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_U.html b/master/corelib/index_global_U.html new file mode 100644 index 0000000000..d4c16eef96 --- /dev/null +++ b/master/corelib/index_global_U.html @@ -0,0 +1,1122 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

U

+uint [inductive, in Corelib.Init.Hexadecimal]
+uint [inductive, in Corelib.Init.Decimal]
+uint [inductive, in Corelib.Init.Number]
+UIntDecimal [constructor, in Corelib.Init.Number]
+UIntHexadecimal [constructor, in Corelib.Init.Number]
+uint_eq_dec [definition, in Corelib.Init.Hexadecimal]
+uint_sind [definition, in Corelib.Init.Hexadecimal]
+uint_rec [definition, in Corelib.Init.Hexadecimal]
+uint_ind [definition, in Corelib.Init.Hexadecimal]
+uint_rect [definition, in Corelib.Init.Hexadecimal]
+uint_of_uint [definition, in Corelib.Init.Decimal]
+uint_eq_dec [definition, in Corelib.Init.Decimal]
+uint_sind [definition, in Corelib.Init.Decimal]
+uint_rec [definition, in Corelib.Init.Decimal]
+uint_ind [definition, in Corelib.Init.Decimal]
+uint_rect [definition, in Corelib.Init.Decimal]
+uint_of_uint [definition, in Corelib.Init.Number]
+uint_eq_dec [definition, in Corelib.Init.Number]
+Uint63 [library]
+Uint63Axioms [library]
+Uint63NotationsInternalA [module, in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+ulp [definition, in Corelib.Floats.FloatOps]
+unary_predicate [definition, in Corelib.Classes.RelationClasses]
+unary_operation [definition, in Corelib.Classes.RelationClasses]
+unconvertible [projection, in Corelib.Classes.Init]
+Unconvertible [record, in Corelib.Classes.Init]
+unconvertible [constructor, in Corelib.Classes.Init]
+Unconvertible [inductive, in Corelib.Classes.Init]
+uncurry [definition, in Corelib.Init.Datatypes]
+UnderE [definition, in Corelib.ssr.ssreflect]
+Under_rel.under_rel_done [lemma, in Corelib.ssr.ssrunder]
+Under_rel.over_rel_done [lemma, in Corelib.ssr.ssrunder]
+Under_rel.over_rel [lemma, in Corelib.ssr.ssrunder]
+Under_rel.Over_rel [definition, in Corelib.ssr.ssrunder]
+Under_rel.Under_relE [lemma, in Corelib.ssr.ssrunder]
+Under_rel.Under_rel_from_rel [lemma, in Corelib.ssr.ssrunder]
+Under_rel.Under_rel [definition, in Corelib.ssr.ssrunder]
+Under_rel [module, in Corelib.ssr.ssrunder]
+'Under[ _ ] [notation, in Corelib.ssr.ssrunder]
+UNDER_REL.under_rel_done [axiom, in Corelib.ssr.ssrunder]
+UNDER_REL.over_rel_done [axiom, in Corelib.ssr.ssrunder]
+UNDER_REL.over_rel [axiom, in Corelib.ssr.ssrunder]
+UNDER_REL.Over_rel [axiom, in Corelib.ssr.ssrunder]
+UNDER_REL.Under_relE [axiom, in Corelib.ssr.ssrunder]
+UNDER_REL.Under_rel_from_rel [axiom, in Corelib.ssr.ssrunder]
+UNDER_REL.Under_rel [axiom, in Corelib.ssr.ssrunder]
+UNDER_REL [module, in Corelib.ssr.ssrunder]
+unfold_in [lemma, in Corelib.ssr.ssrbool]
+Unification [library]
+unique [definition, in Corelib.Init.Logic]
+uniqueness [definition, in Corelib.Init.Logic]
+unique_existence [lemma, in Corelib.Init.Logic]
+unit [inductive, in Corelib.Init.Datatypes]
+unitE [lemma, in Corelib.ssr.ssrfun]
+unit_sind [definition, in Corelib.Init.Datatypes]
+unit_rec [definition, in Corelib.Init.Datatypes]
+unit_ind [definition, in Corelib.Init.Datatypes]
+unit_rect [definition, in Corelib.Init.Datatypes]
+universal_quantification.P [variable, in Corelib.Init.Logic]
+universal_quantification.A [variable, in Corelib.Init.Logic]
+universal_quantification [section, in Corelib.Init.Logic]
+unkeyed [abbreviation, in Corelib.ssr.ssreflect]
+unkey_qualifier [projection, in Corelib.ssr.ssrbool]
+unkey_pred [projection, in Corelib.ssr.ssrbool]
+unless [definition, in Corelib.ssr.ssrbool]
+unlessL [lemma, in Corelib.ssr.ssrbool]
+unlessP [lemma, in Corelib.ssr.ssrbool]
+unlessR [lemma, in Corelib.ssr.ssrbool]
+unless_contra [lemma, in Corelib.ssr.ssrbool]
+unless_sym [lemma, in Corelib.ssr.ssrbool]
+unlock [lemma, in Corelib.ssr.ssreflect]
+unlockable [record, in Corelib.ssr.ssreflect]
+unlocked [projection, in Corelib.ssr.ssreflect]
+unlock_with [lemma, in Corelib.ssr.ssreflect]
+unorm [definition, in Corelib.Init.Hexadecimal]
+unorm [definition, in Corelib.Init.Decimal]
+Unsafe [module, in Ltac2.Constr]
+Unsafe.Case [module, in Ltac2.Constr]
+unwrap [projection, in Corelib.ssr.ssrfun]
+Utils [library]
+

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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

V

+valid_binary [definition, in Corelib.Floats.SpecFloat]
+valid_binary [abbreviation, in Corelib.Floats.FloatAxioms]
+value [definition, in Corelib.Init.Specif]
+vm_compute [projection, in Corelib.ssr.ssreflect]
+vm_compute_eq [record, in Corelib.ssr.ssreflect]
+vm_compute [constructor, in Corelib.ssr.ssreflect]
+vm_compute_eq [inductive, in Corelib.ssr.ssreflect]
+void [abbreviation, in Corelib.ssr.ssrfun]
+

+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

W

+wB [definition, in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+Well_founded.F_ext [variable, in Corelib.Program.Wf]
+Well_founded.F_sub [variable, in Corelib.Program.Wf]
+Well_founded.P [variable, in Corelib.Program.Wf]
+Well_founded.Rwf [variable, in Corelib.Program.Wf]
+Well_founded.R [variable, in Corelib.Program.Wf]
+Well_founded.A [variable, in Corelib.Program.Wf]
+Well_founded [section, in Corelib.Program.Wf]
+well_founded_morphism [instance, in Corelib.Classes.Morphisms_Prop]
+well_founded_induction_type_2 [lemma, in Corelib.Init.Wf]
+Well_founded_2.Rwf [variable, in Corelib.Init.Wf]
+Well_founded_2.FixPoint_2.F [variable, in Corelib.Init.Wf]
+Well_founded_2.FixPoint_2 [section, in Corelib.Init.Wf]
+Well_founded_2.P [variable, in Corelib.Init.Wf]
+Well_founded_2.R [variable, in Corelib.Init.Wf]
+Well_founded_2.B [variable, in Corelib.Init.Wf]
+Well_founded_2.A [variable, in Corelib.Init.Wf]
+Well_founded_2 [section, in Corelib.Init.Wf]
+Well_founded.FixPoint.F_ext [variable, in Corelib.Init.Wf]
+Well_founded.FixPoint.F [variable, in Corelib.Init.Wf]
+Well_founded.FixPoint.P [variable, in Corelib.Init.Wf]
+Well_founded.FixPoint [section, in Corelib.Init.Wf]
+well_founded_ind [lemma, in Corelib.Init.Wf]
+well_founded_induction [lemma, in Corelib.Init.Wf]
+well_founded_induction_type [lemma, in Corelib.Init.Wf]
+Well_founded.Rwf [variable, in Corelib.Init.Wf]
+well_founded [definition, in Corelib.Init.Wf]
+Well_founded.R [variable, in Corelib.Init.Wf]
+Well_founded.A [variable, in Corelib.Init.Wf]
+Well_founded [section, in Corelib.Init.Wf]
+Wf [library]
+Wf [library]
+wlog_neg [lemma, in Corelib.ssr.ssrbool]
+wrap [definition, in Corelib.ssr.ssrfun]
+wrapped [record, in Corelib.ssr.ssrfun]
+

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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_global_X.html b/master/corelib/index_global_X.html new file mode 100644 index 0000000000..c2bf883e22 --- /dev/null +++ b/master/corelib/index_global_X.html @@ -0,0 +1,1313 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

X

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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

Z

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+zero [abbreviation, in Corelib.Init.Hexadecimal]
+zero [abbreviation, in Corelib.Init.Decimal]
+zero [definition, in Corelib.Floats.PrimFloat]
+Zneg [constructor, in Corelib.Numbers.BinNums]
+Zpos [constructor, in Corelib.Numbers.BinNums]
+Z_sind [definition, in Corelib.Numbers.BinNums]
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+_ ÷ _ (Z_scope) [notation, in Corelib.BinNums.IntDef]
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+_ < _ (Z_scope) [notation, in Corelib.BinNums.IntDef]
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+_ ?= _ (Z_scope) [notation, in Corelib.BinNums.IntDef]
+_ ^ _ (Z_scope) [notation, in Corelib.BinNums.IntDef]
+_ * _ (Z_scope) [notation, in Corelib.BinNums.IntDef]
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+- _ (Z_scope) [notation, in Corelib.BinNums.IntDef]
+_ + _ (Z_scope) [notation, in Corelib.BinNums.IntDef]
+Z0 [constructor, in Corelib.Numbers.BinNums]
+

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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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+ +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

A (inductive)

+Acc [in Corelib.Init.Wf]
+alt_spec [in Corelib.ssr.ssrbool]
+and [in Corelib.Init.Logic]
+and3 [in Corelib.ssr.ssrbool]
+and4 [in Corelib.ssr.ssrbool]
+and5 [in Corelib.ssr.ssrbool]
+Antisymmetric [in Corelib.Classes.RelationClasses]
+Antisymmetric [in Corelib.Classes.CRelationClasses]
+apply_subrelation [in Corelib.Classes.CMorphisms]
+apply_subrelation [in Corelib.Classes.Morphisms]
+Asymmetric [in Corelib.Classes.RelationClasses]
+Asymmetric [in Corelib.Classes.CRelationClasses]
+

+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

B (inductive)

+bijective [in Corelib.ssr.ssrfun]
+bool [in Corelib.Init.Datatypes]
+BoolSpec [in Corelib.Init.Datatypes]
+byte [in Corelib.Init.Byte]
+

+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

C (inductive)

+carry [in Corelib.Numbers.Cyclic.Int63.CarryType]
+CompareSpec [in Corelib.Init.Datatypes]
+CompareSpecT [in Corelib.Init.Datatypes]
+comparison [in Corelib.Init.Datatypes]
+

+ +
+ +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

D (inductive)

+decimal [in Corelib.Init.Decimal]
+

+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

E (inductive)

+Empty_set [in Corelib.Init.Datatypes]
+eq [in Corelib.Init.Logic]
+eq_true [in Corelib.Init.Datatypes]
+ex [in Corelib.Init.Logic]
+external_view [in Corelib.ssr.ssreflect]
+ex2 [in Corelib.Init.Logic]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_inductive_F.html b/master/corelib/index_inductive_F.html new file mode 100644 index 0000000000..53d0261be3 --- /dev/null +++ b/master/corelib/index_inductive_F.html @@ -0,0 +1,564 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

F (inductive)

+False [in Corelib.Init.Logic]
+float_class [in Corelib.Floats.FloatClass]
+float_comparison [in Corelib.Floats.PrimFloat]
+Forall [in Corelib.Lists.ListDef]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_inductive_G.html b/master/corelib/index_inductive_G.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_inductive_G.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

H (inductive)

+hexadecimal [in Corelib.Init.Hexadecimal]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_inductive_I.html b/master/corelib/index_inductive_I.html new file mode 100644 index 0000000000..8d990471d0 --- /dev/null +++ b/master/corelib/index_inductive_I.html @@ -0,0 +1,565 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

I (inductive)

+if_spec [in Corelib.ssr.ssrbool]
+implies [in Corelib.ssr.ssrbool]
+inhabited [in Corelib.Init.Logic]
+Irreflexive [in Corelib.Classes.RelationClasses]
+Irreflexive [in Corelib.Classes.CRelationClasses]
+

+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_inductive_L.html b/master/corelib/index_inductive_L.html new file mode 100644 index 0000000000..3911c260dc --- /dev/null +++ b/master/corelib/index_inductive_L.html @@ -0,0 +1,563 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

L (inductive)

+le [in Corelib.Init.Peano]
+list [in Corelib.Init.Datatypes]
+location [in Corelib.Floats.SpecFloat]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_inductive_M.html b/master/corelib/index_inductive_M.html new file mode 100644 index 0000000000..a7a9dba240 --- /dev/null +++ b/master/corelib/index_inductive_M.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

M (inductive)

+mem_pred [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_inductive_N.html b/master/corelib/index_inductive_N.html new file mode 100644 index 0000000000..f05ba953d6 --- /dev/null +++ b/master/corelib/index_inductive_N.html @@ -0,0 +1,567 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

N (inductive)

+N [in Corelib.Numbers.BinNums]
+nat [in Corelib.Init.Datatypes]
+normalization_done [in Corelib.Classes.CMorphisms]
+normalization_done [in Corelib.Classes.Morphisms]
+Normalizes [in Corelib.Classes.CMorphisms]
+Normalizes [in Corelib.Classes.Morphisms]
+number [in Corelib.Init.Number]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_inductive_O.html b/master/corelib/index_inductive_O.html new file mode 100644 index 0000000000..a7819352a6 --- /dev/null +++ b/master/corelib/index_inductive_O.html @@ -0,0 +1,564 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

O (inductive)

+option [in Corelib.Init.Datatypes]
+or [in Corelib.Init.Logic]
+or3 [in Corelib.ssr.ssrbool]
+or4 [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_inductive_P.html b/master/corelib/index_inductive_P.html new file mode 100644 index 0000000000..a913fe68b4 --- /dev/null +++ b/master/corelib/index_inductive_P.html @@ -0,0 +1,573 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

P (inductive)

+PartialOrder [in Corelib.Classes.RelationClasses]
+PartialOrder [in Corelib.Classes.CRelationClasses]
+phant [in Corelib.ssr.ssreflect]
+phantom [in Corelib.ssr.ssreflect]
+positive [in Corelib.Numbers.BinNums]
+pos_neg_int63 [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+Pos.mask [in Corelib.BinNums.PosDef]
+pred_key [in Corelib.ssr.ssrbool]
+prod [in Corelib.Init.Datatypes]
+Proper [in Corelib.Classes.CMorphisms]
+Proper [in Corelib.Classes.Morphisms]
+ProperProxy [in Corelib.Classes.CMorphisms]
+ProperProxy [in Corelib.Classes.Morphisms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_inductive_Q.html b/master/corelib/index_inductive_Q.html new file mode 100644 index 0000000000..35d985aa00 --- /dev/null +++ b/master/corelib/index_inductive_Q.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

Q (inductive)

+qualifier [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_inductive_R.html b/master/corelib/index_inductive_R.html new file mode 100644 index 0000000000..ecce641603 --- /dev/null +++ b/master/corelib/index_inductive_R.html @@ -0,0 +1,565 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

R (inductive)

+reflect [in Corelib.Init.Datatypes]
+Reflexive [in Corelib.Classes.RelationClasses]
+Reflexive [in Corelib.ssr.ssrclasses]
+Reflexive [in Corelib.Classes.CRelationClasses]
+ReflexiveProxy [in Corelib.Classes.Morphisms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_inductive_S.html b/master/corelib/index_inductive_S.html new file mode 100644 index 0000000000..b346d24327 --- /dev/null +++ b/master/corelib/index_inductive_S.html @@ -0,0 +1,576 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

S (inductive)

+sig [in Corelib.Init.Specif]
+signed_int [in Corelib.Init.Hexadecimal]
+signed_int [in Corelib.Init.Decimal]
+signed_int [in Corelib.Init.Number]
+sigT [in Corelib.Init.Specif]
+sigT2 [in Corelib.Init.Specif]
+sig2 [in Corelib.Init.Specif]
+simpl_fun [in Corelib.ssr.ssrfun]
+spec_float [in Corelib.Floats.SpecFloat]
+subrelation [in Corelib.Classes.RelationClasses]
+subrelation [in Corelib.Classes.CRelationClasses]
+sum [in Corelib.Init.Datatypes]
+sumbool [in Corelib.Init.Specif]
+sumor [in Corelib.Init.Specif]
+Symmetric [in Corelib.Classes.RelationClasses]
+Symmetric [in Corelib.Classes.CRelationClasses]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_inductive_T.html b/master/corelib/index_inductive_T.html new file mode 100644 index 0000000000..523de899a0 --- /dev/null +++ b/master/corelib/index_inductive_T.html @@ -0,0 +1,565 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

T (inductive)

+TheCanonical.put [in Corelib.ssr.ssreflect]
+Tlist [in Corelib.Classes.RelationClasses]
+Transitive [in Corelib.Classes.RelationClasses]
+Transitive [in Corelib.Classes.CRelationClasses]
+True [in Corelib.Init.Logic]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_inductive_U.html b/master/corelib/index_inductive_U.html new file mode 100644 index 0000000000..063bf2721b --- /dev/null +++ b/master/corelib/index_inductive_U.html @@ -0,0 +1,565 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

U (inductive)

+uint [in Corelib.Init.Hexadecimal]
+uint [in Corelib.Init.Decimal]
+uint [in Corelib.Init.Number]
+Unconvertible [in Corelib.Classes.Init]
+unit [in Corelib.Init.Datatypes]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_inductive_V.html b/master/corelib/index_inductive_V.html new file mode 100644 index 0000000000..f8356ceabd --- /dev/null +++ b/master/corelib/index_inductive_V.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

V (inductive)

+vm_compute_eq [in Corelib.ssr.ssreflect]
+

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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

Z (inductive)

+Z [in Corelib.Numbers.BinNums]
+

+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_instance_A.html b/master/corelib/index_instance_A.html new file mode 100644 index 0000000000..b0dfd55ec2 --- /dev/null +++ b/master/corelib/index_instance_A.html @@ -0,0 +1,569 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

A (instance)

+Acc_rel_morphism [in Corelib.Classes.Morphisms_Prop]
+Acc_pt_morphism [in Corelib.Classes.Morphisms_Prop]
+all_flip_impl_morphism [in Corelib.Classes.Morphisms_Prop]
+all_impl_morphism [in Corelib.Classes.Morphisms_Prop]
+all_iff_morphism [in Corelib.Classes.Morphisms_Prop]
+and_iff_morphism [in Corelib.Classes.Morphisms_Prop]
+and_impl_morphism [in Corelib.Classes.Morphisms_Prop]
+arrow_Transitive [in Corelib.Classes.CRelationClasses]
+arrow_Reflexive [in Corelib.Classes.CRelationClasses]
+

+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_instance_C.html b/master/corelib/index_instance_C.html new file mode 100644 index 0000000000..4ddf3d65c1 --- /dev/null +++ b/master/corelib/index_instance_C.html @@ -0,0 +1,563 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

C (instance)

+compat_Reflexive [in Corelib.ssr.ssrsetoid]
+compose_proper [in Corelib.Classes.CMorphisms]
+compose_proper [in Corelib.Classes.Morphisms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_instance_D.html b/master/corelib/index_instance_D.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_instance_D.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_instance_E.html b/master/corelib/index_instance_E.html new file mode 100644 index 0000000000..106681e05c --- /dev/null +++ b/master/corelib/index_instance_E.html @@ -0,0 +1,581 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

E (instance)

+equivalence_default [in Corelib.Classes.SetoidTactics]
+Equivalence_PreOrder [in Corelib.Classes.RelationClasses]
+Equivalence_PER [in Corelib.Classes.RelationClasses]
+equivalence_rewrite_crelation [in Corelib.Classes.CRelationClasses]
+Equivalence_PER [in Corelib.Classes.CRelationClasses]
+equiv_transitive [in Corelib.Classes.Equivalence]
+equiv_symmetric [in Corelib.Classes.Equivalence]
+equiv_reflexive [in Corelib.Classes.Equivalence]
+eq_equivalence [in Corelib.Classes.RelationClasses]
+eq_Transitive [in Corelib.Classes.RelationClasses]
+eq_Symmetric [in Corelib.Classes.RelationClasses]
+eq_Reflexive [in Corelib.Classes.RelationClasses]
+eq_Reflexive [in Corelib.ssr.ssrclasses]
+eq_pars [in Corelib.Classes.Morphisms]
+eq_equivalence [in Corelib.Classes.CRelationClasses]
+eq_Transitive [in Corelib.Classes.CRelationClasses]
+eq_Symmetric [in Corelib.Classes.CRelationClasses]
+eq_Reflexive [in Corelib.Classes.CRelationClasses]
+ex_flip_impl_morphism [in Corelib.Classes.Morphisms_Prop]
+ex_impl_morphism [in Corelib.Classes.Morphisms_Prop]
+ex_iff_morphism [in Corelib.Classes.Morphisms_Prop]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_instance_F.html b/master/corelib/index_instance_F.html new file mode 100644 index 0000000000..a577a8c2c0 --- /dev/null +++ b/master/corelib/index_instance_F.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

F (instance)

+flip_pars [in Corelib.Classes.Morphisms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_instance_G.html b/master/corelib/index_instance_G.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_instance_G.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_instance_H.html b/master/corelib/index_instance_H.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_instance_H.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

I (instance)

+iffT_flip_arrow_subrelation [in Corelib.Classes.CMorphisms]
+iffT_arrow_subrelation [in Corelib.Classes.CMorphisms]
+iffT_Transitive [in Corelib.Classes.CRelationClasses]
+iffT_Symmetric [in Corelib.Classes.CRelationClasses]
+iffT_Reflexive [in Corelib.Classes.CRelationClasses]
+iff_equivalence [in Corelib.Classes.RelationClasses]
+iff_Transitive [in Corelib.Classes.RelationClasses]
+iff_Symmetric [in Corelib.Classes.RelationClasses]
+iff_Reflexive [in Corelib.Classes.RelationClasses]
+iff_rewrite_relation [in Corelib.Classes.RelationClasses]
+iff_Reflexive [in Corelib.ssr.ssrclasses]
+iff_flip_impl_subrelation [in Corelib.Classes.CMorphisms]
+iff_impl_subrelation [in Corelib.Classes.CMorphisms]
+iff_pars [in Corelib.Classes.Morphisms]
+iff_flip_impl_subrelation [in Corelib.Classes.Morphisms]
+iff_impl_subrelation [in Corelib.Classes.Morphisms]
+iff_equivalence [in Corelib.Classes.CRelationClasses]
+iff_Transitive [in Corelib.Classes.CRelationClasses]
+iff_Symmetric [in Corelib.Classes.CRelationClasses]
+iff_Reflexive [in Corelib.Classes.CRelationClasses]
+iff_iff_iff_impl_morphism [in Corelib.Classes.Morphisms_Prop]
+impl_Transitive [in Corelib.Classes.RelationClasses]
+impl_Reflexive [in Corelib.Classes.RelationClasses]
+impl_rewrite_relation [in Corelib.Classes.RelationClasses]
+impl_pars [in Corelib.Classes.Morphisms]
+impl_Transitive [in Corelib.Classes.CRelationClasses]
+impl_Reflexive [in Corelib.Classes.CRelationClasses]
+inverse_impl_rewrite_relation [in Corelib.Classes.RelationClasses]
+

+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_instance_K.html b/master/corelib/index_instance_K.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_instance_K.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_instance_M.html b/master/corelib/index_instance_M.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_instance_M.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_instance_N.html b/master/corelib/index_instance_N.html new file mode 100644 index 0000000000..39062754b7 --- /dev/null +++ b/master/corelib/index_instance_N.html @@ -0,0 +1,563 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

N (instance)

+neq_Symmetric [in Corelib.Classes.RelationClasses]
+not_iff_morphism [in Corelib.Classes.Morphisms_Prop]
+not_impl_morphism [in Corelib.Classes.Morphisms_Prop]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_instance_O.html b/master/corelib/index_instance_O.html new file mode 100644 index 0000000000..508d13a777 --- /dev/null +++ b/master/corelib/index_instance_O.html @@ -0,0 +1,562 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

O (instance)

+or_iff_morphism [in Corelib.Classes.Morphisms_Prop]
+or_impl_morphism [in Corelib.Classes.Morphisms_Prop]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_instance_P.html b/master/corelib/index_instance_P.html new file mode 100644 index 0000000000..af28692153 --- /dev/null +++ b/master/corelib/index_instance_P.html @@ -0,0 +1,580 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

P (instance)

+PartialOrder_proper_type [in Corelib.Classes.CMorphisms]
+PartialOrder_proper [in Corelib.Classes.Morphisms]
+partial_order_antisym [in Corelib.Classes.RelationClasses]
+partial_order_antisym [in Corelib.Classes.CRelationClasses]
+PER_type_morphism [in Corelib.Classes.CMorphisms]
+per_partial_app_type_morphism [in Corelib.Classes.CMorphisms]
+PER_morphism [in Corelib.Classes.Morphisms]
+per_partial_app_morphism [in Corelib.Classes.Morphisms]
+pointwise_subrelation [in Corelib.Classes.CMorphisms]
+pointwise_subrelation [in Corelib.Classes.Morphisms]
+pointwise_equivalence [in Corelib.Classes.Equivalence]
+pointwise_transitive [in Corelib.Classes.Equivalence]
+pointwise_symmetric [in Corelib.Classes.Equivalence]
+pointwise_reflexive [in Corelib.Classes.Equivalence]
+predicate_implication_preorder [in Corelib.Classes.RelationClasses]
+predicate_equivalence_equivalence [in Corelib.Classes.RelationClasses]
+proper_proper [in Corelib.Classes.CMorphisms]
+proper_subrelation_proper_arrow [in Corelib.Classes.CMorphisms]
+proper_proper [in Corelib.Classes.Morphisms]
+proper_subrelation_proper [in Corelib.Classes.Morphisms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_instance_Q.html b/master/corelib/index_instance_Q.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_instance_Q.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_instance_R.html b/master/corelib/index_instance_R.html new file mode 100644 index 0000000000..82a7316d69 --- /dev/null +++ b/master/corelib/index_instance_R.html @@ -0,0 +1,572 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

R (instance)

+reflexive_eq_dom_reflexive [in Corelib.Classes.CMorphisms]
+reflexive_eq_dom_reflexive [in Corelib.Classes.Morphisms]
+relation_implication_preorder [in Corelib.Classes.RelationClasses]
+relation_equivalence_equivalence [in Corelib.Classes.RelationClasses]
+relation_equivalence_rewrite_relation [in Corelib.Classes.RelationClasses]
+relation_implication_preorder [in Corelib.Classes.CRelationClasses]
+relation_equivalence_equivalence [in Corelib.Classes.CRelationClasses]
+respectful_morphism [in Corelib.Classes.CMorphisms]
+respectful_per [in Corelib.Classes.CMorphisms]
+respectful_morphism [in Corelib.Classes.Morphisms]
+respectful_per [in Corelib.Classes.Morphisms]
+respecting_equiv [in Corelib.Classes.Equivalence]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_instance_S.html b/master/corelib/index_instance_S.html new file mode 100644 index 0000000000..694224428e --- /dev/null +++ b/master/corelib/index_instance_S.html @@ -0,0 +1,565 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

S (instance)

+StrictOrder_Asymmetric [in Corelib.Classes.RelationClasses]
+StrictOrder_Asymmetric [in Corelib.Classes.CRelationClasses]
+subrelation_partial_order [in Corelib.Classes.RelationClasses]
+subrelation_id_proper [in Corelib.Classes.CMorphisms]
+subrelation_id_proper [in Corelib.Classes.Morphisms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_instance_T.html b/master/corelib/index_instance_T.html new file mode 100644 index 0000000000..3bddcfe926 --- /dev/null +++ b/master/corelib/index_instance_T.html @@ -0,0 +1,572 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

T (instance)

+trans_co_eq_inv_arrow_morphism [in Corelib.Classes.CMorphisms]
+trans_sym_contra_arrow_morphism [in Corelib.Classes.CMorphisms]
+trans_sym_co_inv_impl_type_morphism [in Corelib.Classes.CMorphisms]
+trans_co_impl_type_morphism [in Corelib.Classes.CMorphisms]
+trans_contra_inv_impl_type_morphism [in Corelib.Classes.CMorphisms]
+trans_contra_co_type_morphism [in Corelib.Classes.CMorphisms]
+trans_co_eq_inv_impl_morphism [in Corelib.Classes.Morphisms]
+trans_sym_contra_impl_morphism [in Corelib.Classes.Morphisms]
+trans_sym_co_inv_impl_morphism [in Corelib.Classes.Morphisms]
+trans_co_impl_morphism [in Corelib.Classes.Morphisms]
+trans_contra_inv_impl_morphism [in Corelib.Classes.Morphisms]
+trans_contra_co_morphism [in Corelib.Classes.Morphisms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_instance_U.html b/master/corelib/index_instance_U.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_instance_U.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_instance_V.html b/master/corelib/index_instance_V.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_instance_V.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_instance_W.html b/master/corelib/index_instance_W.html new file mode 100644 index 0000000000..e58c3a00c0 --- /dev/null +++ b/master/corelib/index_instance_W.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

W (instance)

+well_founded_morphism [in Corelib.Classes.Morphisms_Prop]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_instance_X.html b/master/corelib/index_instance_X.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_instance_X.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

A (lemma)

+abstract_context [in Corelib.ssr.ssreflect]
+absurd [in Corelib.Init.Logic]
+absurd_set [in Corelib.Init.Specif]
+Acc_inv [in Corelib.Init.Wf]
+addbA [in Corelib.ssr.ssrbool]
+addbAC [in Corelib.ssr.ssrbool]
+addbACA [in Corelib.ssr.ssrbool]
+addbb [in Corelib.ssr.ssrbool]
+addbC [in Corelib.ssr.ssrbool]
+addbCA [in Corelib.ssr.ssrbool]
+addbF [in Corelib.ssr.ssrbool]
+addbI [in Corelib.ssr.ssrbool]
+addbK [in Corelib.ssr.ssrbool]
+addbN [in Corelib.ssr.ssrbool]
+addbP [in Corelib.ssr.ssrbool]
+addbT [in Corelib.ssr.ssrbool]
+addFb [in Corelib.ssr.ssrbool]
+addIb [in Corelib.ssr.ssrbool]
+addKb [in Corelib.ssr.ssrbool]
+addNb [in Corelib.ssr.ssrbool]
+addTb [in Corelib.ssr.ssrbool]
+all_sig2_cond [in Corelib.ssr.ssrbool]
+all_sig_cond [in Corelib.ssr.ssrbool]
+all_sig_cond_dep [in Corelib.ssr.ssrbool]
+all_tag_cond [in Corelib.ssr.ssrbool]
+all_tag_cond_dep [in Corelib.ssr.ssrbool]
+all_and5 [in Corelib.ssr.ssrbool]
+all_and4 [in Corelib.ssr.ssrbool]
+all_and3 [in Corelib.ssr.ssrbool]
+all_and2 [in Corelib.ssr.ssrbool]
+all_sig2 [in Corelib.ssr.ssrfun]
+all_sig [in Corelib.ssr.ssrfun]
+all_tag2 [in Corelib.ssr.ssrfun]
+all_tag [in Corelib.ssr.ssrfun]
+altP [in Corelib.ssr.ssrbool]
+andbA [in Corelib.ssr.ssrbool]
+andbAC [in Corelib.ssr.ssrbool]
+andbACA [in Corelib.ssr.ssrbool]
+andbb [in Corelib.ssr.ssrbool]
+andbC [in Corelib.ssr.ssrbool]
+andbCA [in Corelib.ssr.ssrbool]
+andbF [in Corelib.ssr.ssrbool]
+andbK [in Corelib.ssr.ssrbool]
+andbN [in Corelib.ssr.ssrbool]
+andbT [in Corelib.ssr.ssrbool]
+andb_true_intro [in Corelib.Init.Datatypes]
+andb_prop [in Corelib.Init.Datatypes]
+andb_addr [in Corelib.ssr.ssrbool]
+andb_addl [in Corelib.ssr.ssrbool]
+andb_id2r [in Corelib.ssr.ssrbool]
+andb_id2l [in Corelib.ssr.ssrbool]
+andb_idr [in Corelib.ssr.ssrbool]
+andb_idl [in Corelib.ssr.ssrbool]
+andb_orr [in Corelib.ssr.ssrbool]
+andb_orl [in Corelib.ssr.ssrbool]
+andFb [in Corelib.ssr.ssrbool]
+andKb [in Corelib.ssr.ssrbool]
+andNb [in Corelib.ssr.ssrbool]
+andP [in Corelib.ssr.ssrbool]
+andPP [in Corelib.ssr.ssrbool]
+andTb [in Corelib.ssr.ssrbool]
+and_assoc [in Corelib.Init.Logic]
+and_comm [in Corelib.Init.Logic]
+and_cancel_r [in Corelib.Init.Logic]
+and_cancel_l [in Corelib.Init.Logic]
+and_iff_compat_r [in Corelib.Init.Logic]
+and_iff_compat_l [in Corelib.Init.Logic]
+and3P [in Corelib.ssr.ssrbool]
+and4P [in Corelib.ssr.ssrbool]
+and5P [in Corelib.ssr.ssrbool]
+appP [in Corelib.ssr.ssrbool]
+app_predE [in Corelib.ssr.ssrbool]
+

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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_B.html b/master/corelib/index_lemma_B.html new file mode 100644 index 0000000000..61b4d41a1d --- /dev/null +++ b/master/corelib/index_lemma_B.html @@ -0,0 +1,568 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

B (lemma)

+bij_can_bij [in Corelib.ssr.ssrfun]
+bij_comp [in Corelib.ssr.ssrfun]
+bij_can_eq [in Corelib.ssr.ssrfun]
+bij_can_sym [in Corelib.ssr.ssrfun]
+bij_inj [in Corelib.ssr.ssrfun]
+bind_unless [in Corelib.ssr.ssrbool]
+boolP [in Corelib.ssr.ssrbool]
+bool_choice [in Corelib.Init.Specif]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_C.html b/master/corelib/index_lemma_C.html new file mode 100644 index 0000000000..ba5b793cb5 --- /dev/null +++ b/master/corelib/index_lemma_C.html @@ -0,0 +1,1100 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

C (lemma)

+canLR [in Corelib.ssr.ssrfun]
+canLR_on [in Corelib.ssr.ssrbool]
+canLR_in [in Corelib.ssr.ssrbool]
+canRL [in Corelib.ssr.ssrfun]
+canRL_on [in Corelib.ssr.ssrbool]
+canRL_in [in Corelib.ssr.ssrbool]
+can_mono_in [in Corelib.ssr.ssrbool]
+can_mono [in Corelib.ssr.ssrbool]
+can_in_comp [in Corelib.ssr.ssrbool]
+can_in_pcan [in Corelib.ssr.ssrbool]
+can_in_inj [in Corelib.ssr.ssrbool]
+can_comp [in Corelib.ssr.ssrfun]
+can_inj [in Corelib.ssr.ssrfun]
+can_pcan [in Corelib.ssr.ssrfun]
+Choice [in Corelib.Init.Specif]
+Choice2 [in Corelib.Init.Specif]
+classicP [in Corelib.ssr.ssrbool]
+classicW [in Corelib.ssr.ssrbool]
+classic_ex [in Corelib.ssr.ssrbool]
+classic_sigW [in Corelib.ssr.ssrbool]
+classic_imply [in Corelib.ssr.ssrbool]
+classic_pick [in Corelib.ssr.ssrbool]
+classic_EM [in Corelib.ssr.ssrbool]
+classic_bind [in Corelib.ssr.ssrbool]
+compA [in Corelib.ssr.ssrfun]
+CompareSpec2Type [in Corelib.Init.Datatypes]
+comparison_eq_stable [in Corelib.Init.Datatypes]
+complement_Symmetric [in Corelib.Classes.RelationClasses]
+complement_Irreflexive [in Corelib.Classes.RelationClasses]
+complement_inverse [in Corelib.Classes.RelationClasses]
+complement_Symmetric [in Corelib.Classes.CRelationClasses]
+complement_Irreflexive [in Corelib.Classes.CRelationClasses]
+complement_inverse [in Corelib.Classes.CRelationClasses]
+CompOpp_iff [in Corelib.Init.Datatypes]
+CompOpp_inj [in Corelib.Init.Datatypes]
+CompOpp_involutive [in Corelib.Init.Datatypes]
+CompSpec2Type [in Corelib.Init.Datatypes]
+contra [in Corelib.ssr.ssrbool]
+contraFF [in Corelib.ssr.ssrbool]
+contraFN [in Corelib.ssr.ssrbool]
+contraFnot [in Corelib.ssr.ssrbool]
+contraFT [in Corelib.ssr.ssrbool]
+contraL [in Corelib.ssr.ssrbool]
+contraLR [in Corelib.ssr.ssrbool]
+contraNF [in Corelib.ssr.ssrbool]
+contraNnot [in Corelib.ssr.ssrbool]
+contraPF [in Corelib.ssr.ssrbool]
+contraPN [in Corelib.ssr.ssrbool]
+contraPnot [in Corelib.ssr.ssrbool]
+contraPT [in Corelib.ssr.ssrbool]
+contraR [in Corelib.ssr.ssrbool]
+contraT [in Corelib.ssr.ssrbool]
+contraTF [in Corelib.ssr.ssrbool]
+contraTnot [in Corelib.ssr.ssrbool]
+contra_notF [in Corelib.ssr.ssrbool]
+contra_notN [in Corelib.ssr.ssrbool]
+contra_notT [in Corelib.ssr.ssrbool]
+contra_not [in Corelib.ssr.ssrbool]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_D.html b/master/corelib/index_lemma_D.html new file mode 100644 index 0000000000..865c13e884 --- /dev/null +++ b/master/corelib/index_lemma_D.html @@ -0,0 +1,564 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

D (lemma)

+decide_right [in Corelib.Init.Tactics]
+decide_left [in Corelib.Init.Tactics]
+decPcases [in Corelib.ssr.ssrbool]
+dependent_choice [in Corelib.Init.Specif]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_E.html b/master/corelib/index_lemma_E.html new file mode 100644 index 0000000000..17112ca2d4 --- /dev/null +++ b/master/corelib/index_lemma_E.html @@ -0,0 +1,1100 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

E (lemma)

+elimF [in Corelib.ssr.ssrbool]
+elimFn [in Corelib.ssr.ssrbool]
+elimN [in Corelib.ssr.ssrbool]
+elimNf [in Corelib.ssr.ssrbool]
+elimNTF [in Corelib.ssr.ssrbool]
+elimT [in Corelib.ssr.ssrbool]
+elimTF [in Corelib.ssr.ssrbool]
+elimTFn [in Corelib.ssr.ssrbool]
+elimTn [in Corelib.ssr.ssrbool]
+eqbLR [in Corelib.ssr.ssrbool]
+eqbRL [in Corelib.ssr.ssrbool]
+equivalence_relP_in [in Corelib.ssr.ssrbool]
+equivalence_relP [in Corelib.ssr.ssrbool]
+equivP [in Corelib.ssr.ssrbool]
+equivPif [in Corelib.ssr.ssrbool]
+equivPifn [in Corelib.ssr.ssrbool]
+eq_true_rect_r [in Corelib.Init.Datatypes]
+eq_true_rec_r [in Corelib.Init.Datatypes]
+eq_true_ind_r [in Corelib.Init.Datatypes]
+eq_subrelation [in Corelib.Classes.CMorphisms]
+eq_proper_proxy [in Corelib.Classes.CMorphisms]
+eq_Fix_F_sub [in Corelib.Program.Wf]
+eq_exist2_curried [in Corelib.Init.Specif]
+eq_existT2_curried [in Corelib.Init.Specif]
+eq_exist_curried [in Corelib.Init.Specif]
+eq_existT_curried_congr [in Corelib.Init.Specif]
+eq_existT_curried_trans [in Corelib.Init.Specif]
+eq_existT_curried_map [in Corelib.Init.Specif]
+eq_existT_curried [in Corelib.Init.Specif]
+eq_bij [in Corelib.ssr.ssrfun]
+eq_can [in Corelib.ssr.ssrfun]
+eq_inj [in Corelib.ssr.ssrfun]
+eq_comp [in Corelib.ssr.ssrfun]
+eq_subrelation [in Corelib.Classes.Morphisms]
+eq_rewrite_relation [in Corelib.Classes.Morphisms]
+eq_proper_proxy [in Corelib.Classes.Morphisms]
+eq_stepl [in Corelib.Init.Logic]
+eq_trans_rew_distr [in Corelib.Init.Logic]
+eq_trans_sym_distr [in Corelib.Init.Logic]
+eq_sym_map_distr [in Corelib.Init.Logic]
+eq_trans_map_distr [in Corelib.Init.Logic]
+eq_refl_map_distr [in Corelib.Init.Logic]
+eq_id_comm_r [in Corelib.Init.Logic]
+eq_id_comm_l [in Corelib.Init.Logic]
+eq_trans_map [in Corelib.Init.Logic]
+eq_trans_assoc [in Corelib.Init.Logic]
+eq_trans_sym_inv_r [in Corelib.Init.Logic]
+eq_trans_sym_inv_l [in Corelib.Init.Logic]
+eq_sym_involutive [in Corelib.Init.Logic]
+eq_trans_refl_r [in Corelib.Init.Logic]
+eq_trans_refl_l [in Corelib.Init.Logic]
+eq_trans_r [in Corelib.Init.Logic]
+eq_trans [in Corelib.Init.Logic]
+eq_sym [in Corelib.Init.Logic]
+esymK [in Corelib.ssr.ssrfun]
+etrans_id [in Corelib.ssr.ssrfun]
+exists_to_inhabited_sig [in Corelib.Init.Specif]
+exists_inhabited [in Corelib.Init.Logic]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_F.html b/master/corelib/index_lemma_F.html new file mode 100644 index 0000000000..6fe73f8967 --- /dev/null +++ b/master/corelib/index_lemma_F.html @@ -0,0 +1,1091 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

F (lemma)

+Fix_sub_rect [in Corelib.Program.Wf]
+Fix_F_sub_rect [in Corelib.Program.Wf]
+fix_sub_eq [in Corelib.Program.Wf]
+Fix_eq [in Corelib.Program.Wf]
+Fix_F_inv [in Corelib.Program.Wf]
+Fix_F_eq [in Corelib.Program.Wf]
+Fix_eq [in Corelib.Init.Wf]
+Fix_F_inv [in Corelib.Init.Wf]
+Fix_F_eq [in Corelib.Init.Wf]
+flip_Equivalence [in Corelib.Classes.RelationClasses]
+flip_PER [in Corelib.Classes.RelationClasses]
+flip_StrictOrder [in Corelib.Classes.RelationClasses]
+flip_PreOrder [in Corelib.Classes.RelationClasses]
+flip_Antisymmetric [in Corelib.Classes.RelationClasses]
+flip_Reflexive [in Corelib.Classes.RelationClasses]
+flip_arrow [in Corelib.Classes.CMorphisms]
+flip_atom [in Corelib.Classes.CMorphisms]
+flip_respectful [in Corelib.Classes.CMorphisms]
+flip_arrow [in Corelib.Classes.Morphisms]
+flip_atom [in Corelib.Classes.Morphisms]
+flip_respectful [in Corelib.Classes.Morphisms]
+flip_Equivalence [in Corelib.Classes.CRelationClasses]
+flip_PER [in Corelib.Classes.CRelationClasses]
+flip_StrictOrder [in Corelib.Classes.CRelationClasses]
+flip_PreOrder [in Corelib.Classes.CRelationClasses]
+flip_Antisymmetric [in Corelib.Classes.CRelationClasses]
+flip_Reflexive [in Corelib.Classes.CRelationClasses]
+flip1 [in Corelib.Classes.CMorphisms]
+flip1 [in Corelib.Classes.Morphisms]
+flip2 [in Corelib.Classes.CMorphisms]
+flip2 [in Corelib.Classes.Morphisms]
+forall_subrelation [in Corelib.Classes.CMorphisms]
+forall_subrelation [in Corelib.Classes.Morphisms]
+forall_exists_coincide_unique_domain [in Corelib.Init.Logic]
+forall_exists_unique_domain_coincide [in Corelib.Init.Logic]
+forE [in Corelib.ssr.ssrbool]
+frefl [in Corelib.ssr.ssrfun]
+fsym [in Corelib.ssr.ssrfun]
+ftrans [in Corelib.ssr.ssrfun]
+fun_if [in Corelib.ssr.ssrbool]
+F_unfold [in Corelib.Program.Wf]
+f_equal_compose [in Corelib.Init.Logic]
+f_equal5 [in Corelib.Init.Logic]
+f_equal4 [in Corelib.Init.Logic]
+f_equal3 [in Corelib.Init.Logic]
+f_equal2 [in Corelib.Init.Logic]
+f_equal_dep2 [in Corelib.Init.Logic]
+f_equal_dep [in Corelib.Init.Logic]
+f_equal [in Corelib.Init.Logic]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_G.html b/master/corelib/index_lemma_G.html new file mode 100644 index 0000000000..ec8f97fcd7 --- /dev/null +++ b/master/corelib/index_lemma_G.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

G (lemma)

+gen [in Corelib.Init.Logic]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_H.html b/master/corelib/index_lemma_H.html new file mode 100644 index 0000000000..0c732076c6 --- /dev/null +++ b/master/corelib/index_lemma_H.html @@ -0,0 +1,569 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

H (lemma)

+homoLR [in Corelib.ssr.ssrbool]
+homoLR_in [in Corelib.ssr.ssrbool]
+homoRL [in Corelib.ssr.ssrbool]
+homoRL_in [in Corelib.ssr.ssrbool]
+homo_sym_in11 [in Corelib.ssr.ssrbool]
+homo_sym_in [in Corelib.ssr.ssrbool]
+homo_sym [in Corelib.ssr.ssrbool]
+homo_mono_in [in Corelib.ssr.ssrbool]
+homo_mono [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_I.html b/master/corelib/index_lemma_I.html new file mode 100644 index 0000000000..33f5d15b69 --- /dev/null +++ b/master/corelib/index_lemma_I.html @@ -0,0 +1,1134 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

I (lemma)

+idP [in Corelib.ssr.ssrbool]
+idPn [in Corelib.ssr.ssrbool]
+ifE [in Corelib.ssr.ssrbool]
+ifF [in Corelib.ssr.ssrbool]
+iffLR [in Corelib.ssr.ssreflect]
+iffLRn [in Corelib.ssr.ssreflect]
+iffP [in Corelib.ssr.ssrbool]
+iffRL [in Corelib.ssr.ssreflect]
+iffRLn [in Corelib.ssr.ssreflect]
+iff_stepl [in Corelib.Init.Logic]
+iff_to_and [in Corelib.Init.Logic]
+iff_and [in Corelib.Init.Logic]
+iff_sym [in Corelib.Init.Logic]
+iff_trans [in Corelib.Init.Logic]
+iff_refl [in Corelib.Init.Logic]
+ifN [in Corelib.ssr.ssrbool]
+ifP [in Corelib.ssr.ssrbool]
+ifPn [in Corelib.ssr.ssrbool]
+ifT [in Corelib.ssr.ssrbool]
+if_arg [in Corelib.ssr.ssrbool]
+if_neg [in Corelib.ssr.ssrbool]
+if_same [in Corelib.ssr.ssrbool]
+impliesP [in Corelib.ssr.ssrbool]
+impliesPn [in Corelib.ssr.ssrbool]
+implybb [in Corelib.ssr.ssrbool]
+implybE [in Corelib.ssr.ssrbool]
+implybF [in Corelib.ssr.ssrbool]
+implybN [in Corelib.ssr.ssrbool]
+implybNN [in Corelib.ssr.ssrbool]
+implybT [in Corelib.ssr.ssrbool]
+implyb_id2l [in Corelib.ssr.ssrbool]
+implyb_idr [in Corelib.ssr.ssrbool]
+implyb_idl [in Corelib.ssr.ssrbool]
+implyFb [in Corelib.ssr.ssrbool]
+implyNb [in Corelib.ssr.ssrbool]
+implyP [in Corelib.ssr.ssrbool]
+implyPP [in Corelib.ssr.ssrbool]
+implyTb [in Corelib.ssr.ssrbool]
+imp_iff_compat_r [in Corelib.Init.Logic]
+imp_iff_compat_l [in Corelib.Init.Logic]
+inhabited_sig_to_exists [in Corelib.Init.Specif]
+inhabited_covariant [in Corelib.Init.Logic]
+injective_projections [in Corelib.Init.Datatypes]
+inj_can_sym_in [in Corelib.ssr.ssrbool]
+inj_can_sym_on [in Corelib.ssr.ssrbool]
+inj_can_sym_in_on [in Corelib.ssr.ssrbool]
+inj_can_eq [in Corelib.ssr.ssrfun]
+inj_compr [in Corelib.ssr.ssrfun]
+inj_comp [in Corelib.ssr.ssrfun]
+inj_can_sym [in Corelib.ssr.ssrfun]
+inj_id [in Corelib.ssr.ssrfun]
+inst [in Corelib.Init.Logic]
+introF [in Corelib.ssr.ssrbool]
+introFn [in Corelib.ssr.ssrbool]
+introN [in Corelib.ssr.ssrbool]
+introNf [in Corelib.ssr.ssrbool]
+introNTF [in Corelib.ssr.ssrbool]
+introP [in Corelib.ssr.ssrbool]
+introT [in Corelib.ssr.ssrbool]
+introTF [in Corelib.ssr.ssrbool]
+introTFn [in Corelib.ssr.ssrbool]
+introTn [in Corelib.ssr.ssrbool]
+inT_bij [in Corelib.ssr.ssrbool]
+inv_bij [in Corelib.ssr.ssrfun]
+inv_inj [in Corelib.ssr.ssrfun]
+inW_bij [in Corelib.ssr.ssrbool]
+in_onS_can [in Corelib.ssr.ssrbool]
+in_onW_can [in Corelib.ssr.ssrbool]
+in_inj_comp [in Corelib.ssr.ssrbool]
+in_on2S [in Corelib.ssr.ssrbool]
+in_on1lS [in Corelib.ssr.ssrbool]
+in_on1S [in Corelib.ssr.ssrbool]
+in_on2W [in Corelib.ssr.ssrbool]
+in_on1lW [in Corelib.ssr.ssrbool]
+in_on1W [in Corelib.ssr.ssrbool]
+in_on2P [in Corelib.ssr.ssrbool]
+in_on1lP [in Corelib.ssr.ssrbool]
+in_on1P [in Corelib.ssr.ssrbool]
+in_simpl [in Corelib.ssr.ssrbool]
+in_collective [in Corelib.ssr.ssrbool]
+in_applicative [in Corelib.ssr.ssrbool]
+in1T [in Corelib.ssr.ssrbool]
+in1W [in Corelib.ssr.ssrbool]
+in1_sig [in Corelib.ssr.ssrbool]
+in2T [in Corelib.ssr.ssrbool]
+in2W [in Corelib.ssr.ssrbool]
+in2_sig [in Corelib.ssr.ssrbool]
+in3T [in Corelib.ssr.ssrbool]
+in3W [in Corelib.ssr.ssrbool]
+in3_sig [in Corelib.ssr.ssrbool]
+is_true_locked_true [in Corelib.ssr.ssrbool]
+is_true_true [in Corelib.ssr.ssrbool]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_J.html b/master/corelib/index_lemma_J.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_lemma_J.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_K.html b/master/corelib/index_lemma_K.html new file mode 100644 index 0000000000..b671f73ee9 --- /dev/null +++ b/master/corelib/index_lemma_K.html @@ -0,0 +1,562 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

K (lemma)

+keyed_qualifier_suproof [in Corelib.ssr.ssrbool]
+keyed_predE [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_L.html b/master/corelib/index_lemma_L.html new file mode 100644 index 0000000000..40d0baaf9b --- /dev/null +++ b/master/corelib/index_lemma_L.html @@ -0,0 +1,566 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

L (lemma)

+le_n_S [in Corelib.Init.Peano]
+le_0_n [in Corelib.Init.Peano]
+le_S_n [in Corelib.Init.Peano]
+le_pred [in Corelib.Init.Peano]
+lock [in Corelib.ssr.ssreflect]
+locked_withE [in Corelib.ssr.ssreflect]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_M.html b/master/corelib/index_lemma_M.html new file mode 100644 index 0000000000..70b7ab2187 --- /dev/null +++ b/master/corelib/index_lemma_M.html @@ -0,0 +1,584 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

M (lemma)

+map_subst_map [in Corelib.Init.Logic]
+map_subst [in Corelib.Init.Logic]
+master_key [in Corelib.ssr.ssreflect]
+max_r [in Corelib.Init.Peano]
+max_l [in Corelib.Init.Peano]
+measure_wf [in Corelib.Program.Wf]
+mem_mem [in Corelib.ssr.ssrbool]
+mem_simpl [in Corelib.ssr.ssrbool]
+mem_topred [in Corelib.ssr.ssrbool]
+min_r [in Corelib.Init.Peano]
+min_l [in Corelib.Init.Peano]
+monoLR [in Corelib.ssr.ssrbool]
+monoLR_in [in Corelib.ssr.ssrbool]
+monoRL [in Corelib.ssr.ssrbool]
+monoRL_in [in Corelib.ssr.ssrbool]
+monoW [in Corelib.ssr.ssrbool]
+monoW_in [in Corelib.ssr.ssrbool]
+mono_sym_in11 [in Corelib.ssr.ssrbool]
+mono_sym_in [in Corelib.ssr.ssrbool]
+mono_sym [in Corelib.ssr.ssrbool]
+mono1W_in [in Corelib.ssr.ssrbool]
+mono2W [in Corelib.ssr.ssrbool]
+mult_n_Sm [in Corelib.Init.Peano]
+mult_n_O [in Corelib.Init.Peano]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_N.html b/master/corelib/index_lemma_N.html new file mode 100644 index 0000000000..ae2e9fb06d --- /dev/null +++ b/master/corelib/index_lemma_N.html @@ -0,0 +1,589 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

N (lemma)

+nandP [in Corelib.ssr.ssrbool]
+nary_congruence [in Corelib.ssr.ssreflect]
+nat_rect_plus [in Corelib.Init.Peano]
+nat_rect_succ_r [in Corelib.Init.Peano]
+nat_double_ind [in Corelib.Init.Peano]
+nat_case [in Corelib.Init.Peano]
+negbF [in Corelib.ssr.ssrbool]
+negbFE [in Corelib.ssr.ssrbool]
+negbK [in Corelib.ssr.ssrbool]
+negbLR [in Corelib.ssr.ssrbool]
+negbNE [in Corelib.ssr.ssrbool]
+negbRL [in Corelib.ssr.ssrbool]
+negbT [in Corelib.ssr.ssrbool]
+negbTE [in Corelib.ssr.ssrbool]
+negb_imply [in Corelib.ssr.ssrbool]
+negb_or [in Corelib.ssr.ssrbool]
+negb_and [in Corelib.ssr.ssrbool]
+negb_inj [in Corelib.ssr.ssrbool]
+negP [in Corelib.ssr.ssrbool]
+negPf [in Corelib.ssr.ssrbool]
+negPn [in Corelib.ssr.ssrbool]
+negPP [in Corelib.ssr.ssrbool]
+neg_false [in Corelib.Init.Logic]
+norP [in Corelib.ssr.ssrbool]
+not_false_is_true [in Corelib.ssr.ssrbool]
+not_eq_S [in Corelib.Init.Peano]
+not_eq_sym [in Corelib.Init.Logic]
+not_iff_compat [in Corelib.Init.Logic]
+n_Sn [in Corelib.Init.Peano]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_O.html b/master/corelib/index_lemma_O.html new file mode 100644 index 0000000000..0199cd07bc --- /dev/null +++ b/master/corelib/index_lemma_O.html @@ -0,0 +1,1107 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

O (lemma)

+oappEmap [in Corelib.ssr.ssrfun]
+oapp_comp_f [in Corelib.ssr.ssrfun]
+oapp_comp [in Corelib.ssr.ssrfun]
+obindEapp [in Corelib.ssr.ssrfun]
+ocan_in_comp [in Corelib.ssr.ssrbool]
+ocan_comp [in Corelib.ssr.ssrfun]
+of_bits_to_bits [in Corelib.Init.Byte]
+of_voidK [in Corelib.ssr.ssrfun]
+olift_comp [in Corelib.ssr.ssrfun]
+omapEapp [in Corelib.ssr.ssrfun]
+omapEbind [in Corelib.ssr.ssrfun]
+omap_comp [in Corelib.ssr.ssrfun]
+onS_can_in [in Corelib.ssr.ssrbool]
+onS_can [in Corelib.ssr.ssrbool]
+onT_bij [in Corelib.ssr.ssrbool]
+onW_can_in [in Corelib.ssr.ssrbool]
+onW_can [in Corelib.ssr.ssrbool]
+onW_bij [in Corelib.ssr.ssrbool]
+on_can_inj [in Corelib.ssr.ssrbool]
+on1lS [in Corelib.ssr.ssrbool]
+on1lS_in [in Corelib.ssr.ssrbool]
+on1lT [in Corelib.ssr.ssrbool]
+on1lW [in Corelib.ssr.ssrbool]
+on1lW_in [in Corelib.ssr.ssrbool]
+on1S [in Corelib.ssr.ssrbool]
+on1S_in [in Corelib.ssr.ssrbool]
+on1T [in Corelib.ssr.ssrbool]
+on1W [in Corelib.ssr.ssrbool]
+on1W_in [in Corelib.ssr.ssrbool]
+on2S [in Corelib.ssr.ssrbool]
+on2S_in [in Corelib.ssr.ssrbool]
+on2T [in Corelib.ssr.ssrbool]
+on2W [in Corelib.ssr.ssrbool]
+on2W_in [in Corelib.ssr.ssrbool]
+orbA [in Corelib.ssr.ssrbool]
+orbAC [in Corelib.ssr.ssrbool]
+orbACA [in Corelib.ssr.ssrbool]
+orbb [in Corelib.ssr.ssrbool]
+orbC [in Corelib.ssr.ssrbool]
+orbCA [in Corelib.ssr.ssrbool]
+orbF [in Corelib.ssr.ssrbool]
+orbK [in Corelib.ssr.ssrbool]
+orbN [in Corelib.ssr.ssrbool]
+orbT [in Corelib.ssr.ssrbool]
+orb_id2r [in Corelib.ssr.ssrbool]
+orb_id2l [in Corelib.ssr.ssrbool]
+orb_idr [in Corelib.ssr.ssrbool]
+orb_idl [in Corelib.ssr.ssrbool]
+orb_andr [in Corelib.ssr.ssrbool]
+orb_andl [in Corelib.ssr.ssrbool]
+orFb [in Corelib.ssr.ssrbool]
+orKb [in Corelib.ssr.ssrbool]
+orNb [in Corelib.ssr.ssrbool]
+orP [in Corelib.ssr.ssrbool]
+orPP [in Corelib.ssr.ssrbool]
+orTb [in Corelib.ssr.ssrbool]
+or_assoc [in Corelib.Init.Logic]
+or_comm [in Corelib.Init.Logic]
+or_cancel_r [in Corelib.Init.Logic]
+or_cancel_l [in Corelib.Init.Logic]
+or_iff_compat_r [in Corelib.Init.Logic]
+or_iff_compat_l [in Corelib.Init.Logic]
+or3P [in Corelib.ssr.ssrbool]
+or4P [in Corelib.ssr.ssrbool]
+O_S [in Corelib.Init.Peano]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_P.html b/master/corelib/index_lemma_P.html new file mode 100644 index 0000000000..fc9bf86da7 --- /dev/null +++ b/master/corelib/index_lemma_P.html @@ -0,0 +1,1080 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

P (lemma)

+pair_equal_spec [in Corelib.Init.Datatypes]
+pair_andP [in Corelib.ssr.ssrbool]
+PartialOrder_inverse [in Corelib.Classes.RelationClasses]
+PartialOrder_StrictOrder [in Corelib.Classes.CMorphisms]
+PartialOrder_StrictOrder [in Corelib.Classes.Morphisms]
+PartialOrder_inverse [in Corelib.Classes.CRelationClasses]
+pcan_in_comp [in Corelib.ssr.ssrbool]
+pcan_in_inj [in Corelib.ssr.ssrbool]
+pcan_pcomp [in Corelib.ssr.ssrfun]
+pcan_inj [in Corelib.ssr.ssrfun]
+plus_Sn_m [in Corelib.Init.Peano]
+plus_n_Sm [in Corelib.Init.Peano]
+plus_O_n [in Corelib.Init.Peano]
+plus_n_O [in Corelib.Init.Peano]
+pointwise_pointwise [in Corelib.Classes.CMorphisms]
+pointwise_pointwise [in Corelib.Classes.Morphisms]
+pred_Sn [in Corelib.Init.Peano]
+Prim2SF_inj [in Corelib.Floats.FloatAxioms]
+prod_sigT_prod [in Corelib.Init.Specif]
+proj1 [in Corelib.Init.Logic]
+proj2 [in Corelib.Init.Logic]
+proper_sym_arrow_iffT_2 [in Corelib.Classes.CMorphisms]
+proper_sym_impl_iff_2 [in Corelib.Classes.CMorphisms]
+proper_sym_arrow_iffT [in Corelib.Classes.CMorphisms]
+proper_sym_impl_iff [in Corelib.Classes.CMorphisms]
+proper_sym_flip_2 [in Corelib.Classes.CMorphisms]
+proper_sym_flip [in Corelib.Classes.CMorphisms]
+proper_normalizes_proper [in Corelib.Classes.CMorphisms]
+proper_eq [in Corelib.Classes.CMorphisms]
+proper_proper_proxy [in Corelib.Classes.CMorphisms]
+proper_sym_impl_iff_2 [in Corelib.Classes.Morphisms]
+proper_sym_impl_iff [in Corelib.Classes.Morphisms]
+proper_sym_flip_2 [in Corelib.Classes.Morphisms]
+proper_sym_flip [in Corelib.Classes.Morphisms]
+proper_normalizes_proper [in Corelib.Classes.Morphisms]
+proper_eq [in Corelib.Classes.Morphisms]
+proper_proper_proxy [in Corelib.Classes.Morphisms]
+prop_congr [in Corelib.ssr.ssrbool]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_Q.html b/master/corelib/index_lemma_Q.html new file mode 100644 index 0000000000..80c3136b30 --- /dev/null +++ b/master/corelib/index_lemma_Q.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

Q (lemma)

+qualifE [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_R.html b/master/corelib/index_lemma_R.html new file mode 100644 index 0000000000..43663f594b --- /dev/null +++ b/master/corelib/index_lemma_R.html @@ -0,0 +1,586 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

R (lemma)

+reflexive_proper [in Corelib.Classes.CMorphisms]
+Reflexive_partial_app_morphism [in Corelib.Classes.CMorphisms]
+reflexive_proper_proxy [in Corelib.Classes.CMorphisms]
+Reflexive_partial_app_morphism [in Corelib.Classes.Morphisms]
+reflexive_reflexive_proxy [in Corelib.Classes.Morphisms]
+reflexive_proper_proxy [in Corelib.Classes.Morphisms]
+reflexive_proper [in Corelib.Classes.Morphisms]
+rev_trans [in Corelib.ssr.ssrbool]
+rewrite_relation_eq_dom [in Corelib.Classes.Morphisms]
+rewrite_relation_pointwise [in Corelib.Classes.Morphisms]
+rew_pair [in Corelib.Init.Datatypes]
+rew_sig2 [in Corelib.Init.Specif]
+rew_sigT2 [in Corelib.Init.Specif]
+rew_sig [in Corelib.Init.Specif]
+rew_sigT [in Corelib.Init.Specif]
+rew_ex2 [in Corelib.Init.Logic]
+rew_ex [in Corelib.Init.Logic]
+rew_const [in Corelib.Init.Logic]
+rew_compose [in Corelib.Init.Logic]
+rew_swap [in Corelib.Init.Logic]
+rew_map [in Corelib.Init.Logic]
+rew_opp_l [in Corelib.Init.Logic]
+rew_opp_r [in Corelib.Init.Logic]
+rrefl [in Corelib.ssr.ssrfun]
+rwP [in Corelib.ssr.ssrbool]
+rwP2 [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_S.html b/master/corelib/index_lemma_S.html new file mode 100644 index 0000000000..709e711a7a --- /dev/null +++ b/master/corelib/index_lemma_S.html @@ -0,0 +1,1087 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

S (lemma)

+sameP [in Corelib.ssr.ssrbool]
+SF2Prim_inj [in Corelib.Floats.FloatAxioms]
+sigT_prod_sigT [in Corelib.Init.Specif]
+simpl_predE [in Corelib.ssr.ssrbool]
+Some_inj [in Corelib.ssr.ssrfun]
+ssr_congr_arrow [in Corelib.ssr.ssreflect]
+ssr_have_upoly [in Corelib.ssr.ssreflect]
+ssr_have [in Corelib.ssr.ssreflect]
+StrictOrder_PartialOrder [in Corelib.Classes.CMorphisms]
+StrictOrder_PreOrder [in Corelib.Classes.CMorphisms]
+StrictOrder_PartialOrder [in Corelib.Classes.Morphisms]
+StrictOrder_PreOrder [in Corelib.Classes.Morphisms]
+subon_bij [in Corelib.ssr.ssrbool]
+subon1 [in Corelib.ssr.ssrbool]
+subon1l [in Corelib.ssr.ssrbool]
+subon2 [in Corelib.ssr.ssrbool]
+subrelation_symmetric [in Corelib.Classes.RelationClasses]
+subrelation_proper [in Corelib.Classes.CMorphisms]
+subrelation_refl [in Corelib.Classes.CMorphisms]
+subrelation_respectful [in Corelib.Classes.CMorphisms]
+subrelation_proper [in Corelib.Classes.Morphisms]
+subrelation_refl [in Corelib.Classes.Morphisms]
+subrelation_respectful [in Corelib.Classes.Morphisms]
+subrelation_symmetric [in Corelib.Classes.CRelationClasses]
+subrelUl [in Corelib.ssr.ssrbool]
+subrelUr [in Corelib.ssr.ssrbool]
+sub_in21 [in Corelib.ssr.ssrbool]
+sub_in12 [in Corelib.ssr.ssrbool]
+sub_in3 [in Corelib.ssr.ssrbool]
+sub_in2 [in Corelib.ssr.ssrbool]
+sub_in_bij [in Corelib.ssr.ssrbool]
+sub_in111 [in Corelib.ssr.ssrbool]
+sub_in11 [in Corelib.ssr.ssrbool]
+sub_in1 [in Corelib.ssr.ssrbool]
+sub_refl [in Corelib.ssr.ssrbool]
+sumboolP [in Corelib.ssr.ssrbool]
+surjective_pairing [in Corelib.Init.Datatypes]
+svalP [in Corelib.ssr.ssrfun]
+symmetric_from_pre [in Corelib.ssr.ssrbool]
+symmetric_equiv_flip [in Corelib.Classes.CMorphisms]
+symmetric_equiv_flip [in Corelib.Classes.Morphisms]
+sym_right_transitive [in Corelib.ssr.ssrbool]
+sym_left_transitive [in Corelib.ssr.ssrbool]
+s2valP [in Corelib.ssr.ssrfun]
+s2valP' [in Corelib.ssr.ssrfun]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_T.html b/master/corelib/index_lemma_T.html new file mode 100644 index 0000000000..67575606d5 --- /dev/null +++ b/master/corelib/index_lemma_T.html @@ -0,0 +1,562 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

T (lemma)

+topredE [in Corelib.ssr.ssrbool]
+to_bits_of_bits [in Corelib.Init.Byte]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_U.html b/master/corelib/index_lemma_U.html new file mode 100644 index 0000000000..cf3e662600 --- /dev/null +++ b/master/corelib/index_lemma_U.html @@ -0,0 +1,575 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

U (lemma)

+Under_rel.under_rel_done [in Corelib.ssr.ssrunder]
+Under_rel.over_rel_done [in Corelib.ssr.ssrunder]
+Under_rel.over_rel [in Corelib.ssr.ssrunder]
+Under_rel.Under_relE [in Corelib.ssr.ssrunder]
+Under_rel.Under_rel_from_rel [in Corelib.ssr.ssrunder]
+unfold_in [in Corelib.ssr.ssrbool]
+unique_existence [in Corelib.Init.Logic]
+unitE [in Corelib.ssr.ssrfun]
+unlessL [in Corelib.ssr.ssrbool]
+unlessP [in Corelib.ssr.ssrbool]
+unlessR [in Corelib.ssr.ssrbool]
+unless_contra [in Corelib.ssr.ssrbool]
+unless_sym [in Corelib.ssr.ssrbool]
+unlock [in Corelib.ssr.ssreflect]
+unlock_with [in Corelib.ssr.ssreflect]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_V.html b/master/corelib/index_lemma_V.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_lemma_V.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_W.html b/master/corelib/index_lemma_W.html new file mode 100644 index 0000000000..318dd93617 --- /dev/null +++ b/master/corelib/index_lemma_W.html @@ -0,0 +1,565 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

W (lemma)

+well_founded_induction_type_2 [in Corelib.Init.Wf]
+well_founded_ind [in Corelib.Init.Wf]
+well_founded_induction [in Corelib.Init.Wf]
+well_founded_induction_type [in Corelib.Init.Wf]
+wlog_neg [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_X.html b/master/corelib/index_lemma_X.html new file mode 100644 index 0000000000..6e13c405a8 --- /dev/null +++ b/master/corelib/index_lemma_X.html @@ -0,0 +1,562 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

X (lemma)

+xorPif [in Corelib.ssr.ssrbool]
+xorPifn [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_Y.html b/master/corelib/index_lemma_Y.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_lemma_Y.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_lemma_Z.html b/master/corelib/index_lemma_Z.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_lemma_Z.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
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Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
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Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
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Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
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Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
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Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
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Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
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Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
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Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
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Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
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Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
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Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
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Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
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Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
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Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
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Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
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Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
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Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
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Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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R (library)

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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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S (library)

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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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T (library)

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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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U (library)

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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
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Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
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Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
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Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
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Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
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Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
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Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
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Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
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Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

B (module)

+Binder [in Ltac2.Constr]
+BoolNotations [in Ltac2.Bool]
+ByteSyntaxNotations [in Corelib.Init.Byte]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module_C.html b/master/corelib/index_module_C.html new file mode 100644 index 0000000000..1607370ca8 --- /dev/null +++ b/master/corelib/index_module_C.html @@ -0,0 +1,562 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

C (module)

+Cast [in Ltac2.Constr]
+Char63Notations [in Corelib.Strings.PrimString]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module_D.html b/master/corelib/index_module_D.html new file mode 100644 index 0000000000..1c2ea2d1c6 --- /dev/null +++ b/master/corelib/index_module_D.html @@ -0,0 +1,562 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

D (module)

+DeclarePredSortOfSimpl [in Corelib.ssr.ssrbool]
+DefaultKeying [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module_E.html b/master/corelib/index_module_E.html new file mode 100644 index 0000000000..6a01083a3d --- /dev/null +++ b/master/corelib/index_module_E.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

E (module)

+EqNotations [in Corelib.Init.Logic]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module_F.html b/master/corelib/index_module_F.html new file mode 100644 index 0000000000..94450810ef --- /dev/null +++ b/master/corelib/index_module_F.html @@ -0,0 +1,562 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

F (module)

+Format [in Ltac2.Message]
+Free [in Ltac2.Fresh]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module_G.html b/master/corelib/index_module_G.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_module_G.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module_H.html b/master/corelib/index_module_H.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_module_H.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module_I.html b/master/corelib/index_module_I.html new file mode 100644 index 0000000000..dcadcc9c63 --- /dev/null +++ b/master/corelib/index_module_I.html @@ -0,0 +1,563 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

I (module)

+IfNotations [in Corelib.Init.Notations]
+Int63NotationsInternalA [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+ipat [in Corelib.ssr.ssreflect]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module_J.html b/master/corelib/index_module_J.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_module_J.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module_K.html b/master/corelib/index_module_K.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_module_K.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module_L.html b/master/corelib/index_module_L.html new file mode 100644 index 0000000000..9b02944616 --- /dev/null +++ b/master/corelib/index_module_L.html @@ -0,0 +1,566 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

L (module)

+Leibniz [in Corelib.Floats.FloatAxioms]
+Leibniz [in Corelib.Floats.PrimFloat]
+Little [in Corelib.Init.Hexadecimal]
+Little [in Corelib.Init.Decimal]
+Ltac2 [in Ltac2.Compat.Coq818]
+Ltac2.Array [in Ltac2.Compat.Coq818]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module_M.html b/master/corelib/index_module_M.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_module_M.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module_N.html b/master/corelib/index_module_N.html new file mode 100644 index 0000000000..479fe6de97 --- /dev/null +++ b/master/corelib/index_module_N.html @@ -0,0 +1,565 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

N (module)

+N [in Corelib.BinNums.NatDef]
+NonPropType [in Corelib.ssr.ssreflect]
+NonPropType.Exports [in Corelib.ssr.ssreflect]
+Notations [in Ltac2.RedFlags]
+Notations [in Ltac2.Lazy]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module_O.html b/master/corelib/index_module_O.html new file mode 100644 index 0000000000..e5ea774ec2 --- /dev/null +++ b/master/corelib/index_module_O.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

O (module)

+Option [in Corelib.ssr.ssrfun]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module_P.html b/master/corelib/index_module_P.html new file mode 100644 index 0000000000..11d282f1ee --- /dev/null +++ b/master/corelib/index_module_P.html @@ -0,0 +1,574 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

P (module)

+PArrayNotations [in Corelib.Array.PrimArray]
+Pos [in Corelib.BinNums.PosDef]
+PredOfSimpl [in Corelib.ssr.ssrbool]
+PredSortOfSimplCoercion [in Corelib.ssr.ssrbool]
+PredSortOfSimplSignature [in Corelib.ssr.ssrbool]
+Pretype [in Ltac2.Constr]
+Pretype.Flags [in Ltac2.Constr]
+PrimFloatNotations [in Corelib.Floats.PrimFloat]
+PrimFloatNotationsInternalA [in Corelib.Floats.PrimFloat]
+PrimFloatNotationsInternalB [in Corelib.Floats.PrimFloat]
+PrimInt63Notations [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+ProperNotations [in Corelib.Classes.CMorphisms]
+ProperNotations [in Corelib.Classes.Morphisms]
+PStringNotations [in Corelib.Strings.PrimString]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module_Q.html b/master/corelib/index_module_Q.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_module_Q.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module_R.html b/master/corelib/index_module_R.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_module_R.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module_S.html b/master/corelib/index_module_S.html new file mode 100644 index 0000000000..0c93bcf92c --- /dev/null +++ b/master/corelib/index_module_S.html @@ -0,0 +1,563 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

S (module)

+SigTNotations [in Corelib.Init.Specif]
+SsrMatchingSyntax [in Corelib.ssrmatching.ssrmatching]
+SsrSyntax [in Corelib.ssr.ssreflect]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module_T.html b/master/corelib/index_module_T.html new file mode 100644 index 0000000000..05eada01a7 --- /dev/null +++ b/master/corelib/index_module_T.html @@ -0,0 +1,562 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

T (module)

+Tags [in Ltac2.FSet]
+TheCanonical [in Corelib.ssr.ssreflect]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module_U.html b/master/corelib/index_module_U.html new file mode 100644 index 0000000000..ba1d975e51 --- /dev/null +++ b/master/corelib/index_module_U.html @@ -0,0 +1,565 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

U (module)

+Uint63NotationsInternalA [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+Under_rel [in Corelib.ssr.ssrunder]
+UNDER_REL [in Corelib.ssr.ssrunder]
+Unsafe [in Ltac2.Constr]
+Unsafe.Case [in Ltac2.Constr]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module_V.html b/master/corelib/index_module_V.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_module_V.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module_W.html b/master/corelib/index_module_W.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_module_W.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module_Y.html b/master/corelib/index_module_Y.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_module_Y.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

Z (module)

+Z [in Corelib.BinNums.IntDef]
+Z [in Corelib.Floats.FloatOps]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_module__.html b/master/corelib/index_module__.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_module__.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_notation_*.html b/master/corelib/index_notation_*.html new file mode 100644 index 0000000000..ca7ad67c68 --- /dev/null +++ b/master/corelib/index_notation_*.html @@ -0,0 +1,1280 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

other (notation)

+if _ as _ return _ then _ else _ (boolean_if_scope) [in Corelib.ssr.ssreflect]
+if _ then _ else _ (boolean_if_scope) [in Corelib.ssr.ssreflect]
+if _ return _ then _ else _ (boolean_if_scope) [in Corelib.ssr.ssreflect]
+_ && _ (bool_scope) [in Corelib.Init.Datatypes]
+_ || _ (bool_scope) [in Corelib.Init.Datatypes]
+_ \is an _ (bool_scope) [in Corelib.ssr.ssrbool]
+_ \is a _ (bool_scope) [in Corelib.ssr.ssrbool]
+_ \is _ (bool_scope) [in Corelib.ssr.ssrbool]
+_ \in _ (bool_scope) [in Corelib.ssr.ssrbool]
+_ \isn't an _ (bool_scope) [in Corelib.ssr.ssrbool]
+_ \isn't a _ (bool_scope) [in Corelib.ssr.ssrbool]
+_ \isn't _ (bool_scope) [in Corelib.ssr.ssrbool]
+_ \is an _ (bool_scope) [in Corelib.ssr.ssrbool]
+_ \is an _ (bool_scope) [in Corelib.ssr.ssrbool]
+_ \is a _ (bool_scope) [in Corelib.ssr.ssrbool]
+_ \is a _ (bool_scope) [in Corelib.ssr.ssrbool]
+_ \is _ (bool_scope) [in Corelib.ssr.ssrbool]
+_ \is _ (bool_scope) [in Corelib.ssr.ssrbool]
+_ \notin _ (bool_scope) [in Corelib.ssr.ssrbool]
+_ \in _ (bool_scope) [in Corelib.ssr.ssrbool]
+_ \in _ (bool_scope) [in Corelib.ssr.ssrbool]
+[ ==> _ => _ ] (bool_scope) [in Corelib.ssr.ssrbool]
+[ ==> _ , _ , .. , _ => _ ] (bool_scope) [in Corelib.ssr.ssrbool]
+[ || _ , _ , .. , _ | _ ] (bool_scope) [in Corelib.ssr.ssrbool]
+[ || _ | _ ] (bool_scope) [in Corelib.ssr.ssrbool]
+[ && _ , _ , .. , _ & _ ] (bool_scope) [in Corelib.ssr.ssrbool]
+[ && _ & _ ] (bool_scope) [in Corelib.ssr.ssrbool]
+_ (+) _ (bool_scope) [in Corelib.ssr.ssrbool]
+_ ==> _ (bool_scope) [in Corelib.ssr.ssrbool]
+~~ _ (bool_scope) [in Corelib.ssr.ssrbool]
+( _ , _ , .. , _ ) (core_scope) [in Corelib.Init.Datatypes]
+_ =~= _ (equiv_scope) [in Corelib.Classes.Equivalence]
+_ =/= _ (equiv_scope) [in Corelib.Classes.Equivalence]
+_ === _ (equiv_scope) [in Corelib.Classes.Equivalence]
+[ qualify an _ : _ | _ ] (form_scope) [in Corelib.ssr.ssrbool]
+[ qualify an _ | _ ] (form_scope) [in Corelib.ssr.ssrbool]
+[ qualify a _ : _ | _ ] (form_scope) [in Corelib.ssr.ssrbool]
+[ qualify a _ | _ ] (form_scope) [in Corelib.ssr.ssrbool]
+[ qualify _ : _ | _ ] (form_scope) [in Corelib.ssr.ssrbool]
+[ qualify _ | _ ] (form_scope) [in Corelib.ssr.ssrbool]
+[ predType of _ ] (form_scope) [in Corelib.ssr.ssrbool]
+[ unlockable fun _ ] (form_scope) [in Corelib.ssr.ssreflect]
+[ unlockable of _ ] (form_scope) [in Corelib.ssr.ssreflect]
+=^~ _ (form_scope) [in Corelib.ssr.ssreflect]
+[ the _ of _ ] (form_scope) [in Corelib.ssr.ssreflect]
+[ the _ of _ by _ ] (form_scope) [in Corelib.ssr.ssreflect]
+[ the _ of _ ] (form_scope) [in Corelib.ssr.ssreflect]
+[ the _ of _ by _ ] (form_scope) [in Corelib.ssr.ssreflect]
+[ rel _ _ in _ ] (function_scope) [in Corelib.ssr.ssrbool]
+[ rel _ _ in _ | _ ] (function_scope) [in Corelib.ssr.ssrbool]
+[ rel _ _ in _ & _ ] (function_scope) [in Corelib.ssr.ssrbool]
+[ rel _ _ in _ & _ | _ ] (function_scope) [in Corelib.ssr.ssrbool]
+[ pred _ in _ | _ & _ ] (function_scope) [in Corelib.ssr.ssrbool]
+[ pred _ in _ | _ ] (function_scope) [in Corelib.ssr.ssrbool]
+[ pred _ in _ ] (function_scope) [in Corelib.ssr.ssrbool]
+[ preim _ of _ ] (function_scope) [in Corelib.ssr.ssrbool]
+[ predC _ ] (function_scope) [in Corelib.ssr.ssrbool]
+[ predD _ & _ ] (function_scope) [in Corelib.ssr.ssrbool]
+[ predU _ & _ ] (function_scope) [in Corelib.ssr.ssrbool]
+[ predI _ & _ ] (function_scope) [in Corelib.ssr.ssrbool]
+[ mem _ ] (function_scope) [in Corelib.ssr.ssrbool]
+[ in _ ] (function_scope) [in Corelib.ssr.ssrbool]
+[ rel _ _ : _ | _ ] (function_scope) [in Corelib.ssr.ssrbool]
+[ rel _ _ | _ ] (function_scope) [in Corelib.ssr.ssrbool]
+[ pred _ : _ | _ & _ ] (function_scope) [in Corelib.ssr.ssrbool]
+[ pred _ : _ | _ ] (function_scope) [in Corelib.ssr.ssrbool]
+[ pred _ | _ & _ ] (function_scope) [in Corelib.ssr.ssrbool]
+[ pred _ | _ ] (function_scope) [in Corelib.ssr.ssrbool]
+[ pred : _ | _ ] (function_scope) [in Corelib.ssr.ssrbool]
+@ sval (function_scope) [in Corelib.ssr.ssrfun]
+@ id _ (function_scope) [in Corelib.ssr.ssrfun]
+fun => _ (function_scope) [in Corelib.ssr.ssrfun]
+[ eta _ ] (function_scope) [in Corelib.ssr.ssrfun]
+_ \; _ (function_scope) [in Corelib.ssr.ssrfun]
+_ \o _ (function_scope) [in Corelib.ssr.ssrfun]
+[ fun ( _ : _ ) ( _ : _ ) => _ ] (function_scope) [in Corelib.ssr.ssrfun]
+[ fun _ ( _ : _ ) => _ ] (function_scope) [in Corelib.ssr.ssrfun]
+[ fun ( _ : _ ) _ => _ ] (function_scope) [in Corelib.ssr.ssrfun]
+[ fun _ _ : _ => _ ] (function_scope) [in Corelib.ssr.ssrfun]
+[ fun _ : _ => _ ] (function_scope) [in Corelib.ssr.ssrfun]
+[ fun _ _ => _ ] (function_scope) [in Corelib.ssr.ssrfun]
+[ fun _ => _ ] (function_scope) [in Corelib.ssr.ssrfun]
+[ fun : _ => _ ] (function_scope) [in Corelib.ssr.ssrfun]
+@^~ _ (function_scope) [in Corelib.ssr.ssrfun]
+_ ^~ _ (function_scope) [in Corelib.ssr.ssrfun]
+if _ as _ return _ then _ else _ (general_if_scope) [in Corelib.ssr.ssreflect]
+if _ return _ then _ else _ (general_if_scope) [in Corelib.ssr.ssreflect]
+if _ then _ else _ (general_if_scope) [in Corelib.ssr.ssreflect]
+_ ++ _ (list_scope) [in Corelib.Init.Datatypes]
+_ :: _ (list_scope) [in Corelib.Init.Datatypes]
+_ mod _ (nat_scope) [in Corelib.Init.Nat]
+_ / _ (nat_scope) [in Corelib.Init.Nat]
+_ ^ _ (nat_scope) [in Corelib.Init.Nat]
+_ ?= _ (nat_scope) [in Corelib.Init.Nat]
+_ <? _ (nat_scope) [in Corelib.Init.Nat]
+_ <=? _ (nat_scope) [in Corelib.Init.Nat]
+_ =? _ (nat_scope) [in Corelib.Init.Nat]
+_ - _ (nat_scope) [in Corelib.Init.Nat]
+_ * _ (nat_scope) [in Corelib.Init.Nat]
+_ + _ (nat_scope) [in Corelib.Init.Nat]
+_ < _ <= _ (nat_scope) [in Corelib.Init.Peano]
+_ < _ < _ (nat_scope) [in Corelib.Init.Peano]
+_ <= _ < _ (nat_scope) [in Corelib.Init.Peano]
+_ <= _ <= _ (nat_scope) [in Corelib.Init.Peano]
+_ > _ (nat_scope) [in Corelib.Init.Peano]
+_ >= _ (nat_scope) [in Corelib.Init.Peano]
+_ < _ (nat_scope) [in Corelib.Init.Peano]
+_ <= _ (nat_scope) [in Corelib.Init.Peano]
+_ - _ (nat_scope) [in Corelib.Init.Peano]
+_ * _ (nat_scope) [in Corelib.Init.Peano]
+_ + _ (nat_scope) [in Corelib.Init.Peano]
+_ .2 (pair_scope) [in Corelib.ssr.ssrfun]
+_ .1 (pair_scope) [in Corelib.ssr.ssrfun]
+3 (positive_scope) [in Corelib.BinNums.PosDef]
+2 (positive_scope) [in Corelib.BinNums.PosDef]
+1 (positive_scope) [in Corelib.BinNums.PosDef]
+_ ~ 0 (positive_scope) [in Corelib.BinNums.PosDef]
+_ ~ 1 (positive_scope) [in Corelib.BinNums.PosDef]
+∙⊥∙ (predicate_scope) [in Corelib.Classes.RelationClasses]
+∙⊤∙ (predicate_scope) [in Corelib.Classes.RelationClasses]
+_ \∙/ _ (predicate_scope) [in Corelib.Classes.RelationClasses]
+_ /∙\ _ (predicate_scope) [in Corelib.Classes.RelationClasses]
+_ -∙> _ (predicate_scope) [in Corelib.Classes.RelationClasses]
+_ <∙> _ (predicate_scope) [in Corelib.Classes.RelationClasses]
+_ ∘ _ (program_scope) [in Corelib.Program.Basics]
+` _ (program_scope) [in Corelib.Program.Utils]
+! (program_scope) [in Corelib.Program.Utils]
+_ (* _ *) (ssr_scope) [in Corelib.ssr.ssreflect]
+<hidden _ > (ssr_scope) [in Corelib.ssr.ssreflect]
+_ * _ (type_scope) [in Corelib.Init.Datatypes]
+_ + _ (type_scope) [in Corelib.Init.Datatypes]
+{ on _ , bijective _ } (type_scope) [in Corelib.ssr.ssrbool]
+{ in _ , bijective _ } (type_scope) [in Corelib.ssr.ssrbool]
+{ on _ , _ & _ } (type_scope) [in Corelib.ssr.ssrbool]
+{ on _ & , _ } (type_scope) [in Corelib.ssr.ssrbool]
+{ on _ , _ } (type_scope) [in Corelib.ssr.ssrbool]
+{ in _ & & , _ } (type_scope) [in Corelib.ssr.ssrbool]
+{ in _ & _ & , _ } (type_scope) [in Corelib.ssr.ssrbool]
+{ in _ & & _ , _ } (type_scope) [in Corelib.ssr.ssrbool]
+{ in _ & _ & _ , _ } (type_scope) [in Corelib.ssr.ssrbool]
+{ in _ & , _ } (type_scope) [in Corelib.ssr.ssrbool]
+{ in _ & _ , _ } (type_scope) [in Corelib.ssr.ssrbool]
+{ in _ , _ } (type_scope) [in Corelib.ssr.ssrbool]
+{ for _ , _ } (type_scope) [in Corelib.ssr.ssrbool]
+{ subset _ <= _ } (type_scope) [in Corelib.ssr.ssrbool]
+_ =i _ (type_scope) [in Corelib.ssr.ssrbool]
+{ : _ } (type_scope) [in Corelib.ssr.ssrbool]
+{ pred _ } (type_scope) [in Corelib.ssr.ssrbool]
+[ \/ _ , _ , _ | _ ] (type_scope) [in Corelib.ssr.ssrbool]
+[ \/ _ , _ | _ ] (type_scope) [in Corelib.ssr.ssrbool]
+[ \/ _ | _ ] (type_scope) [in Corelib.ssr.ssrbool]
+[ /\ _ , _ , _ , _ & _ ] (type_scope) [in Corelib.ssr.ssrbool]
+[ /\ _ , _ , _ & _ ] (type_scope) [in Corelib.ssr.ssrbool]
+[ /\ _ , _ & _ ] (type_scope) [in Corelib.ssr.ssrbool]
+[ /\ _ & _ ] (type_scope) [in Corelib.ssr.ssrbool]
+\unless _ , _ (type_scope) [in Corelib.ssr.ssrbool]
+{ type of _ for _ } (type_scope) [in Corelib.ssr.ssreflect]
+_ + { _ } (type_scope) [in Corelib.Init.Specif]
+{ _ } + { _ } (type_scope) [in Corelib.Init.Specif]
+{ ' _ : _ & _ & _ } (type_scope) [in Corelib.Init.Specif]
+{ ' _ : _ & _ } (type_scope) [in Corelib.Init.Specif]
+{ ' _ & _ & _ } (type_scope) [in Corelib.Init.Specif]
+{ ' _ & _ } (type_scope) [in Corelib.Init.Specif]
+{ ' _ : _ | _ & _ } (type_scope) [in Corelib.Init.Specif]
+{ ' _ : _ | _ } (type_scope) [in Corelib.Init.Specif]
+{ ' _ | _ & _ } (type_scope) [in Corelib.Init.Specif]
+{ ' _ | _ } (type_scope) [in Corelib.Init.Specif]
+{ _ : _ & _ & _ } (type_scope) [in Corelib.Init.Specif]
+{ _ : _ & _ } (type_scope) [in Corelib.Init.Specif]
+{ _ & _ & _ } (type_scope) [in Corelib.Init.Specif]
+{ _ & _ } (type_scope) [in Corelib.Init.Specif]
+{ _ : _ | _ & _ } (type_scope) [in Corelib.Init.Specif]
+{ _ : _ | _ } (type_scope) [in Corelib.Init.Specif]
+{ _ | _ & _ } (type_scope) [in Corelib.Init.Specif]
+{ _ | _ } (type_scope) [in Corelib.Init.Specif]
+{ mono _ : _ _ /~ _ } (type_scope) [in Corelib.ssr.ssrfun]
+{ mono _ : _ _ / _ } (type_scope) [in Corelib.ssr.ssrfun]
+{ mono _ : _ _ / _ >-> _ } (type_scope) [in Corelib.ssr.ssrfun]
+{ mono _ : _ / _ } (type_scope) [in Corelib.ssr.ssrfun]
+{ mono _ : _ / _ >-> _ } (type_scope) [in Corelib.ssr.ssrfun]
+{ homo _ : _ _ /~ _ } (type_scope) [in Corelib.ssr.ssrfun]
+{ homo _ : _ _ / _ } (type_scope) [in Corelib.ssr.ssrfun]
+{ homo _ : _ _ / _ >-> _ } (type_scope) [in Corelib.ssr.ssrfun]
+{ homo _ : _ / _ } (type_scope) [in Corelib.ssr.ssrfun]
+{ homo _ : _ / _ >-> _ } (type_scope) [in Corelib.ssr.ssrfun]
+{ morph _ : _ _ / _ } (type_scope) [in Corelib.ssr.ssrfun]
+{ morph _ : _ _ / _ >-> _ } (type_scope) [in Corelib.ssr.ssrfun]
+{ morph _ : _ / _ } (type_scope) [in Corelib.ssr.ssrfun]
+{ morph _ : _ / _ >-> _ } (type_scope) [in Corelib.ssr.ssrfun]
+_ =2 _ :> _ (type_scope) [in Corelib.ssr.ssrfun]
+_ =2 _ (type_scope) [in Corelib.ssr.ssrfun]
+_ =1 _ :> _ (type_scope) [in Corelib.ssr.ssrfun]
+_ =1 _ (type_scope) [in Corelib.ssr.ssrfun]
+exists ! _ .. _ , _ (type_scope) [in Corelib.Init.Logic]
+_ <> _ (type_scope) [in Corelib.Init.Logic]
+_ <> _ :> _ (type_scope) [in Corelib.Init.Logic]
+_ = _ (type_scope) [in Corelib.Init.Logic]
+_ = _ :> _ (type_scope) [in Corelib.Init.Logic]
+exists2 ' _ : _ , _ & _ (type_scope) [in Corelib.Init.Logic]
+exists2 ' _ , _ & _ (type_scope) [in Corelib.Init.Logic]
+exists2 _ : _ , _ & _ (type_scope) [in Corelib.Init.Logic]
+exists2 _ , _ & _ (type_scope) [in Corelib.Init.Logic]
+exists _ .. _ , _ (type_scope) [in Corelib.Init.Logic]
+_ <-> _ (type_scope) [in Corelib.Init.Logic]
+_ \/ _ (type_scope) [in Corelib.Init.Logic]
+_ /\ _ (type_scope) [in Corelib.Init.Logic]
+~ _ (type_scope) [in Corelib.Init.Logic]
+_ -> _ (type_scope) [in Corelib.Init.Logic]
+{ ( _ , _ ) : _ | _ } (type_scope) [in Corelib.Program.Utils]
+_ <= _ < _ (Z_scope) [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+_ < _ (Z_scope) [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+_ <= _ (Z_scope) [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+_ ^ _ (Z_scope) [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+_ * _ (Z_scope) [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+_ - _ (Z_scope) [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+_ + _ (Z_scope) [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+2 (Z_scope) [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+1 (Z_scope) [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+0 (Z_scope) [in Corelib.Numbers.Cyclic.Int63.Uint63Axioms]
+_ < _ (Z_scope) [in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+_ <= _ (Z_scope) [in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+_ ^ _ (Z_scope) [in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+2 (Z_scope) [in Corelib.Numbers.Cyclic.Int63.Sint63Axioms]
+_ :: _ [in Corelib.Classes.RelationClasses]
+_ .3 [in Corelib.Init.Specif]
+0 [in Corelib.BinNums.IntDef]
+0 [in Corelib.Init.Byte]
+0 [in Corelib.Init.Nat]
+0 [in Corelib.Init.Peano]
+1 [in Corelib.BinNums.IntDef]
+1 [in Corelib.Init.Byte]
+1 [in Corelib.Init.Nat]
+2 [in Corelib.BinNums.IntDef]
+2 [in Corelib.Init.Nat]
+[ elaborate _ ] [in Corelib.ssr.ssreflect]
+{ all3 _ } [in Corelib.ssr.ssrbool]
+{ all2 _ } [in Corelib.ssr.ssrbool]
+{ all1 _ } [in Corelib.ssr.ssrbool]
+

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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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+ +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

E (notation)

+rew dependent <- [ _ ] _ in _ [in Corelib.Init.Logic]
+rew dependent -> [ _ ] _ in _ [in Corelib.Init.Logic]
+rew dependent [ _ ] _ in _ [in Corelib.Init.Logic]
+rew dependent <- [ fun _ _ => _ ] _ in _ [in Corelib.Init.Logic]
+rew dependent -> [ fun _ _ => _ ] _ in _ [in Corelib.Init.Logic]
+rew dependent [ fun _ _ => _ ] _ in _ [in Corelib.Init.Logic]
+rew dependent <- _ in _ [in Corelib.Init.Logic]
+rew dependent -> _ in _ [in Corelib.Init.Logic]
+rew dependent _ in _ [in Corelib.Init.Logic]
+rew -> [ _ ] _ in _ [in Corelib.Init.Logic]
+rew -> _ in _ [in Corelib.Init.Logic]
+rew <- [ _ ] _ in _ [in Corelib.Init.Logic]
+rew <- _ in _ [in Corelib.Init.Logic]
+rew [ _ ] _ in _ [in Corelib.Init.Logic]
+rew _ in _ [in Corelib.Init.Logic]
+

+ +
+ +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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I (notation)

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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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+ + + diff --git a/master/corelib/index_notation_P.html b/master/corelib/index_notation_P.html new file mode 100644 index 0000000000..a9c2f70ca9 --- /dev/null +++ b/master/corelib/index_notation_P.html @@ -0,0 +1,577 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

P (notation)

+_ .[ _ <- _ ] [in Corelib.Array.PrimArray]
+_ .[ _ ] [in Corelib.Array.PrimArray]
+_ / _ (float_scope) [in Corelib.Floats.PrimFloat]
+_ - _ (float_scope) [in Corelib.Floats.PrimFloat]
+_ + _ (float_scope) [in Corelib.Floats.PrimFloat]
+_ * _ (float_scope) [in Corelib.Floats.PrimFloat]
+_ ?= _ (float_scope) [in Corelib.Floats.PrimFloat]
+_ <=? _ (float_scope) [in Corelib.Floats.PrimFloat]
+_ <? _ (float_scope) [in Corelib.Floats.PrimFloat]
+_ =? _ (float_scope) [in Corelib.Floats.PrimFloat]
+- _ (float_scope) [in Corelib.Floats.PrimFloat]
+_ --> _ (signatureT_scope) [in Corelib.Classes.CMorphisms]
+_ ==> _ (signatureT_scope) [in Corelib.Classes.CMorphisms]
+_ ++> _ (signatureT_scope) [in Corelib.Classes.CMorphisms]
+_ --> _ (signature_scope) [in Corelib.Classes.Morphisms]
+_ ==> _ (signature_scope) [in Corelib.Classes.Morphisms]
+_ ++> _ (signature_scope) [in Corelib.Classes.Morphisms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_notation_Q.html b/master/corelib/index_notation_Q.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_notation_Q.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_notation_R.html b/master/corelib/index_notation_R.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_notation_R.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_notation_S.html b/master/corelib/index_notation_S.html new file mode 100644 index 0000000000..c863c539c4 --- /dev/null +++ b/master/corelib/index_notation_S.html @@ -0,0 +1,565 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

S (notation)

+_ .2 [in Corelib.Init.Specif]
+_ .1 [in Corelib.Init.Specif]
+( _ ; _ ) [in Corelib.Init.Specif]
+(= _ ; _ ) [in Corelib.Init.Specif]
+( _ in _ ) (ssrpatternscope) [in Corelib.ssrmatching.ssrmatching]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_notation_T.html b/master/corelib/index_notation_T.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_notation_T.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_notation_U.html b/master/corelib/index_notation_U.html new file mode 100644 index 0000000000..74452d4bee --- /dev/null +++ b/master/corelib/index_notation_U.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

U (notation)

+'Under[ _ ] [in Corelib.ssr.ssrunder]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_notation_V.html b/master/corelib/index_notation_V.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_notation_V.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_notation_W.html b/master/corelib/index_notation_W.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_notation_W.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

Z (notation)

+_ ÷ _ (Z_scope) [in Corelib.BinNums.IntDef]
+_ > _ (Z_scope) [in Corelib.BinNums.IntDef]
+_ >= _ (Z_scope) [in Corelib.BinNums.IntDef]
+_ < _ (Z_scope) [in Corelib.BinNums.IntDef]
+_ <= _ (Z_scope) [in Corelib.BinNums.IntDef]
+_ ?= _ (Z_scope) [in Corelib.BinNums.IntDef]
+_ ^ _ (Z_scope) [in Corelib.BinNums.IntDef]
+_ * _ (Z_scope) [in Corelib.BinNums.IntDef]
+_ - _ (Z_scope) [in Corelib.BinNums.IntDef]
+- _ (Z_scope) [in Corelib.BinNums.IntDef]
+_ + _ (Z_scope) [in Corelib.BinNums.IntDef]
+

+ +
+ +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

A (projection)

+antisymmetry [in Corelib.Classes.RelationClasses]
+antisymmetry [in Corelib.Classes.CRelationClasses]
+applicative_mem_pred_value [in Corelib.ssr.ssrbool]
+applicative_pred_value [in Corelib.ssr.ssrbool]
+asymmetry [in Corelib.Classes.RelationClasses]
+asymmetry [in Corelib.Classes.CRelationClasses]
+

+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

C (projection)

+char63_wrap [in Corelib.Strings.PrimString]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_projection_D.html b/master/corelib/index_projection_D.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_projection_D.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_projection_E.html b/master/corelib/index_projection_E.html new file mode 100644 index 0000000000..a6aa908efd --- /dev/null +++ b/master/corelib/index_projection_E.html @@ -0,0 +1,569 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

E (projection)

+Equivalence_Transitive [in Corelib.Classes.RelationClasses]
+Equivalence_Symmetric [in Corelib.Classes.RelationClasses]
+Equivalence_Reflexive [in Corelib.Classes.RelationClasses]
+Equivalence_Transitive [in Corelib.Classes.CRelationClasses]
+Equivalence_Symmetric [in Corelib.Classes.CRelationClasses]
+Equivalence_Reflexive [in Corelib.Classes.CRelationClasses]
+equiv_sym [in Corelib.Relations.Relation_Definitions]
+equiv_trans [in Corelib.Relations.Relation_Definitions]
+equiv_refl [in Corelib.Relations.Relation_Definitions]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_projection_F.html b/master/corelib/index_projection_F.html new file mode 100644 index 0000000000..d91c7eee34 --- /dev/null +++ b/master/corelib/index_projection_F.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

F (projection)

+float_wrap [in Corelib.Floats.PrimFloat]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_projection_G.html b/master/corelib/index_projection_G.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_projection_G.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_projection_H.html b/master/corelib/index_projection_H.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_projection_H.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_projection_I.html b/master/corelib/index_projection_I.html new file mode 100644 index 0000000000..e10517303f --- /dev/null +++ b/master/corelib/index_projection_I.html @@ -0,0 +1,565 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

I (projection)

+int_wrap [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+irreflexivity [in Corelib.Classes.RelationClasses]
+irreflexivity [in Corelib.Classes.CRelationClasses]
+is_subrelation [in Corelib.Classes.RelationClasses]
+is_subrelation [in Corelib.Classes.CRelationClasses]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_projection_J.html b/master/corelib/index_projection_J.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_projection_J.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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+ +
+ +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

M (projection)

+mem_pred_value [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_projection_N.html b/master/corelib/index_projection_N.html new file mode 100644 index 0000000000..5ee072fbb2 --- /dev/null +++ b/master/corelib/index_projection_N.html @@ -0,0 +1,567 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

N (projection)

+NonPropType.callee [in Corelib.ssr.ssreflect]
+NonPropType.condition [in Corelib.ssr.ssreflect]
+NonPropType.frame [in Corelib.ssr.ssreflect]
+NonPropType.result [in Corelib.ssr.ssreflect]
+NonPropType.test [in Corelib.ssr.ssreflect]
+normalizes [in Corelib.Classes.CMorphisms]
+normalizes [in Corelib.Classes.Morphisms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_projection_O.html b/master/corelib/index_projection_O.html new file mode 100644 index 0000000000..8f98f0ab0a --- /dev/null +++ b/master/corelib/index_projection_O.html @@ -0,0 +1,563 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

O (projection)

+ord_antisym [in Corelib.Relations.Relation_Definitions]
+ord_trans [in Corelib.Relations.Relation_Definitions]
+ord_refl [in Corelib.Relations.Relation_Definitions]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_projection_P.html b/master/corelib/index_projection_P.html new file mode 100644 index 0000000000..65e9e68711 --- /dev/null +++ b/master/corelib/index_projection_P.html @@ -0,0 +1,580 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

P (projection)

+partial_order_equivalence [in Corelib.Classes.RelationClasses]
+partial_order_equivalence [in Corelib.Classes.CRelationClasses]
+PER_Transitive [in Corelib.Classes.RelationClasses]
+PER_Symmetric [in Corelib.Classes.RelationClasses]
+PER_Transitive [in Corelib.Classes.CRelationClasses]
+PER_Symmetric [in Corelib.Classes.CRelationClasses]
+per_trans [in Corelib.Relations.Relation_Definitions]
+per_sym [in Corelib.Relations.Relation_Definitions]
+pred_sort [in Corelib.ssr.ssrbool]
+PreOrder_Transitive [in Corelib.Classes.RelationClasses]
+PreOrder_Reflexive [in Corelib.Classes.RelationClasses]
+PreOrder_Transitive [in Corelib.Classes.CRelationClasses]
+PreOrder_Reflexive [in Corelib.Classes.CRelationClasses]
+preord_trans [in Corelib.Relations.Relation_Definitions]
+preord_refl [in Corelib.Relations.Relation_Definitions]
+proper_proxy [in Corelib.Classes.CMorphisms]
+proper_prf [in Corelib.Classes.CMorphisms]
+proper_proxy [in Corelib.Classes.Morphisms]
+proper_prf [in Corelib.Classes.Morphisms]
+PStringNotations.string_wrap [in Corelib.Strings.PrimString]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_projection_Q.html b/master/corelib/index_projection_Q.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_projection_Q.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_projection_R.html b/master/corelib/index_projection_R.html new file mode 100644 index 0000000000..af82c68f1f --- /dev/null +++ b/master/corelib/index_projection_R.html @@ -0,0 +1,564 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

R (projection)

+reflexive_proxy [in Corelib.Classes.Morphisms]
+reflexivity [in Corelib.Classes.RelationClasses]
+reflexivity [in Corelib.ssr.ssrclasses]
+reflexivity [in Corelib.Classes.CRelationClasses]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_projection_S.html b/master/corelib/index_projection_S.html new file mode 100644 index 0000000000..2a9d9df558 --- /dev/null +++ b/master/corelib/index_projection_S.html @@ -0,0 +1,570 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

S (projection)

+shr_s [in Corelib.Floats.SpecFloat]
+shr_r [in Corelib.Floats.SpecFloat]
+shr_m [in Corelib.Floats.SpecFloat]
+simpl_pred_value [in Corelib.ssr.ssrbool]
+StrictOrder_Transitive [in Corelib.Classes.RelationClasses]
+StrictOrder_Irreflexive [in Corelib.Classes.RelationClasses]
+StrictOrder_Transitive [in Corelib.Classes.CRelationClasses]
+StrictOrder_Irreflexive [in Corelib.Classes.CRelationClasses]
+symmetry [in Corelib.Classes.RelationClasses]
+symmetry [in Corelib.Classes.CRelationClasses]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_projection_T.html b/master/corelib/index_projection_T.html new file mode 100644 index 0000000000..43eb235141 --- /dev/null +++ b/master/corelib/index_projection_T.html @@ -0,0 +1,563 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

T (projection)

+topred [in Corelib.ssr.ssrbool]
+transitivity [in Corelib.Classes.RelationClasses]
+transitivity [in Corelib.Classes.CRelationClasses]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_projection_U.html b/master/corelib/index_projection_U.html new file mode 100644 index 0000000000..c47db57cf9 --- /dev/null +++ b/master/corelib/index_projection_U.html @@ -0,0 +1,565 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

U (projection)

+unconvertible [in Corelib.Classes.Init]
+unkey_qualifier [in Corelib.ssr.ssrbool]
+unkey_pred [in Corelib.ssr.ssrbool]
+unlocked [in Corelib.ssr.ssreflect]
+unwrap [in Corelib.ssr.ssrfun]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_projection_V.html b/master/corelib/index_projection_V.html new file mode 100644 index 0000000000..b0c1614774 --- /dev/null +++ b/master/corelib/index_projection_V.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

V (projection)

+vm_compute [in Corelib.ssr.ssreflect]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_projection_W.html b/master/corelib/index_projection_W.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_projection_W.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_projection_X.html b/master/corelib/index_projection_X.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_projection_X.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_projection_Y.html b/master/corelib/index_projection_Y.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_projection_Y.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
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Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
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Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

A (record)

+Antisymmetric [in Corelib.Classes.RelationClasses]
+Antisymmetric [in Corelib.Classes.CRelationClasses]
+applicative_mem_pred [in Corelib.ssr.ssrbool]
+Asymmetric [in Corelib.Classes.RelationClasses]
+Asymmetric [in Corelib.Classes.CRelationClasses]
+

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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

C (record)

+char63_wrapper [in Corelib.Strings.PrimString]
+

+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

D (record)

+DefaultRelation [in Corelib.Classes.SetoidTactics]
+

+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

E (record)

+Equivalence [in Corelib.Classes.RelationClasses]
+Equivalence [in Corelib.Classes.CRelationClasses]
+equivalence [in Corelib.Relations.Relation_Definitions]
+

+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

F (record)

+float_wrapper [in Corelib.Floats.PrimFloat]
+

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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
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+ +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
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+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

I (record)

+int_wrapper [in Corelib.Numbers.Cyclic.Int63.PrimInt63]
+Irreflexive [in Corelib.Classes.RelationClasses]
+Irreflexive [in Corelib.Classes.CRelationClasses]
+

+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_record_K.html b/master/corelib/index_record_K.html new file mode 100644 index 0000000000..e75f466775 --- /dev/null +++ b/master/corelib/index_record_K.html @@ -0,0 +1,562 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

K (record)

+keyed_qualifier [in Corelib.ssr.ssrbool]
+keyed_pred [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_record_L.html b/master/corelib/index_record_L.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_record_L.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_record_M.html b/master/corelib/index_record_M.html new file mode 100644 index 0000000000..0db1c2e4e8 --- /dev/null +++ b/master/corelib/index_record_M.html @@ -0,0 +1,562 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

M (record)

+manifest_mem_pred [in Corelib.ssr.ssrbool]
+manifest_simpl_pred [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

N (record)

+NonPropType.call_of [in Corelib.ssr.ssreflect]
+NonPropType.test_of [in Corelib.ssr.ssreflect]
+NonPropType.type [in Corelib.ssr.ssreflect]
+Normalizes [in Corelib.Classes.CMorphisms]
+Normalizes [in Corelib.Classes.Morphisms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_record_O.html b/master/corelib/index_record_O.html new file mode 100644 index 0000000000..cc45fd9b42 --- /dev/null +++ b/master/corelib/index_record_O.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

O (record)

+order [in Corelib.Relations.Relation_Definitions]
+

+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

P (record)

+Params [in Corelib.Classes.CMorphisms]
+Params [in Corelib.Classes.Morphisms]
+PartialApplication [in Corelib.Classes.CMorphisms]
+PartialApplication [in Corelib.Classes.Morphisms]
+PartialOrder [in Corelib.Classes.RelationClasses]
+PartialOrder [in Corelib.Classes.CRelationClasses]
+PER [in Corelib.Classes.RelationClasses]
+PER [in Corelib.Classes.CRelationClasses]
+PER [in Corelib.Relations.Relation_Definitions]
+predType [in Corelib.ssr.ssrbool]
+PreOrder [in Corelib.Classes.RelationClasses]
+PreOrder [in Corelib.Classes.CRelationClasses]
+preorder [in Corelib.Relations.Relation_Definitions]
+Proper [in Corelib.Classes.CMorphisms]
+Proper [in Corelib.Classes.Morphisms]
+ProperProxy [in Corelib.Classes.CMorphisms]
+ProperProxy [in Corelib.Classes.Morphisms]
+PStringNotations.string_wrapper [in Corelib.Strings.PrimString]
+

+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_record_R.html b/master/corelib/index_record_R.html new file mode 100644 index 0000000000..fade41dbf4 --- /dev/null +++ b/master/corelib/index_record_R.html @@ -0,0 +1,567 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

R (record)

+Reflexive [in Corelib.Classes.RelationClasses]
+Reflexive [in Corelib.ssr.ssrclasses]
+Reflexive [in Corelib.Classes.CRelationClasses]
+ReflexiveProxy [in Corelib.Classes.Morphisms]
+registered_applicative_pred [in Corelib.ssr.ssrbool]
+RewriteRelation [in Corelib.Classes.RelationClasses]
+RewriteRelation [in Corelib.Classes.CRelationClasses]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_record_S.html b/master/corelib/index_record_S.html new file mode 100644 index 0000000000..aff014ce47 --- /dev/null +++ b/master/corelib/index_record_S.html @@ -0,0 +1,567 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

S (record)

+shr_record [in Corelib.Floats.SpecFloat]
+StrictOrder [in Corelib.Classes.RelationClasses]
+StrictOrder [in Corelib.Classes.CRelationClasses]
+subrelation [in Corelib.Classes.RelationClasses]
+subrelation [in Corelib.Classes.CRelationClasses]
+Symmetric [in Corelib.Classes.RelationClasses]
+Symmetric [in Corelib.Classes.CRelationClasses]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_record_T.html b/master/corelib/index_record_T.html new file mode 100644 index 0000000000..66ecfbea52 --- /dev/null +++ b/master/corelib/index_record_T.html @@ -0,0 +1,562 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

T (record)

+Transitive [in Corelib.Classes.RelationClasses]
+Transitive [in Corelib.Classes.CRelationClasses]
+

+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
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Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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+ + + diff --git a/master/corelib/index_section_A.html b/master/corelib/index_section_A.html new file mode 100644 index 0000000000..f9ad0f4957 --- /dev/null +++ b/master/corelib/index_section_A.html @@ -0,0 +1,563 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

A (section)

+Acc_generator [in Corelib.Init.Wf]
+AllAnd [in Corelib.ssr.ssrbool]
+ApplyIff [in Corelib.ssr.ssreflect]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_section_B.html b/master/corelib/index_section_B.html new file mode 100644 index 0000000000..ef4c2331e8 --- /dev/null +++ b/master/corelib/index_section_B.html @@ -0,0 +1,565 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

B (section)

+Bijections [in Corelib.ssr.ssrfun]
+BijectionsTheory [in Corelib.ssr.ssrfun]
+Binary [in Corelib.Classes.RelationClasses]
+Binary [in Corelib.Classes.CRelationClasses]
+BoolIf [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_section_C.html b/master/corelib/index_section_C.html new file mode 100644 index 0000000000..b408f63607 --- /dev/null +++ b/master/corelib/index_section_C.html @@ -0,0 +1,567 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

C (section)

+CancelOn [in Corelib.ssr.ssrbool]
+Choice_lemmas [in Corelib.Init.Specif]
+Compare [in Corelib.Lists.ListDef]
+Composition [in Corelib.ssr.ssrfun]
+Conjunction [in Corelib.Init.Logic]
+connectives [in Corelib.Init.Sumbool]
+Cutting [in Corelib.Lists.ListDef]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_section_D.html b/master/corelib/index_section_D.html new file mode 100644 index 0000000000..02bff4f94d --- /dev/null +++ b/master/corelib/index_section_D.html @@ -0,0 +1,571 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

D (section)

+Defs [in Corelib.Classes.RelationClasses]
+Defs [in Corelib.ssr.ssrclasses]
+Defs [in Corelib.Classes.CRelationClasses]
+Defs.complement [in Corelib.Classes.RelationClasses]
+Defs.complement [in Corelib.Classes.CRelationClasses]
+Defs.flip [in Corelib.Classes.RelationClasses]
+Defs.flip [in Corelib.Classes.CRelationClasses]
+Defs.Leibniz [in Corelib.Classes.RelationClasses]
+Defs.Leibniz [in Corelib.Classes.CRelationClasses]
+Defs.LeibnizNot [in Corelib.Classes.RelationClasses]
+Dependent_choice_lemmas [in Corelib.Init.Specif]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_section_E.html b/master/corelib/index_section_E.html new file mode 100644 index 0000000000..4a250f24ef --- /dev/null +++ b/master/corelib/index_section_E.html @@ -0,0 +1,572 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

E (section)

+Elts [in Corelib.Lists.ListDef]
+equality_dep [in Corelib.Init.Logic]
+Equivalence [in Corelib.Init.Logic]
+ex [in Corelib.Init.Logic]
+Exc [in Corelib.Init.Specif]
+Exists_Forall.One_predicate [in Corelib.Lists.ListDef]
+Exists_Forall [in Corelib.Lists.ListDef]
+ExtensionalEquality [in Corelib.ssr.ssrfun]
+ex_Prop [in Corelib.Init.Logic]
+ex2 [in Corelib.Init.Logic]
+ex2_Prop [in Corelib.Init.Logic]
+ex2_Projections [in Corelib.Init.Logic]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_section_F.html b/master/corelib/index_section_F.html new file mode 100644 index 0000000000..ce879aa89b --- /dev/null +++ b/master/corelib/index_section_F.html @@ -0,0 +1,566 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

F (section)

+Fix_rects [in Corelib.Program.Wf]
+FloatOps [in Corelib.Floats.SpecFloat]
+FloatOps.Iter [in Corelib.Floats.SpecFloat]
+FloatOps.Rounding [in Corelib.Floats.SpecFloat]
+FloatOps.ValidBinary [in Corelib.Floats.SpecFloat]
+FloatOps.Zdigits2 [in Corelib.Floats.SpecFloat]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_section_G.html b/master/corelib/index_section_G.html new file mode 100644 index 0000000000..09ad40037d --- /dev/null +++ b/master/corelib/index_section_G.html @@ -0,0 +1,562 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

G (section)

+GenericInstances [in Corelib.Classes.CMorphisms]
+GenericInstances [in Corelib.Classes.Morphisms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_section_H.html b/master/corelib/index_section_H.html new file mode 100644 index 0000000000..dabec42d7d --- /dev/null +++ b/master/corelib/index_section_H.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

H (section)

+HomoMonoMorphismFlip [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_section_I.html b/master/corelib/index_section_I.html new file mode 100644 index 0000000000..ec50442fdb --- /dev/null +++ b/master/corelib/index_section_I.html @@ -0,0 +1,565 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

I (section)

+Injections [in Corelib.ssr.ssrfun]
+InjectionsTheory [in Corelib.ssr.ssrfun]
+inj_can_sym_in_on [in Corelib.ssr.ssrbool]
+Involutions [in Corelib.ssr.ssrfun]
+in_sig [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_section_J.html b/master/corelib/index_section_J.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_section_J.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_section_K.html b/master/corelib/index_section_K.html new file mode 100644 index 0000000000..02ca373fc2 --- /dev/null +++ b/master/corelib/index_section_K.html @@ -0,0 +1,562 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

K (section)

+KeyedQualifier [in Corelib.ssr.ssrbool]
+KeyPred [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_section_L.html b/master/corelib/index_section_L.html new file mode 100644 index 0000000000..17306ba509 --- /dev/null +++ b/master/corelib/index_section_L.html @@ -0,0 +1,564 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

L (section)

+LocalGlobal [in Corelib.ssr.ssrbool]
+LocalProperties [in Corelib.ssr.ssrbool]
+Logic_lemmas.equality [in Corelib.Init.Logic]
+Logic_lemmas [in Corelib.Init.Logic]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_section_M.html b/master/corelib/index_section_M.html new file mode 100644 index 0000000000..ab53982a09 --- /dev/null +++ b/master/corelib/index_section_M.html @@ -0,0 +1,565 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

M (section)

+Map [in Corelib.Lists.ListDef]
+Measure_well_founded [in Corelib.Program.Wf]
+MonoHomoMorphismTheory [in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in [in Corelib.ssr.ssrbool]
+Morphism [in Corelib.ssr.ssrfun]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_section_N.html b/master/corelib/index_section_N.html new file mode 100644 index 0000000000..706e0a6dd4 --- /dev/null +++ b/master/corelib/index_section_N.html @@ -0,0 +1,563 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

N (section)

+NatSeq [in Corelib.Lists.ListDef]
+Normalize [in Corelib.Classes.CMorphisms]
+Normalize [in Corelib.Classes.Morphisms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_section_O.html b/master/corelib/index_section_O.html new file mode 100644 index 0000000000..4314a2482a --- /dev/null +++ b/master/corelib/index_section_O.html @@ -0,0 +1,567 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

O (section)

+OperationProperties [in Corelib.ssr.ssrfun]
+OperationProperties.SopSisS [in Corelib.ssr.ssrfun]
+OperationProperties.SopSisT [in Corelib.ssr.ssrfun]
+OperationProperties.SopTisR [in Corelib.ssr.ssrfun]
+OperationProperties.SopTisS [in Corelib.ssr.ssrfun]
+OperationProperties.SopTisT [in Corelib.ssr.ssrfun]
+OptionTheory [in Corelib.ssr.ssrfun]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_section_P.html b/master/corelib/index_section_P.html new file mode 100644 index 0000000000..46f3c96a45 --- /dev/null +++ b/master/corelib/index_section_P.html @@ -0,0 +1,568 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

P (section)

+PredicateSimplification [in Corelib.ssr.ssrbool]
+ProdSigT [in Corelib.Init.Specif]
+projections [in Corelib.Init.Datatypes]
+Projections [in Corelib.Init.Specif]
+Projections [in Corelib.Init.Logic]
+Projections2 [in Corelib.Init.Specif]
+Proper [in Corelib.Classes.CMorphisms]
+Proper [in Corelib.Classes.Morphisms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_section_Q.html b/master/corelib/index_section_Q.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_section_Q.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_section_R.html b/master/corelib/index_section_R.html new file mode 100644 index 0000000000..8f47d1adc8 --- /dev/null +++ b/master/corelib/index_section_R.html @@ -0,0 +1,575 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

R (section)

+Reflect [in Corelib.ssr.ssrbool]
+ReflectCombinators [in Corelib.ssr.ssrbool]
+ReflectConnectives [in Corelib.ssr.ssrbool]
+ReflectCore [in Corelib.ssr.ssrbool]
+ReflectNegCore [in Corelib.ssr.ssrbool]
+RelationProperties [in Corelib.ssr.ssrbool]
+RelationProperties.PER [in Corelib.ssr.ssrbool]
+Relations [in Corelib.Classes.CMorphisms]
+Relations [in Corelib.Classes.Morphisms]
+Relation_Definition.Relations_of_Relations [in Corelib.Relations.Relation_Definitions]
+Relation_Definition.Sets_of_Relations [in Corelib.Relations.Relation_Definitions]
+Relation_Definition.General_Properties_of_Relations [in Corelib.Relations.Relation_Definitions]
+Relation_Definition [in Corelib.Relations.Relation_Definitions]
+Repeat [in Corelib.Lists.ListDef]
+Respecting [in Corelib.Classes.Equivalence]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_section_S.html b/master/corelib/index_section_S.html new file mode 100644 index 0000000000..488a282124 --- /dev/null +++ b/master/corelib/index_section_S.html @@ -0,0 +1,568 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

S (section)

+sig [in Corelib.Init.Specif]
+Sig [in Corelib.ssr.ssrfun]
+sigT [in Corelib.Init.Specif]
+sigT2 [in Corelib.Init.Specif]
+sig2 [in Corelib.Init.Specif]
+SimplFun [in Corelib.ssr.ssrfun]
+Subset_projections2 [in Corelib.Init.Specif]
+Subset_projections [in Corelib.Init.Specif]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_section_T.html b/master/corelib/index_section_T.html new file mode 100644 index 0000000000..5934d30617 --- /dev/null +++ b/master/corelib/index_section_T.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

T (section)

+Tag [in Corelib.ssr.ssrfun]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_section_U.html b/master/corelib/index_section_U.html new file mode 100644 index 0000000000..c742990f05 --- /dev/null +++ b/master/corelib/index_section_U.html @@ -0,0 +1,561 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

U (section)

+universal_quantification [in Corelib.Init.Logic]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_section_V.html b/master/corelib/index_section_V.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_section_V.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_section_W.html b/master/corelib/index_section_W.html new file mode 100644 index 0000000000..f324931015 --- /dev/null +++ b/master/corelib/index_section_W.html @@ -0,0 +1,565 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

W (section)

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+Well_founded_2 [in Corelib.Init.Wf]
+Well_founded.FixPoint [in Corelib.Init.Wf]
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Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
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Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

A (variable)

+Acc_generator.R [in Corelib.Init.Wf]
+Acc_generator.A [in Corelib.Init.Wf]
+AllAnd.P1 [in Corelib.ssr.ssrbool]
+AllAnd.P2 [in Corelib.ssr.ssrbool]
+AllAnd.P3 [in Corelib.ssr.ssrbool]
+AllAnd.P4 [in Corelib.ssr.ssrbool]
+AllAnd.P5 [in Corelib.ssr.ssrbool]
+AllAnd.T [in Corelib.ssr.ssrbool]
+ApplyIff.eqPQ [in Corelib.ssr.ssreflect]
+ApplyIff.P [in Corelib.ssr.ssreflect]
+ApplyIff.Q [in Corelib.ssr.ssreflect]
+

+ +
+ +
+ + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

B (variable)

+BijectionsTheory.A [in Corelib.ssr.ssrfun]
+BijectionsTheory.B [in Corelib.ssr.ssrfun]
+BijectionsTheory.C [in Corelib.ssr.ssrfun]
+BijectionsTheory.f [in Corelib.ssr.ssrfun]
+BijectionsTheory.h [in Corelib.ssr.ssrfun]
+Bijections.A [in Corelib.ssr.ssrfun]
+Bijections.B [in Corelib.ssr.ssrfun]
+Bijections.bijf [in Corelib.ssr.ssrfun]
+Bijections.f [in Corelib.ssr.ssrfun]
+Binary.A [in Corelib.Classes.RelationClasses]
+Binary.A [in Corelib.Classes.CRelationClasses]
+BoolIf.A [in Corelib.ssr.ssrbool]
+BoolIf.b [in Corelib.ssr.ssrbool]
+BoolIf.B [in Corelib.ssr.ssrbool]
+BoolIf.f [in Corelib.ssr.ssrbool]
+BoolIf.vF [in Corelib.ssr.ssrbool]
+BoolIf.vT [in Corelib.ssr.ssrbool]
+BoolIf.x [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_C.html b/master/corelib/index_variable_C.html new file mode 100644 index 0000000000..ca069789ef --- /dev/null +++ b/master/corelib/index_variable_C.html @@ -0,0 +1,586 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

C (variable)

+CancelOn.aD [in Corelib.ssr.ssrbool]
+CancelOn.aT [in Corelib.ssr.ssrbool]
+CancelOn.f [in Corelib.ssr.ssrbool]
+CancelOn.g [in Corelib.ssr.ssrbool]
+CancelOn.rD [in Corelib.ssr.ssrbool]
+CancelOn.rT [in Corelib.ssr.ssrbool]
+Choice_lemmas.R2 [in Corelib.Init.Specif]
+Choice_lemmas.R1 [in Corelib.Init.Specif]
+Choice_lemmas.R' [in Corelib.Init.Specif]
+Choice_lemmas.R [in Corelib.Init.Specif]
+Choice_lemmas.S' [in Corelib.Init.Specif]
+Choice_lemmas.S [in Corelib.Init.Specif]
+Compare.A [in Corelib.Lists.ListDef]
+Compare.cmp [in Corelib.Lists.ListDef]
+Composition.A [in Corelib.ssr.ssrfun]
+Composition.B [in Corelib.ssr.ssrfun]
+Composition.C [in Corelib.ssr.ssrfun]
+Conjunction.A [in Corelib.Init.Logic]
+Conjunction.B [in Corelib.Init.Logic]
+connectives.A [in Corelib.Init.Sumbool]
+connectives.B [in Corelib.Init.Sumbool]
+connectives.C [in Corelib.Init.Sumbool]
+connectives.D [in Corelib.Init.Sumbool]
+connectives.H1 [in Corelib.Init.Sumbool]
+connectives.H2 [in Corelib.Init.Sumbool]
+Cutting.A [in Corelib.Lists.ListDef]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_D.html b/master/corelib/index_variable_D.html new file mode 100644 index 0000000000..2aa7a8ac3a --- /dev/null +++ b/master/corelib/index_variable_D.html @@ -0,0 +1,565 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

D (variable)

+Defs.A [in Corelib.Classes.RelationClasses]
+Defs.A [in Corelib.ssr.ssrclasses]
+Defs.A [in Corelib.Classes.CRelationClasses]
+Dependent_choice_lemmas.R [in Corelib.Init.Specif]
+Dependent_choice_lemmas.X [in Corelib.Init.Specif]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_E.html b/master/corelib/index_variable_E.html new file mode 100644 index 0000000000..5a17b2fb80 --- /dev/null +++ b/master/corelib/index_variable_E.html @@ -0,0 +1,580 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

E (variable)

+Elts.A [in Corelib.Lists.ListDef]
+equality_dep.y [in Corelib.Init.Logic]
+equality_dep.x [in Corelib.Init.Logic]
+equality_dep.f [in Corelib.Init.Logic]
+equality_dep.B [in Corelib.Init.Logic]
+equality_dep.A [in Corelib.Init.Logic]
+Exc.A [in Corelib.Init.Specif]
+Exists_Forall.One_predicate.P [in Corelib.Lists.ListDef]
+Exists_Forall.A [in Corelib.Lists.ListDef]
+ExtensionalEquality.A [in Corelib.ssr.ssrfun]
+ExtensionalEquality.B [in Corelib.ssr.ssrfun]
+ExtensionalEquality.C [in Corelib.ssr.ssrfun]
+ex_Prop.P [in Corelib.Init.Logic]
+ex_Prop.A [in Corelib.Init.Logic]
+ex2_Prop.Q [in Corelib.Init.Logic]
+ex2_Prop.P [in Corelib.Init.Logic]
+ex2_Prop.A [in Corelib.Init.Logic]
+ex2_Projections.Q [in Corelib.Init.Logic]
+ex2_Projections.P [in Corelib.Init.Logic]
+ex2_Projections.A [in Corelib.Init.Logic]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_F.html b/master/corelib/index_variable_F.html new file mode 100644 index 0000000000..0039e2decf --- /dev/null +++ b/master/corelib/index_variable_F.html @@ -0,0 +1,570 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

F (variable)

+Fix_rects.equiv_lowers [in Corelib.Program.Wf]
+Fix_rects.f [in Corelib.Program.Wf]
+Fix_rects.Rwf [in Corelib.Program.Wf]
+Fix_rects.R [in Corelib.Program.Wf]
+Fix_rects.P [in Corelib.Program.Wf]
+Fix_rects.A [in Corelib.Program.Wf]
+FloatOps.emax [in Corelib.Floats.SpecFloat]
+FloatOps.Iter.A [in Corelib.Floats.SpecFloat]
+FloatOps.Iter.f [in Corelib.Floats.SpecFloat]
+FloatOps.prec [in Corelib.Floats.SpecFloat]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_G.html b/master/corelib/index_variable_G.html new file mode 100644 index 0000000000..ec32567d5b --- /dev/null +++ b/master/corelib/index_variable_G.html @@ -0,0 +1,564 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

G (variable)

+GenericInstances.A [in Corelib.Classes.Morphisms]
+GenericInstances.B [in Corelib.Classes.Morphisms]
+GenericInstances.C [in Corelib.Classes.Morphisms]
+GenericInstances.U [in Corelib.Classes.Morphisms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_H.html b/master/corelib/index_variable_H.html new file mode 100644 index 0000000000..cd4dc2af88 --- /dev/null +++ b/master/corelib/index_variable_H.html @@ -0,0 +1,567 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

H (variable)

+HomoMonoMorphismFlip.aD [in Corelib.ssr.ssrbool]
+HomoMonoMorphismFlip.aD' [in Corelib.ssr.ssrbool]
+HomoMonoMorphismFlip.aR [in Corelib.ssr.ssrbool]
+HomoMonoMorphismFlip.aT [in Corelib.ssr.ssrbool]
+HomoMonoMorphismFlip.f [in Corelib.ssr.ssrbool]
+HomoMonoMorphismFlip.rR [in Corelib.ssr.ssrbool]
+HomoMonoMorphismFlip.rT [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_I.html b/master/corelib/index_variable_I.html new file mode 100644 index 0000000000..010da95839 --- /dev/null +++ b/master/corelib/index_variable_I.html @@ -0,0 +1,587 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

I (variable)

+InjectionsTheory.A [in Corelib.ssr.ssrfun]
+InjectionsTheory.B [in Corelib.ssr.ssrfun]
+InjectionsTheory.C [in Corelib.ssr.ssrfun]
+InjectionsTheory.f [in Corelib.ssr.ssrfun]
+InjectionsTheory.g [in Corelib.ssr.ssrfun]
+InjectionsTheory.h [in Corelib.ssr.ssrfun]
+Injections.aT [in Corelib.ssr.ssrfun]
+Injections.f [in Corelib.ssr.ssrfun]
+Injections.rT [in Corelib.ssr.ssrfun]
+inj_can_sym_in_on.g [in Corelib.ssr.ssrbool]
+inj_can_sym_in_on.f [in Corelib.ssr.ssrbool]
+inj_can_sym_in_on.rD [in Corelib.ssr.ssrbool]
+inj_can_sym_in_on.aD [in Corelib.ssr.ssrbool]
+inj_can_sym_in_on.rT [in Corelib.ssr.ssrbool]
+inj_can_sym_in_on.aT [in Corelib.ssr.ssrbool]
+Involutions.A [in Corelib.ssr.ssrfun]
+Involutions.f [in Corelib.ssr.ssrfun]
+Involutions.Hf [in Corelib.ssr.ssrfun]
+in_sig.P3 [in Corelib.ssr.ssrbool]
+in_sig.P2 [in Corelib.ssr.ssrbool]
+in_sig.P1 [in Corelib.ssr.ssrbool]
+in_sig.D3 [in Corelib.ssr.ssrbool]
+in_sig.D2 [in Corelib.ssr.ssrbool]
+in_sig.D1 [in Corelib.ssr.ssrbool]
+in_sig.T3 [in Corelib.ssr.ssrbool]
+in_sig.T2 [in Corelib.ssr.ssrbool]
+in_sig.T1 [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_J.html b/master/corelib/index_variable_J.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_variable_J.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_K.html b/master/corelib/index_variable_K.html new file mode 100644 index 0000000000..1dc0209d00 --- /dev/null +++ b/master/corelib/index_variable_K.html @@ -0,0 +1,569 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

K (variable)

+KeyedQualifier.k [in Corelib.ssr.ssrbool]
+KeyedQualifier.k_q [in Corelib.ssr.ssrbool]
+KeyedQualifier.n [in Corelib.ssr.ssrbool]
+KeyedQualifier.q [in Corelib.ssr.ssrbool]
+KeyedQualifier.T [in Corelib.ssr.ssrbool]
+KeyPred.k [in Corelib.ssr.ssrbool]
+KeyPred.k_p [in Corelib.ssr.ssrbool]
+KeyPred.p [in Corelib.ssr.ssrbool]
+KeyPred.T [in Corelib.ssr.ssrbool]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_L.html b/master/corelib/index_variable_L.html new file mode 100644 index 0000000000..f15fea7ed8 --- /dev/null +++ b/master/corelib/index_variable_L.html @@ -0,0 +1,1083 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

L (variable)

+LocalGlobal.allQ1 [in Corelib.ssr.ssrbool]
+LocalGlobal.allQ1l [in Corelib.ssr.ssrbool]
+LocalGlobal.allQ2 [in Corelib.ssr.ssrbool]
+LocalGlobal.d1 [in Corelib.ssr.ssrbool]
+LocalGlobal.D1 [in Corelib.ssr.ssrbool]
+LocalGlobal.d1' [in Corelib.ssr.ssrbool]
+LocalGlobal.d2 [in Corelib.ssr.ssrbool]
+LocalGlobal.D2 [in Corelib.ssr.ssrbool]
+LocalGlobal.d2' [in Corelib.ssr.ssrbool]
+LocalGlobal.d3 [in Corelib.ssr.ssrbool]
+LocalGlobal.D3 [in Corelib.ssr.ssrbool]
+LocalGlobal.d3' [in Corelib.ssr.ssrbool]
+LocalGlobal.f [in Corelib.ssr.ssrbool]
+LocalGlobal.f' [in Corelib.ssr.ssrbool]
+LocalGlobal.g [in Corelib.ssr.ssrbool]
+LocalGlobal.h [in Corelib.ssr.ssrbool]
+LocalGlobal.P1 [in Corelib.ssr.ssrbool]
+LocalGlobal.P2 [in Corelib.ssr.ssrbool]
+LocalGlobal.P3 [in Corelib.ssr.ssrbool]
+LocalGlobal.Q1 [in Corelib.ssr.ssrbool]
+LocalGlobal.Q1l [in Corelib.ssr.ssrbool]
+LocalGlobal.Q2 [in Corelib.ssr.ssrbool]
+LocalGlobal.sub1 [in Corelib.ssr.ssrbool]
+LocalGlobal.sub2 [in Corelib.ssr.ssrbool]
+LocalGlobal.sub3 [in Corelib.ssr.ssrbool]
+LocalGlobal.T1 [in Corelib.ssr.ssrbool]
+LocalGlobal.T2 [in Corelib.ssr.ssrbool]
+LocalGlobal.T3 [in Corelib.ssr.ssrbool]
+LocalProperties.d1 [in Corelib.ssr.ssrbool]
+LocalProperties.d2 [in Corelib.ssr.ssrbool]
+LocalProperties.d3 [in Corelib.ssr.ssrbool]
+LocalProperties.f [in Corelib.ssr.ssrbool]
+LocalProperties.T1 [in Corelib.ssr.ssrbool]
+LocalProperties.T2 [in Corelib.ssr.ssrbool]
+LocalProperties.T3 [in Corelib.ssr.ssrbool]
+Logic_lemmas.equality.z [in Corelib.Init.Logic]
+Logic_lemmas.equality.y [in Corelib.Init.Logic]
+Logic_lemmas.equality.x [in Corelib.Init.Logic]
+Logic_lemmas.equality.f [in Corelib.Init.Logic]
+Logic_lemmas.equality.B [in Corelib.Init.Logic]
+Logic_lemmas.equality.A [in Corelib.Init.Logic]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_M.html b/master/corelib/index_variable_M.html new file mode 100644 index 0000000000..7df1ee99a9 --- /dev/null +++ b/master/corelib/index_variable_M.html @@ -0,0 +1,1076 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

M (variable)

+Map.A [in Corelib.Lists.ListDef]
+Map.B [in Corelib.Lists.ListDef]
+Map.f [in Corelib.Lists.ListDef]
+Measure_well_founded.m [in Corelib.Program.Wf]
+Measure_well_founded.wf [in Corelib.Program.Wf]
+Measure_well_founded.R [in Corelib.Program.Wf]
+Measure_well_founded.M [in Corelib.Program.Wf]
+Measure_well_founded.T [in Corelib.Program.Wf]
+MonoHomoMorphismTheory_in.mem_g [in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.fgK [in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.rR [in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.aR [in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.rP [in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.aP [in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.rD [in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.aD [in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.g [in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.f [in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.rT [in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory_in.aT [in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory.aP [in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory.aR [in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory.aT [in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory.f [in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory.fgK [in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory.g [in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory.rP [in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory.rR [in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory.rT [in Corelib.ssr.ssrbool]
+MonoHomoMorphismTheory.sT [in Corelib.ssr.ssrbool]
+Morphism.aT [in Corelib.ssr.ssrfun]
+Morphism.f [in Corelib.ssr.ssrfun]
+Morphism.rT [in Corelib.ssr.ssrfun]
+Morphism.sT [in Corelib.ssr.ssrfun]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_N.html b/master/corelib/index_variable_N.html new file mode 100644 index 0000000000..b5f5997dcd --- /dev/null +++ b/master/corelib/index_variable_N.html @@ -0,0 +1,562 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

N (variable)

+Normalize.A [in Corelib.Classes.CMorphisms]
+Normalize.A [in Corelib.Classes.Morphisms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_O.html b/master/corelib/index_variable_O.html new file mode 100644 index 0000000000..72e05ca626 --- /dev/null +++ b/master/corelib/index_variable_O.html @@ -0,0 +1,568 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

O (variable)

+OperationProperties.R [in Corelib.ssr.ssrfun]
+OperationProperties.S [in Corelib.ssr.ssrfun]
+OperationProperties.T [in Corelib.ssr.ssrfun]
+OptionTheory.aT [in Corelib.ssr.ssrfun]
+OptionTheory.f [in Corelib.ssr.ssrfun]
+OptionTheory.g [in Corelib.ssr.ssrfun]
+OptionTheory.rT [in Corelib.ssr.ssrfun]
+OptionTheory.sT [in Corelib.ssr.ssrfun]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_P.html b/master/corelib/index_variable_P.html new file mode 100644 index 0000000000..1131570de8 --- /dev/null +++ b/master/corelib/index_variable_P.html @@ -0,0 +1,576 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

P (variable)

+PredicateSimplification.T [in Corelib.ssr.ssrbool]
+ProdSigT.A [in Corelib.Init.Specif]
+ProdSigT.B [in Corelib.Init.Specif]
+projections.A [in Corelib.Init.Datatypes]
+Projections.A [in Corelib.Init.Specif]
+Projections.A [in Corelib.Init.Logic]
+projections.B [in Corelib.Init.Datatypes]
+Projections.P [in Corelib.Init.Specif]
+Projections.P [in Corelib.Init.Logic]
+Projections2.A [in Corelib.Init.Specif]
+Projections2.P [in Corelib.Init.Specif]
+Projections2.Q [in Corelib.Init.Specif]
+Proper.A [in Corelib.Classes.CMorphisms]
+Proper.A [in Corelib.Classes.Morphisms]
+Proper.B [in Corelib.Classes.Morphisms]
+Proper.U [in Corelib.Classes.Morphisms]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_Q.html b/master/corelib/index_variable_Q.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_variable_Q.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_R.html b/master/corelib/index_variable_R.html new file mode 100644 index 0000000000..02df818ee1 --- /dev/null +++ b/master/corelib/index_variable_R.html @@ -0,0 +1,1082 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

R (variable)

+ReflectCombinators.p [in Corelib.ssr.ssrbool]
+ReflectCombinators.P [in Corelib.ssr.ssrbool]
+ReflectCombinators.q [in Corelib.ssr.ssrbool]
+ReflectCombinators.Q [in Corelib.ssr.ssrbool]
+ReflectCombinators.rP [in Corelib.ssr.ssrbool]
+ReflectCombinators.rQ [in Corelib.ssr.ssrbool]
+ReflectConnectives.b1 [in Corelib.ssr.ssrbool]
+ReflectConnectives.b2 [in Corelib.ssr.ssrbool]
+ReflectConnectives.b3 [in Corelib.ssr.ssrbool]
+ReflectConnectives.b4 [in Corelib.ssr.ssrbool]
+ReflectConnectives.b5 [in Corelib.ssr.ssrbool]
+ReflectCore.b [in Corelib.ssr.ssrbool]
+ReflectCore.c [in Corelib.ssr.ssrbool]
+ReflectCore.Hb [in Corelib.ssr.ssrbool]
+ReflectCore.P [in Corelib.ssr.ssrbool]
+ReflectCore.Q [in Corelib.ssr.ssrbool]
+ReflectNegCore.b [in Corelib.ssr.ssrbool]
+ReflectNegCore.c [in Corelib.ssr.ssrbool]
+ReflectNegCore.Hb [in Corelib.ssr.ssrbool]
+ReflectNegCore.P [in Corelib.ssr.ssrbool]
+ReflectNegCore.Q [in Corelib.ssr.ssrbool]
+Reflect.b [in Corelib.ssr.ssrbool]
+Reflect.b' [in Corelib.ssr.ssrbool]
+Reflect.c [in Corelib.ssr.ssrbool]
+Reflect.P [in Corelib.ssr.ssrbool]
+Reflect.Pb [in Corelib.ssr.ssrbool]
+Reflect.Pb' [in Corelib.ssr.ssrbool]
+Reflect.Q [in Corelib.ssr.ssrbool]
+RelationProperties.PER.symR [in Corelib.ssr.ssrbool]
+RelationProperties.PER.trR [in Corelib.ssr.ssrbool]
+RelationProperties.R [in Corelib.ssr.ssrbool]
+RelationProperties.T [in Corelib.ssr.ssrbool]
+Relations.A [in Corelib.Classes.CMorphisms]
+Relations.A [in Corelib.Classes.Morphisms]
+Relations.B [in Corelib.Classes.Morphisms]
+Relations.P [in Corelib.Classes.Morphisms]
+Relations.U [in Corelib.Classes.Morphisms]
+Relation_Definition.R [in Corelib.Relations.Relation_Definitions]
+Relation_Definition.A [in Corelib.Relations.Relation_Definitions]
+Repeat.A [in Corelib.Lists.ListDef]
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_S.html b/master/corelib/index_variable_S.html new file mode 100644 index 0000000000..2bec828585 --- /dev/null +++ b/master/corelib/index_variable_S.html @@ -0,0 +1,570 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

S (variable)

+Sig.P [in Corelib.ssr.ssrfun]
+Sig.Q [in Corelib.ssr.ssrfun]
+Sig.T [in Corelib.ssr.ssrfun]
+SimplFun.aT [in Corelib.ssr.ssrfun]
+SimplFun.rT [in Corelib.ssr.ssrfun]
+Subset_projections2.Q [in Corelib.Init.Specif]
+Subset_projections2.P [in Corelib.Init.Specif]
+Subset_projections2.A [in Corelib.Init.Specif]
+Subset_projections.P [in Corelib.Init.Specif]
+Subset_projections.A [in Corelib.Init.Specif]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_T.html b/master/corelib/index_variable_T.html new file mode 100644 index 0000000000..65e7b5400d --- /dev/null +++ b/master/corelib/index_variable_T.html @@ -0,0 +1,564 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

T (variable)

+Tag.i [in Corelib.ssr.ssrfun]
+Tag.I [in Corelib.ssr.ssrfun]
+Tag.T_ [in Corelib.ssr.ssrfun]
+Tag.U_ [in Corelib.ssr.ssrfun]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_U.html b/master/corelib/index_variable_U.html new file mode 100644 index 0000000000..42c9a83d5d --- /dev/null +++ b/master/corelib/index_variable_U.html @@ -0,0 +1,562 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

U (variable)

+universal_quantification.P [in Corelib.Init.Logic]
+universal_quantification.A [in Corelib.Init.Logic]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_V.html b/master/corelib/index_variable_V.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_variable_V.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_W.html b/master/corelib/index_variable_W.html new file mode 100644 index 0000000000..40bf872717 --- /dev/null +++ b/master/corelib/index_variable_W.html @@ -0,0 +1,578 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+

W (variable)

+Well_founded.F_ext [in Corelib.Program.Wf]
+Well_founded.F_sub [in Corelib.Program.Wf]
+Well_founded.P [in Corelib.Program.Wf]
+Well_founded.Rwf [in Corelib.Program.Wf]
+Well_founded.R [in Corelib.Program.Wf]
+Well_founded.A [in Corelib.Program.Wf]
+Well_founded_2.Rwf [in Corelib.Init.Wf]
+Well_founded_2.FixPoint_2.F [in Corelib.Init.Wf]
+Well_founded_2.P [in Corelib.Init.Wf]
+Well_founded_2.R [in Corelib.Init.Wf]
+Well_founded_2.B [in Corelib.Init.Wf]
+Well_founded_2.A [in Corelib.Init.Wf]
+Well_founded.FixPoint.F_ext [in Corelib.Init.Wf]
+Well_founded.FixPoint.F [in Corelib.Init.Wf]
+Well_founded.FixPoint.P [in Corelib.Init.Wf]
+Well_founded.Rwf [in Corelib.Init.Wf]
+Well_founded.R [in Corelib.Init.Wf]
+Well_founded.A [in Corelib.Init.Wf]
+

+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_X.html b/master/corelib/index_variable_X.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_variable_X.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_Y.html b/master/corelib/index_variable_Y.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_variable_Y.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
+ + + + +
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Global IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(3486 entries)
Notation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(293 entries)
Module IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(51 entries)
Variable IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(312 entries)
Library IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(100 entries)
Constructor IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(435 entries)
Lemma IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(611 entries)
Axiom IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(149 entries)
Inductive IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(99 entries)
Projection IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(76 entries)
Instance IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(117 entries)
Section IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(111 entries)
Abbreviation IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(108 entries)
Definition IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(962 entries)
Record IndexABCDEFGHIJKLMNOPQRSTUVWXYZ_other(62 entries)
+
+ +
+ +
+ + + +
+ + + diff --git a/master/corelib/index_variable_Z.html b/master/corelib/index_variable_Z.html new file mode 100644 index 0000000000..7447058421 --- /dev/null +++ b/master/corelib/index_variable_Z.html @@ -0,0 +1,559 @@ + + + + + + + + + + + + + +Standard Library | The Coq Proof Assistant + + + + + +
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When it is not found, a full rebuild will be done. +config: 76f3259802bd63a83d97c93e84a2f8f6 +tags: 645f666f9bcd5a90fca523b33c5a78b7 diff --git a/master/refman-stdlib/.doctrees/changes.doctree b/master/refman-stdlib/.doctrees/changes.doctree new file mode 100644 index 0000000000..6fbefb0a7e Binary files /dev/null and b/master/refman-stdlib/.doctrees/changes.doctree differ diff --git a/master/refman-stdlib/.doctrees/environment.pickle b/master/refman-stdlib/.doctrees/environment.pickle new file mode 100644 index 0000000000..b273d8b7cb Binary files /dev/null and b/master/refman-stdlib/.doctrees/environment.pickle differ diff --git a/master/refman-stdlib/.doctrees/index.doctree b/master/refman-stdlib/.doctrees/index.doctree new file mode 100644 index 0000000000..da3a81c5b1 Binary files /dev/null and b/master/refman-stdlib/.doctrees/index.doctree differ diff --git a/master/refman-stdlib/.doctrees/language/coq-library.doctree b/master/refman-stdlib/.doctrees/language/coq-library.doctree new file mode 100644 index 0000000000..49d9e77587 Binary files /dev/null and b/master/refman-stdlib/.doctrees/language/coq-library.doctree differ diff --git a/master/refman-stdlib/.doctrees/license.doctree b/master/refman-stdlib/.doctrees/license.doctree new file mode 100644 index 0000000000..97dd1c6f65 Binary files /dev/null and b/master/refman-stdlib/.doctrees/license.doctree differ diff --git a/master/refman-stdlib/.doctrees/zebibliography.doctree b/master/refman-stdlib/.doctrees/zebibliography.doctree new file mode 100644 index 0000000000..e51bbcad43 Binary files /dev/null and b/master/refman-stdlib/.doctrees/zebibliography.doctree differ diff --git a/master/refman-stdlib/_sources/changes.rst.txt b/master/refman-stdlib/_sources/changes.rst.txt new file mode 100644 index 0000000000..f8acfc2e45 --- /dev/null +++ b/master/refman-stdlib/_sources/changes.rst.txt @@ -0,0 +1,15 @@ +.. _changes: + +-------------- +Recent changes +-------------- + +.. ifconfig:: not is_a_released_version + + .. include:: ../unreleased.rst + +Previous versions +----------------- + +The standard library historically used to be distributed with Coq, +please look in Coq own changelog for details about older changes. diff --git a/master/refman-stdlib/_sources/index.rst.txt b/master/refman-stdlib/_sources/index.rst.txt new file mode 100644 index 0000000000..b06c179ead --- /dev/null +++ b/master/refman-stdlib/_sources/index.rst.txt @@ -0,0 +1,25 @@ +========================== +Introduction and Contents +========================== + +.. include:: introduction.rst + +Contents +-------- + +.. toctree:: + + self + +.. toctree:: + :caption: Overview + + language/coq-library + +.. toctree:: + :caption: Appendix + + changes + zebibliography + +.. include:: license.rst diff --git a/master/refman-stdlib/_sources/language/coq-library.rst.txt b/master/refman-stdlib/_sources/language/coq-library.rst.txt new file mode 100644 index 0000000000..befc0502bb --- /dev/null +++ b/master/refman-stdlib/_sources/language/coq-library.rst.txt @@ -0,0 +1,393 @@ +The standard library +-------------------- + +Survey +~~~~~~ + +The standard library is structured into the following +subdirectories: + + * **Logic** : Classical logic and dependent equality + * **Arith** : Basic Peano arithmetic + * **PArith** : Basic positive integer arithmetic + * **NArith** : Basic binary natural number arithmetic + * **ZArith** : Basic relative integer arithmetic + * **Numbers** : Various approaches to natural, integer and cyclic numbers (currently axiomatically and on top of 2^31 binary words) + * **Bool** : Booleans (basic functions and results) + * **Lists** : Monomorphic and polymorphic lists (basic functions and results), Streams (infinite sequences defined with coinductive types) + * **Sets** : Sets (classical, constructive, finite, infinite, power set, etc.) + * **FSets** : Specification and implementations of finite sets and finite maps (by lists and by AVL trees) + * **Reals** : Axiomatization of real numbers (classical, basic functions, integer part, fractional part, limit, derivative, Cauchy series, power series and results,...) + * **Floats** : Machine implementation of floating-point arithmetic (for the binary64 format) + * **Relations** : Relations (definitions and basic results) + * **Sorting** : Sorted list (basic definitions and heapsort correctness) + * **Strings** : 8-bits characters and strings + * **Wellfounded** : Well-founded relations (basic results) + + +These directories belong to the initial load path of the system, and +the modules they provide are compiled at installation time. So they +are directly accessible with the command ``Require``. + +The different modules of the Coq standard library are documented +online at https://coq.inria.fr/stdlib/. + +Peano’s arithmetic (nat) +~~~~~~~~~~~~~~~~~~~~~~~~ + +.. index:: + single: Peano's arithmetic + single: nat_scope + +While in the initial state, many operations and predicates of Peano's +arithmetic are defined, further operations and results belong to other +modules. For instance, the decidability of the basic predicates are +defined here. This is provided by requiring the module ``Arith``. + +The following table describes the notations available in scope +``nat_scope`` : + +=============== =================== +Notation Interpretation +=============== =================== +``_ < _`` ``lt`` +``_ <= _`` ``le`` +``_ > _`` ``gt`` +``_ >= _`` ``ge`` +``x < y < z`` ``x < y /\ y < z`` +``x < y <= z`` ``x < y /\ y <= z`` +``x <= y < z`` ``x <= y /\ y < z`` +``x <= y <= z`` ``x <= y /\ y <= z`` +``_ + _`` ``plus`` +``_ - _`` ``minus`` +``_ * _`` ``mult`` +=============== =================== + + +Notations for integer arithmetic +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. index:: + single: Arithmetical notations + single: + (term) + single: * (term) + single: - (term) + singel: / (term) + single: <= (term) + single: >= (term) + single: < (term) + single: > (term) + single: ?= (term) + single: mod (term) + + +The following table describes the syntax of expressions +for integer arithmetic. It is provided by requiring and opening the module ``ZArith`` and opening scope ``Z_scope``. +It specifies how notations are interpreted and, when not +already reserved, the precedence and associativity. + +=============== ==================== ========== ============= +Notation Interpretation Precedence Associativity +=============== ==================== ========== ============= +``_ < _`` ``Z.lt`` +``_ <= _`` ``Z.le`` +``_ > _`` ``Z.gt`` +``_ >= _`` ``Z.ge`` +``x < y < z`` ``x < y /\ y < z`` +``x < y <= z`` ``x < y /\ y <= z`` +``x <= y < z`` ``x <= y /\ y < z`` +``x <= y <= z`` ``x <= y /\ y <= z`` +``_ ?= _`` ``Z.compare`` 70 no +``_ + _`` ``Z.add`` +``_ - _`` ``Z.sub`` +``_ * _`` ``Z.mul`` +``_ / _`` ``Z.div`` +``_ mod _`` ``Z.modulo`` 40 no +``- _`` ``Z.opp`` +``_ ^ _`` ``Z.pow`` +=============== ==================== ========== ============= + + +.. example:: + + .. rocqtop:: all reset + + From Stdlib Require Import ZArith. + Check (2 + 3)%Z. + Open Scope Z_scope. + Check 2 + 3. + + +Real numbers library +~~~~~~~~~~~~~~~~~~~~ + +Notations for real numbers +++++++++++++++++++++++++++ + +This is provided by requiring and opening the module ``Reals`` and +opening scope ``R_scope``. This set of notations is very similar to +the notation for integer arithmetic. The inverse function was added. + +=============== =================== +Notation Interpretation +=============== =================== +``_ < _`` ``Rlt`` +``_ <= _`` ``Rle`` +``_ > _`` ``Rgt`` +``_ >= _`` ``Rge`` +``x < y < z`` ``x < y /\ y < z`` +``x < y <= z`` ``x < y /\ y <= z`` +``x <= y < z`` ``x <= y /\ y < z`` +``x <= y <= z`` ``x <= y /\ y <= z`` +``_ + _`` ``Rplus`` +``_ - _`` ``Rminus`` +``_ * _`` ``Rmult`` +``_ / _`` ``Rdiv`` +``- _`` ``Ropp`` +``/ _`` ``Rinv`` +``_ ^ _`` ``pow`` +=============== =================== + +.. example:: + + .. rocqtop:: all reset + + From Stdlib Require Import Reals. + Check (2 + 3)%R. + Open Scope R_scope. + Check 2 + 3. + +Some tactics for real numbers ++++++++++++++++++++++++++++++ + +In addition to the powerful ``ring``, ``field`` and ``lra`` +tactics (see Chapters ring and micromega), there are also: + +.. tacn:: discrR + + Proves that two real integer constants are different. + +.. example:: + + .. rocqtop:: all reset + + From Stdlib Require Import DiscrR. + Open Scope R_scope. + Goal 5 <> 0. + discrR. + +.. tacn:: split_Rabs + + Allows unfolding the ``Rabs`` constant and splits corresponding conjunctions. + +.. example:: + + .. rocqtop:: all reset + + From Stdlib Require Import Reals. + Open Scope R_scope. + Goal forall x:R, x <= Rabs x. + intro; split_Rabs. + +.. tacn:: split_Rmult + + Splits a condition that a product is non-null into subgoals + corresponding to the condition on each operand of the product. + +.. example:: + + .. rocqtop:: all reset + + From Stdlib Require Import Reals. + Open Scope R_scope. + Goal forall x y z:R, x * y * z <> 0. + intros; split_Rmult. + +List library +~~~~~~~~~~~~ + +.. index:: + single: Notations for lists + single: length (term) + single: head (term) + single: tail (term) + single: app (term) + single: rev (term) + single: nth (term) + single: map (term) + single: flat_map (term) + single: fold_left (term) + single: fold_right (term) + +Some elementary operations on polymorphic lists are defined here. +They can be accessed by requiring module ``List``. + +It defines the following notions: + + * ``length`` + * ``head`` : first element (with default) + * ``tail`` : all but first element + * ``app`` : concatenation + * ``rev`` : reverse + * ``nth`` : accessing n-th element (with default) + * ``map`` : applying a function + * ``flat_map`` : applying a function returning lists + * ``fold_left`` : iterator (from head to tail) + * ``fold_right`` : iterator (from tail to head) + +The following table shows notations available when opening scope ``list_scope``. + +========== ============== ========== ============= +Notation Interpretation Precedence Associativity +========== ============== ========== ============= +``_ ++ _`` ``app`` 60 right +``_ :: _`` ``cons`` 60 right +========== ============== ========== ============= + +.. _floats_library: + +Floats library +~~~~~~~~~~~~~~ + +The standard library has a small ``Floats`` module for accessing +processor floating-point operations through the Coq kernel. +However, while this module supports computation and has a bit-level +specification, it doesn't include elaborate theorems, such as a link +to real arithmetic or various error bounds. To do proofs by +reflection, use ``Floats`` in conjunction with the complementary +`Flocq `_ library, which provides +many such theorems. + +The library of primitive floating-point arithmetic can be loaded by +requiring module ``Floats``: + +.. rocqtop:: in + + From Stdlib Require Import Floats. + +It exports the module ``PrimFloat`` that provides a primitive type +named ``float``, defined in the kernel +as well as two variant types ``float_comparison`` and ``float_class``: + + +.. rocqtop:: all + + Print float. + Print float_comparison. + Print float_class. + +It then defines the primitive operators below, using the processor +floating-point operators for binary64 in rounding-to-nearest even: + +* ``abs`` +* ``opp`` +* ``sub`` +* ``add`` +* ``mul`` +* ``div`` +* ``sqrt`` +* ``compare`` : compare two floats and return a ``float_comparison`` +* ``classify`` : analyze a float and return a ``float_class`` +* ``of_int63`` : round a primitive integer and convert it into a float +* ``normfr_mantissa`` : take a float in ``[0.5; 1.0)`` and return its mantissa +* ``frshiftexp`` : convert a float to fractional part in ``[0.5; 1.0)`` and integer part +* ``ldshiftexp`` : multiply a float by an integral power of ``2`` +* ``next_up`` : return the next float towards positive infinity +* ``next_down`` : return the next float towards negative infinity + +For special floating-point values, the following constants are also +defined: + +* ``zero`` +* ``neg_zero`` +* ``one`` +* ``two`` +* ``infinity`` +* ``neg_infinity`` +* ``nan`` : Not a Number (assumed to be unique: the "payload" of NaNs is ignored) + +The following table shows the notations available when opening scope +``float_scope``. + +=========== ============== +Notation Interpretation +=========== ============== +``- _`` ``opp`` +``_ - _`` ``sub`` +``_ + _`` ``add`` +``_ * _`` ``mul`` +``_ / _`` ``div`` +``_ =? _`` ``eqb`` +``_ tbody > tr > td > ul { + padding-left: 0em; +} + +table.indextable tr.pcap { + height: 10px; +} + +table.indextable tr.cap { + margin-top: 10px; 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0000000000..e1bfd708b7 --- /dev/null +++ b/master/refman-stdlib/_static/doctools.js @@ -0,0 +1,358 @@ +/* + * doctools.js + * ~~~~~~~~~~~ + * + * Sphinx JavaScript utilities for all documentation. + * + * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ + +/** + * select a different prefix for underscore + */ +$u = _.noConflict(); + +/** + * make the code below compatible with browsers without + * an installed firebug like debugger +if (!window.console || !console.firebug) { + var names = ["log", "debug", "info", "warn", "error", "assert", "dir", + "dirxml", "group", "groupEnd", "time", "timeEnd", "count", "trace", + "profile", "profileEnd"]; + window.console = {}; + for (var i = 0; i < names.length; ++i) + window.console[names[i]] = function() {}; +} + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} + +/** + * Small JavaScript module for the documentation. + */ +var Documentation = { + + init : function() { + this.fixFirefoxAnchorBug(); + this.highlightSearchWords(); + this.initIndexTable(); + this.initOnKeyListeners(); + }, + + /** + * i18n support + */ + TRANSLATIONS : {}, + PLURAL_EXPR : function(n) { return n === 1 ? 0 : 1; }, + LOCALE : 'unknown', + + // gettext and ngettext don't access this so that the functions + // can safely bound to a different name (_ = Documentation.gettext) + gettext : function(string) { + var translated = Documentation.TRANSLATIONS[string]; + if (typeof translated === 'undefined') + return string; + return (typeof translated === 'string') ? translated : translated[0]; + }, + + ngettext : function(singular, plural, n) { + var translated = Documentation.TRANSLATIONS[singular]; + if (typeof translated === 'undefined') + return (n == 1) ? singular : plural; + return translated[Documentation.PLURALEXPR(n)]; + }, + + addTranslations : function(catalog) { + for (var key in catalog.messages) + this.TRANSLATIONS[key] = catalog.messages[key]; + this.PLURAL_EXPR = new Function('n', 'return +(' + catalog.plural_expr + ')'); + this.LOCALE = catalog.locale; + }, + + /** + * add context elements like header anchor links + */ + addContextElements : function() { + $('div[id] > :header:first').each(function() { + $('\u00B6'). + attr('href', '#' + this.id). + attr('title', _('Permalink to this headline')). + appendTo(this); + }); + $('dt[id]').each(function() { + $('\u00B6'). + attr('href', '#' + this.id). + attr('title', _('Permalink to this definition')). + appendTo(this); + }); + }, + + /** + * workaround a firefox stupidity + * see: https://bugzilla.mozilla.org/show_bug.cgi?id=645075 + */ + fixFirefoxAnchorBug : function() { + if (document.location.hash && $.browser.mozilla) + window.setTimeout(function() { + document.location.href += ''; + }, 10); + }, + + /** + * highlight the search words provided in the url in the text + */ + highlightSearchWords : function() { + var params = $.getQueryParameters(); + var terms = (params.highlight) ? params.highlight[0].split(/\s+/) : []; + if (terms.length) { + var body = $('div.body'); + if (!body.length) { + body = $('body'); + } + window.setTimeout(function() { + $.each(terms, function() { + body.highlightText(this.toLowerCase(), 'highlighted'); + }); + }, 10); + $('

' + _('Hide Search Matches') + '

') + .appendTo($('#searchbox')); + } + }, + + /** + * init the domain index toggle buttons + */ + initIndexTable : function() { + var togglers = $('img.toggler').click(function() { + var src = $(this).attr('src'); + var idnum = $(this).attr('id').substr(7); + $('tr.cg-' + idnum).toggle(); + if (src.substr(-9) === 'minus.png') + $(this).attr('src', src.substr(0, src.length-9) + 'plus.png'); + else + $(this).attr('src', src.substr(0, src.length-8) + 'minus.png'); + }).css('display', ''); + if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) { + togglers.click(); + } + }, + + /** + * helper function to hide the search marks again + */ + hideSearchWords : function() { + $('#searchbox .highlight-link').fadeOut(300); + $('span.highlighted').removeClass('highlighted'); + var url = new URL(window.location); + url.searchParams.delete('highlight'); + window.history.replaceState({}, '', url); + }, + + /** + * helper function to focus on search bar + */ + focusSearchBar : function() { + $('input[name=q]').first().focus(); + }, + + /** + * make the url absolute + */ + makeURL : function(relativeURL) { + return DOCUMENTATION_OPTIONS.URL_ROOT + '/' + relativeURL; + }, + + /** + * get the current relative url + */ + getCurrentURL : function() { + var path = document.location.pathname; + var parts = path.split(/\//); + $.each(DOCUMENTATION_OPTIONS.URL_ROOT.split(/\//), function() { + if (this === '..') + parts.pop(); + }); + var url = parts.join('/'); + return path.substring(url.lastIndexOf('/') + 1, path.length - 1); + }, + + initOnKeyListeners: function() { + // only install a listener if it is really needed + if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS && + !DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) + return; + + $(document).keydown(function(event) { + var activeElementType = document.activeElement.tagName; + // don't navigate when in search box, textarea, dropdown or button + if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT' + && activeElementType !== 'BUTTON') { + if (event.altKey || event.ctrlKey || event.metaKey) + return; + + if (!event.shiftKey) { + switch (event.key) { + case 'ArrowLeft': + if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) + break; + var prevHref = $('link[rel="prev"]').prop('href'); + if (prevHref) { + window.location.href = prevHref; + return false; + } + break; + case 'ArrowRight': + if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) + break; + var nextHref = $('link[rel="next"]').prop('href'); + if (nextHref) { + window.location.href = nextHref; + return false; + } + break; + case 'Escape': + if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) + break; + Documentation.hideSearchWords(); + return false; + } + } + + // some keyboard layouts may need Shift to get / + switch (event.key) { + case '/': + if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) + break; + Documentation.focusSearchBar(); + return false; + } + } + }); + } +}; + +// quick alias for translations +_ = Documentation.gettext; + +$(document).ready(function() { + Documentation.init(); +}); diff --git a/master/refman-stdlib/_static/documentation_options.js b/master/refman-stdlib/_static/documentation_options.js new file mode 100644 index 0000000000..c8ac6acbc0 --- /dev/null +++ b/master/refman-stdlib/_static/documentation_options.js @@ -0,0 +1,14 @@ +var DOCUMENTATION_OPTIONS = { + URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'), + VERSION: '9.0+alpha', + LANGUAGE: 'en', + COLLAPSE_INDEX: false, + BUILDER: 'html', + FILE_SUFFIX: '.html', + LINK_SUFFIX: '.html', + HAS_SOURCE: true, + SOURCELINK_SUFFIX: '.txt', + NAVIGATION_WITH_KEYS: false, + SHOW_SEARCH_SUMMARY: true, + ENABLE_SEARCH_SHORTCUTS: true, +}; \ No newline at end of file diff --git a/master/refman-stdlib/_static/file.png b/master/refman-stdlib/_static/file.png new file mode 100644 index 0000000000..a858a410e4 Binary files /dev/null and b/master/refman-stdlib/_static/file.png differ diff --git a/master/refman-stdlib/_static/jquery-3.5.1.js b/master/refman-stdlib/_static/jquery-3.5.1.js new file mode 100644 index 0000000000..50937333b9 --- /dev/null +++ b/master/refman-stdlib/_static/jquery-3.5.1.js @@ -0,0 +1,10872 @@ +/*! + * jQuery JavaScript Library v3.5.1 + * https://jquery.com/ + * + * Includes Sizzle.js + * https://sizzlejs.com/ + * + * Copyright JS Foundation and other contributors + * Released under the MIT license + * https://jquery.org/license + * + * Date: 2020-05-04T22:49Z + */ +( function( global, factory ) { + + "use strict"; + + if ( typeof module === "object" && typeof module.exports === "object" ) { + + // For CommonJS and CommonJS-like environments where a proper `window` + // is present, execute the factory and get jQuery. + // For environments that do not have a `window` with a `document` + // (such as Node.js), expose a factory as module.exports. + // This accentuates the need for the creation of a real `window`. + // e.g. var jQuery = require("jquery")(window); + // See ticket #14549 for more info. + module.exports = global.document ? + factory( global, true ) : + function( w ) { + if ( !w.document ) { + throw new Error( "jQuery requires a window with a document" ); + } + return factory( w ); + }; + } else { + factory( global ); + } + +// Pass this if window is not defined yet +} )( typeof window !== "undefined" ? window : this, function( window, noGlobal ) { + +// Edge <= 12 - 13+, Firefox <=18 - 45+, IE 10 - 11, Safari 5.1 - 9+, iOS 6 - 9.1 +// throw exceptions when non-strict code (e.g., ASP.NET 4.5) accesses strict mode +// arguments.callee.caller (trac-13335). But as of jQuery 3.0 (2016), strict mode should be common +// enough that all such attempts are guarded in a try block. +"use strict"; + +var arr = []; + +var getProto = Object.getPrototypeOf; + +var slice = arr.slice; + +var flat = arr.flat ? function( array ) { + return arr.flat.call( array ); +} : function( array ) { + return arr.concat.apply( [], array ); +}; + + +var push = arr.push; + +var indexOf = arr.indexOf; + +var class2type = {}; + +var toString = class2type.toString; + +var hasOwn = class2type.hasOwnProperty; + +var fnToString = hasOwn.toString; + +var ObjectFunctionString = fnToString.call( Object ); + +var support = {}; + +var isFunction = function isFunction( obj ) { + + // Support: Chrome <=57, Firefox <=52 + // In some browsers, typeof returns "function" for HTML elements + // (i.e., `typeof document.createElement( "object" ) === "function"`). + // We don't want to classify *any* DOM node as a function. + return typeof obj === "function" && typeof obj.nodeType !== "number"; + }; + + +var isWindow = function isWindow( obj ) { + return obj != null && obj === obj.window; + }; + + +var document = window.document; + + + + var preservedScriptAttributes = { + type: true, + src: true, + nonce: true, + noModule: true + }; + + function DOMEval( code, node, doc ) { + doc = doc || document; + + var i, val, + script = doc.createElement( "script" ); + + script.text = code; + if ( node ) { + for ( i in preservedScriptAttributes ) { + + // Support: Firefox 64+, Edge 18+ + // Some browsers don't support the "nonce" property on scripts. + // On the other hand, just using `getAttribute` is not enough as + // the `nonce` attribute is reset to an empty string whenever it + // becomes browsing-context connected. + // See https://github.com/whatwg/html/issues/2369 + // See https://html.spec.whatwg.org/#nonce-attributes + // The `node.getAttribute` check was added for the sake of + // `jQuery.globalEval` so that it can fake a nonce-containing node + // via an object. + val = node[ i ] || node.getAttribute && node.getAttribute( i ); + if ( val ) { + script.setAttribute( i, val ); + } + } + } + doc.head.appendChild( script ).parentNode.removeChild( script ); + } + + +function toType( obj ) { + if ( obj == null ) { + return obj + ""; + } + + // Support: Android <=2.3 only (functionish RegExp) + return typeof obj === "object" || typeof obj === "function" ? + class2type[ toString.call( obj ) ] || "object" : + typeof obj; +} +/* global Symbol */ +// Defining this global in .eslintrc.json would create a danger of using the global +// unguarded in another place, it seems safer to define global only for this module + + + +var + version = "3.5.1", + + // Define a local copy of jQuery + jQuery = function( selector, context ) { + + // The jQuery object is actually just the init constructor 'enhanced' + // Need init if jQuery is called (just allow error to be thrown if not included) + return new jQuery.fn.init( selector, context ); + }; + +jQuery.fn = jQuery.prototype = { + + // The current version of jQuery being used + jquery: version, + + constructor: jQuery, + + // The default length of a jQuery object is 0 + length: 0, + + toArray: function() { + return slice.call( this ); + }, + + // Get the Nth element in the matched element set OR + // Get the whole matched element set as a clean array + get: function( num ) { + + // Return all the elements in a clean array + if ( num == null ) { + return slice.call( this ); + } + + // Return just the one element from the set + return num < 0 ? this[ num + this.length ] : this[ num ]; + }, + + // Take an array of elements and push it onto the stack + // (returning the new matched element set) + pushStack: function( elems ) { + + // Build a new jQuery matched element set + var ret = jQuery.merge( this.constructor(), elems ); + + // Add the old object onto the stack (as a reference) + ret.prevObject = this; + + // Return the newly-formed element set + return ret; + }, + + // Execute a callback for every element in the matched set. + each: function( callback ) { + return jQuery.each( this, callback ); + }, + + map: function( callback ) { + return this.pushStack( jQuery.map( this, function( elem, i ) { + return callback.call( elem, i, elem ); + } ) ); + }, + + slice: function() { + return this.pushStack( slice.apply( this, arguments ) ); + }, + + first: function() { + return this.eq( 0 ); + }, + + last: function() { + return this.eq( -1 ); + }, + + even: function() { + return this.pushStack( jQuery.grep( this, function( _elem, i ) { + return ( i + 1 ) % 2; + } ) ); + }, + + odd: function() { + return this.pushStack( jQuery.grep( this, function( _elem, i ) { + return i % 2; + } ) ); + }, + + eq: function( i ) { + var len = this.length, + j = +i + ( i < 0 ? len : 0 ); + return this.pushStack( j >= 0 && j < len ? [ this[ j ] ] : [] ); + }, + + end: function() { + return this.prevObject || this.constructor(); + }, + + // For internal use only. + // Behaves like an Array's method, not like a jQuery method. + push: push, + sort: arr.sort, + splice: arr.splice +}; + +jQuery.extend = jQuery.fn.extend = function() { + var options, name, src, copy, copyIsArray, clone, + target = arguments[ 0 ] || {}, + i = 1, + length = arguments.length, + deep = false; + + // Handle a deep copy situation + if ( typeof target === "boolean" ) { + deep = target; + + // Skip the boolean and the target + target = arguments[ i ] || {}; + i++; + } + + // Handle case when target is a string or something (possible in deep copy) + if ( typeof target !== "object" && !isFunction( target ) ) { + target = {}; + } + + // Extend jQuery itself if only one argument is passed + if ( i === length ) { + target = this; + i--; + } + + for ( ; i < length; i++ ) { + + // Only deal with non-null/undefined values + if ( ( options = arguments[ i ] ) != null ) { + + // Extend the base object + for ( name in options ) { + copy = options[ name ]; + + // Prevent Object.prototype pollution + // Prevent never-ending loop + if ( name === "__proto__" || target === copy ) { + continue; + } + + // Recurse if we're merging plain objects or arrays + if ( deep && copy && ( jQuery.isPlainObject( copy ) || + ( copyIsArray = Array.isArray( copy ) ) ) ) { + src = target[ name ]; + + // Ensure proper type for the source value + if ( copyIsArray && !Array.isArray( src ) ) { + clone = []; + } else if ( !copyIsArray && !jQuery.isPlainObject( src ) ) { + clone = {}; + } else { + clone = src; + } + copyIsArray = false; + + // Never move original objects, clone them + target[ name ] = jQuery.extend( deep, clone, copy ); + + // Don't bring in undefined values + } else if ( copy !== undefined ) { + target[ name ] = copy; + } + } + } + } + + // Return the modified object + return target; +}; + +jQuery.extend( { + + // Unique for each copy of jQuery on the page + expando: "jQuery" + ( version + Math.random() ).replace( /\D/g, "" ), + + // Assume jQuery is ready without the ready module + isReady: true, + + error: function( msg ) { + throw new Error( msg ); + }, + + noop: function() {}, + + isPlainObject: function( obj ) { + var proto, Ctor; + + // Detect obvious negatives + // Use toString instead of jQuery.type to catch host objects + if ( !obj || toString.call( obj ) !== "[object Object]" ) { + return false; + } + + proto = getProto( obj ); + + // Objects with no prototype (e.g., `Object.create( null )`) are plain + if ( !proto ) { + return true; + } + + // Objects with prototype are plain iff they were constructed by a global Object function + Ctor = hasOwn.call( proto, "constructor" ) && proto.constructor; + return typeof Ctor === "function" && fnToString.call( Ctor ) === ObjectFunctionString; + }, + + isEmptyObject: function( obj ) { + var name; + + for ( name in obj ) { + return false; + } + return true; + }, + + // Evaluates a script in a provided context; falls back to the global one + // if not specified. + globalEval: function( code, options, doc ) { + DOMEval( code, { nonce: options && options.nonce }, doc ); + }, + + each: function( obj, callback ) { + var length, i = 0; + + if ( isArrayLike( obj ) ) { + length = obj.length; + for ( ; i < length; i++ ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } else { + for ( i in obj ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } + + return obj; + }, + + // results is for internal usage only + makeArray: function( arr, results ) { + var ret = results || []; + + if ( arr != null ) { + if ( isArrayLike( Object( arr ) ) ) { + jQuery.merge( ret, + typeof arr === "string" ? + [ arr ] : arr + ); + } else { + push.call( ret, arr ); + } + } + + return ret; + }, + + inArray: function( elem, arr, i ) { + return arr == null ? -1 : indexOf.call( arr, elem, i ); + }, + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + merge: function( first, second ) { + var len = +second.length, + j = 0, + i = first.length; + + for ( ; j < len; j++ ) { + first[ i++ ] = second[ j ]; + } + + first.length = i; + + return first; + }, + + grep: function( elems, callback, invert ) { + var callbackInverse, + matches = [], + i = 0, + length = elems.length, + callbackExpect = !invert; + + // Go through the array, only saving the items + // that pass the validator function + for ( ; i < length; i++ ) { + callbackInverse = !callback( elems[ i ], i ); + if ( callbackInverse !== callbackExpect ) { + matches.push( elems[ i ] ); + } + } + + return matches; + }, + + // arg is for internal usage only + map: function( elems, callback, arg ) { + var length, value, + i = 0, + ret = []; + + // Go through the array, translating each of the items to their new values + if ( isArrayLike( elems ) ) { + length = elems.length; + for ( ; i < length; i++ ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + + // Go through every key on the object, + } else { + for ( i in elems ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + } + + // Flatten any nested arrays + return flat( ret ); + }, + + // A global GUID counter for objects + guid: 1, + + // jQuery.support is not used in Core but other projects attach their + // properties to it so it needs to exist. + support: support +} ); + +if ( typeof Symbol === "function" ) { + jQuery.fn[ Symbol.iterator ] = arr[ Symbol.iterator ]; +} + +// Populate the class2type map +jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ), +function( _i, name ) { + class2type[ "[object " + name + "]" ] = name.toLowerCase(); +} ); + +function isArrayLike( obj ) { + + // Support: real iOS 8.2 only (not reproducible in simulator) + // `in` check used to prevent JIT error (gh-2145) + // hasOwn isn't used here due to false negatives + // regarding Nodelist length in IE + var length = !!obj && "length" in obj && obj.length, + type = toType( obj ); + + if ( isFunction( obj ) || isWindow( obj ) ) { + return false; + } + + return type === "array" || length === 0 || + typeof length === "number" && length > 0 && ( length - 1 ) in obj; +} +var Sizzle = +/*! + * Sizzle CSS Selector Engine v2.3.5 + * https://sizzlejs.com/ + * + * Copyright JS Foundation and other contributors + * Released under the MIT license + * https://js.foundation/ + * + * Date: 2020-03-14 + */ +( function( window ) { +var i, + support, + Expr, + getText, + isXML, + tokenize, + compile, + select, + outermostContext, + sortInput, + hasDuplicate, + + // Local document vars + setDocument, + document, + docElem, + documentIsHTML, + rbuggyQSA, + rbuggyMatches, + matches, + contains, + + // Instance-specific data + expando = "sizzle" + 1 * new Date(), + preferredDoc = window.document, + dirruns = 0, + done = 0, + classCache = createCache(), + tokenCache = createCache(), + compilerCache = createCache(), + nonnativeSelectorCache = createCache(), + sortOrder = function( a, b ) { + if ( a === b ) { + hasDuplicate = true; + } + return 0; + }, + + // Instance methods + hasOwn = ( {} ).hasOwnProperty, + arr = [], + pop = arr.pop, + pushNative = arr.push, + push = arr.push, + slice = arr.slice, + + // Use a stripped-down indexOf as it's faster than native + // https://jsperf.com/thor-indexof-vs-for/5 + indexOf = function( list, elem ) { + var i = 0, + len = list.length; + for ( ; i < len; i++ ) { + if ( list[ i ] === elem ) { + return i; + } + } + return -1; + }, + + booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|" + + "ismap|loop|multiple|open|readonly|required|scoped", + + // Regular expressions + + // http://www.w3.org/TR/css3-selectors/#whitespace + whitespace = "[\\x20\\t\\r\\n\\f]", + + // https://www.w3.org/TR/css-syntax-3/#ident-token-diagram + identifier = "(?:\\\\[\\da-fA-F]{1,6}" + whitespace + + "?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+", + + // Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors + attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace + + + // Operator (capture 2) + "*([*^$|!~]?=)" + whitespace + + + // "Attribute values must be CSS identifiers [capture 5] + // or strings [capture 3 or capture 4]" + "*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" + + whitespace + "*\\]", + + pseudos = ":(" + identifier + ")(?:\\((" + + + // To reduce the number of selectors needing tokenize in the preFilter, prefer arguments: + // 1. quoted (capture 3; capture 4 or capture 5) + "('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" + + + // 2. simple (capture 6) + "((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" + + + // 3. anything else (capture 2) + ".*" + + ")\\)|)", + + // Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter + rwhitespace = new RegExp( whitespace + "+", "g" ), + rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" + + whitespace + "+$", "g" ), + + rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ), + rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace + + "*" ), + rdescend = new RegExp( whitespace + "|>" ), + + rpseudo = new RegExp( pseudos ), + ridentifier = new RegExp( "^" + identifier + "$" ), + + matchExpr = { + "ID": new RegExp( "^#(" + identifier + ")" ), + "CLASS": new RegExp( "^\\.(" + identifier + ")" ), + "TAG": new RegExp( "^(" + identifier + "|[*])" ), + "ATTR": new RegExp( "^" + attributes ), + "PSEUDO": new RegExp( "^" + pseudos ), + "CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" + + whitespace + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" + + whitespace + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ), + "bool": new RegExp( "^(?:" + booleans + ")$", "i" ), + + // For use in libraries implementing .is() + // We use this for POS matching in `select` + "needsContext": new RegExp( "^" + whitespace + + "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + whitespace + + "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" ) + }, + + rhtml = /HTML$/i, + rinputs = /^(?:input|select|textarea|button)$/i, + rheader = /^h\d$/i, + + rnative = /^[^{]+\{\s*\[native \w/, + + // Easily-parseable/retrievable ID or TAG or CLASS selectors + rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/, + + rsibling = /[+~]/, + + // CSS escapes + // http://www.w3.org/TR/CSS21/syndata.html#escaped-characters + runescape = new RegExp( "\\\\[\\da-fA-F]{1,6}" + whitespace + "?|\\\\([^\\r\\n\\f])", "g" ), + funescape = function( escape, nonHex ) { + var high = "0x" + escape.slice( 1 ) - 0x10000; + + return nonHex ? + + // Strip the backslash prefix from a non-hex escape sequence + nonHex : + + // Replace a hexadecimal escape sequence with the encoded Unicode code point + // Support: IE <=11+ + // For values outside the Basic Multilingual Plane (BMP), manually construct a + // surrogate pair + high < 0 ? + String.fromCharCode( high + 0x10000 ) : + String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 ); + }, + + // CSS string/identifier serialization + // https://drafts.csswg.org/cssom/#common-serializing-idioms + rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g, + fcssescape = function( ch, asCodePoint ) { + if ( asCodePoint ) { + + // U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER + if ( ch === "\0" ) { + return "\uFFFD"; + } + + // Control characters and (dependent upon position) numbers get escaped as code points + return ch.slice( 0, -1 ) + "\\" + + ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " "; + } + + // Other potentially-special ASCII characters get backslash-escaped + return "\\" + ch; + }, + + // Used for iframes + // See setDocument() + // Removing the function wrapper causes a "Permission Denied" + // error in IE + unloadHandler = function() { + setDocument(); + }, + + inDisabledFieldset = addCombinator( + function( elem ) { + return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset"; + }, + { dir: "parentNode", next: "legend" } + ); + +// Optimize for push.apply( _, NodeList ) +try { + push.apply( + ( arr = slice.call( preferredDoc.childNodes ) ), + preferredDoc.childNodes + ); + + // Support: Android<4.0 + // Detect silently failing push.apply + // eslint-disable-next-line no-unused-expressions + arr[ preferredDoc.childNodes.length ].nodeType; +} catch ( e ) { + push = { apply: arr.length ? + + // Leverage slice if possible + function( target, els ) { + pushNative.apply( target, slice.call( els ) ); + } : + + // Support: IE<9 + // Otherwise append directly + function( target, els ) { + var j = target.length, + i = 0; + + // Can't trust NodeList.length + while ( ( target[ j++ ] = els[ i++ ] ) ) {} + target.length = j - 1; + } + }; +} + +function Sizzle( selector, context, results, seed ) { + var m, i, elem, nid, match, groups, newSelector, + newContext = context && context.ownerDocument, + + // nodeType defaults to 9, since context defaults to document + nodeType = context ? context.nodeType : 9; + + results = results || []; + + // Return early from calls with invalid selector or context + if ( typeof selector !== "string" || !selector || + nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) { + + return results; + } + + // Try to shortcut find operations (as opposed to filters) in HTML documents + if ( !seed ) { + setDocument( context ); + context = context || document; + + if ( documentIsHTML ) { + + // If the selector is sufficiently simple, try using a "get*By*" DOM method + // (excepting DocumentFragment context, where the methods don't exist) + if ( nodeType !== 11 && ( match = rquickExpr.exec( selector ) ) ) { + + // ID selector + if ( ( m = match[ 1 ] ) ) { + + // Document context + if ( nodeType === 9 ) { + if ( ( elem = context.getElementById( m ) ) ) { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( elem.id === m ) { + results.push( elem ); + return results; + } + } else { + return results; + } + + // Element context + } else { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( newContext && ( elem = newContext.getElementById( m ) ) && + contains( context, elem ) && + elem.id === m ) { + + results.push( elem ); + return results; + } + } + + // Type selector + } else if ( match[ 2 ] ) { + push.apply( results, context.getElementsByTagName( selector ) ); + return results; + + // Class selector + } else if ( ( m = match[ 3 ] ) && support.getElementsByClassName && + context.getElementsByClassName ) { + + push.apply( results, context.getElementsByClassName( m ) ); + return results; + } + } + + // Take advantage of querySelectorAll + if ( support.qsa && + !nonnativeSelectorCache[ selector + " " ] && + ( !rbuggyQSA || !rbuggyQSA.test( selector ) ) && + + // Support: IE 8 only + // Exclude object elements + ( nodeType !== 1 || context.nodeName.toLowerCase() !== "object" ) ) { + + newSelector = selector; + newContext = context; + + // qSA considers elements outside a scoping root when evaluating child or + // descendant combinators, which is not what we want. + // In such cases, we work around the behavior by prefixing every selector in the + // list with an ID selector referencing the scope context. + // The technique has to be used as well when a leading combinator is used + // as such selectors are not recognized by querySelectorAll. + // Thanks to Andrew Dupont for this technique. + if ( nodeType === 1 && + ( rdescend.test( selector ) || rcombinators.test( selector ) ) ) { + + // Expand context for sibling selectors + newContext = rsibling.test( selector ) && testContext( context.parentNode ) || + context; + + // We can use :scope instead of the ID hack if the browser + // supports it & if we're not changing the context. + if ( newContext !== context || !support.scope ) { + + // Capture the context ID, setting it first if necessary + if ( ( nid = context.getAttribute( "id" ) ) ) { + nid = nid.replace( rcssescape, fcssescape ); + } else { + context.setAttribute( "id", ( nid = expando ) ); + } + } + + // Prefix every selector in the list + groups = tokenize( selector ); + i = groups.length; + while ( i-- ) { + groups[ i ] = ( nid ? "#" + nid : ":scope" ) + " " + + toSelector( groups[ i ] ); + } + newSelector = groups.join( "," ); + } + + try { + push.apply( results, + newContext.querySelectorAll( newSelector ) + ); + return results; + } catch ( qsaError ) { + nonnativeSelectorCache( selector, true ); + } finally { + if ( nid === expando ) { + context.removeAttribute( "id" ); + } + } + } + } + } + + // All others + return select( selector.replace( rtrim, "$1" ), context, results, seed ); +} + +/** + * Create key-value caches of limited size + * @returns {function(string, object)} Returns the Object data after storing it on itself with + * property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength) + * deleting the oldest entry + */ +function createCache() { + var keys = []; + + function cache( key, value ) { + + // Use (key + " ") to avoid collision with native prototype properties (see Issue #157) + if ( keys.push( key + " " ) > Expr.cacheLength ) { + + // Only keep the most recent entries + delete cache[ keys.shift() ]; + } + return ( cache[ key + " " ] = value ); + } + return cache; +} + +/** + * Mark a function for special use by Sizzle + * @param {Function} fn The function to mark + */ +function markFunction( fn ) { + fn[ expando ] = true; + return fn; +} + +/** + * Support testing using an element + * @param {Function} fn Passed the created element and returns a boolean result + */ +function assert( fn ) { + var el = document.createElement( "fieldset" ); + + try { + return !!fn( el ); + } catch ( e ) { + return false; + } finally { + + // Remove from its parent by default + if ( el.parentNode ) { + el.parentNode.removeChild( el ); + } + + // release memory in IE + el = null; + } +} + +/** + * Adds the same handler for all of the specified attrs + * @param {String} attrs Pipe-separated list of attributes + * @param {Function} handler The method that will be applied + */ +function addHandle( attrs, handler ) { + var arr = attrs.split( "|" ), + i = arr.length; + + while ( i-- ) { + Expr.attrHandle[ arr[ i ] ] = handler; + } +} + +/** + * Checks document order of two siblings + * @param {Element} a + * @param {Element} b + * @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b + */ +function siblingCheck( a, b ) { + var cur = b && a, + diff = cur && a.nodeType === 1 && b.nodeType === 1 && + a.sourceIndex - b.sourceIndex; + + // Use IE sourceIndex if available on both nodes + if ( diff ) { + return diff; + } + + // Check if b follows a + if ( cur ) { + while ( ( cur = cur.nextSibling ) ) { + if ( cur === b ) { + return -1; + } + } + } + + return a ? 1 : -1; +} + +/** + * Returns a function to use in pseudos for input types + * @param {String} type + */ +function createInputPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for buttons + * @param {String} type + */ +function createButtonPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return ( name === "input" || name === "button" ) && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for :enabled/:disabled + * @param {Boolean} disabled true for :disabled; false for :enabled + */ +function createDisabledPseudo( disabled ) { + + // Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable + return function( elem ) { + + // Only certain elements can match :enabled or :disabled + // https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled + // https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled + if ( "form" in elem ) { + + // Check for inherited disabledness on relevant non-disabled elements: + // * listed form-associated elements in a disabled fieldset + // https://html.spec.whatwg.org/multipage/forms.html#category-listed + // https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled + // * option elements in a disabled optgroup + // https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled + // All such elements have a "form" property. + if ( elem.parentNode && elem.disabled === false ) { + + // Option elements defer to a parent optgroup if present + if ( "label" in elem ) { + if ( "label" in elem.parentNode ) { + return elem.parentNode.disabled === disabled; + } else { + return elem.disabled === disabled; + } + } + + // Support: IE 6 - 11 + // Use the isDisabled shortcut property to check for disabled fieldset ancestors + return elem.isDisabled === disabled || + + // Where there is no isDisabled, check manually + /* jshint -W018 */ + elem.isDisabled !== !disabled && + inDisabledFieldset( elem ) === disabled; + } + + return elem.disabled === disabled; + + // Try to winnow out elements that can't be disabled before trusting the disabled property. + // Some victims get caught in our net (label, legend, menu, track), but it shouldn't + // even exist on them, let alone have a boolean value. + } else if ( "label" in elem ) { + return elem.disabled === disabled; + } + + // Remaining elements are neither :enabled nor :disabled + return false; + }; +} + +/** + * Returns a function to use in pseudos for positionals + * @param {Function} fn + */ +function createPositionalPseudo( fn ) { + return markFunction( function( argument ) { + argument = +argument; + return markFunction( function( seed, matches ) { + var j, + matchIndexes = fn( [], seed.length, argument ), + i = matchIndexes.length; + + // Match elements found at the specified indexes + while ( i-- ) { + if ( seed[ ( j = matchIndexes[ i ] ) ] ) { + seed[ j ] = !( matches[ j ] = seed[ j ] ); + } + } + } ); + } ); +} + +/** + * Checks a node for validity as a Sizzle context + * @param {Element|Object=} context + * @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value + */ +function testContext( context ) { + return context && typeof context.getElementsByTagName !== "undefined" && context; +} + +// Expose support vars for convenience +support = Sizzle.support = {}; + +/** + * Detects XML nodes + * @param {Element|Object} elem An element or a document + * @returns {Boolean} True iff elem is a non-HTML XML node + */ +isXML = Sizzle.isXML = function( elem ) { + var namespace = elem.namespaceURI, + docElem = ( elem.ownerDocument || elem ).documentElement; + + // Support: IE <=8 + // Assume HTML when documentElement doesn't yet exist, such as inside loading iframes + // https://bugs.jquery.com/ticket/4833 + return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" ); +}; + +/** + * Sets document-related variables once based on the current document + * @param {Element|Object} [doc] An element or document object to use to set the document + * @returns {Object} Returns the current document + */ +setDocument = Sizzle.setDocument = function( node ) { + var hasCompare, subWindow, + doc = node ? node.ownerDocument || node : preferredDoc; + + // Return early if doc is invalid or already selected + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( doc == document || doc.nodeType !== 9 || !doc.documentElement ) { + return document; + } + + // Update global variables + document = doc; + docElem = document.documentElement; + documentIsHTML = !isXML( document ); + + // Support: IE 9 - 11+, Edge 12 - 18+ + // Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936) + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( preferredDoc != document && + ( subWindow = document.defaultView ) && subWindow.top !== subWindow ) { + + // Support: IE 11, Edge + if ( subWindow.addEventListener ) { + subWindow.addEventListener( "unload", unloadHandler, false ); + + // Support: IE 9 - 10 only + } else if ( subWindow.attachEvent ) { + subWindow.attachEvent( "onunload", unloadHandler ); + } + } + + // Support: IE 8 - 11+, Edge 12 - 18+, Chrome <=16 - 25 only, Firefox <=3.6 - 31 only, + // Safari 4 - 5 only, Opera <=11.6 - 12.x only + // IE/Edge & older browsers don't support the :scope pseudo-class. + // Support: Safari 6.0 only + // Safari 6.0 supports :scope but it's an alias of :root there. + support.scope = assert( function( el ) { + docElem.appendChild( el ).appendChild( document.createElement( "div" ) ); + return typeof el.querySelectorAll !== "undefined" && + !el.querySelectorAll( ":scope fieldset div" ).length; + } ); + + /* Attributes + ---------------------------------------------------------------------- */ + + // Support: IE<8 + // Verify that getAttribute really returns attributes and not properties + // (excepting IE8 booleans) + support.attributes = assert( function( el ) { + el.className = "i"; + return !el.getAttribute( "className" ); + } ); + + /* getElement(s)By* + ---------------------------------------------------------------------- */ + + // Check if getElementsByTagName("*") returns only elements + support.getElementsByTagName = assert( function( el ) { + el.appendChild( document.createComment( "" ) ); + return !el.getElementsByTagName( "*" ).length; + } ); + + // Support: IE<9 + support.getElementsByClassName = rnative.test( document.getElementsByClassName ); + + // Support: IE<10 + // Check if getElementById returns elements by name + // The broken getElementById methods don't pick up programmatically-set names, + // so use a roundabout getElementsByName test + support.getById = assert( function( el ) { + docElem.appendChild( el ).id = expando; + return !document.getElementsByName || !document.getElementsByName( expando ).length; + } ); + + // ID filter and find + if ( support.getById ) { + Expr.filter[ "ID" ] = function( id ) { + var attrId = id.replace( runescape, funescape ); + return function( elem ) { + return elem.getAttribute( "id" ) === attrId; + }; + }; + Expr.find[ "ID" ] = function( id, context ) { + if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { + var elem = context.getElementById( id ); + return elem ? [ elem ] : []; + } + }; + } else { + Expr.filter[ "ID" ] = function( id ) { + var attrId = id.replace( runescape, funescape ); + return function( elem ) { + var node = typeof elem.getAttributeNode !== "undefined" && + elem.getAttributeNode( "id" ); + return node && node.value === attrId; + }; + }; + + // Support: IE 6 - 7 only + // getElementById is not reliable as a find shortcut + Expr.find[ "ID" ] = function( id, context ) { + if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { + var node, i, elems, + elem = context.getElementById( id ); + + if ( elem ) { + + // Verify the id attribute + node = elem.getAttributeNode( "id" ); + if ( node && node.value === id ) { + return [ elem ]; + } + + // Fall back on getElementsByName + elems = context.getElementsByName( id ); + i = 0; + while ( ( elem = elems[ i++ ] ) ) { + node = elem.getAttributeNode( "id" ); + if ( node && node.value === id ) { + return [ elem ]; + } + } + } + + return []; + } + }; + } + + // Tag + Expr.find[ "TAG" ] = support.getElementsByTagName ? + function( tag, context ) { + if ( typeof context.getElementsByTagName !== "undefined" ) { + return context.getElementsByTagName( tag ); + + // DocumentFragment nodes don't have gEBTN + } else if ( support.qsa ) { + return context.querySelectorAll( tag ); + } + } : + + function( tag, context ) { + var elem, + tmp = [], + i = 0, + + // By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too + results = context.getElementsByTagName( tag ); + + // Filter out possible comments + if ( tag === "*" ) { + while ( ( elem = results[ i++ ] ) ) { + if ( elem.nodeType === 1 ) { + tmp.push( elem ); + } + } + + return tmp; + } + return results; + }; + + // Class + Expr.find[ "CLASS" ] = support.getElementsByClassName && function( className, context ) { + if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) { + return context.getElementsByClassName( className ); + } + }; + + /* QSA/matchesSelector + ---------------------------------------------------------------------- */ + + // QSA and matchesSelector support + + // matchesSelector(:active) reports false when true (IE9/Opera 11.5) + rbuggyMatches = []; + + // qSa(:focus) reports false when true (Chrome 21) + // We allow this because of a bug in IE8/9 that throws an error + // whenever `document.activeElement` is accessed on an iframe + // So, we allow :focus to pass through QSA all the time to avoid the IE error + // See https://bugs.jquery.com/ticket/13378 + rbuggyQSA = []; + + if ( ( support.qsa = rnative.test( document.querySelectorAll ) ) ) { + + // Build QSA regex + // Regex strategy adopted from Diego Perini + assert( function( el ) { + + var input; + + // Select is set to empty string on purpose + // This is to test IE's treatment of not explicitly + // setting a boolean content attribute, + // since its presence should be enough + // https://bugs.jquery.com/ticket/12359 + docElem.appendChild( el ).innerHTML = "" + + ""; + + // Support: IE8, Opera 11-12.16 + // Nothing should be selected when empty strings follow ^= or $= or *= + // The test attribute must be unknown in Opera but "safe" for WinRT + // https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section + if ( el.querySelectorAll( "[msallowcapture^='']" ).length ) { + rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" ); + } + + // Support: IE8 + // Boolean attributes and "value" are not treated correctly + if ( !el.querySelectorAll( "[selected]" ).length ) { + rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" ); + } + + // Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+ + if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) { + rbuggyQSA.push( "~=" ); + } + + // Support: IE 11+, Edge 15 - 18+ + // IE 11/Edge don't find elements on a `[name='']` query in some cases. + // Adding a temporary attribute to the document before the selection works + // around the issue. + // Interestingly, IE 10 & older don't seem to have the issue. + input = document.createElement( "input" ); + input.setAttribute( "name", "" ); + el.appendChild( input ); + if ( !el.querySelectorAll( "[name='']" ).length ) { + rbuggyQSA.push( "\\[" + whitespace + "*name" + whitespace + "*=" + + whitespace + "*(?:''|\"\")" ); + } + + // Webkit/Opera - :checked should return selected option elements + // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked + // IE8 throws error here and will not see later tests + if ( !el.querySelectorAll( ":checked" ).length ) { + rbuggyQSA.push( ":checked" ); + } + + // Support: Safari 8+, iOS 8+ + // https://bugs.webkit.org/show_bug.cgi?id=136851 + // In-page `selector#id sibling-combinator selector` fails + if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) { + rbuggyQSA.push( ".#.+[+~]" ); + } + + // Support: Firefox <=3.6 - 5 only + // Old Firefox doesn't throw on a badly-escaped identifier. + el.querySelectorAll( "\\\f" ); + rbuggyQSA.push( "[\\r\\n\\f]" ); + } ); + + assert( function( el ) { + el.innerHTML = "" + + ""; + + // Support: Windows 8 Native Apps + // The type and name attributes are restricted during .innerHTML assignment + var input = document.createElement( "input" ); + input.setAttribute( "type", "hidden" ); + el.appendChild( input ).setAttribute( "name", "D" ); + + // Support: IE8 + // Enforce case-sensitivity of name attribute + if ( el.querySelectorAll( "[name=d]" ).length ) { + rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" ); + } + + // FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled) + // IE8 throws error here and will not see later tests + if ( el.querySelectorAll( ":enabled" ).length !== 2 ) { + rbuggyQSA.push( ":enabled", ":disabled" ); + } + + // Support: IE9-11+ + // IE's :disabled selector does not pick up the children of disabled fieldsets + docElem.appendChild( el ).disabled = true; + if ( el.querySelectorAll( ":disabled" ).length !== 2 ) { + rbuggyQSA.push( ":enabled", ":disabled" ); + } + + // Support: Opera 10 - 11 only + // Opera 10-11 does not throw on post-comma invalid pseudos + el.querySelectorAll( "*,:x" ); + rbuggyQSA.push( ",.*:" ); + } ); + } + + if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches || + docElem.webkitMatchesSelector || + docElem.mozMatchesSelector || + docElem.oMatchesSelector || + docElem.msMatchesSelector ) ) ) ) { + + assert( function( el ) { + + // Check to see if it's possible to do matchesSelector + // on a disconnected node (IE 9) + support.disconnectedMatch = matches.call( el, "*" ); + + // This should fail with an exception + // Gecko does not error, returns false instead + matches.call( el, "[s!='']:x" ); + rbuggyMatches.push( "!=", pseudos ); + } ); + } + + rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) ); + rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) ); + + /* Contains + ---------------------------------------------------------------------- */ + hasCompare = rnative.test( docElem.compareDocumentPosition ); + + // Element contains another + // Purposefully self-exclusive + // As in, an element does not contain itself + contains = hasCompare || rnative.test( docElem.contains ) ? + function( a, b ) { + var adown = a.nodeType === 9 ? a.documentElement : a, + bup = b && b.parentNode; + return a === bup || !!( bup && bup.nodeType === 1 && ( + adown.contains ? + adown.contains( bup ) : + a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16 + ) ); + } : + function( a, b ) { + if ( b ) { + while ( ( b = b.parentNode ) ) { + if ( b === a ) { + return true; + } + } + } + return false; + }; + + /* Sorting + ---------------------------------------------------------------------- */ + + // Document order sorting + sortOrder = hasCompare ? + function( a, b ) { + + // Flag for duplicate removal + if ( a === b ) { + hasDuplicate = true; + return 0; + } + + // Sort on method existence if only one input has compareDocumentPosition + var compare = !a.compareDocumentPosition - !b.compareDocumentPosition; + if ( compare ) { + return compare; + } + + // Calculate position if both inputs belong to the same document + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + compare = ( a.ownerDocument || a ) == ( b.ownerDocument || b ) ? + a.compareDocumentPosition( b ) : + + // Otherwise we know they are disconnected + 1; + + // Disconnected nodes + if ( compare & 1 || + ( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) { + + // Choose the first element that is related to our preferred document + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( a == document || a.ownerDocument == preferredDoc && + contains( preferredDoc, a ) ) { + return -1; + } + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( b == document || b.ownerDocument == preferredDoc && + contains( preferredDoc, b ) ) { + return 1; + } + + // Maintain original order + return sortInput ? + ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : + 0; + } + + return compare & 4 ? -1 : 1; + } : + function( a, b ) { + + // Exit early if the nodes are identical + if ( a === b ) { + hasDuplicate = true; + return 0; + } + + var cur, + i = 0, + aup = a.parentNode, + bup = b.parentNode, + ap = [ a ], + bp = [ b ]; + + // Parentless nodes are either documents or disconnected + if ( !aup || !bup ) { + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + /* eslint-disable eqeqeq */ + return a == document ? -1 : + b == document ? 1 : + /* eslint-enable eqeqeq */ + aup ? -1 : + bup ? 1 : + sortInput ? + ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : + 0; + + // If the nodes are siblings, we can do a quick check + } else if ( aup === bup ) { + return siblingCheck( a, b ); + } + + // Otherwise we need full lists of their ancestors for comparison + cur = a; + while ( ( cur = cur.parentNode ) ) { + ap.unshift( cur ); + } + cur = b; + while ( ( cur = cur.parentNode ) ) { + bp.unshift( cur ); + } + + // Walk down the tree looking for a discrepancy + while ( ap[ i ] === bp[ i ] ) { + i++; + } + + return i ? + + // Do a sibling check if the nodes have a common ancestor + siblingCheck( ap[ i ], bp[ i ] ) : + + // Otherwise nodes in our document sort first + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + /* eslint-disable eqeqeq */ + ap[ i ] == preferredDoc ? -1 : + bp[ i ] == preferredDoc ? 1 : + /* eslint-enable eqeqeq */ + 0; + }; + + return document; +}; + +Sizzle.matches = function( expr, elements ) { + return Sizzle( expr, null, null, elements ); +}; + +Sizzle.matchesSelector = function( elem, expr ) { + setDocument( elem ); + + if ( support.matchesSelector && documentIsHTML && + !nonnativeSelectorCache[ expr + " " ] && + ( !rbuggyMatches || !rbuggyMatches.test( expr ) ) && + ( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) { + + try { + var ret = matches.call( elem, expr ); + + // IE 9's matchesSelector returns false on disconnected nodes + if ( ret || support.disconnectedMatch || + + // As well, disconnected nodes are said to be in a document + // fragment in IE 9 + elem.document && elem.document.nodeType !== 11 ) { + return ret; + } + } catch ( e ) { + nonnativeSelectorCache( expr, true ); + } + } + + return Sizzle( expr, document, null, [ elem ] ).length > 0; +}; + +Sizzle.contains = function( context, elem ) { + + // Set document vars if needed + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( ( context.ownerDocument || context ) != document ) { + setDocument( context ); + } + return contains( context, elem ); +}; + +Sizzle.attr = function( elem, name ) { + + // Set document vars if needed + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( ( elem.ownerDocument || elem ) != document ) { + setDocument( elem ); + } + + var fn = Expr.attrHandle[ name.toLowerCase() ], + + // Don't get fooled by Object.prototype properties (jQuery #13807) + val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ? + fn( elem, name, !documentIsHTML ) : + undefined; + + return val !== undefined ? + val : + support.attributes || !documentIsHTML ? + elem.getAttribute( name ) : + ( val = elem.getAttributeNode( name ) ) && val.specified ? + val.value : + null; +}; + +Sizzle.escape = function( sel ) { + return ( sel + "" ).replace( rcssescape, fcssescape ); +}; + +Sizzle.error = function( msg ) { + throw new Error( "Syntax error, unrecognized expression: " + msg ); +}; + +/** + * Document sorting and removing duplicates + * @param {ArrayLike} results + */ +Sizzle.uniqueSort = function( results ) { + var elem, + duplicates = [], + j = 0, + i = 0; + + // Unless we *know* we can detect duplicates, assume their presence + hasDuplicate = !support.detectDuplicates; + sortInput = !support.sortStable && results.slice( 0 ); + results.sort( sortOrder ); + + if ( hasDuplicate ) { + while ( ( elem = results[ i++ ] ) ) { + if ( elem === results[ i ] ) { + j = duplicates.push( i ); + } + } + while ( j-- ) { + results.splice( duplicates[ j ], 1 ); + } + } + + // Clear input after sorting to release objects + // See https://github.com/jquery/sizzle/pull/225 + sortInput = null; + + return results; +}; + +/** + * Utility function for retrieving the text value of an array of DOM nodes + * @param {Array|Element} elem + */ +getText = Sizzle.getText = function( elem ) { + var node, + ret = "", + i = 0, + nodeType = elem.nodeType; + + if ( !nodeType ) { + + // If no nodeType, this is expected to be an array + while ( ( node = elem[ i++ ] ) ) { + + // Do not traverse comment nodes + ret += getText( node ); + } + } else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) { + + // Use textContent for elements + // innerText usage removed for consistency of new lines (jQuery #11153) + if ( typeof elem.textContent === "string" ) { + return elem.textContent; + } else { + + // Traverse its children + for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { + ret += getText( elem ); + } + } + } else if ( nodeType === 3 || nodeType === 4 ) { + return elem.nodeValue; + } + + // Do not include comment or processing instruction nodes + + return ret; +}; + +Expr = Sizzle.selectors = { + + // Can be adjusted by the user + cacheLength: 50, + + createPseudo: markFunction, + + match: matchExpr, + + attrHandle: {}, + + find: {}, + + relative: { + ">": { dir: "parentNode", first: true }, + " ": { dir: "parentNode" }, + "+": { dir: "previousSibling", first: true }, + "~": { dir: "previousSibling" } + }, + + preFilter: { + "ATTR": function( match ) { + match[ 1 ] = match[ 1 ].replace( runescape, funescape ); + + // Move the given value to match[3] whether quoted or unquoted + match[ 3 ] = ( match[ 3 ] || match[ 4 ] || + match[ 5 ] || "" ).replace( runescape, funescape ); + + if ( match[ 2 ] === "~=" ) { + match[ 3 ] = " " + match[ 3 ] + " "; + } + + return match.slice( 0, 4 ); + }, + + "CHILD": function( match ) { + + /* matches from matchExpr["CHILD"] + 1 type (only|nth|...) + 2 what (child|of-type) + 3 argument (even|odd|\d*|\d*n([+-]\d+)?|...) + 4 xn-component of xn+y argument ([+-]?\d*n|) + 5 sign of xn-component + 6 x of xn-component + 7 sign of y-component + 8 y of y-component + */ + match[ 1 ] = match[ 1 ].toLowerCase(); + + if ( match[ 1 ].slice( 0, 3 ) === "nth" ) { + + // nth-* requires argument + if ( !match[ 3 ] ) { + Sizzle.error( match[ 0 ] ); + } + + // numeric x and y parameters for Expr.filter.CHILD + // remember that false/true cast respectively to 0/1 + match[ 4 ] = +( match[ 4 ] ? + match[ 5 ] + ( match[ 6 ] || 1 ) : + 2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) ); + match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" ); + + // other types prohibit arguments + } else if ( match[ 3 ] ) { + Sizzle.error( match[ 0 ] ); + } + + return match; + }, + + "PSEUDO": function( match ) { + var excess, + unquoted = !match[ 6 ] && match[ 2 ]; + + if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) { + return null; + } + + // Accept quoted arguments as-is + if ( match[ 3 ] ) { + match[ 2 ] = match[ 4 ] || match[ 5 ] || ""; + + // Strip excess characters from unquoted arguments + } else if ( unquoted && rpseudo.test( unquoted ) && + + // Get excess from tokenize (recursively) + ( excess = tokenize( unquoted, true ) ) && + + // advance to the next closing parenthesis + ( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) { + + // excess is a negative index + match[ 0 ] = match[ 0 ].slice( 0, excess ); + match[ 2 ] = unquoted.slice( 0, excess ); + } + + // Return only captures needed by the pseudo filter method (type and argument) + return match.slice( 0, 3 ); + } + }, + + filter: { + + "TAG": function( nodeNameSelector ) { + var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase(); + return nodeNameSelector === "*" ? + function() { + return true; + } : + function( elem ) { + return elem.nodeName && elem.nodeName.toLowerCase() === nodeName; + }; + }, + + "CLASS": function( className ) { + var pattern = classCache[ className + " " ]; + + return pattern || + ( pattern = new RegExp( "(^|" + whitespace + + ")" + className + "(" + whitespace + "|$)" ) ) && classCache( + className, function( elem ) { + return pattern.test( + typeof elem.className === "string" && elem.className || + typeof elem.getAttribute !== "undefined" && + elem.getAttribute( "class" ) || + "" + ); + } ); + }, + + "ATTR": function( name, operator, check ) { + return function( elem ) { + var result = Sizzle.attr( elem, name ); + + if ( result == null ) { + return operator === "!="; + } + if ( !operator ) { + return true; + } + + result += ""; + + /* eslint-disable max-len */ + + return operator === "=" ? result === check : + operator === "!=" ? result !== check : + operator === "^=" ? check && result.indexOf( check ) === 0 : + operator === "*=" ? check && result.indexOf( check ) > -1 : + operator === "$=" ? check && result.slice( -check.length ) === check : + operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 : + operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" : + false; + /* eslint-enable max-len */ + + }; + }, + + "CHILD": function( type, what, _argument, first, last ) { + var simple = type.slice( 0, 3 ) !== "nth", + forward = type.slice( -4 ) !== "last", + ofType = what === "of-type"; + + return first === 1 && last === 0 ? + + // Shortcut for :nth-*(n) + function( elem ) { + return !!elem.parentNode; + } : + + function( elem, _context, xml ) { + var cache, uniqueCache, outerCache, node, nodeIndex, start, + dir = simple !== forward ? "nextSibling" : "previousSibling", + parent = elem.parentNode, + name = ofType && elem.nodeName.toLowerCase(), + useCache = !xml && !ofType, + diff = false; + + if ( parent ) { + + // :(first|last|only)-(child|of-type) + if ( simple ) { + while ( dir ) { + node = elem; + while ( ( node = node[ dir ] ) ) { + if ( ofType ? + node.nodeName.toLowerCase() === name : + node.nodeType === 1 ) { + + return false; + } + } + + // Reverse direction for :only-* (if we haven't yet done so) + start = dir = type === "only" && !start && "nextSibling"; + } + return true; + } + + start = [ forward ? parent.firstChild : parent.lastChild ]; + + // non-xml :nth-child(...) stores cache data on `parent` + if ( forward && useCache ) { + + // Seek `elem` from a previously-cached index + + // ...in a gzip-friendly way + node = parent; + outerCache = node[ expando ] || ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + cache = uniqueCache[ type ] || []; + nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; + diff = nodeIndex && cache[ 2 ]; + node = nodeIndex && parent.childNodes[ nodeIndex ]; + + while ( ( node = ++nodeIndex && node && node[ dir ] || + + // Fallback to seeking `elem` from the start + ( diff = nodeIndex = 0 ) || start.pop() ) ) { + + // When found, cache indexes on `parent` and break + if ( node.nodeType === 1 && ++diff && node === elem ) { + uniqueCache[ type ] = [ dirruns, nodeIndex, diff ]; + break; + } + } + + } else { + + // Use previously-cached element index if available + if ( useCache ) { + + // ...in a gzip-friendly way + node = elem; + outerCache = node[ expando ] || ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + cache = uniqueCache[ type ] || []; + nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; + diff = nodeIndex; + } + + // xml :nth-child(...) + // or :nth-last-child(...) or :nth(-last)?-of-type(...) + if ( diff === false ) { + + // Use the same loop as above to seek `elem` from the start + while ( ( node = ++nodeIndex && node && node[ dir ] || + ( diff = nodeIndex = 0 ) || start.pop() ) ) { + + if ( ( ofType ? + node.nodeName.toLowerCase() === name : + node.nodeType === 1 ) && + ++diff ) { + + // Cache the index of each encountered element + if ( useCache ) { + outerCache = node[ expando ] || + ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + uniqueCache[ type ] = [ dirruns, diff ]; + } + + if ( node === elem ) { + break; + } + } + } + } + } + + // Incorporate the offset, then check against cycle size + diff -= last; + return diff === first || ( diff % first === 0 && diff / first >= 0 ); + } + }; + }, + + "PSEUDO": function( pseudo, argument ) { + + // pseudo-class names are case-insensitive + // http://www.w3.org/TR/selectors/#pseudo-classes + // Prioritize by case sensitivity in case custom pseudos are added with uppercase letters + // Remember that setFilters inherits from pseudos + var args, + fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] || + Sizzle.error( "unsupported pseudo: " + pseudo ); + + // The user may use createPseudo to indicate that + // arguments are needed to create the filter function + // just as Sizzle does + if ( fn[ expando ] ) { + return fn( argument ); + } + + // But maintain support for old signatures + if ( fn.length > 1 ) { + args = [ pseudo, pseudo, "", argument ]; + return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ? + markFunction( function( seed, matches ) { + var idx, + matched = fn( seed, argument ), + i = matched.length; + while ( i-- ) { + idx = indexOf( seed, matched[ i ] ); + seed[ idx ] = !( matches[ idx ] = matched[ i ] ); + } + } ) : + function( elem ) { + return fn( elem, 0, args ); + }; + } + + return fn; + } + }, + + pseudos: { + + // Potentially complex pseudos + "not": markFunction( function( selector ) { + + // Trim the selector passed to compile + // to avoid treating leading and trailing + // spaces as combinators + var input = [], + results = [], + matcher = compile( selector.replace( rtrim, "$1" ) ); + + return matcher[ expando ] ? + markFunction( function( seed, matches, _context, xml ) { + var elem, + unmatched = matcher( seed, null, xml, [] ), + i = seed.length; + + // Match elements unmatched by `matcher` + while ( i-- ) { + if ( ( elem = unmatched[ i ] ) ) { + seed[ i ] = !( matches[ i ] = elem ); + } + } + } ) : + function( elem, _context, xml ) { + input[ 0 ] = elem; + matcher( input, null, xml, results ); + + // Don't keep the element (issue #299) + input[ 0 ] = null; + return !results.pop(); + }; + } ), + + "has": markFunction( function( selector ) { + return function( elem ) { + return Sizzle( selector, elem ).length > 0; + }; + } ), + + "contains": markFunction( function( text ) { + text = text.replace( runescape, funescape ); + return function( elem ) { + return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1; + }; + } ), + + // "Whether an element is represented by a :lang() selector + // is based solely on the element's language value + // being equal to the identifier C, + // or beginning with the identifier C immediately followed by "-". + // The matching of C against the element's language value is performed case-insensitively. + // The identifier C does not have to be a valid language name." + // http://www.w3.org/TR/selectors/#lang-pseudo + "lang": markFunction( function( lang ) { + + // lang value must be a valid identifier + if ( !ridentifier.test( lang || "" ) ) { + Sizzle.error( "unsupported lang: " + lang ); + } + lang = lang.replace( runescape, funescape ).toLowerCase(); + return function( elem ) { + var elemLang; + do { + if ( ( elemLang = documentIsHTML ? + elem.lang : + elem.getAttribute( "xml:lang" ) || elem.getAttribute( "lang" ) ) ) { + + elemLang = elemLang.toLowerCase(); + return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0; + } + } while ( ( elem = elem.parentNode ) && elem.nodeType === 1 ); + return false; + }; + } ), + + // Miscellaneous + "target": function( elem ) { + var hash = window.location && window.location.hash; + return hash && hash.slice( 1 ) === elem.id; + }, + + "root": function( elem ) { + return elem === docElem; + }, + + "focus": function( elem ) { + return elem === document.activeElement && + ( !document.hasFocus || document.hasFocus() ) && + !!( elem.type || elem.href || ~elem.tabIndex ); + }, + + // Boolean properties + "enabled": createDisabledPseudo( false ), + "disabled": createDisabledPseudo( true ), + + "checked": function( elem ) { + + // In CSS3, :checked should return both checked and selected elements + // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked + var nodeName = elem.nodeName.toLowerCase(); + return ( nodeName === "input" && !!elem.checked ) || + ( nodeName === "option" && !!elem.selected ); + }, + + "selected": function( elem ) { + + // Accessing this property makes selected-by-default + // options in Safari work properly + if ( elem.parentNode ) { + // eslint-disable-next-line no-unused-expressions + elem.parentNode.selectedIndex; + } + + return elem.selected === true; + }, + + // Contents + "empty": function( elem ) { + + // http://www.w3.org/TR/selectors/#empty-pseudo + // :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5), + // but not by others (comment: 8; processing instruction: 7; etc.) + // nodeType < 6 works because attributes (2) do not appear as children + for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { + if ( elem.nodeType < 6 ) { + return false; + } + } + return true; + }, + + "parent": function( elem ) { + return !Expr.pseudos[ "empty" ]( elem ); + }, + + // Element/input types + "header": function( elem ) { + return rheader.test( elem.nodeName ); + }, + + "input": function( elem ) { + return rinputs.test( elem.nodeName ); + }, + + "button": function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === "button" || name === "button"; + }, + + "text": function( elem ) { + var attr; + return elem.nodeName.toLowerCase() === "input" && + elem.type === "text" && + + // Support: IE<8 + // New HTML5 attribute values (e.g., "search") appear with elem.type === "text" + ( ( attr = elem.getAttribute( "type" ) ) == null || + attr.toLowerCase() === "text" ); + }, + + // Position-in-collection + "first": createPositionalPseudo( function() { + return [ 0 ]; + } ), + + "last": createPositionalPseudo( function( _matchIndexes, length ) { + return [ length - 1 ]; + } ), + + "eq": createPositionalPseudo( function( _matchIndexes, length, argument ) { + return [ argument < 0 ? argument + length : argument ]; + } ), + + "even": createPositionalPseudo( function( matchIndexes, length ) { + var i = 0; + for ( ; i < length; i += 2 ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "odd": createPositionalPseudo( function( matchIndexes, length ) { + var i = 1; + for ( ; i < length; i += 2 ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "lt": createPositionalPseudo( function( matchIndexes, length, argument ) { + var i = argument < 0 ? + argument + length : + argument > length ? + length : + argument; + for ( ; --i >= 0; ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "gt": createPositionalPseudo( function( matchIndexes, length, argument ) { + var i = argument < 0 ? argument + length : argument; + for ( ; ++i < length; ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ) + } +}; + +Expr.pseudos[ "nth" ] = Expr.pseudos[ "eq" ]; + +// Add button/input type pseudos +for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) { + Expr.pseudos[ i ] = createInputPseudo( i ); +} +for ( i in { submit: true, reset: true } ) { + Expr.pseudos[ i ] = createButtonPseudo( i ); +} + +// Easy API for creating new setFilters +function setFilters() {} +setFilters.prototype = Expr.filters = Expr.pseudos; +Expr.setFilters = new setFilters(); + +tokenize = Sizzle.tokenize = function( selector, parseOnly ) { + var matched, match, tokens, type, + soFar, groups, preFilters, + cached = tokenCache[ selector + " " ]; + + if ( cached ) { + return parseOnly ? 0 : cached.slice( 0 ); + } + + soFar = selector; + groups = []; + preFilters = Expr.preFilter; + + while ( soFar ) { + + // Comma and first run + if ( !matched || ( match = rcomma.exec( soFar ) ) ) { + if ( match ) { + + // Don't consume trailing commas as valid + soFar = soFar.slice( match[ 0 ].length ) || soFar; + } + groups.push( ( tokens = [] ) ); + } + + matched = false; + + // Combinators + if ( ( match = rcombinators.exec( soFar ) ) ) { + matched = match.shift(); + tokens.push( { + value: matched, + + // Cast descendant combinators to space + type: match[ 0 ].replace( rtrim, " " ) + } ); + soFar = soFar.slice( matched.length ); + } + + // Filters + for ( type in Expr.filter ) { + if ( ( match = matchExpr[ type ].exec( soFar ) ) && ( !preFilters[ type ] || + ( match = preFilters[ type ]( match ) ) ) ) { + matched = match.shift(); + tokens.push( { + value: matched, + type: type, + matches: match + } ); + soFar = soFar.slice( matched.length ); + } + } + + if ( !matched ) { + break; + } + } + + // Return the length of the invalid excess + // if we're just parsing + // Otherwise, throw an error or return tokens + return parseOnly ? + soFar.length : + soFar ? + Sizzle.error( selector ) : + + // Cache the tokens + tokenCache( selector, groups ).slice( 0 ); +}; + +function toSelector( tokens ) { + var i = 0, + len = tokens.length, + selector = ""; + for ( ; i < len; i++ ) { + selector += tokens[ i ].value; + } + return selector; +} + +function addCombinator( matcher, combinator, base ) { + var dir = combinator.dir, + skip = combinator.next, + key = skip || dir, + checkNonElements = base && key === "parentNode", + doneName = done++; + + return combinator.first ? + + // Check against closest ancestor/preceding element + function( elem, context, xml ) { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + return matcher( elem, context, xml ); + } + } + return false; + } : + + // Check against all ancestor/preceding elements + function( elem, context, xml ) { + var oldCache, uniqueCache, outerCache, + newCache = [ dirruns, doneName ]; + + // We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching + if ( xml ) { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + if ( matcher( elem, context, xml ) ) { + return true; + } + } + } + } else { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + outerCache = elem[ expando ] || ( elem[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ elem.uniqueID ] || + ( outerCache[ elem.uniqueID ] = {} ); + + if ( skip && skip === elem.nodeName.toLowerCase() ) { + elem = elem[ dir ] || elem; + } else if ( ( oldCache = uniqueCache[ key ] ) && + oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) { + + // Assign to newCache so results back-propagate to previous elements + return ( newCache[ 2 ] = oldCache[ 2 ] ); + } else { + + // Reuse newcache so results back-propagate to previous elements + uniqueCache[ key ] = newCache; + + // A match means we're done; a fail means we have to keep checking + if ( ( newCache[ 2 ] = matcher( elem, context, xml ) ) ) { + return true; + } + } + } + } + } + return false; + }; +} + +function elementMatcher( matchers ) { + return matchers.length > 1 ? + function( elem, context, xml ) { + var i = matchers.length; + while ( i-- ) { + if ( !matchers[ i ]( elem, context, xml ) ) { + return false; + } + } + return true; + } : + matchers[ 0 ]; +} + +function multipleContexts( selector, contexts, results ) { + var i = 0, + len = contexts.length; + for ( ; i < len; i++ ) { + Sizzle( selector, contexts[ i ], results ); + } + return results; +} + +function condense( unmatched, map, filter, context, xml ) { + var elem, + newUnmatched = [], + i = 0, + len = unmatched.length, + mapped = map != null; + + for ( ; i < len; i++ ) { + if ( ( elem = unmatched[ i ] ) ) { + if ( !filter || filter( elem, context, xml ) ) { + newUnmatched.push( elem ); + if ( mapped ) { + map.push( i ); + } + } + } + } + + return newUnmatched; +} + +function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) { + if ( postFilter && !postFilter[ expando ] ) { + postFilter = setMatcher( postFilter ); + } + if ( postFinder && !postFinder[ expando ] ) { + postFinder = setMatcher( postFinder, postSelector ); + } + return markFunction( function( seed, results, context, xml ) { + var temp, i, elem, + preMap = [], + postMap = [], + preexisting = results.length, + + // Get initial elements from seed or context + elems = seed || multipleContexts( + selector || "*", + context.nodeType ? [ context ] : context, + [] + ), + + // Prefilter to get matcher input, preserving a map for seed-results synchronization + matcherIn = preFilter && ( seed || !selector ) ? + condense( elems, preMap, preFilter, context, xml ) : + elems, + + matcherOut = matcher ? + + // If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results, + postFinder || ( seed ? preFilter : preexisting || postFilter ) ? + + // ...intermediate processing is necessary + [] : + + // ...otherwise use results directly + results : + matcherIn; + + // Find primary matches + if ( matcher ) { + matcher( matcherIn, matcherOut, context, xml ); + } + + // Apply postFilter + if ( postFilter ) { + temp = condense( matcherOut, postMap ); + postFilter( temp, [], context, xml ); + + // Un-match failing elements by moving them back to matcherIn + i = temp.length; + while ( i-- ) { + if ( ( elem = temp[ i ] ) ) { + matcherOut[ postMap[ i ] ] = !( matcherIn[ postMap[ i ] ] = elem ); + } + } + } + + if ( seed ) { + if ( postFinder || preFilter ) { + if ( postFinder ) { + + // Get the final matcherOut by condensing this intermediate into postFinder contexts + temp = []; + i = matcherOut.length; + while ( i-- ) { + if ( ( elem = matcherOut[ i ] ) ) { + + // Restore matcherIn since elem is not yet a final match + temp.push( ( matcherIn[ i ] = elem ) ); + } + } + postFinder( null, ( matcherOut = [] ), temp, xml ); + } + + // Move matched elements from seed to results to keep them synchronized + i = matcherOut.length; + while ( i-- ) { + if ( ( elem = matcherOut[ i ] ) && + ( temp = postFinder ? indexOf( seed, elem ) : preMap[ i ] ) > -1 ) { + + seed[ temp ] = !( results[ temp ] = elem ); + } + } + } + + // Add elements to results, through postFinder if defined + } else { + matcherOut = condense( + matcherOut === results ? + matcherOut.splice( preexisting, matcherOut.length ) : + matcherOut + ); + if ( postFinder ) { + postFinder( null, results, matcherOut, xml ); + } else { + push.apply( results, matcherOut ); + } + } + } ); +} + +function matcherFromTokens( tokens ) { + var checkContext, matcher, j, + len = tokens.length, + leadingRelative = Expr.relative[ tokens[ 0 ].type ], + implicitRelative = leadingRelative || Expr.relative[ " " ], + i = leadingRelative ? 1 : 0, + + // The foundational matcher ensures that elements are reachable from top-level context(s) + matchContext = addCombinator( function( elem ) { + return elem === checkContext; + }, implicitRelative, true ), + matchAnyContext = addCombinator( function( elem ) { + return indexOf( checkContext, elem ) > -1; + }, implicitRelative, true ), + matchers = [ function( elem, context, xml ) { + var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || ( + ( checkContext = context ).nodeType ? + matchContext( elem, context, xml ) : + matchAnyContext( elem, context, xml ) ); + + // Avoid hanging onto element (issue #299) + checkContext = null; + return ret; + } ]; + + for ( ; i < len; i++ ) { + if ( ( matcher = Expr.relative[ tokens[ i ].type ] ) ) { + matchers = [ addCombinator( elementMatcher( matchers ), matcher ) ]; + } else { + matcher = Expr.filter[ tokens[ i ].type ].apply( null, tokens[ i ].matches ); + + // Return special upon seeing a positional matcher + if ( matcher[ expando ] ) { + + // Find the next relative operator (if any) for proper handling + j = ++i; + for ( ; j < len; j++ ) { + if ( Expr.relative[ tokens[ j ].type ] ) { + break; + } + } + return setMatcher( + i > 1 && elementMatcher( matchers ), + i > 1 && toSelector( + + // If the preceding token was a descendant combinator, insert an implicit any-element `*` + tokens + .slice( 0, i - 1 ) + .concat( { value: tokens[ i - 2 ].type === " " ? "*" : "" } ) + ).replace( rtrim, "$1" ), + matcher, + i < j && matcherFromTokens( tokens.slice( i, j ) ), + j < len && matcherFromTokens( ( tokens = tokens.slice( j ) ) ), + j < len && toSelector( tokens ) + ); + } + matchers.push( matcher ); + } + } + + return elementMatcher( matchers ); +} + +function matcherFromGroupMatchers( elementMatchers, setMatchers ) { + var bySet = setMatchers.length > 0, + byElement = elementMatchers.length > 0, + superMatcher = function( seed, context, xml, results, outermost ) { + var elem, j, matcher, + matchedCount = 0, + i = "0", + unmatched = seed && [], + setMatched = [], + contextBackup = outermostContext, + + // We must always have either seed elements or outermost context + elems = seed || byElement && Expr.find[ "TAG" ]( "*", outermost ), + + // Use integer dirruns iff this is the outermost matcher + dirrunsUnique = ( dirruns += contextBackup == null ? 1 : Math.random() || 0.1 ), + len = elems.length; + + if ( outermost ) { + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + outermostContext = context == document || context || outermost; + } + + // Add elements passing elementMatchers directly to results + // Support: IE<9, Safari + // Tolerate NodeList properties (IE: "length"; Safari: ) matching elements by id + for ( ; i !== len && ( elem = elems[ i ] ) != null; i++ ) { + if ( byElement && elem ) { + j = 0; + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( !context && elem.ownerDocument != document ) { + setDocument( elem ); + xml = !documentIsHTML; + } + while ( ( matcher = elementMatchers[ j++ ] ) ) { + if ( matcher( elem, context || document, xml ) ) { + results.push( elem ); + break; + } + } + if ( outermost ) { + dirruns = dirrunsUnique; + } + } + + // Track unmatched elements for set filters + if ( bySet ) { + + // They will have gone through all possible matchers + if ( ( elem = !matcher && elem ) ) { + matchedCount--; + } + + // Lengthen the array for every element, matched or not + if ( seed ) { + unmatched.push( elem ); + } + } + } + + // `i` is now the count of elements visited above, and adding it to `matchedCount` + // makes the latter nonnegative. + matchedCount += i; + + // Apply set filters to unmatched elements + // NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount` + // equals `i`), unless we didn't visit _any_ elements in the above loop because we have + // no element matchers and no seed. + // Incrementing an initially-string "0" `i` allows `i` to remain a string only in that + // case, which will result in a "00" `matchedCount` that differs from `i` but is also + // numerically zero. + if ( bySet && i !== matchedCount ) { + j = 0; + while ( ( matcher = setMatchers[ j++ ] ) ) { + matcher( unmatched, setMatched, context, xml ); + } + + if ( seed ) { + + // Reintegrate element matches to eliminate the need for sorting + if ( matchedCount > 0 ) { + while ( i-- ) { + if ( !( unmatched[ i ] || setMatched[ i ] ) ) { + setMatched[ i ] = pop.call( results ); + } + } + } + + // Discard index placeholder values to get only actual matches + setMatched = condense( setMatched ); + } + + // Add matches to results + push.apply( results, setMatched ); + + // Seedless set matches succeeding multiple successful matchers stipulate sorting + if ( outermost && !seed && setMatched.length > 0 && + ( matchedCount + setMatchers.length ) > 1 ) { + + Sizzle.uniqueSort( results ); + } + } + + // Override manipulation of globals by nested matchers + if ( outermost ) { + dirruns = dirrunsUnique; + outermostContext = contextBackup; + } + + return unmatched; + }; + + return bySet ? + markFunction( superMatcher ) : + superMatcher; +} + +compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) { + var i, + setMatchers = [], + elementMatchers = [], + cached = compilerCache[ selector + " " ]; + + if ( !cached ) { + + // Generate a function of recursive functions that can be used to check each element + if ( !match ) { + match = tokenize( selector ); + } + i = match.length; + while ( i-- ) { + cached = matcherFromTokens( match[ i ] ); + if ( cached[ expando ] ) { + setMatchers.push( cached ); + } else { + elementMatchers.push( cached ); + } + } + + // Cache the compiled function + cached = compilerCache( + selector, + matcherFromGroupMatchers( elementMatchers, setMatchers ) + ); + + // Save selector and tokenization + cached.selector = selector; + } + return cached; +}; + +/** + * A low-level selection function that works with Sizzle's compiled + * selector functions + * @param {String|Function} selector A selector or a pre-compiled + * selector function built with Sizzle.compile + * @param {Element} context + * @param {Array} [results] + * @param {Array} [seed] A set of elements to match against + */ +select = Sizzle.select = function( selector, context, results, seed ) { + var i, tokens, token, type, find, + compiled = typeof selector === "function" && selector, + match = !seed && tokenize( ( selector = compiled.selector || selector ) ); + + results = results || []; + + // Try to minimize operations if there is only one selector in the list and no seed + // (the latter of which guarantees us context) + if ( match.length === 1 ) { + + // Reduce context if the leading compound selector is an ID + tokens = match[ 0 ] = match[ 0 ].slice( 0 ); + if ( tokens.length > 2 && ( token = tokens[ 0 ] ).type === "ID" && + context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[ 1 ].type ] ) { + + context = ( Expr.find[ "ID" ]( token.matches[ 0 ] + .replace( runescape, funescape ), context ) || [] )[ 0 ]; + if ( !context ) { + return results; + + // Precompiled matchers will still verify ancestry, so step up a level + } else if ( compiled ) { + context = context.parentNode; + } + + selector = selector.slice( tokens.shift().value.length ); + } + + // Fetch a seed set for right-to-left matching + i = matchExpr[ "needsContext" ].test( selector ) ? 0 : tokens.length; + while ( i-- ) { + token = tokens[ i ]; + + // Abort if we hit a combinator + if ( Expr.relative[ ( type = token.type ) ] ) { + break; + } + if ( ( find = Expr.find[ type ] ) ) { + + // Search, expanding context for leading sibling combinators + if ( ( seed = find( + token.matches[ 0 ].replace( runescape, funescape ), + rsibling.test( tokens[ 0 ].type ) && testContext( context.parentNode ) || + context + ) ) ) { + + // If seed is empty or no tokens remain, we can return early + tokens.splice( i, 1 ); + selector = seed.length && toSelector( tokens ); + if ( !selector ) { + push.apply( results, seed ); + return results; + } + + break; + } + } + } + } + + // Compile and execute a filtering function if one is not provided + // Provide `match` to avoid retokenization if we modified the selector above + ( compiled || compile( selector, match ) )( + seed, + context, + !documentIsHTML, + results, + !context || rsibling.test( selector ) && testContext( context.parentNode ) || context + ); + return results; +}; + +// One-time assignments + +// Sort stability +support.sortStable = expando.split( "" ).sort( sortOrder ).join( "" ) === expando; + +// Support: Chrome 14-35+ +// Always assume duplicates if they aren't passed to the comparison function +support.detectDuplicates = !!hasDuplicate; + +// Initialize against the default document +setDocument(); + +// Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27) +// Detached nodes confoundingly follow *each other* +support.sortDetached = assert( function( el ) { + + // Should return 1, but returns 4 (following) + return el.compareDocumentPosition( document.createElement( "fieldset" ) ) & 1; +} ); + +// Support: IE<8 +// Prevent attribute/property "interpolation" +// https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx +if ( !assert( function( el ) { + el.innerHTML = ""; + return el.firstChild.getAttribute( "href" ) === "#"; +} ) ) { + addHandle( "type|href|height|width", function( elem, name, isXML ) { + if ( !isXML ) { + return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 ); + } + } ); +} + +// Support: IE<9 +// Use defaultValue in place of getAttribute("value") +if ( !support.attributes || !assert( function( el ) { + el.innerHTML = ""; + el.firstChild.setAttribute( "value", "" ); + return el.firstChild.getAttribute( "value" ) === ""; +} ) ) { + addHandle( "value", function( elem, _name, isXML ) { + if ( !isXML && elem.nodeName.toLowerCase() === "input" ) { + return elem.defaultValue; + } + } ); +} + +// Support: IE<9 +// Use getAttributeNode to fetch booleans when getAttribute lies +if ( !assert( function( el ) { + return el.getAttribute( "disabled" ) == null; +} ) ) { + addHandle( booleans, function( elem, name, isXML ) { + var val; + if ( !isXML ) { + return elem[ name ] === true ? name.toLowerCase() : + ( val = elem.getAttributeNode( name ) ) && val.specified ? + val.value : + null; + } + } ); +} + +return Sizzle; + +} )( window ); + + + +jQuery.find = Sizzle; +jQuery.expr = Sizzle.selectors; + +// Deprecated +jQuery.expr[ ":" ] = jQuery.expr.pseudos; +jQuery.uniqueSort = jQuery.unique = Sizzle.uniqueSort; +jQuery.text = Sizzle.getText; +jQuery.isXMLDoc = Sizzle.isXML; +jQuery.contains = Sizzle.contains; +jQuery.escapeSelector = Sizzle.escape; + + + + +var dir = function( elem, dir, until ) { + var matched = [], + truncate = until !== undefined; + + while ( ( elem = elem[ dir ] ) && elem.nodeType !== 9 ) { + if ( elem.nodeType === 1 ) { + if ( truncate && jQuery( elem ).is( until ) ) { + break; + } + matched.push( elem ); + } + } + return matched; +}; + + +var siblings = function( n, elem ) { + var matched = []; + + for ( ; n; n = n.nextSibling ) { + if ( n.nodeType === 1 && n !== elem ) { + matched.push( n ); + } + } + + return matched; +}; + + +var rneedsContext = jQuery.expr.match.needsContext; + + + +function nodeName( elem, name ) { + + return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase(); + +}; +var rsingleTag = ( /^<([a-z][^\/\0>:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i ); + + + +// Implement the identical functionality for filter and not +function winnow( elements, qualifier, not ) { + if ( isFunction( qualifier ) ) { + return jQuery.grep( elements, function( elem, i ) { + return !!qualifier.call( elem, i, elem ) !== not; + } ); + } + + // Single element + if ( qualifier.nodeType ) { + return jQuery.grep( elements, function( elem ) { + return ( elem === qualifier ) !== not; + } ); + } + + // Arraylike of elements (jQuery, arguments, Array) + if ( typeof qualifier !== "string" ) { + return jQuery.grep( elements, function( elem ) { + return ( indexOf.call( qualifier, elem ) > -1 ) !== not; + } ); + } + + // Filtered directly for both simple and complex selectors + return jQuery.filter( qualifier, elements, not ); +} + +jQuery.filter = function( expr, elems, not ) { + var elem = elems[ 0 ]; + + if ( not ) { + expr = ":not(" + expr + ")"; + } + + if ( elems.length === 1 && elem.nodeType === 1 ) { + return jQuery.find.matchesSelector( elem, expr ) ? [ elem ] : []; + } + + return jQuery.find.matches( expr, jQuery.grep( elems, function( elem ) { + return elem.nodeType === 1; + } ) ); +}; + +jQuery.fn.extend( { + find: function( selector ) { + var i, ret, + len = this.length, + self = this; + + if ( typeof selector !== "string" ) { + return this.pushStack( jQuery( selector ).filter( function() { + for ( i = 0; i < len; i++ ) { + if ( jQuery.contains( self[ i ], this ) ) { + return true; + } + } + } ) ); + } + + ret = this.pushStack( [] ); + + for ( i = 0; i < len; i++ ) { + jQuery.find( selector, self[ i ], ret ); + } + + return len > 1 ? jQuery.uniqueSort( ret ) : ret; + }, + filter: function( selector ) { + return this.pushStack( winnow( this, selector || [], false ) ); + }, + not: function( selector ) { + return this.pushStack( winnow( this, selector || [], true ) ); + }, + is: function( selector ) { + return !!winnow( + this, + + // If this is a positional/relative selector, check membership in the returned set + // so $("p:first").is("p:last") won't return true for a doc with two "p". + typeof selector === "string" && rneedsContext.test( selector ) ? + jQuery( selector ) : + selector || [], + false + ).length; + } +} ); + + +// Initialize a jQuery object + + +// A central reference to the root jQuery(document) +var rootjQuery, + + // A simple way to check for HTML strings + // Prioritize #id over to avoid XSS via location.hash (#9521) + // Strict HTML recognition (#11290: must start with <) + // Shortcut simple #id case for speed + rquickExpr = /^(?:\s*(<[\w\W]+>)[^>]*|#([\w-]+))$/, + + init = jQuery.fn.init = function( selector, context, root ) { + var match, elem; + + // HANDLE: $(""), $(null), $(undefined), $(false) + if ( !selector ) { + return this; + } + + // Method init() accepts an alternate rootjQuery + // so migrate can support jQuery.sub (gh-2101) + root = root || rootjQuery; + + // Handle HTML strings + if ( typeof selector === "string" ) { + if ( selector[ 0 ] === "<" && + selector[ selector.length - 1 ] === ">" && + selector.length >= 3 ) { + + // Assume that strings that start and end with <> are HTML and skip the regex check + match = [ null, selector, null ]; + + } else { + match = rquickExpr.exec( selector ); + } + + // Match html or make sure no context is specified for #id + if ( match && ( match[ 1 ] || !context ) ) { + + // HANDLE: $(html) -> $(array) + if ( match[ 1 ] ) { + context = context instanceof jQuery ? context[ 0 ] : context; + + // Option to run scripts is true for back-compat + // Intentionally let the error be thrown if parseHTML is not present + jQuery.merge( this, jQuery.parseHTML( + match[ 1 ], + context && context.nodeType ? context.ownerDocument || context : document, + true + ) ); + + // HANDLE: $(html, props) + if ( rsingleTag.test( match[ 1 ] ) && jQuery.isPlainObject( context ) ) { + for ( match in context ) { + + // Properties of context are called as methods if possible + if ( isFunction( this[ match ] ) ) { + this[ match ]( context[ match ] ); + + // ...and otherwise set as attributes + } else { + this.attr( match, context[ match ] ); + } + } + } + + return this; + + // HANDLE: $(#id) + } else { + elem = document.getElementById( match[ 2 ] ); + + if ( elem ) { + + // Inject the element directly into the jQuery object + this[ 0 ] = elem; + this.length = 1; + } + return this; + } + + // HANDLE: $(expr, $(...)) + } else if ( !context || context.jquery ) { + return ( context || root ).find( selector ); + + // HANDLE: $(expr, context) + // (which is just equivalent to: $(context).find(expr) + } else { + return this.constructor( context ).find( selector ); + } + + // HANDLE: $(DOMElement) + } else if ( selector.nodeType ) { + this[ 0 ] = selector; + this.length = 1; + return this; + + // HANDLE: $(function) + // Shortcut for document ready + } else if ( isFunction( selector ) ) { + return root.ready !== undefined ? + root.ready( selector ) : + + // Execute immediately if ready is not present + selector( jQuery ); + } + + return jQuery.makeArray( selector, this ); + }; + +// Give the init function the jQuery prototype for later instantiation +init.prototype = jQuery.fn; + +// Initialize central reference +rootjQuery = jQuery( document ); + + +var rparentsprev = /^(?:parents|prev(?:Until|All))/, + + // Methods guaranteed to produce a unique set when starting from a unique set + guaranteedUnique = { + children: true, + contents: true, + next: true, + prev: true + }; + +jQuery.fn.extend( { + has: function( target ) { + var targets = jQuery( target, this ), + l = targets.length; + + return this.filter( function() { + var i = 0; + for ( ; i < l; i++ ) { + if ( jQuery.contains( this, targets[ i ] ) ) { + return true; + } + } + } ); + }, + + closest: function( selectors, context ) { + var cur, + i = 0, + l = this.length, + matched = [], + targets = typeof selectors !== "string" && jQuery( selectors ); + + // Positional selectors never match, since there's no _selection_ context + if ( !rneedsContext.test( selectors ) ) { + for ( ; i < l; i++ ) { + for ( cur = this[ i ]; cur && cur !== context; cur = cur.parentNode ) { + + // Always skip document fragments + if ( cur.nodeType < 11 && ( targets ? + targets.index( cur ) > -1 : + + // Don't pass non-elements to Sizzle + cur.nodeType === 1 && + jQuery.find.matchesSelector( cur, selectors ) ) ) { + + matched.push( cur ); + break; + } + } + } + } + + return this.pushStack( matched.length > 1 ? jQuery.uniqueSort( matched ) : matched ); + }, + + // Determine the position of an element within the set + index: function( elem ) { + + // No argument, return index in parent + if ( !elem ) { + return ( this[ 0 ] && this[ 0 ].parentNode ) ? this.first().prevAll().length : -1; + } + + // Index in selector + if ( typeof elem === "string" ) { + return indexOf.call( jQuery( elem ), this[ 0 ] ); + } + + // Locate the position of the desired element + return indexOf.call( this, + + // If it receives a jQuery object, the first element is used + elem.jquery ? elem[ 0 ] : elem + ); + }, + + add: function( selector, context ) { + return this.pushStack( + jQuery.uniqueSort( + jQuery.merge( this.get(), jQuery( selector, context ) ) + ) + ); + }, + + addBack: function( selector ) { + return this.add( selector == null ? + this.prevObject : this.prevObject.filter( selector ) + ); + } +} ); + +function sibling( cur, dir ) { + while ( ( cur = cur[ dir ] ) && cur.nodeType !== 1 ) {} + return cur; +} + +jQuery.each( { + parent: function( elem ) { + var parent = elem.parentNode; + return parent && parent.nodeType !== 11 ? parent : null; + }, + parents: function( elem ) { + return dir( elem, "parentNode" ); + }, + parentsUntil: function( elem, _i, until ) { + return dir( elem, "parentNode", until ); + }, + next: function( elem ) { + return sibling( elem, "nextSibling" ); + }, + prev: function( elem ) { + return sibling( elem, "previousSibling" ); + }, + nextAll: function( elem ) { + return dir( elem, "nextSibling" ); + }, + prevAll: function( elem ) { + return dir( elem, "previousSibling" ); + }, + nextUntil: function( elem, _i, until ) { + return dir( elem, "nextSibling", until ); + }, + prevUntil: function( elem, _i, until ) { + return dir( elem, "previousSibling", until ); + }, + siblings: function( elem ) { + return siblings( ( elem.parentNode || {} ).firstChild, elem ); + }, + children: function( elem ) { + return siblings( elem.firstChild ); + }, + contents: function( elem ) { + if ( elem.contentDocument != null && + + // Support: IE 11+ + // elements with no `data` attribute has an object + // `contentDocument` with a `null` prototype. + getProto( elem.contentDocument ) ) { + + return elem.contentDocument; + } + + // Support: IE 9 - 11 only, iOS 7 only, Android Browser <=4.3 only + // Treat the template element as a regular one in browsers that + // don't support it. + if ( nodeName( elem, "template" ) ) { + elem = elem.content || elem; + } + + return jQuery.merge( [], elem.childNodes ); + } +}, function( name, fn ) { + jQuery.fn[ name ] = function( until, selector ) { + var matched = jQuery.map( this, fn, until ); + + if ( name.slice( -5 ) !== "Until" ) { + selector = until; + } + + if ( selector && typeof selector === "string" ) { + matched = jQuery.filter( selector, matched ); + } + + if ( this.length > 1 ) { + + // Remove duplicates + if ( !guaranteedUnique[ name ] ) { + jQuery.uniqueSort( matched ); + } + + // Reverse order for parents* and prev-derivatives + if ( rparentsprev.test( name ) ) { + matched.reverse(); + } + } + + return this.pushStack( matched ); + }; +} ); +var rnothtmlwhite = ( /[^\x20\t\r\n\f]+/g ); + + + +// Convert String-formatted options into Object-formatted ones +function createOptions( options ) { + var object = {}; + jQuery.each( options.match( rnothtmlwhite ) || [], function( _, flag ) { + object[ flag ] = true; + } ); + return object; +} + +/* + * Create a callback list using the following parameters: + * + * options: an optional list of space-separated options that will change how + * the callback list behaves or a more traditional option object + * + * By default a callback list will act like an event callback list and can be + * "fired" multiple times. + * + * Possible options: + * + * once: will ensure the callback list can only be fired once (like a Deferred) + * + * memory: will keep track of previous values and will call any callback added + * after the list has been fired right away with the latest "memorized" + * values (like a Deferred) + * + * unique: will ensure a callback can only be added once (no duplicate in the list) + * + * stopOnFalse: interrupt callings when a callback returns false + * + */ +jQuery.Callbacks = function( options ) { + + // Convert options from String-formatted to Object-formatted if needed + // (we check in cache first) + options = typeof options === "string" ? + createOptions( options ) : + jQuery.extend( {}, options ); + + var // Flag to know if list is currently firing + firing, + + // Last fire value for non-forgettable lists + memory, + + // Flag to know if list was already fired + fired, + + // Flag to prevent firing + locked, + + // Actual callback list + list = [], + + // Queue of execution data for repeatable lists + queue = [], + + // Index of currently firing callback (modified by add/remove as needed) + firingIndex = -1, + + // Fire callbacks + fire = function() { + + // Enforce single-firing + locked = locked || options.once; + + // Execute callbacks for all pending executions, + // respecting firingIndex overrides and runtime changes + fired = firing = true; + for ( ; queue.length; firingIndex = -1 ) { + memory = queue.shift(); + while ( ++firingIndex < list.length ) { + + // Run callback and check for early termination + if ( list[ firingIndex ].apply( memory[ 0 ], memory[ 1 ] ) === false && + options.stopOnFalse ) { + + // Jump to end and forget the data so .add doesn't re-fire + firingIndex = list.length; + memory = false; + } + } + } + + // Forget the data if we're done with it + if ( !options.memory ) { + memory = false; + } + + firing = false; + + // Clean up if we're done firing for good + if ( locked ) { + + // Keep an empty list if we have data for future add calls + if ( memory ) { + list = []; + + // Otherwise, this object is spent + } else { + list = ""; + } + } + }, + + // Actual Callbacks object + self = { + + // Add a callback or a collection of callbacks to the list + add: function() { + if ( list ) { + + // If we have memory from a past run, we should fire after adding + if ( memory && !firing ) { + firingIndex = list.length - 1; + queue.push( memory ); + } + + ( function add( args ) { + jQuery.each( args, function( _, arg ) { + if ( isFunction( arg ) ) { + if ( !options.unique || !self.has( arg ) ) { + list.push( arg ); + } + } else if ( arg && arg.length && toType( arg ) !== "string" ) { + + // Inspect recursively + add( arg ); + } + } ); + } )( arguments ); + + if ( memory && !firing ) { + fire(); + } + } + return this; + }, + + // Remove a callback from the list + remove: function() { + jQuery.each( arguments, function( _, arg ) { + var index; + while ( ( index = jQuery.inArray( arg, list, index ) ) > -1 ) { + list.splice( index, 1 ); + + // Handle firing indexes + if ( index <= firingIndex ) { + firingIndex--; + } + } + } ); + return this; + }, + + // Check if a given callback is in the list. + // If no argument is given, return whether or not list has callbacks attached. + has: function( fn ) { + return fn ? + jQuery.inArray( fn, list ) > -1 : + list.length > 0; + }, + + // Remove all callbacks from the list + empty: function() { + if ( list ) { + list = []; + } + return this; + }, + + // Disable .fire and .add + // Abort any current/pending executions + // Clear all callbacks and values + disable: function() { + locked = queue = []; + list = memory = ""; + return this; + }, + disabled: function() { + return !list; + }, + + // Disable .fire + // Also disable .add unless we have memory (since it would have no effect) + // Abort any pending executions + lock: function() { + locked = queue = []; + if ( !memory && !firing ) { + list = memory = ""; + } + return this; + }, + locked: function() { + return !!locked; + }, + + // Call all callbacks with the given context and arguments + fireWith: function( context, args ) { + if ( !locked ) { + args = args || []; + args = [ context, args.slice ? args.slice() : args ]; + queue.push( args ); + if ( !firing ) { + fire(); + } + } + return this; + }, + + // Call all the callbacks with the given arguments + fire: function() { + self.fireWith( this, arguments ); + return this; + }, + + // To know if the callbacks have already been called at least once + fired: function() { + return !!fired; + } + }; + + return self; +}; + + +function Identity( v ) { + return v; +} +function Thrower( ex ) { + throw ex; +} + +function adoptValue( value, resolve, reject, noValue ) { + var method; + + try { + + // Check for promise aspect first to privilege synchronous behavior + if ( value && isFunction( ( method = value.promise ) ) ) { + method.call( value ).done( resolve ).fail( reject ); + + // Other thenables + } else if ( value && isFunction( ( method = value.then ) ) ) { + method.call( value, resolve, reject ); + + // Other non-thenables + } else { + + // Control `resolve` arguments by letting Array#slice cast boolean `noValue` to integer: + // * false: [ value ].slice( 0 ) => resolve( value ) + // * true: [ value ].slice( 1 ) => resolve() + resolve.apply( undefined, [ value ].slice( noValue ) ); + } + + // For Promises/A+, convert exceptions into rejections + // Since jQuery.when doesn't unwrap thenables, we can skip the extra checks appearing in + // Deferred#then to conditionally suppress rejection. + } catch ( value ) { + + // Support: Android 4.0 only + // Strict mode functions invoked without .call/.apply get global-object context + reject.apply( undefined, [ value ] ); + } +} + +jQuery.extend( { + + Deferred: function( func ) { + var tuples = [ + + // action, add listener, callbacks, + // ... .then handlers, argument index, [final state] + [ "notify", "progress", jQuery.Callbacks( "memory" ), + jQuery.Callbacks( "memory" ), 2 ], + [ "resolve", "done", jQuery.Callbacks( "once memory" ), + jQuery.Callbacks( "once memory" ), 0, "resolved" ], + [ "reject", "fail", jQuery.Callbacks( "once memory" ), + jQuery.Callbacks( "once memory" ), 1, "rejected" ] + ], + state = "pending", + promise = { + state: function() { + return state; + }, + always: function() { + deferred.done( arguments ).fail( arguments ); + return this; + }, + "catch": function( fn ) { + return promise.then( null, fn ); + }, + + // Keep pipe for back-compat + pipe: function( /* fnDone, fnFail, fnProgress */ ) { + var fns = arguments; + + return jQuery.Deferred( function( newDefer ) { + jQuery.each( tuples, function( _i, tuple ) { + + // Map tuples (progress, done, fail) to arguments (done, fail, progress) + var fn = isFunction( fns[ tuple[ 4 ] ] ) && fns[ tuple[ 4 ] ]; + + // deferred.progress(function() { bind to newDefer or newDefer.notify }) + // deferred.done(function() { bind to newDefer or newDefer.resolve }) + // deferred.fail(function() { bind to newDefer or newDefer.reject }) + deferred[ tuple[ 1 ] ]( function() { + var returned = fn && fn.apply( this, arguments ); + if ( returned && isFunction( returned.promise ) ) { + returned.promise() + .progress( newDefer.notify ) + .done( newDefer.resolve ) + .fail( newDefer.reject ); + } else { + newDefer[ tuple[ 0 ] + "With" ]( + this, + fn ? [ returned ] : arguments + ); + } + } ); + } ); + fns = null; + } ).promise(); + }, + then: function( onFulfilled, onRejected, onProgress ) { + var maxDepth = 0; + function resolve( depth, deferred, handler, special ) { + return function() { + var that = this, + args = arguments, + mightThrow = function() { + var returned, then; + + // Support: Promises/A+ section 2.3.3.3.3 + // https://promisesaplus.com/#point-59 + // Ignore double-resolution attempts + if ( depth < maxDepth ) { + return; + } + + returned = handler.apply( that, args ); + + // Support: Promises/A+ section 2.3.1 + // https://promisesaplus.com/#point-48 + if ( returned === deferred.promise() ) { + throw new TypeError( "Thenable self-resolution" ); + } + + // Support: Promises/A+ sections 2.3.3.1, 3.5 + // https://promisesaplus.com/#point-54 + // https://promisesaplus.com/#point-75 + // Retrieve `then` only once + then = returned && + + // Support: Promises/A+ section 2.3.4 + // https://promisesaplus.com/#point-64 + // Only check objects and functions for thenability + ( typeof returned === "object" || + typeof returned === "function" ) && + returned.then; + + // Handle a returned thenable + if ( isFunction( then ) ) { + + // Special processors (notify) just wait for resolution + if ( special ) { + then.call( + returned, + resolve( maxDepth, deferred, Identity, special ), + resolve( maxDepth, deferred, Thrower, special ) + ); + + // Normal processors (resolve) also hook into progress + } else { + + // ...and disregard older resolution values + maxDepth++; + + then.call( + returned, + resolve( maxDepth, deferred, Identity, special ), + resolve( maxDepth, deferred, Thrower, special ), + resolve( maxDepth, deferred, Identity, + deferred.notifyWith ) + ); + } + + // Handle all other returned values + } else { + + // Only substitute handlers pass on context + // and multiple values (non-spec behavior) + if ( handler !== Identity ) { + that = undefined; + args = [ returned ]; + } + + // Process the value(s) + // Default process is resolve + ( special || deferred.resolveWith )( that, args ); + } + }, + + // Only normal processors (resolve) catch and reject exceptions + process = special ? + mightThrow : + function() { + try { + mightThrow(); + } catch ( e ) { + + if ( jQuery.Deferred.exceptionHook ) { + jQuery.Deferred.exceptionHook( e, + process.stackTrace ); + } + + // Support: Promises/A+ section 2.3.3.3.4.1 + // https://promisesaplus.com/#point-61 + // Ignore post-resolution exceptions + if ( depth + 1 >= maxDepth ) { + + // Only substitute handlers pass on context + // and multiple values (non-spec behavior) + if ( handler !== Thrower ) { + that = undefined; + args = [ e ]; + } + + deferred.rejectWith( that, args ); + } + } + }; + + // Support: Promises/A+ section 2.3.3.3.1 + // https://promisesaplus.com/#point-57 + // Re-resolve promises immediately to dodge false rejection from + // subsequent errors + if ( depth ) { + process(); + } else { + + // Call an optional hook to record the stack, in case of exception + // since it's otherwise lost when execution goes async + if ( jQuery.Deferred.getStackHook ) { + process.stackTrace = jQuery.Deferred.getStackHook(); + } + window.setTimeout( process ); + } + }; + } + + return jQuery.Deferred( function( newDefer ) { + + // progress_handlers.add( ... ) + tuples[ 0 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onProgress ) ? + onProgress : + Identity, + newDefer.notifyWith + ) + ); + + // fulfilled_handlers.add( ... ) + tuples[ 1 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onFulfilled ) ? + onFulfilled : + Identity + ) + ); + + // rejected_handlers.add( ... ) + tuples[ 2 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onRejected ) ? + onRejected : + Thrower + ) + ); + } ).promise(); + }, + + // Get a promise for this deferred + // If obj is provided, the promise aspect is added to the object + promise: function( obj ) { + return obj != null ? jQuery.extend( obj, promise ) : promise; + } + }, + deferred = {}; + + // Add list-specific methods + jQuery.each( tuples, function( i, tuple ) { + var list = tuple[ 2 ], + stateString = tuple[ 5 ]; + + // promise.progress = list.add + // promise.done = list.add + // promise.fail = list.add + promise[ tuple[ 1 ] ] = list.add; + + // Handle state + if ( stateString ) { + list.add( + function() { + + // state = "resolved" (i.e., fulfilled) + // state = "rejected" + state = stateString; + }, + + // rejected_callbacks.disable + // fulfilled_callbacks.disable + tuples[ 3 - i ][ 2 ].disable, + + // rejected_handlers.disable + // fulfilled_handlers.disable + tuples[ 3 - i ][ 3 ].disable, + + // progress_callbacks.lock + tuples[ 0 ][ 2 ].lock, + + // progress_handlers.lock + tuples[ 0 ][ 3 ].lock + ); + } + + // progress_handlers.fire + // fulfilled_handlers.fire + // rejected_handlers.fire + list.add( tuple[ 3 ].fire ); + + // deferred.notify = function() { deferred.notifyWith(...) } + // deferred.resolve = function() { deferred.resolveWith(...) } + // deferred.reject = function() { deferred.rejectWith(...) } + deferred[ tuple[ 0 ] ] = function() { + deferred[ tuple[ 0 ] + "With" ]( this === deferred ? undefined : this, arguments ); + return this; + }; + + // deferred.notifyWith = list.fireWith + // deferred.resolveWith = list.fireWith + // deferred.rejectWith = list.fireWith + deferred[ tuple[ 0 ] + "With" ] = list.fireWith; + } ); + + // Make the deferred a promise + promise.promise( deferred ); + + // Call given func if any + if ( func ) { + func.call( deferred, deferred ); + } + + // All done! + return deferred; + }, + + // Deferred helper + when: function( singleValue ) { + var + + // count of uncompleted subordinates + remaining = arguments.length, + + // count of unprocessed arguments + i = remaining, + + // subordinate fulfillment data + resolveContexts = Array( i ), + resolveValues = slice.call( arguments ), + + // the master Deferred + master = jQuery.Deferred(), + + // subordinate callback factory + updateFunc = function( i ) { + return function( value ) { + resolveContexts[ i ] = this; + resolveValues[ i ] = arguments.length > 1 ? slice.call( arguments ) : value; + if ( !( --remaining ) ) { + master.resolveWith( resolveContexts, resolveValues ); + } + }; + }; + + // Single- and empty arguments are adopted like Promise.resolve + if ( remaining <= 1 ) { + adoptValue( singleValue, master.done( updateFunc( i ) ).resolve, master.reject, + !remaining ); + + // Use .then() to unwrap secondary thenables (cf. gh-3000) + if ( master.state() === "pending" || + isFunction( resolveValues[ i ] && resolveValues[ i ].then ) ) { + + return master.then(); + } + } + + // Multiple arguments are aggregated like Promise.all array elements + while ( i-- ) { + adoptValue( resolveValues[ i ], updateFunc( i ), master.reject ); + } + + return master.promise(); + } +} ); + + +// These usually indicate a programmer mistake during development, +// warn about them ASAP rather than swallowing them by default. +var rerrorNames = /^(Eval|Internal|Range|Reference|Syntax|Type|URI)Error$/; + +jQuery.Deferred.exceptionHook = function( error, stack ) { + + // Support: IE 8 - 9 only + // Console exists when dev tools are open, which can happen at any time + if ( window.console && window.console.warn && error && rerrorNames.test( error.name ) ) { + window.console.warn( "jQuery.Deferred exception: " + error.message, error.stack, stack ); + } +}; + + + + +jQuery.readyException = function( error ) { + window.setTimeout( function() { + throw error; + } ); +}; + + + + +// The deferred used on DOM ready +var readyList = jQuery.Deferred(); + +jQuery.fn.ready = function( fn ) { + + readyList + .then( fn ) + + // Wrap jQuery.readyException in a function so that the lookup + // happens at the time of error handling instead of callback + // registration. + .catch( function( error ) { + jQuery.readyException( error ); + } ); + + return this; +}; + +jQuery.extend( { + + // Is the DOM ready to be used? Set to true once it occurs. + isReady: false, + + // A counter to track how many items to wait for before + // the ready event fires. See #6781 + readyWait: 1, + + // Handle when the DOM is ready + ready: function( wait ) { + + // Abort if there are pending holds or we're already ready + if ( wait === true ? --jQuery.readyWait : jQuery.isReady ) { + return; + } + + // Remember that the DOM is ready + jQuery.isReady = true; + + // If a normal DOM Ready event fired, decrement, and wait if need be + if ( wait !== true && --jQuery.readyWait > 0 ) { + return; + } + + // If there are functions bound, to execute + readyList.resolveWith( document, [ jQuery ] ); + } +} ); + +jQuery.ready.then = readyList.then; + +// The ready event handler and self cleanup method +function completed() { + document.removeEventListener( "DOMContentLoaded", completed ); + window.removeEventListener( "load", completed ); + jQuery.ready(); +} + +// Catch cases where $(document).ready() is called +// after the browser event has already occurred. +// Support: IE <=9 - 10 only +// Older IE sometimes signals "interactive" too soon +if ( document.readyState === "complete" || + ( document.readyState !== "loading" && !document.documentElement.doScroll ) ) { + + // Handle it asynchronously to allow scripts the opportunity to delay ready + window.setTimeout( jQuery.ready ); + +} else { + + // Use the handy event callback + document.addEventListener( "DOMContentLoaded", completed ); + + // A fallback to window.onload, that will always work + window.addEventListener( "load", completed ); +} + + + + +// Multifunctional method to get and set values of a collection +// The value/s can optionally be executed if it's a function +var access = function( elems, fn, key, value, chainable, emptyGet, raw ) { + var i = 0, + len = elems.length, + bulk = key == null; + + // Sets many values + if ( toType( key ) === "object" ) { + chainable = true; + for ( i in key ) { + access( elems, fn, i, key[ i ], true, emptyGet, raw ); + } + + // Sets one value + } else if ( value !== undefined ) { + chainable = true; + + if ( !isFunction( value ) ) { + raw = true; + } + + if ( bulk ) { + + // Bulk operations run against the entire set + if ( raw ) { + fn.call( elems, value ); + fn = null; + + // ...except when executing function values + } else { + bulk = fn; + fn = function( elem, _key, value ) { + return bulk.call( jQuery( elem ), value ); + }; + } + } + + if ( fn ) { + for ( ; i < len; i++ ) { + fn( + elems[ i ], key, raw ? + value : + value.call( elems[ i ], i, fn( elems[ i ], key ) ) + ); + } + } + } + + if ( chainable ) { + return elems; + } + + // Gets + if ( bulk ) { + return fn.call( elems ); + } + + return len ? fn( elems[ 0 ], key ) : emptyGet; +}; + + +// Matches dashed string for camelizing +var rmsPrefix = /^-ms-/, + rdashAlpha = /-([a-z])/g; + +// Used by camelCase as callback to replace() +function fcamelCase( _all, letter ) { + return letter.toUpperCase(); +} + +// Convert dashed to camelCase; used by the css and data modules +// Support: IE <=9 - 11, Edge 12 - 15 +// Microsoft forgot to hump their vendor prefix (#9572) +function camelCase( string ) { + return string.replace( rmsPrefix, "ms-" ).replace( rdashAlpha, fcamelCase ); +} +var acceptData = function( owner ) { + + // Accepts only: + // - Node + // - Node.ELEMENT_NODE + // - Node.DOCUMENT_NODE + // - Object + // - Any + return owner.nodeType === 1 || owner.nodeType === 9 || !( +owner.nodeType ); +}; + + + + +function Data() { + this.expando = jQuery.expando + Data.uid++; +} + +Data.uid = 1; + +Data.prototype = { + + cache: function( owner ) { + + // Check if the owner object already has a cache + var value = owner[ this.expando ]; + + // If not, create one + if ( !value ) { + value = {}; + + // We can accept data for non-element nodes in modern browsers, + // but we should not, see #8335. + // Always return an empty object. + if ( acceptData( owner ) ) { + + // If it is a node unlikely to be stringify-ed or looped over + // use plain assignment + if ( owner.nodeType ) { + owner[ this.expando ] = value; + + // Otherwise secure it in a non-enumerable property + // configurable must be true to allow the property to be + // deleted when data is removed + } else { + Object.defineProperty( owner, this.expando, { + value: value, + configurable: true + } ); + } + } + } + + return value; + }, + set: function( owner, data, value ) { + var prop, + cache = this.cache( owner ); + + // Handle: [ owner, key, value ] args + // Always use camelCase key (gh-2257) + if ( typeof data === "string" ) { + cache[ camelCase( data ) ] = value; + + // Handle: [ owner, { properties } ] args + } else { + + // Copy the properties one-by-one to the cache object + for ( prop in data ) { + cache[ camelCase( prop ) ] = data[ prop ]; + } + } + return cache; + }, + get: function( owner, key ) { + return key === undefined ? + this.cache( owner ) : + + // Always use camelCase key (gh-2257) + owner[ this.expando ] && owner[ this.expando ][ camelCase( key ) ]; + }, + access: function( owner, key, value ) { + + // In cases where either: + // + // 1. No key was specified + // 2. A string key was specified, but no value provided + // + // Take the "read" path and allow the get method to determine + // which value to return, respectively either: + // + // 1. The entire cache object + // 2. The data stored at the key + // + if ( key === undefined || + ( ( key && typeof key === "string" ) && value === undefined ) ) { + + return this.get( owner, key ); + } + + // When the key is not a string, or both a key and value + // are specified, set or extend (existing objects) with either: + // + // 1. An object of properties + // 2. A key and value + // + this.set( owner, key, value ); + + // Since the "set" path can have two possible entry points + // return the expected data based on which path was taken[*] + return value !== undefined ? value : key; + }, + remove: function( owner, key ) { + var i, + cache = owner[ this.expando ]; + + if ( cache === undefined ) { + return; + } + + if ( key !== undefined ) { + + // Support array or space separated string of keys + if ( Array.isArray( key ) ) { + + // If key is an array of keys... + // We always set camelCase keys, so remove that. + key = key.map( camelCase ); + } else { + key = camelCase( key ); + + // If a key with the spaces exists, use it. + // Otherwise, create an array by matching non-whitespace + key = key in cache ? + [ key ] : + ( key.match( rnothtmlwhite ) || [] ); + } + + i = key.length; + + while ( i-- ) { + delete cache[ key[ i ] ]; + } + } + + // Remove the expando if there's no more data + if ( key === undefined || jQuery.isEmptyObject( cache ) ) { + + // Support: Chrome <=35 - 45 + // Webkit & Blink performance suffers when deleting properties + // from DOM nodes, so set to undefined instead + // https://bugs.chromium.org/p/chromium/issues/detail?id=378607 (bug restricted) + if ( owner.nodeType ) { + owner[ this.expando ] = undefined; + } else { + delete owner[ this.expando ]; + } + } + }, + hasData: function( owner ) { + var cache = owner[ this.expando ]; + return cache !== undefined && !jQuery.isEmptyObject( cache ); + } +}; +var dataPriv = new Data(); + +var dataUser = new Data(); + + + +// Implementation Summary +// +// 1. Enforce API surface and semantic compatibility with 1.9.x branch +// 2. Improve the module's maintainability by reducing the storage +// paths to a single mechanism. +// 3. Use the same single mechanism to support "private" and "user" data. +// 4. _Never_ expose "private" data to user code (TODO: Drop _data, _removeData) +// 5. Avoid exposing implementation details on user objects (eg. expando properties) +// 6. Provide a clear path for implementation upgrade to WeakMap in 2014 + +var rbrace = /^(?:\{[\w\W]*\}|\[[\w\W]*\])$/, + rmultiDash = /[A-Z]/g; + +function getData( data ) { + if ( data === "true" ) { + return true; + } + + if ( data === "false" ) { + return false; + } + + if ( data === "null" ) { + return null; + } + + // Only convert to a number if it doesn't change the string + if ( data === +data + "" ) { + return +data; + } + + if ( rbrace.test( data ) ) { + return JSON.parse( data ); + } + + return data; +} + +function dataAttr( elem, key, data ) { + var name; + + // If nothing was found internally, try to fetch any + // data from the HTML5 data-* attribute + if ( data === undefined && elem.nodeType === 1 ) { + name = "data-" + key.replace( rmultiDash, "-$&" ).toLowerCase(); + data = elem.getAttribute( name ); + + if ( typeof data === "string" ) { + try { + data = getData( data ); + } catch ( e ) {} + + // Make sure we set the data so it isn't changed later + dataUser.set( elem, key, data ); + } else { + data = undefined; + } + } + return data; +} + +jQuery.extend( { + hasData: function( elem ) { + return dataUser.hasData( elem ) || dataPriv.hasData( elem ); + }, + + data: function( elem, name, data ) { + return dataUser.access( elem, name, data ); + }, + + removeData: function( elem, name ) { + dataUser.remove( elem, name ); + }, + + // TODO: Now that all calls to _data and _removeData have been replaced + // with direct calls to dataPriv methods, these can be deprecated. + _data: function( elem, name, data ) { + return dataPriv.access( elem, name, data ); + }, + + _removeData: function( elem, name ) { + dataPriv.remove( elem, name ); + } +} ); + +jQuery.fn.extend( { + data: function( key, value ) { + var i, name, data, + elem = this[ 0 ], + attrs = elem && elem.attributes; + + // Gets all values + if ( key === undefined ) { + if ( this.length ) { + data = dataUser.get( elem ); + + if ( elem.nodeType === 1 && !dataPriv.get( elem, "hasDataAttrs" ) ) { + i = attrs.length; + while ( i-- ) { + + // Support: IE 11 only + // The attrs elements can be null (#14894) + if ( attrs[ i ] ) { + name = attrs[ i ].name; + if ( name.indexOf( "data-" ) === 0 ) { + name = camelCase( name.slice( 5 ) ); + dataAttr( elem, name, data[ name ] ); + } + } + } + dataPriv.set( elem, "hasDataAttrs", true ); + } + } + + return data; + } + + // Sets multiple values + if ( typeof key === "object" ) { + return this.each( function() { + dataUser.set( this, key ); + } ); + } + + return access( this, function( value ) { + var data; + + // The calling jQuery object (element matches) is not empty + // (and therefore has an element appears at this[ 0 ]) and the + // `value` parameter was not undefined. An empty jQuery object + // will result in `undefined` for elem = this[ 0 ] which will + // throw an exception if an attempt to read a data cache is made. + if ( elem && value === undefined ) { + + // Attempt to get data from the cache + // The key will always be camelCased in Data + data = dataUser.get( elem, key ); + if ( data !== undefined ) { + return data; + } + + // Attempt to "discover" the data in + // HTML5 custom data-* attrs + data = dataAttr( elem, key ); + if ( data !== undefined ) { + return data; + } + + // We tried really hard, but the data doesn't exist. + return; + } + + // Set the data... + this.each( function() { + + // We always store the camelCased key + dataUser.set( this, key, value ); + } ); + }, null, value, arguments.length > 1, null, true ); + }, + + removeData: function( key ) { + return this.each( function() { + dataUser.remove( this, key ); + } ); + } +} ); + + +jQuery.extend( { + queue: function( elem, type, data ) { + var queue; + + if ( elem ) { + type = ( type || "fx" ) + "queue"; + queue = dataPriv.get( elem, type ); + + // Speed up dequeue by getting out quickly if this is just a lookup + if ( data ) { + if ( !queue || Array.isArray( data ) ) { + queue = dataPriv.access( elem, type, jQuery.makeArray( data ) ); + } else { + queue.push( data ); + } + } + return queue || []; + } + }, + + dequeue: function( elem, type ) { + type = type || "fx"; + + var queue = jQuery.queue( elem, type ), + startLength = queue.length, + fn = queue.shift(), + hooks = jQuery._queueHooks( elem, type ), + next = function() { + jQuery.dequeue( elem, type ); + }; + + // If the fx queue is dequeued, always remove the progress sentinel + if ( fn === "inprogress" ) { + fn = queue.shift(); + startLength--; + } + + if ( fn ) { + + // Add a progress sentinel to prevent the fx queue from being + // automatically dequeued + if ( type === "fx" ) { + queue.unshift( "inprogress" ); + } + + // Clear up the last queue stop function + delete hooks.stop; + fn.call( elem, next, hooks ); + } + + if ( !startLength && hooks ) { + hooks.empty.fire(); + } + }, + + // Not public - generate a queueHooks object, or return the current one + _queueHooks: function( elem, type ) { + var key = type + "queueHooks"; + return dataPriv.get( elem, key ) || dataPriv.access( elem, key, { + empty: jQuery.Callbacks( "once memory" ).add( function() { + dataPriv.remove( elem, [ type + "queue", key ] ); + } ) + } ); + } +} ); + +jQuery.fn.extend( { + queue: function( type, data ) { + var setter = 2; + + if ( typeof type !== "string" ) { + data = type; + type = "fx"; + setter--; + } + + if ( arguments.length < setter ) { + return jQuery.queue( this[ 0 ], type ); + } + + return data === undefined ? + this : + this.each( function() { + var queue = jQuery.queue( this, type, data ); + + // Ensure a hooks for this queue + jQuery._queueHooks( this, type ); + + if ( type === "fx" && queue[ 0 ] !== "inprogress" ) { + jQuery.dequeue( this, type ); + } + } ); + }, + dequeue: function( type ) { + return this.each( function() { + jQuery.dequeue( this, type ); + } ); + }, + clearQueue: function( type ) { + return this.queue( type || "fx", [] ); + }, + + // Get a promise resolved when queues of a certain type + // are emptied (fx is the type by default) + promise: function( type, obj ) { + var tmp, + count = 1, + defer = jQuery.Deferred(), + elements = this, + i = this.length, + resolve = function() { + if ( !( --count ) ) { + defer.resolveWith( elements, [ elements ] ); + } + }; + + if ( typeof type !== "string" ) { + obj = type; + type = undefined; + } + type = type || "fx"; + + while ( i-- ) { + tmp = dataPriv.get( elements[ i ], type + "queueHooks" ); + if ( tmp && tmp.empty ) { + count++; + tmp.empty.add( resolve ); + } + } + resolve(); + return defer.promise( obj ); + } +} ); +var pnum = ( /[+-]?(?:\d*\.|)\d+(?:[eE][+-]?\d+|)/ ).source; + +var rcssNum = new RegExp( "^(?:([+-])=|)(" + pnum + ")([a-z%]*)$", "i" ); + + +var cssExpand = [ "Top", "Right", "Bottom", "Left" ]; + +var documentElement = document.documentElement; + + + + var isAttached = function( elem ) { + return jQuery.contains( elem.ownerDocument, elem ); + }, + composed = { composed: true }; + + // Support: IE 9 - 11+, Edge 12 - 18+, iOS 10.0 - 10.2 only + // Check attachment across shadow DOM boundaries when possible (gh-3504) + // Support: iOS 10.0-10.2 only + // Early iOS 10 versions support `attachShadow` but not `getRootNode`, + // leading to errors. We need to check for `getRootNode`. + if ( documentElement.getRootNode ) { + isAttached = function( elem ) { + return jQuery.contains( elem.ownerDocument, elem ) || + elem.getRootNode( composed ) === elem.ownerDocument; + }; + } +var isHiddenWithinTree = function( elem, el ) { + + // isHiddenWithinTree might be called from jQuery#filter function; + // in that case, element will be second argument + elem = el || elem; + + // Inline style trumps all + return elem.style.display === "none" || + elem.style.display === "" && + + // Otherwise, check computed style + // Support: Firefox <=43 - 45 + // Disconnected elements can have computed display: none, so first confirm that elem is + // in the document. + isAttached( elem ) && + + jQuery.css( elem, "display" ) === "none"; + }; + + + +function adjustCSS( elem, prop, valueParts, tween ) { + var adjusted, scale, + maxIterations = 20, + currentValue = tween ? + function() { + return tween.cur(); + } : + function() { + return jQuery.css( elem, prop, "" ); + }, + initial = currentValue(), + unit = valueParts && valueParts[ 3 ] || ( jQuery.cssNumber[ prop ] ? "" : "px" ), + + // Starting value computation is required for potential unit mismatches + initialInUnit = elem.nodeType && + ( jQuery.cssNumber[ prop ] || unit !== "px" && +initial ) && + rcssNum.exec( jQuery.css( elem, prop ) ); + + if ( initialInUnit && initialInUnit[ 3 ] !== unit ) { + + // Support: Firefox <=54 + // Halve the iteration target value to prevent interference from CSS upper bounds (gh-2144) + initial = initial / 2; + + // Trust units reported by jQuery.css + unit = unit || initialInUnit[ 3 ]; + + // Iteratively approximate from a nonzero starting point + initialInUnit = +initial || 1; + + while ( maxIterations-- ) { + + // Evaluate and update our best guess (doubling guesses that zero out). + // Finish if the scale equals or crosses 1 (making the old*new product non-positive). + jQuery.style( elem, prop, initialInUnit + unit ); + if ( ( 1 - scale ) * ( 1 - ( scale = currentValue() / initial || 0.5 ) ) <= 0 ) { + maxIterations = 0; + } + initialInUnit = initialInUnit / scale; + + } + + initialInUnit = initialInUnit * 2; + jQuery.style( elem, prop, initialInUnit + unit ); + + // Make sure we update the tween properties later on + valueParts = valueParts || []; + } + + if ( valueParts ) { + initialInUnit = +initialInUnit || +initial || 0; + + // Apply relative offset (+=/-=) if specified + adjusted = valueParts[ 1 ] ? + initialInUnit + ( valueParts[ 1 ] + 1 ) * valueParts[ 2 ] : + +valueParts[ 2 ]; + if ( tween ) { + tween.unit = unit; + tween.start = initialInUnit; + tween.end = adjusted; + } + } + return adjusted; +} + + +var defaultDisplayMap = {}; + +function getDefaultDisplay( elem ) { + var temp, + doc = elem.ownerDocument, + nodeName = elem.nodeName, + display = defaultDisplayMap[ nodeName ]; + + if ( display ) { + return display; + } + + temp = doc.body.appendChild( doc.createElement( nodeName ) ); + display = jQuery.css( temp, "display" ); + + temp.parentNode.removeChild( temp ); + + if ( display === "none" ) { + display = "block"; + } + defaultDisplayMap[ nodeName ] = display; + + return display; +} + +function showHide( elements, show ) { + var display, elem, + values = [], + index = 0, + length = elements.length; + + // Determine new display value for elements that need to change + for ( ; index < length; index++ ) { + elem = elements[ index ]; + if ( !elem.style ) { + continue; + } + + display = elem.style.display; + if ( show ) { + + // Since we force visibility upon cascade-hidden elements, an immediate (and slow) + // check is required in this first loop unless we have a nonempty display value (either + // inline or about-to-be-restored) + if ( display === "none" ) { + values[ index ] = dataPriv.get( elem, "display" ) || null; + if ( !values[ index ] ) { + elem.style.display = ""; + } + } + if ( elem.style.display === "" && isHiddenWithinTree( elem ) ) { + values[ index ] = getDefaultDisplay( elem ); + } + } else { + if ( display !== "none" ) { + values[ index ] = "none"; + + // Remember what we're overwriting + dataPriv.set( elem, "display", display ); + } + } + } + + // Set the display of the elements in a second loop to avoid constant reflow + for ( index = 0; index < length; index++ ) { + if ( values[ index ] != null ) { + elements[ index ].style.display = values[ index ]; + } + } + + return elements; +} + +jQuery.fn.extend( { + show: function() { + return showHide( this, true ); + }, + hide: function() { + return showHide( this ); + }, + toggle: function( state ) { + if ( typeof state === "boolean" ) { + return state ? this.show() : this.hide(); + } + + return this.each( function() { + if ( isHiddenWithinTree( this ) ) { + jQuery( this ).show(); + } else { + jQuery( this ).hide(); + } + } ); + } +} ); +var rcheckableType = ( /^(?:checkbox|radio)$/i ); + +var rtagName = ( /<([a-z][^\/\0>\x20\t\r\n\f]*)/i ); + +var rscriptType = ( /^$|^module$|\/(?:java|ecma)script/i ); + + + +( function() { + var fragment = document.createDocumentFragment(), + div = fragment.appendChild( document.createElement( "div" ) ), + input = document.createElement( "input" ); + + // Support: Android 4.0 - 4.3 only + // Check state lost if the name is set (#11217) + // Support: Windows Web Apps (WWA) + // `name` and `type` must use .setAttribute for WWA (#14901) + input.setAttribute( "type", "radio" ); + input.setAttribute( "checked", "checked" ); + input.setAttribute( "name", "t" ); + + div.appendChild( input ); + + // Support: Android <=4.1 only + // Older WebKit doesn't clone checked state correctly in fragments + support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked; + + // Support: IE <=11 only + // Make sure textarea (and checkbox) defaultValue is properly cloned + div.innerHTML = ""; + support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue; + + // Support: IE <=9 only + // IE <=9 replaces "; + support.option = !!div.lastChild; +} )(); + + +// We have to close these tags to support XHTML (#13200) +var wrapMap = { + + // XHTML parsers do not magically insert elements in the + // same way that tag soup parsers do. So we cannot shorten + // this by omitting or other required elements. + thead: [ 1, "", "
" ], + col: [ 2, "", "
" ], + tr: [ 2, "", "
" ], + td: [ 3, "", "
" ], + + _default: [ 0, "", "" ] +}; + +wrapMap.tbody = wrapMap.tfoot = wrapMap.colgroup = wrapMap.caption = wrapMap.thead; +wrapMap.th = wrapMap.td; + +// Support: IE <=9 only +if ( !support.option ) { + wrapMap.optgroup = wrapMap.option = [ 1, "" ]; +} + + +function getAll( context, tag ) { + + // Support: IE <=9 - 11 only + // Use typeof to avoid zero-argument method invocation on host objects (#15151) + var ret; + + if ( typeof context.getElementsByTagName !== "undefined" ) { + ret = context.getElementsByTagName( tag || "*" ); + + } else if ( typeof context.querySelectorAll !== "undefined" ) { + ret = context.querySelectorAll( tag || "*" ); + + } else { + ret = []; + } + + if ( tag === undefined || tag && nodeName( context, tag ) ) { + return jQuery.merge( [ context ], ret ); + } + + return ret; +} + + +// Mark scripts as having already been evaluated +function setGlobalEval( elems, refElements ) { + var i = 0, + l = elems.length; + + for ( ; i < l; i++ ) { + dataPriv.set( + elems[ i ], + "globalEval", + !refElements || dataPriv.get( refElements[ i ], "globalEval" ) + ); + } +} + + +var rhtml = /<|&#?\w+;/; + +function buildFragment( elems, context, scripts, selection, ignored ) { + var elem, tmp, tag, wrap, attached, j, + fragment = context.createDocumentFragment(), + nodes = [], + i = 0, + l = elems.length; + + for ( ; i < l; i++ ) { + elem = elems[ i ]; + + if ( elem || elem === 0 ) { + + // Add nodes directly + if ( toType( elem ) === "object" ) { + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( nodes, elem.nodeType ? [ elem ] : elem ); + + // Convert non-html into a text node + } else if ( !rhtml.test( elem ) ) { + nodes.push( context.createTextNode( elem ) ); + + // Convert html into DOM nodes + } else { + tmp = tmp || fragment.appendChild( context.createElement( "div" ) ); + + // Deserialize a standard representation + tag = ( rtagName.exec( elem ) || [ "", "" ] )[ 1 ].toLowerCase(); + wrap = wrapMap[ tag ] || wrapMap._default; + tmp.innerHTML = wrap[ 1 ] + jQuery.htmlPrefilter( elem ) + wrap[ 2 ]; + + // Descend through wrappers to the right content + j = wrap[ 0 ]; + while ( j-- ) { + tmp = tmp.lastChild; + } + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( nodes, tmp.childNodes ); + + // Remember the top-level container + tmp = fragment.firstChild; + + // Ensure the created nodes are orphaned (#12392) + tmp.textContent = ""; + } + } + } + + // Remove wrapper from fragment + fragment.textContent = ""; + + i = 0; + while ( ( elem = nodes[ i++ ] ) ) { + + // Skip elements already in the context collection (trac-4087) + if ( selection && jQuery.inArray( elem, selection ) > -1 ) { + if ( ignored ) { + ignored.push( elem ); + } + continue; + } + + attached = isAttached( elem ); + + // Append to fragment + tmp = getAll( fragment.appendChild( elem ), "script" ); + + // Preserve script evaluation history + if ( attached ) { + setGlobalEval( tmp ); + } + + // Capture executables + if ( scripts ) { + j = 0; + while ( ( elem = tmp[ j++ ] ) ) { + if ( rscriptType.test( elem.type || "" ) ) { + scripts.push( elem ); + } + } + } + } + + return fragment; +} + + +var + rkeyEvent = /^key/, + rmouseEvent = /^(?:mouse|pointer|contextmenu|drag|drop)|click/, + rtypenamespace = /^([^.]*)(?:\.(.+)|)/; + +function returnTrue() { + return true; +} + +function returnFalse() { + return false; +} + +// Support: IE <=9 - 11+ +// focus() and blur() are asynchronous, except when they are no-op. +// So expect focus to be synchronous when the element is already active, +// and blur to be synchronous when the element is not already active. +// (focus and blur are always synchronous in other supported browsers, +// this just defines when we can count on it). +function expectSync( elem, type ) { + return ( elem === safeActiveElement() ) === ( type === "focus" ); +} + +// Support: IE <=9 only +// Accessing document.activeElement can throw unexpectedly +// https://bugs.jquery.com/ticket/13393 +function safeActiveElement() { + try { + return document.activeElement; + } catch ( err ) { } +} + +function on( elem, types, selector, data, fn, one ) { + var origFn, type; + + // Types can be a map of types/handlers + if ( typeof types === "object" ) { + + // ( types-Object, selector, data ) + if ( typeof selector !== "string" ) { + + // ( types-Object, data ) + data = data || selector; + selector = undefined; + } + for ( type in types ) { + on( elem, type, selector, data, types[ type ], one ); + } + return elem; + } + + if ( data == null && fn == null ) { + + // ( types, fn ) + fn = selector; + data = selector = undefined; + } else if ( fn == null ) { + if ( typeof selector === "string" ) { + + // ( types, selector, fn ) + fn = data; + data = undefined; + } else { + + // ( types, data, fn ) + fn = data; + data = selector; + selector = undefined; + } + } + if ( fn === false ) { + fn = returnFalse; + } else if ( !fn ) { + return elem; + } + + if ( one === 1 ) { + origFn = fn; + fn = function( event ) { + + // Can use an empty set, since event contains the info + jQuery().off( event ); + return origFn.apply( this, arguments ); + }; + + // Use same guid so caller can remove using origFn + fn.guid = origFn.guid || ( origFn.guid = jQuery.guid++ ); + } + return elem.each( function() { + jQuery.event.add( this, types, fn, data, selector ); + } ); +} + +/* + * Helper functions for managing events -- not part of the public interface. + * Props to Dean Edwards' addEvent library for many of the ideas. + */ +jQuery.event = { + + global: {}, + + add: function( elem, types, handler, data, selector ) { + + var handleObjIn, eventHandle, tmp, + events, t, handleObj, + special, handlers, type, namespaces, origType, + elemData = dataPriv.get( elem ); + + // Only attach events to objects that accept data + if ( !acceptData( elem ) ) { + return; + } + + // Caller can pass in an object of custom data in lieu of the handler + if ( handler.handler ) { + handleObjIn = handler; + handler = handleObjIn.handler; + selector = handleObjIn.selector; + } + + // Ensure that invalid selectors throw exceptions at attach time + // Evaluate against documentElement in case elem is a non-element node (e.g., document) + if ( selector ) { + jQuery.find.matchesSelector( documentElement, selector ); + } + + // Make sure that the handler has a unique ID, used to find/remove it later + if ( !handler.guid ) { + handler.guid = jQuery.guid++; + } + + // Init the element's event structure and main handler, if this is the first + if ( !( events = elemData.events ) ) { + events = elemData.events = Object.create( null ); + } + if ( !( eventHandle = elemData.handle ) ) { + eventHandle = elemData.handle = function( e ) { + + // Discard the second event of a jQuery.event.trigger() and + // when an event is called after a page has unloaded + return typeof jQuery !== "undefined" && jQuery.event.triggered !== e.type ? + jQuery.event.dispatch.apply( elem, arguments ) : undefined; + }; + } + + // Handle multiple events separated by a space + types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; + t = types.length; + while ( t-- ) { + tmp = rtypenamespace.exec( types[ t ] ) || []; + type = origType = tmp[ 1 ]; + namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); + + // There *must* be a type, no attaching namespace-only handlers + if ( !type ) { + continue; + } + + // If event changes its type, use the special event handlers for the changed type + special = jQuery.event.special[ type ] || {}; + + // If selector defined, determine special event api type, otherwise given type + type = ( selector ? special.delegateType : special.bindType ) || type; + + // Update special based on newly reset type + special = jQuery.event.special[ type ] || {}; + + // handleObj is passed to all event handlers + handleObj = jQuery.extend( { + type: type, + origType: origType, + data: data, + handler: handler, + guid: handler.guid, + selector: selector, + needsContext: selector && jQuery.expr.match.needsContext.test( selector ), + namespace: namespaces.join( "." ) + }, handleObjIn ); + + // Init the event handler queue if we're the first + if ( !( handlers = events[ type ] ) ) { + handlers = events[ type ] = []; + handlers.delegateCount = 0; + + // Only use addEventListener if the special events handler returns false + if ( !special.setup || + special.setup.call( elem, data, namespaces, eventHandle ) === false ) { + + if ( elem.addEventListener ) { + elem.addEventListener( type, eventHandle ); + } + } + } + + if ( special.add ) { + special.add.call( elem, handleObj ); + + if ( !handleObj.handler.guid ) { + handleObj.handler.guid = handler.guid; + } + } + + // Add to the element's handler list, delegates in front + if ( selector ) { + handlers.splice( handlers.delegateCount++, 0, handleObj ); + } else { + handlers.push( handleObj ); + } + + // Keep track of which events have ever been used, for event optimization + jQuery.event.global[ type ] = true; + } + + }, + + // Detach an event or set of events from an element + remove: function( elem, types, handler, selector, mappedTypes ) { + + var j, origCount, tmp, + events, t, handleObj, + special, handlers, type, namespaces, origType, + elemData = dataPriv.hasData( elem ) && dataPriv.get( elem ); + + if ( !elemData || !( events = elemData.events ) ) { + return; + } + + // Once for each type.namespace in types; type may be omitted + types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; + t = types.length; + while ( t-- ) { + tmp = rtypenamespace.exec( types[ t ] ) || []; + type = origType = tmp[ 1 ]; + namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); + + // Unbind all events (on this namespace, if provided) for the element + if ( !type ) { + for ( type in events ) { + jQuery.event.remove( elem, type + types[ t ], handler, selector, true ); + } + continue; + } + + special = jQuery.event.special[ type ] || {}; + type = ( selector ? special.delegateType : special.bindType ) || type; + handlers = events[ type ] || []; + tmp = tmp[ 2 ] && + new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ); + + // Remove matching events + origCount = j = handlers.length; + while ( j-- ) { + handleObj = handlers[ j ]; + + if ( ( mappedTypes || origType === handleObj.origType ) && + ( !handler || handler.guid === handleObj.guid ) && + ( !tmp || tmp.test( handleObj.namespace ) ) && + ( !selector || selector === handleObj.selector || + selector === "**" && handleObj.selector ) ) { + handlers.splice( j, 1 ); + + if ( handleObj.selector ) { + handlers.delegateCount--; + } + if ( special.remove ) { + special.remove.call( elem, handleObj ); + } + } + } + + // Remove generic event handler if we removed something and no more handlers exist + // (avoids potential for endless recursion during removal of special event handlers) + if ( origCount && !handlers.length ) { + if ( !special.teardown || + special.teardown.call( elem, namespaces, elemData.handle ) === false ) { + + jQuery.removeEvent( elem, type, elemData.handle ); + } + + delete events[ type ]; + } + } + + // Remove data and the expando if it's no longer used + if ( jQuery.isEmptyObject( events ) ) { + dataPriv.remove( elem, "handle events" ); + } + }, + + dispatch: function( nativeEvent ) { + + var i, j, ret, matched, handleObj, handlerQueue, + args = new Array( arguments.length ), + + // Make a writable jQuery.Event from the native event object + event = jQuery.event.fix( nativeEvent ), + + handlers = ( + dataPriv.get( this, "events" ) || Object.create( null ) + )[ event.type ] || [], + special = jQuery.event.special[ event.type ] || {}; + + // Use the fix-ed jQuery.Event rather than the (read-only) native event + args[ 0 ] = event; + + for ( i = 1; i < arguments.length; i++ ) { + args[ i ] = arguments[ i ]; + } + + event.delegateTarget = this; + + // Call the preDispatch hook for the mapped type, and let it bail if desired + if ( special.preDispatch && special.preDispatch.call( this, event ) === false ) { + return; + } + + // Determine handlers + handlerQueue = jQuery.event.handlers.call( this, event, handlers ); + + // Run delegates first; they may want to stop propagation beneath us + i = 0; + while ( ( matched = handlerQueue[ i++ ] ) && !event.isPropagationStopped() ) { + event.currentTarget = matched.elem; + + j = 0; + while ( ( handleObj = matched.handlers[ j++ ] ) && + !event.isImmediatePropagationStopped() ) { + + // If the event is namespaced, then each handler is only invoked if it is + // specially universal or its namespaces are a superset of the event's. + if ( !event.rnamespace || handleObj.namespace === false || + event.rnamespace.test( handleObj.namespace ) ) { + + event.handleObj = handleObj; + event.data = handleObj.data; + + ret = ( ( jQuery.event.special[ handleObj.origType ] || {} ).handle || + handleObj.handler ).apply( matched.elem, args ); + + if ( ret !== undefined ) { + if ( ( event.result = ret ) === false ) { + event.preventDefault(); + event.stopPropagation(); + } + } + } + } + } + + // Call the postDispatch hook for the mapped type + if ( special.postDispatch ) { + special.postDispatch.call( this, event ); + } + + return event.result; + }, + + handlers: function( event, handlers ) { + var i, handleObj, sel, matchedHandlers, matchedSelectors, + handlerQueue = [], + delegateCount = handlers.delegateCount, + cur = event.target; + + // Find delegate handlers + if ( delegateCount && + + // Support: IE <=9 + // Black-hole SVG instance trees (trac-13180) + cur.nodeType && + + // Support: Firefox <=42 + // Suppress spec-violating clicks indicating a non-primary pointer button (trac-3861) + // https://www.w3.org/TR/DOM-Level-3-Events/#event-type-click + // Support: IE 11 only + // ...but not arrow key "clicks" of radio inputs, which can have `button` -1 (gh-2343) + !( event.type === "click" && event.button >= 1 ) ) { + + for ( ; cur !== this; cur = cur.parentNode || this ) { + + // Don't check non-elements (#13208) + // Don't process clicks on disabled elements (#6911, #8165, #11382, #11764) + if ( cur.nodeType === 1 && !( event.type === "click" && cur.disabled === true ) ) { + matchedHandlers = []; + matchedSelectors = {}; + for ( i = 0; i < delegateCount; i++ ) { + handleObj = handlers[ i ]; + + // Don't conflict with Object.prototype properties (#13203) + sel = handleObj.selector + " "; + + if ( matchedSelectors[ sel ] === undefined ) { + matchedSelectors[ sel ] = handleObj.needsContext ? + jQuery( sel, this ).index( cur ) > -1 : + jQuery.find( sel, this, null, [ cur ] ).length; + } + if ( matchedSelectors[ sel ] ) { + matchedHandlers.push( handleObj ); + } + } + if ( matchedHandlers.length ) { + handlerQueue.push( { elem: cur, handlers: matchedHandlers } ); + } + } + } + } + + // Add the remaining (directly-bound) handlers + cur = this; + if ( delegateCount < handlers.length ) { + handlerQueue.push( { elem: cur, handlers: handlers.slice( delegateCount ) } ); + } + + return handlerQueue; + }, + + addProp: function( name, hook ) { + Object.defineProperty( jQuery.Event.prototype, name, { + enumerable: true, + configurable: true, + + get: isFunction( hook ) ? + function() { + if ( this.originalEvent ) { + return hook( this.originalEvent ); + } + } : + function() { + if ( this.originalEvent ) { + return this.originalEvent[ name ]; + } + }, + + set: function( value ) { + Object.defineProperty( this, name, { + enumerable: true, + configurable: true, + writable: true, + value: value + } ); + } + } ); + }, + + fix: function( originalEvent ) { + return originalEvent[ jQuery.expando ] ? + originalEvent : + new jQuery.Event( originalEvent ); + }, + + special: { + load: { + + // Prevent triggered image.load events from bubbling to window.load + noBubble: true + }, + click: { + + // Utilize native event to ensure correct state for checkable inputs + setup: function( data ) { + + // For mutual compressibility with _default, replace `this` access with a local var. + // `|| data` is dead code meant only to preserve the variable through minification. + var el = this || data; + + // Claim the first handler + if ( rcheckableType.test( el.type ) && + el.click && nodeName( el, "input" ) ) { + + // dataPriv.set( el, "click", ... ) + leverageNative( el, "click", returnTrue ); + } + + // Return false to allow normal processing in the caller + return false; + }, + trigger: function( data ) { + + // For mutual compressibility with _default, replace `this` access with a local var. + // `|| data` is dead code meant only to preserve the variable through minification. + var el = this || data; + + // Force setup before triggering a click + if ( rcheckableType.test( el.type ) && + el.click && nodeName( el, "input" ) ) { + + leverageNative( el, "click" ); + } + + // Return non-false to allow normal event-path propagation + return true; + }, + + // For cross-browser consistency, suppress native .click() on links + // Also prevent it if we're currently inside a leveraged native-event stack + _default: function( event ) { + var target = event.target; + return rcheckableType.test( target.type ) && + target.click && nodeName( target, "input" ) && + dataPriv.get( target, "click" ) || + nodeName( target, "a" ); + } + }, + + beforeunload: { + postDispatch: function( event ) { + + // Support: Firefox 20+ + // Firefox doesn't alert if the returnValue field is not set. + if ( event.result !== undefined && event.originalEvent ) { + event.originalEvent.returnValue = event.result; + } + } + } + } +}; + +// Ensure the presence of an event listener that handles manually-triggered +// synthetic events by interrupting progress until reinvoked in response to +// *native* events that it fires directly, ensuring that state changes have +// already occurred before other listeners are invoked. +function leverageNative( el, type, expectSync ) { + + // Missing expectSync indicates a trigger call, which must force setup through jQuery.event.add + if ( !expectSync ) { + if ( dataPriv.get( el, type ) === undefined ) { + jQuery.event.add( el, type, returnTrue ); + } + return; + } + + // Register the controller as a special universal handler for all event namespaces + dataPriv.set( el, type, false ); + jQuery.event.add( el, type, { + namespace: false, + handler: function( event ) { + var notAsync, result, + saved = dataPriv.get( this, type ); + + if ( ( event.isTrigger & 1 ) && this[ type ] ) { + + // Interrupt processing of the outer synthetic .trigger()ed event + // Saved data should be false in such cases, but might be a leftover capture object + // from an async native handler (gh-4350) + if ( !saved.length ) { + + // Store arguments for use when handling the inner native event + // There will always be at least one argument (an event object), so this array + // will not be confused with a leftover capture object. + saved = slice.call( arguments ); + dataPriv.set( this, type, saved ); + + // Trigger the native event and capture its result + // Support: IE <=9 - 11+ + // focus() and blur() are asynchronous + notAsync = expectSync( this, type ); + this[ type ](); + result = dataPriv.get( this, type ); + if ( saved !== result || notAsync ) { + dataPriv.set( this, type, false ); + } else { + result = {}; + } + if ( saved !== result ) { + + // Cancel the outer synthetic event + event.stopImmediatePropagation(); + event.preventDefault(); + return result.value; + } + + // If this is an inner synthetic event for an event with a bubbling surrogate + // (focus or blur), assume that the surrogate already propagated from triggering the + // native event and prevent that from happening again here. + // This technically gets the ordering wrong w.r.t. to `.trigger()` (in which the + // bubbling surrogate propagates *after* the non-bubbling base), but that seems + // less bad than duplication. + } else if ( ( jQuery.event.special[ type ] || {} ).delegateType ) { + event.stopPropagation(); + } + + // If this is a native event triggered above, everything is now in order + // Fire an inner synthetic event with the original arguments + } else if ( saved.length ) { + + // ...and capture the result + dataPriv.set( this, type, { + value: jQuery.event.trigger( + + // Support: IE <=9 - 11+ + // Extend with the prototype to reset the above stopImmediatePropagation() + jQuery.extend( saved[ 0 ], jQuery.Event.prototype ), + saved.slice( 1 ), + this + ) + } ); + + // Abort handling of the native event + event.stopImmediatePropagation(); + } + } + } ); +} + +jQuery.removeEvent = function( elem, type, handle ) { + + // This "if" is needed for plain objects + if ( elem.removeEventListener ) { + elem.removeEventListener( type, handle ); + } +}; + +jQuery.Event = function( src, props ) { + + // Allow instantiation without the 'new' keyword + if ( !( this instanceof jQuery.Event ) ) { + return new jQuery.Event( src, props ); + } + + // Event object + if ( src && src.type ) { + this.originalEvent = src; + this.type = src.type; + + // Events bubbling up the document may have been marked as prevented + // by a handler lower down the tree; reflect the correct value. + this.isDefaultPrevented = src.defaultPrevented || + src.defaultPrevented === undefined && + + // Support: Android <=2.3 only + src.returnValue === false ? + returnTrue : + returnFalse; + + // Create target properties + // Support: Safari <=6 - 7 only + // Target should not be a text node (#504, #13143) + this.target = ( src.target && src.target.nodeType === 3 ) ? + src.target.parentNode : + src.target; + + this.currentTarget = src.currentTarget; + this.relatedTarget = src.relatedTarget; + + // Event type + } else { + this.type = src; + } + + // Put explicitly provided properties onto the event object + if ( props ) { + jQuery.extend( this, props ); + } + + // Create a timestamp if incoming event doesn't have one + this.timeStamp = src && src.timeStamp || Date.now(); + + // Mark it as fixed + this[ jQuery.expando ] = true; +}; + +// jQuery.Event is based on DOM3 Events as specified by the ECMAScript Language Binding +// https://www.w3.org/TR/2003/WD-DOM-Level-3-Events-20030331/ecma-script-binding.html +jQuery.Event.prototype = { + constructor: jQuery.Event, + isDefaultPrevented: returnFalse, + isPropagationStopped: returnFalse, + isImmediatePropagationStopped: returnFalse, + isSimulated: false, + + preventDefault: function() { + var e = this.originalEvent; + + this.isDefaultPrevented = returnTrue; + + if ( e && !this.isSimulated ) { + e.preventDefault(); + } + }, + stopPropagation: function() { + var e = this.originalEvent; + + this.isPropagationStopped = returnTrue; + + if ( e && !this.isSimulated ) { + e.stopPropagation(); + } + }, + stopImmediatePropagation: function() { + var e = this.originalEvent; + + this.isImmediatePropagationStopped = returnTrue; + + if ( e && !this.isSimulated ) { + e.stopImmediatePropagation(); + } + + this.stopPropagation(); + } +}; + +// Includes all common event props including KeyEvent and MouseEvent specific props +jQuery.each( { + altKey: true, + bubbles: true, + cancelable: true, + changedTouches: true, + ctrlKey: true, + detail: true, + eventPhase: true, + metaKey: true, + pageX: true, + pageY: true, + shiftKey: true, + view: true, + "char": true, + code: true, + charCode: true, + key: true, + keyCode: true, + button: true, + buttons: true, + clientX: true, + clientY: true, + offsetX: true, + offsetY: true, + pointerId: true, + pointerType: true, + screenX: true, + screenY: true, + targetTouches: true, + toElement: true, + touches: true, + + which: function( event ) { + var button = event.button; + + // Add which for key events + if ( event.which == null && rkeyEvent.test( event.type ) ) { + return event.charCode != null ? event.charCode : event.keyCode; + } + + // Add which for click: 1 === left; 2 === middle; 3 === right + if ( !event.which && button !== undefined && rmouseEvent.test( event.type ) ) { + if ( button & 1 ) { + return 1; + } + + if ( button & 2 ) { + return 3; + } + + if ( button & 4 ) { + return 2; + } + + return 0; + } + + return event.which; + } +}, jQuery.event.addProp ); + +jQuery.each( { focus: "focusin", blur: "focusout" }, function( type, delegateType ) { + jQuery.event.special[ type ] = { + + // Utilize native event if possible so blur/focus sequence is correct + setup: function() { + + // Claim the first handler + // dataPriv.set( this, "focus", ... ) + // dataPriv.set( this, "blur", ... ) + leverageNative( this, type, expectSync ); + + // Return false to allow normal processing in the caller + return false; + }, + trigger: function() { + + // Force setup before trigger + leverageNative( this, type ); + + // Return non-false to allow normal event-path propagation + return true; + }, + + delegateType: delegateType + }; +} ); + +// Create mouseenter/leave events using mouseover/out and event-time checks +// so that event delegation works in jQuery. +// Do the same for pointerenter/pointerleave and pointerover/pointerout +// +// Support: Safari 7 only +// Safari sends mouseenter too often; see: +// https://bugs.chromium.org/p/chromium/issues/detail?id=470258 +// for the description of the bug (it existed in older Chrome versions as well). +jQuery.each( { + mouseenter: "mouseover", + mouseleave: "mouseout", + pointerenter: "pointerover", + pointerleave: "pointerout" +}, function( orig, fix ) { + jQuery.event.special[ orig ] = { + delegateType: fix, + bindType: fix, + + handle: function( event ) { + var ret, + target = this, + related = event.relatedTarget, + handleObj = event.handleObj; + + // For mouseenter/leave call the handler if related is outside the target. + // NB: No relatedTarget if the mouse left/entered the browser window + if ( !related || ( related !== target && !jQuery.contains( target, related ) ) ) { + event.type = handleObj.origType; + ret = handleObj.handler.apply( this, arguments ); + event.type = fix; + } + return ret; + } + }; +} ); + +jQuery.fn.extend( { + + on: function( types, selector, data, fn ) { + return on( this, types, selector, data, fn ); + }, + one: function( types, selector, data, fn ) { + return on( this, types, selector, data, fn, 1 ); + }, + off: function( types, selector, fn ) { + var handleObj, type; + if ( types && types.preventDefault && types.handleObj ) { + + // ( event ) dispatched jQuery.Event + handleObj = types.handleObj; + jQuery( types.delegateTarget ).off( + handleObj.namespace ? + handleObj.origType + "." + handleObj.namespace : + handleObj.origType, + handleObj.selector, + handleObj.handler + ); + return this; + } + if ( typeof types === "object" ) { + + // ( types-object [, selector] ) + for ( type in types ) { + this.off( type, selector, types[ type ] ); + } + return this; + } + if ( selector === false || typeof selector === "function" ) { + + // ( types [, fn] ) + fn = selector; + selector = undefined; + } + if ( fn === false ) { + fn = returnFalse; + } + return this.each( function() { + jQuery.event.remove( this, types, fn, selector ); + } ); + } +} ); + + +var + + // Support: IE <=10 - 11, Edge 12 - 13 only + // In IE/Edge using regex groups here causes severe slowdowns. + // See https://connect.microsoft.com/IE/feedback/details/1736512/ + rnoInnerhtml = /\s*$/g; + +// Prefer a tbody over its parent table for containing new rows +function manipulationTarget( elem, content ) { + if ( nodeName( elem, "table" ) && + nodeName( content.nodeType !== 11 ? content : content.firstChild, "tr" ) ) { + + return jQuery( elem ).children( "tbody" )[ 0 ] || elem; + } + + return elem; +} + +// Replace/restore the type attribute of script elements for safe DOM manipulation +function disableScript( elem ) { + elem.type = ( elem.getAttribute( "type" ) !== null ) + "/" + elem.type; + return elem; +} +function restoreScript( elem ) { + if ( ( elem.type || "" ).slice( 0, 5 ) === "true/" ) { + elem.type = elem.type.slice( 5 ); + } else { + elem.removeAttribute( "type" ); + } + + return elem; +} + +function cloneCopyEvent( src, dest ) { + var i, l, type, pdataOld, udataOld, udataCur, events; + + if ( dest.nodeType !== 1 ) { + return; + } + + // 1. Copy private data: events, handlers, etc. + if ( dataPriv.hasData( src ) ) { + pdataOld = dataPriv.get( src ); + events = pdataOld.events; + + if ( events ) { + dataPriv.remove( dest, "handle events" ); + + for ( type in events ) { + for ( i = 0, l = events[ type ].length; i < l; i++ ) { + jQuery.event.add( dest, type, events[ type ][ i ] ); + } + } + } + } + + // 2. Copy user data + if ( dataUser.hasData( src ) ) { + udataOld = dataUser.access( src ); + udataCur = jQuery.extend( {}, udataOld ); + + dataUser.set( dest, udataCur ); + } +} + +// Fix IE bugs, see support tests +function fixInput( src, dest ) { + var nodeName = dest.nodeName.toLowerCase(); + + // Fails to persist the checked state of a cloned checkbox or radio button. + if ( nodeName === "input" && rcheckableType.test( src.type ) ) { + dest.checked = src.checked; + + // Fails to return the selected option to the default selected state when cloning options + } else if ( nodeName === "input" || nodeName === "textarea" ) { + dest.defaultValue = src.defaultValue; + } +} + +function domManip( collection, args, callback, ignored ) { + + // Flatten any nested arrays + args = flat( args ); + + var fragment, first, scripts, hasScripts, node, doc, + i = 0, + l = collection.length, + iNoClone = l - 1, + value = args[ 0 ], + valueIsFunction = isFunction( value ); + + // We can't cloneNode fragments that contain checked, in WebKit + if ( valueIsFunction || + ( l > 1 && typeof value === "string" && + !support.checkClone && rchecked.test( value ) ) ) { + return collection.each( function( index ) { + var self = collection.eq( index ); + if ( valueIsFunction ) { + args[ 0 ] = value.call( this, index, self.html() ); + } + domManip( self, args, callback, ignored ); + } ); + } + + if ( l ) { + fragment = buildFragment( args, collection[ 0 ].ownerDocument, false, collection, ignored ); + first = fragment.firstChild; + + if ( fragment.childNodes.length === 1 ) { + fragment = first; + } + + // Require either new content or an interest in ignored elements to invoke the callback + if ( first || ignored ) { + scripts = jQuery.map( getAll( fragment, "script" ), disableScript ); + hasScripts = scripts.length; + + // Use the original fragment for the last item + // instead of the first because it can end up + // being emptied incorrectly in certain situations (#8070). + for ( ; i < l; i++ ) { + node = fragment; + + if ( i !== iNoClone ) { + node = jQuery.clone( node, true, true ); + + // Keep references to cloned scripts for later restoration + if ( hasScripts ) { + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( scripts, getAll( node, "script" ) ); + } + } + + callback.call( collection[ i ], node, i ); + } + + if ( hasScripts ) { + doc = scripts[ scripts.length - 1 ].ownerDocument; + + // Reenable scripts + jQuery.map( scripts, restoreScript ); + + // Evaluate executable scripts on first document insertion + for ( i = 0; i < hasScripts; i++ ) { + node = scripts[ i ]; + if ( rscriptType.test( node.type || "" ) && + !dataPriv.access( node, "globalEval" ) && + jQuery.contains( doc, node ) ) { + + if ( node.src && ( node.type || "" ).toLowerCase() !== "module" ) { + + // Optional AJAX dependency, but won't run scripts if not present + if ( jQuery._evalUrl && !node.noModule ) { + jQuery._evalUrl( node.src, { + nonce: node.nonce || node.getAttribute( "nonce" ) + }, doc ); + } + } else { + DOMEval( node.textContent.replace( rcleanScript, "" ), node, doc ); + } + } + } + } + } + } + + return collection; +} + +function remove( elem, selector, keepData ) { + var node, + nodes = selector ? jQuery.filter( selector, elem ) : elem, + i = 0; + + for ( ; ( node = nodes[ i ] ) != null; i++ ) { + if ( !keepData && node.nodeType === 1 ) { + jQuery.cleanData( getAll( node ) ); + } + + if ( node.parentNode ) { + if ( keepData && isAttached( node ) ) { + setGlobalEval( getAll( node, "script" ) ); + } + node.parentNode.removeChild( node ); + } + } + + return elem; +} + +jQuery.extend( { + htmlPrefilter: function( html ) { + return html; + }, + + clone: function( elem, dataAndEvents, deepDataAndEvents ) { + var i, l, srcElements, destElements, + clone = elem.cloneNode( true ), + inPage = isAttached( elem ); + + // Fix IE cloning issues + if ( !support.noCloneChecked && ( elem.nodeType === 1 || elem.nodeType === 11 ) && + !jQuery.isXMLDoc( elem ) ) { + + // We eschew Sizzle here for performance reasons: https://jsperf.com/getall-vs-sizzle/2 + destElements = getAll( clone ); + srcElements = getAll( elem ); + + for ( i = 0, l = srcElements.length; i < l; i++ ) { + fixInput( srcElements[ i ], destElements[ i ] ); + } + } + + // Copy the events from the original to the clone + if ( dataAndEvents ) { + if ( deepDataAndEvents ) { + srcElements = srcElements || getAll( elem ); + destElements = destElements || getAll( clone ); + + for ( i = 0, l = srcElements.length; i < l; i++ ) { + cloneCopyEvent( srcElements[ i ], destElements[ i ] ); + } + } else { + cloneCopyEvent( elem, clone ); + } + } + + // Preserve script evaluation history + destElements = getAll( clone, "script" ); + if ( destElements.length > 0 ) { + setGlobalEval( destElements, !inPage && getAll( elem, "script" ) ); + } + + // Return the cloned set + return clone; + }, + + cleanData: function( elems ) { + var data, elem, type, + special = jQuery.event.special, + i = 0; + + for ( ; ( elem = elems[ i ] ) !== undefined; i++ ) { + if ( acceptData( elem ) ) { + if ( ( data = elem[ dataPriv.expando ] ) ) { + if ( data.events ) { + for ( type in data.events ) { + if ( special[ type ] ) { + jQuery.event.remove( elem, type ); + + // This is a shortcut to avoid jQuery.event.remove's overhead + } else { + jQuery.removeEvent( elem, type, data.handle ); + } + } + } + + // Support: Chrome <=35 - 45+ + // Assign undefined instead of using delete, see Data#remove + elem[ dataPriv.expando ] = undefined; + } + if ( elem[ dataUser.expando ] ) { + + // Support: Chrome <=35 - 45+ + // Assign undefined instead of using delete, see Data#remove + elem[ dataUser.expando ] = undefined; + } + } + } + } +} ); + +jQuery.fn.extend( { + detach: function( selector ) { + return remove( this, selector, true ); + }, + + remove: function( selector ) { + return remove( this, selector ); + }, + + text: function( value ) { + return access( this, function( value ) { + return value === undefined ? + jQuery.text( this ) : + this.empty().each( function() { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + this.textContent = value; + } + } ); + }, null, value, arguments.length ); + }, + + append: function() { + return domManip( this, arguments, function( elem ) { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + var target = manipulationTarget( this, elem ); + target.appendChild( elem ); + } + } ); + }, + + prepend: function() { + return domManip( this, arguments, function( elem ) { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + var target = manipulationTarget( this, elem ); + target.insertBefore( elem, target.firstChild ); + } + } ); + }, + + before: function() { + return domManip( this, arguments, function( elem ) { + if ( this.parentNode ) { + this.parentNode.insertBefore( elem, this ); + } + } ); + }, + + after: function() { + return domManip( this, arguments, function( elem ) { + if ( this.parentNode ) { + this.parentNode.insertBefore( elem, this.nextSibling ); + } + } ); + }, + + empty: function() { + var elem, + i = 0; + + for ( ; ( elem = this[ i ] ) != null; i++ ) { + if ( elem.nodeType === 1 ) { + + // Prevent memory leaks + jQuery.cleanData( getAll( elem, false ) ); + + // Remove any remaining nodes + elem.textContent = ""; + } + } + + return this; + }, + + clone: function( dataAndEvents, deepDataAndEvents ) { + dataAndEvents = dataAndEvents == null ? false : dataAndEvents; + deepDataAndEvents = deepDataAndEvents == null ? dataAndEvents : deepDataAndEvents; + + return this.map( function() { + return jQuery.clone( this, dataAndEvents, deepDataAndEvents ); + } ); + }, + + html: function( value ) { + return access( this, function( value ) { + var elem = this[ 0 ] || {}, + i = 0, + l = this.length; + + if ( value === undefined && elem.nodeType === 1 ) { + return elem.innerHTML; + } + + // See if we can take a shortcut and just use innerHTML + if ( typeof value === "string" && !rnoInnerhtml.test( value ) && + !wrapMap[ ( rtagName.exec( value ) || [ "", "" ] )[ 1 ].toLowerCase() ] ) { + + value = jQuery.htmlPrefilter( value ); + + try { + for ( ; i < l; i++ ) { + elem = this[ i ] || {}; + + // Remove element nodes and prevent memory leaks + if ( elem.nodeType === 1 ) { + jQuery.cleanData( getAll( elem, false ) ); + elem.innerHTML = value; + } + } + + elem = 0; + + // If using innerHTML throws an exception, use the fallback method + } catch ( e ) {} + } + + if ( elem ) { + this.empty().append( value ); + } + }, null, value, arguments.length ); + }, + + replaceWith: function() { + var ignored = []; + + // Make the changes, replacing each non-ignored context element with the new content + return domManip( this, arguments, function( elem ) { + var parent = this.parentNode; + + if ( jQuery.inArray( this, ignored ) < 0 ) { + jQuery.cleanData( getAll( this ) ); + if ( parent ) { + parent.replaceChild( elem, this ); + } + } + + // Force callback invocation + }, ignored ); + } +} ); + +jQuery.each( { + appendTo: "append", + prependTo: "prepend", + insertBefore: "before", + insertAfter: "after", + replaceAll: "replaceWith" +}, function( name, original ) { + jQuery.fn[ name ] = function( selector ) { + var elems, + ret = [], + insert = jQuery( selector ), + last = insert.length - 1, + i = 0; + + for ( ; i <= last; i++ ) { + elems = i === last ? this : this.clone( true ); + jQuery( insert[ i ] )[ original ]( elems ); + + // Support: Android <=4.0 only, PhantomJS 1 only + // .get() because push.apply(_, arraylike) throws on ancient WebKit + push.apply( ret, elems.get() ); + } + + return this.pushStack( ret ); + }; +} ); +var rnumnonpx = new RegExp( "^(" + pnum + ")(?!px)[a-z%]+$", "i" ); + +var getStyles = function( elem ) { + + // Support: IE <=11 only, Firefox <=30 (#15098, #14150) + // IE throws on elements created in popups + // FF meanwhile throws on frame elements through "defaultView.getComputedStyle" + var view = elem.ownerDocument.defaultView; + + if ( !view || !view.opener ) { + view = window; + } + + return view.getComputedStyle( elem ); + }; + +var swap = function( elem, options, callback ) { + var ret, name, + old = {}; + + // Remember the old values, and insert the new ones + for ( name in options ) { + old[ name ] = elem.style[ name ]; + elem.style[ name ] = options[ name ]; + } + + ret = callback.call( elem ); + + // Revert the old values + for ( name in options ) { + elem.style[ name ] = old[ name ]; + } + + return ret; +}; + + +var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" ); + + + +( function() { + + // Executing both pixelPosition & boxSizingReliable tests require only one layout + // so they're executed at the same time to save the second computation. + function computeStyleTests() { + + // This is a singleton, we need to execute it only once + if ( !div ) { + return; + } + + container.style.cssText = "position:absolute;left:-11111px;width:60px;" + + "margin-top:1px;padding:0;border:0"; + div.style.cssText = + "position:relative;display:block;box-sizing:border-box;overflow:scroll;" + + "margin:auto;border:1px;padding:1px;" + + "width:60%;top:1%"; + documentElement.appendChild( container ).appendChild( div ); + + var divStyle = window.getComputedStyle( div ); + pixelPositionVal = divStyle.top !== "1%"; + + // Support: Android 4.0 - 4.3 only, Firefox <=3 - 44 + reliableMarginLeftVal = roundPixelMeasures( divStyle.marginLeft ) === 12; + + // Support: Android 4.0 - 4.3 only, Safari <=9.1 - 10.1, iOS <=7.0 - 9.3 + // Some styles come back with percentage values, even though they shouldn't + div.style.right = "60%"; + pixelBoxStylesVal = roundPixelMeasures( divStyle.right ) === 36; + + // Support: IE 9 - 11 only + // Detect misreporting of content dimensions for box-sizing:border-box elements + boxSizingReliableVal = roundPixelMeasures( divStyle.width ) === 36; + + // Support: IE 9 only + // Detect overflow:scroll screwiness (gh-3699) + // Support: Chrome <=64 + // Don't get tricked when zoom affects offsetWidth (gh-4029) + div.style.position = "absolute"; + scrollboxSizeVal = roundPixelMeasures( div.offsetWidth / 3 ) === 12; + + documentElement.removeChild( container ); + + // Nullify the div so it wouldn't be stored in the memory and + // it will also be a sign that checks already performed + div = null; + } + + function roundPixelMeasures( measure ) { + return Math.round( parseFloat( measure ) ); + } + + var pixelPositionVal, boxSizingReliableVal, scrollboxSizeVal, pixelBoxStylesVal, + reliableTrDimensionsVal, reliableMarginLeftVal, + container = document.createElement( "div" ), + div = document.createElement( "div" ); + + // Finish early in limited (non-browser) environments + if ( !div.style ) { + return; + } + + // Support: IE <=9 - 11 only + // Style of cloned element affects source element cloned (#8908) + div.style.backgroundClip = "content-box"; + div.cloneNode( true ).style.backgroundClip = ""; + support.clearCloneStyle = div.style.backgroundClip === "content-box"; + + jQuery.extend( support, { + boxSizingReliable: function() { + computeStyleTests(); + return boxSizingReliableVal; + }, + pixelBoxStyles: function() { + computeStyleTests(); + return pixelBoxStylesVal; + }, + pixelPosition: function() { + computeStyleTests(); + return pixelPositionVal; + }, + reliableMarginLeft: function() { + computeStyleTests(); + return reliableMarginLeftVal; + }, + scrollboxSize: function() { + computeStyleTests(); + return scrollboxSizeVal; + }, + + // Support: IE 9 - 11+, Edge 15 - 18+ + // IE/Edge misreport `getComputedStyle` of table rows with width/height + // set in CSS while `offset*` properties report correct values. + // Behavior in IE 9 is more subtle than in newer versions & it passes + // some versions of this test; make sure not to make it pass there! + reliableTrDimensions: function() { + var table, tr, trChild, trStyle; + if ( reliableTrDimensionsVal == null ) { + table = document.createElement( "table" ); + tr = document.createElement( "tr" ); + trChild = document.createElement( "div" ); + + table.style.cssText = "position:absolute;left:-11111px"; + tr.style.height = "1px"; + trChild.style.height = "9px"; + + documentElement + .appendChild( table ) + .appendChild( tr ) + .appendChild( trChild ); + + trStyle = window.getComputedStyle( tr ); + reliableTrDimensionsVal = parseInt( trStyle.height ) > 3; + + documentElement.removeChild( table ); + } + return reliableTrDimensionsVal; + } + } ); +} )(); + + +function curCSS( elem, name, computed ) { + var width, minWidth, maxWidth, ret, + + // Support: Firefox 51+ + // Retrieving style before computed somehow + // fixes an issue with getting wrong values + // on detached elements + style = elem.style; + + computed = computed || getStyles( elem ); + + // getPropertyValue is needed for: + // .css('filter') (IE 9 only, #12537) + // .css('--customProperty) (#3144) + if ( computed ) { + ret = computed.getPropertyValue( name ) || computed[ name ]; + + if ( ret === "" && !isAttached( elem ) ) { + ret = jQuery.style( elem, name ); + } + + // A tribute to the "awesome hack by Dean Edwards" + // Android Browser returns percentage for some values, + // but width seems to be reliably pixels. + // This is against the CSSOM draft spec: + // https://drafts.csswg.org/cssom/#resolved-values + if ( !support.pixelBoxStyles() && rnumnonpx.test( ret ) && rboxStyle.test( name ) ) { + + // Remember the original values + width = style.width; + minWidth = style.minWidth; + maxWidth = style.maxWidth; + + // Put in the new values to get a computed value out + style.minWidth = style.maxWidth = style.width = ret; + ret = computed.width; + + // Revert the changed values + style.width = width; + style.minWidth = minWidth; + style.maxWidth = maxWidth; + } + } + + return ret !== undefined ? + + // Support: IE <=9 - 11 only + // IE returns zIndex value as an integer. + ret + "" : + ret; +} + + +function addGetHookIf( conditionFn, hookFn ) { + + // Define the hook, we'll check on the first run if it's really needed. + return { + get: function() { + if ( conditionFn() ) { + + // Hook not needed (or it's not possible to use it due + // to missing dependency), remove it. + delete this.get; + return; + } + + // Hook needed; redefine it so that the support test is not executed again. + return ( this.get = hookFn ).apply( this, arguments ); + } + }; +} + + +var cssPrefixes = [ "Webkit", "Moz", "ms" ], + emptyStyle = document.createElement( "div" ).style, + vendorProps = {}; + +// Return a vendor-prefixed property or undefined +function vendorPropName( name ) { + + // Check for vendor prefixed names + var capName = name[ 0 ].toUpperCase() + name.slice( 1 ), + i = cssPrefixes.length; + + while ( i-- ) { + name = cssPrefixes[ i ] + capName; + if ( name in emptyStyle ) { + return name; + } + } +} + +// Return a potentially-mapped jQuery.cssProps or vendor prefixed property +function finalPropName( name ) { + var final = jQuery.cssProps[ name ] || vendorProps[ name ]; + + if ( final ) { + return final; + } + if ( name in emptyStyle ) { + return name; + } + return vendorProps[ name ] = vendorPropName( name ) || name; +} + + +var + + // Swappable if display is none or starts with table + // except "table", "table-cell", or "table-caption" + // See here for display values: https://developer.mozilla.org/en-US/docs/CSS/display + rdisplayswap = /^(none|table(?!-c[ea]).+)/, + rcustomProp = /^--/, + cssShow = { position: "absolute", visibility: "hidden", display: "block" }, + cssNormalTransform = { + letterSpacing: "0", + fontWeight: "400" + }; + +function setPositiveNumber( _elem, value, subtract ) { + + // Any relative (+/-) values have already been + // normalized at this point + var matches = rcssNum.exec( value ); + return matches ? + + // Guard against undefined "subtract", e.g., when used as in cssHooks + Math.max( 0, matches[ 2 ] - ( subtract || 0 ) ) + ( matches[ 3 ] || "px" ) : + value; +} + +function boxModelAdjustment( elem, dimension, box, isBorderBox, styles, computedVal ) { + var i = dimension === "width" ? 1 : 0, + extra = 0, + delta = 0; + + // Adjustment may not be necessary + if ( box === ( isBorderBox ? "border" : "content" ) ) { + return 0; + } + + for ( ; i < 4; i += 2 ) { + + // Both box models exclude margin + if ( box === "margin" ) { + delta += jQuery.css( elem, box + cssExpand[ i ], true, styles ); + } + + // If we get here with a content-box, we're seeking "padding" or "border" or "margin" + if ( !isBorderBox ) { + + // Add padding + delta += jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); + + // For "border" or "margin", add border + if ( box !== "padding" ) { + delta += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + + // But still keep track of it otherwise + } else { + extra += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + } + + // If we get here with a border-box (content + padding + border), we're seeking "content" or + // "padding" or "margin" + } else { + + // For "content", subtract padding + if ( box === "content" ) { + delta -= jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); + } + + // For "content" or "padding", subtract border + if ( box !== "margin" ) { + delta -= jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + } + } + } + + // Account for positive content-box scroll gutter when requested by providing computedVal + if ( !isBorderBox && computedVal >= 0 ) { + + // offsetWidth/offsetHeight is a rounded sum of content, padding, scroll gutter, and border + // Assuming integer scroll gutter, subtract the rest and round down + delta += Math.max( 0, Math.ceil( + elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - + computedVal - + delta - + extra - + 0.5 + + // If offsetWidth/offsetHeight is unknown, then we can't determine content-box scroll gutter + // Use an explicit zero to avoid NaN (gh-3964) + ) ) || 0; + } + + return delta; +} + +function getWidthOrHeight( elem, dimension, extra ) { + + // Start with computed style + var styles = getStyles( elem ), + + // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-4322). + // Fake content-box until we know it's needed to know the true value. + boxSizingNeeded = !support.boxSizingReliable() || extra, + isBorderBox = boxSizingNeeded && + jQuery.css( elem, "boxSizing", false, styles ) === "border-box", + valueIsBorderBox = isBorderBox, + + val = curCSS( elem, dimension, styles ), + offsetProp = "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ); + + // Support: Firefox <=54 + // Return a confounding non-pixel value or feign ignorance, as appropriate. + if ( rnumnonpx.test( val ) ) { + if ( !extra ) { + return val; + } + val = "auto"; + } + + + // Support: IE 9 - 11 only + // Use offsetWidth/offsetHeight for when box sizing is unreliable. + // In those cases, the computed value can be trusted to be border-box. + if ( ( !support.boxSizingReliable() && isBorderBox || + + // Support: IE 10 - 11+, Edge 15 - 18+ + // IE/Edge misreport `getComputedStyle` of table rows with width/height + // set in CSS while `offset*` properties report correct values. + // Interestingly, in some cases IE 9 doesn't suffer from this issue. + !support.reliableTrDimensions() && nodeName( elem, "tr" ) || + + // Fall back to offsetWidth/offsetHeight when value is "auto" + // This happens for inline elements with no explicit setting (gh-3571) + val === "auto" || + + // Support: Android <=4.1 - 4.3 only + // Also use offsetWidth/offsetHeight for misreported inline dimensions (gh-3602) + !parseFloat( val ) && jQuery.css( elem, "display", false, styles ) === "inline" ) && + + // Make sure the element is visible & connected + elem.getClientRects().length ) { + + isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box"; + + // Where available, offsetWidth/offsetHeight approximate border box dimensions. + // Where not available (e.g., SVG), assume unreliable box-sizing and interpret the + // retrieved value as a content box dimension. + valueIsBorderBox = offsetProp in elem; + if ( valueIsBorderBox ) { + val = elem[ offsetProp ]; + } + } + + // Normalize "" and auto + val = parseFloat( val ) || 0; + + // Adjust for the element's box model + return ( val + + boxModelAdjustment( + elem, + dimension, + extra || ( isBorderBox ? "border" : "content" ), + valueIsBorderBox, + styles, + + // Provide the current computed size to request scroll gutter calculation (gh-3589) + val + ) + ) + "px"; +} + +jQuery.extend( { + + // Add in style property hooks for overriding the default + // behavior of getting and setting a style property + cssHooks: { + opacity: { + get: function( elem, computed ) { + if ( computed ) { + + // We should always get a number back from opacity + var ret = curCSS( elem, "opacity" ); + return ret === "" ? "1" : ret; + } + } + } + }, + + // Don't automatically add "px" to these possibly-unitless properties + cssNumber: { + "animationIterationCount": true, + "columnCount": true, + "fillOpacity": true, + "flexGrow": true, + "flexShrink": true, + "fontWeight": true, + "gridArea": true, + "gridColumn": true, + "gridColumnEnd": true, + "gridColumnStart": true, + "gridRow": true, + "gridRowEnd": true, + "gridRowStart": true, + "lineHeight": true, + "opacity": true, + "order": true, + "orphans": true, + "widows": true, + "zIndex": true, + "zoom": true + }, + + // Add in properties whose names you wish to fix before + // setting or getting the value + cssProps: {}, + + // Get and set the style property on a DOM Node + style: function( elem, name, value, extra ) { + + // Don't set styles on text and comment nodes + if ( !elem || elem.nodeType === 3 || elem.nodeType === 8 || !elem.style ) { + return; + } + + // Make sure that we're working with the right name + var ret, type, hooks, + origName = camelCase( name ), + isCustomProp = rcustomProp.test( name ), + style = elem.style; + + // Make sure that we're working with the right name. We don't + // want to query the value if it is a CSS custom property + // since they are user-defined. + if ( !isCustomProp ) { + name = finalPropName( origName ); + } + + // Gets hook for the prefixed version, then unprefixed version + hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; + + // Check if we're setting a value + if ( value !== undefined ) { + type = typeof value; + + // Convert "+=" or "-=" to relative numbers (#7345) + if ( type === "string" && ( ret = rcssNum.exec( value ) ) && ret[ 1 ] ) { + value = adjustCSS( elem, name, ret ); + + // Fixes bug #9237 + type = "number"; + } + + // Make sure that null and NaN values aren't set (#7116) + if ( value == null || value !== value ) { + return; + } + + // If a number was passed in, add the unit (except for certain CSS properties) + // The isCustomProp check can be removed in jQuery 4.0 when we only auto-append + // "px" to a few hardcoded values. + if ( type === "number" && !isCustomProp ) { + value += ret && ret[ 3 ] || ( jQuery.cssNumber[ origName ] ? "" : "px" ); + } + + // background-* props affect original clone's values + if ( !support.clearCloneStyle && value === "" && name.indexOf( "background" ) === 0 ) { + style[ name ] = "inherit"; + } + + // If a hook was provided, use that value, otherwise just set the specified value + if ( !hooks || !( "set" in hooks ) || + ( value = hooks.set( elem, value, extra ) ) !== undefined ) { + + if ( isCustomProp ) { + style.setProperty( name, value ); + } else { + style[ name ] = value; + } + } + + } else { + + // If a hook was provided get the non-computed value from there + if ( hooks && "get" in hooks && + ( ret = hooks.get( elem, false, extra ) ) !== undefined ) { + + return ret; + } + + // Otherwise just get the value from the style object + return style[ name ]; + } + }, + + css: function( elem, name, extra, styles ) { + var val, num, hooks, + origName = camelCase( name ), + isCustomProp = rcustomProp.test( name ); + + // Make sure that we're working with the right name. We don't + // want to modify the value if it is a CSS custom property + // since they are user-defined. + if ( !isCustomProp ) { + name = finalPropName( origName ); + } + + // Try prefixed name followed by the unprefixed name + hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; + + // If a hook was provided get the computed value from there + if ( hooks && "get" in hooks ) { + val = hooks.get( elem, true, extra ); + } + + // Otherwise, if a way to get the computed value exists, use that + if ( val === undefined ) { + val = curCSS( elem, name, styles ); + } + + // Convert "normal" to computed value + if ( val === "normal" && name in cssNormalTransform ) { + val = cssNormalTransform[ name ]; + } + + // Make numeric if forced or a qualifier was provided and val looks numeric + if ( extra === "" || extra ) { + num = parseFloat( val ); + return extra === true || isFinite( num ) ? num || 0 : val; + } + + return val; + } +} ); + +jQuery.each( [ "height", "width" ], function( _i, dimension ) { + jQuery.cssHooks[ dimension ] = { + get: function( elem, computed, extra ) { + if ( computed ) { + + // Certain elements can have dimension info if we invisibly show them + // but it must have a current display style that would benefit + return rdisplayswap.test( jQuery.css( elem, "display" ) ) && + + // Support: Safari 8+ + // Table columns in Safari have non-zero offsetWidth & zero + // getBoundingClientRect().width unless display is changed. + // Support: IE <=11 only + // Running getBoundingClientRect on a disconnected node + // in IE throws an error. + ( !elem.getClientRects().length || !elem.getBoundingClientRect().width ) ? + swap( elem, cssShow, function() { + return getWidthOrHeight( elem, dimension, extra ); + } ) : + getWidthOrHeight( elem, dimension, extra ); + } + }, + + set: function( elem, value, extra ) { + var matches, + styles = getStyles( elem ), + + // Only read styles.position if the test has a chance to fail + // to avoid forcing a reflow. + scrollboxSizeBuggy = !support.scrollboxSize() && + styles.position === "absolute", + + // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-3991) + boxSizingNeeded = scrollboxSizeBuggy || extra, + isBorderBox = boxSizingNeeded && + jQuery.css( elem, "boxSizing", false, styles ) === "border-box", + subtract = extra ? + boxModelAdjustment( + elem, + dimension, + extra, + isBorderBox, + styles + ) : + 0; + + // Account for unreliable border-box dimensions by comparing offset* to computed and + // faking a content-box to get border and padding (gh-3699) + if ( isBorderBox && scrollboxSizeBuggy ) { + subtract -= Math.ceil( + elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - + parseFloat( styles[ dimension ] ) - + boxModelAdjustment( elem, dimension, "border", false, styles ) - + 0.5 + ); + } + + // Convert to pixels if value adjustment is needed + if ( subtract && ( matches = rcssNum.exec( value ) ) && + ( matches[ 3 ] || "px" ) !== "px" ) { + + elem.style[ dimension ] = value; + value = jQuery.css( elem, dimension ); + } + + return setPositiveNumber( elem, value, subtract ); + } + }; +} ); + +jQuery.cssHooks.marginLeft = addGetHookIf( support.reliableMarginLeft, + function( elem, computed ) { + if ( computed ) { + return ( parseFloat( curCSS( elem, "marginLeft" ) ) || + elem.getBoundingClientRect().left - + swap( elem, { marginLeft: 0 }, function() { + return elem.getBoundingClientRect().left; + } ) + ) + "px"; + } + } +); + +// These hooks are used by animate to expand properties +jQuery.each( { + margin: "", + padding: "", + border: "Width" +}, function( prefix, suffix ) { + jQuery.cssHooks[ prefix + suffix ] = { + expand: function( value ) { + var i = 0, + expanded = {}, + + // Assumes a single number if not a string + parts = typeof value === "string" ? value.split( " " ) : [ value ]; + + for ( ; i < 4; i++ ) { + expanded[ prefix + cssExpand[ i ] + suffix ] = + parts[ i ] || parts[ i - 2 ] || parts[ 0 ]; + } + + return expanded; + } + }; + + if ( prefix !== "margin" ) { + jQuery.cssHooks[ prefix + suffix ].set = setPositiveNumber; + } +} ); + +jQuery.fn.extend( { + css: function( name, value ) { + return access( this, function( elem, name, value ) { + var styles, len, + map = {}, + i = 0; + + if ( Array.isArray( name ) ) { + styles = getStyles( elem ); + len = name.length; + + for ( ; i < len; i++ ) { + map[ name[ i ] ] = jQuery.css( elem, name[ i ], false, styles ); + } + + return map; + } + + return value !== undefined ? + jQuery.style( elem, name, value ) : + jQuery.css( elem, name ); + }, name, value, arguments.length > 1 ); + } +} ); + + +function Tween( elem, options, prop, end, easing ) { + return new Tween.prototype.init( elem, options, prop, end, easing ); +} +jQuery.Tween = Tween; + +Tween.prototype = { + constructor: Tween, + init: function( elem, options, prop, end, easing, unit ) { + this.elem = elem; + this.prop = prop; + this.easing = easing || jQuery.easing._default; + this.options = options; + this.start = this.now = this.cur(); + this.end = end; + this.unit = unit || ( jQuery.cssNumber[ prop ] ? "" : "px" ); + }, + cur: function() { + var hooks = Tween.propHooks[ this.prop ]; + + return hooks && hooks.get ? + hooks.get( this ) : + Tween.propHooks._default.get( this ); + }, + run: function( percent ) { + var eased, + hooks = Tween.propHooks[ this.prop ]; + + if ( this.options.duration ) { + this.pos = eased = jQuery.easing[ this.easing ]( + percent, this.options.duration * percent, 0, 1, this.options.duration + ); + } else { + this.pos = eased = percent; + } + this.now = ( this.end - this.start ) * eased + this.start; + + if ( this.options.step ) { + this.options.step.call( this.elem, this.now, this ); + } + + if ( hooks && hooks.set ) { + hooks.set( this ); + } else { + Tween.propHooks._default.set( this ); + } + return this; + } +}; + +Tween.prototype.init.prototype = Tween.prototype; + +Tween.propHooks = { + _default: { + get: function( tween ) { + var result; + + // Use a property on the element directly when it is not a DOM element, + // or when there is no matching style property that exists. + if ( tween.elem.nodeType !== 1 || + tween.elem[ tween.prop ] != null && tween.elem.style[ tween.prop ] == null ) { + return tween.elem[ tween.prop ]; + } + + // Passing an empty string as a 3rd parameter to .css will automatically + // attempt a parseFloat and fallback to a string if the parse fails. + // Simple values such as "10px" are parsed to Float; + // complex values such as "rotate(1rad)" are returned as-is. + result = jQuery.css( tween.elem, tween.prop, "" ); + + // Empty strings, null, undefined and "auto" are converted to 0. + return !result || result === "auto" ? 0 : result; + }, + set: function( tween ) { + + // Use step hook for back compat. + // Use cssHook if its there. + // Use .style if available and use plain properties where available. + if ( jQuery.fx.step[ tween.prop ] ) { + jQuery.fx.step[ tween.prop ]( tween ); + } else if ( tween.elem.nodeType === 1 && ( + jQuery.cssHooks[ tween.prop ] || + tween.elem.style[ finalPropName( tween.prop ) ] != null ) ) { + jQuery.style( tween.elem, tween.prop, tween.now + tween.unit ); + } else { + tween.elem[ tween.prop ] = tween.now; + } + } + } +}; + +// Support: IE <=9 only +// Panic based approach to setting things on disconnected nodes +Tween.propHooks.scrollTop = Tween.propHooks.scrollLeft = { + set: function( tween ) { + if ( tween.elem.nodeType && tween.elem.parentNode ) { + tween.elem[ tween.prop ] = tween.now; + } + } +}; + +jQuery.easing = { + linear: function( p ) { + return p; + }, + swing: function( p ) { + return 0.5 - Math.cos( p * Math.PI ) / 2; + }, + _default: "swing" +}; + +jQuery.fx = Tween.prototype.init; + +// Back compat <1.8 extension point +jQuery.fx.step = {}; + + + + +var + fxNow, inProgress, + rfxtypes = /^(?:toggle|show|hide)$/, + rrun = /queueHooks$/; + +function schedule() { + if ( inProgress ) { + if ( document.hidden === false && window.requestAnimationFrame ) { + window.requestAnimationFrame( schedule ); + } else { + window.setTimeout( schedule, jQuery.fx.interval ); + } + + jQuery.fx.tick(); + } +} + +// Animations created synchronously will run synchronously +function createFxNow() { + window.setTimeout( function() { + fxNow = undefined; + } ); + return ( fxNow = Date.now() ); +} + +// Generate parameters to create a standard animation +function genFx( type, includeWidth ) { + var which, + i = 0, + attrs = { height: type }; + + // If we include width, step value is 1 to do all cssExpand values, + // otherwise step value is 2 to skip over Left and Right + includeWidth = includeWidth ? 1 : 0; + for ( ; i < 4; i += 2 - includeWidth ) { + which = cssExpand[ i ]; + attrs[ "margin" + which ] = attrs[ "padding" + which ] = type; + } + + if ( includeWidth ) { + attrs.opacity = attrs.width = type; + } + + return attrs; +} + +function createTween( value, prop, animation ) { + var tween, + collection = ( Animation.tweeners[ prop ] || [] ).concat( Animation.tweeners[ "*" ] ), + index = 0, + length = collection.length; + for ( ; index < length; index++ ) { + if ( ( tween = collection[ index ].call( animation, prop, value ) ) ) { + + // We're done with this property + return tween; + } + } +} + +function defaultPrefilter( elem, props, opts ) { + var prop, value, toggle, hooks, oldfire, propTween, restoreDisplay, display, + isBox = "width" in props || "height" in props, + anim = this, + orig = {}, + style = elem.style, + hidden = elem.nodeType && isHiddenWithinTree( elem ), + dataShow = dataPriv.get( elem, "fxshow" ); + + // Queue-skipping animations hijack the fx hooks + if ( !opts.queue ) { + hooks = jQuery._queueHooks( elem, "fx" ); + if ( hooks.unqueued == null ) { + hooks.unqueued = 0; + oldfire = hooks.empty.fire; + hooks.empty.fire = function() { + if ( !hooks.unqueued ) { + oldfire(); + } + }; + } + hooks.unqueued++; + + anim.always( function() { + + // Ensure the complete handler is called before this completes + anim.always( function() { + hooks.unqueued--; + if ( !jQuery.queue( elem, "fx" ).length ) { + hooks.empty.fire(); + } + } ); + } ); + } + + // Detect show/hide animations + for ( prop in props ) { + value = props[ prop ]; + if ( rfxtypes.test( value ) ) { + delete props[ prop ]; + toggle = toggle || value === "toggle"; + if ( value === ( hidden ? "hide" : "show" ) ) { + + // Pretend to be hidden if this is a "show" and + // there is still data from a stopped show/hide + if ( value === "show" && dataShow && dataShow[ prop ] !== undefined ) { + hidden = true; + + // Ignore all other no-op show/hide data + } else { + continue; + } + } + orig[ prop ] = dataShow && dataShow[ prop ] || jQuery.style( elem, prop ); + } + } + + // Bail out if this is a no-op like .hide().hide() + propTween = !jQuery.isEmptyObject( props ); + if ( !propTween && jQuery.isEmptyObject( orig ) ) { + return; + } + + // Restrict "overflow" and "display" styles during box animations + if ( isBox && elem.nodeType === 1 ) { + + // Support: IE <=9 - 11, Edge 12 - 15 + // Record all 3 overflow attributes because IE does not infer the shorthand + // from identically-valued overflowX and overflowY and Edge just mirrors + // the overflowX value there. + opts.overflow = [ style.overflow, style.overflowX, style.overflowY ]; + + // Identify a display type, preferring old show/hide data over the CSS cascade + restoreDisplay = dataShow && dataShow.display; + if ( restoreDisplay == null ) { + restoreDisplay = dataPriv.get( elem, "display" ); + } + display = jQuery.css( elem, "display" ); + if ( display === "none" ) { + if ( restoreDisplay ) { + display = restoreDisplay; + } else { + + // Get nonempty value(s) by temporarily forcing visibility + showHide( [ elem ], true ); + restoreDisplay = elem.style.display || restoreDisplay; + display = jQuery.css( elem, "display" ); + showHide( [ elem ] ); + } + } + + // Animate inline elements as inline-block + if ( display === "inline" || display === "inline-block" && restoreDisplay != null ) { + if ( jQuery.css( elem, "float" ) === "none" ) { + + // Restore the original display value at the end of pure show/hide animations + if ( !propTween ) { + anim.done( function() { + style.display = restoreDisplay; + } ); + if ( restoreDisplay == null ) { + display = style.display; + restoreDisplay = display === "none" ? "" : display; + } + } + style.display = "inline-block"; + } + } + } + + if ( opts.overflow ) { + style.overflow = "hidden"; + anim.always( function() { + style.overflow = opts.overflow[ 0 ]; + style.overflowX = opts.overflow[ 1 ]; + style.overflowY = opts.overflow[ 2 ]; + } ); + } + + // Implement show/hide animations + propTween = false; + for ( prop in orig ) { + + // General show/hide setup for this element animation + if ( !propTween ) { + if ( dataShow ) { + if ( "hidden" in dataShow ) { + hidden = dataShow.hidden; + } + } else { + dataShow = dataPriv.access( elem, "fxshow", { display: restoreDisplay } ); + } + + // Store hidden/visible for toggle so `.stop().toggle()` "reverses" + if ( toggle ) { + dataShow.hidden = !hidden; + } + + // Show elements before animating them + if ( hidden ) { + showHide( [ elem ], true ); + } + + /* eslint-disable no-loop-func */ + + anim.done( function() { + + /* eslint-enable no-loop-func */ + + // The final step of a "hide" animation is actually hiding the element + if ( !hidden ) { + showHide( [ elem ] ); + } + dataPriv.remove( elem, "fxshow" ); + for ( prop in orig ) { + jQuery.style( elem, prop, orig[ prop ] ); + } + } ); + } + + // Per-property setup + propTween = createTween( hidden ? dataShow[ prop ] : 0, prop, anim ); + if ( !( prop in dataShow ) ) { + dataShow[ prop ] = propTween.start; + if ( hidden ) { + propTween.end = propTween.start; + propTween.start = 0; + } + } + } +} + +function propFilter( props, specialEasing ) { + var index, name, easing, value, hooks; + + // camelCase, specialEasing and expand cssHook pass + for ( index in props ) { + name = camelCase( index ); + easing = specialEasing[ name ]; + value = props[ index ]; + if ( Array.isArray( value ) ) { + easing = value[ 1 ]; + value = props[ index ] = value[ 0 ]; + } + + if ( index !== name ) { + props[ name ] = value; + delete props[ index ]; + } + + hooks = jQuery.cssHooks[ name ]; + if ( hooks && "expand" in hooks ) { + value = hooks.expand( value ); + delete props[ name ]; + + // Not quite $.extend, this won't overwrite existing keys. + // Reusing 'index' because we have the correct "name" + for ( index in value ) { + if ( !( index in props ) ) { + props[ index ] = value[ index ]; + specialEasing[ index ] = easing; + } + } + } else { + specialEasing[ name ] = easing; + } + } +} + +function Animation( elem, properties, options ) { + var result, + stopped, + index = 0, + length = Animation.prefilters.length, + deferred = jQuery.Deferred().always( function() { + + // Don't match elem in the :animated selector + delete tick.elem; + } ), + tick = function() { + if ( stopped ) { + return false; + } + var currentTime = fxNow || createFxNow(), + remaining = Math.max( 0, animation.startTime + animation.duration - currentTime ), + + // Support: Android 2.3 only + // Archaic crash bug won't allow us to use `1 - ( 0.5 || 0 )` (#12497) + temp = remaining / animation.duration || 0, + percent = 1 - temp, + index = 0, + length = animation.tweens.length; + + for ( ; index < length; index++ ) { + animation.tweens[ index ].run( percent ); + } + + deferred.notifyWith( elem, [ animation, percent, remaining ] ); + + // If there's more to do, yield + if ( percent < 1 && length ) { + return remaining; + } + + // If this was an empty animation, synthesize a final progress notification + if ( !length ) { + deferred.notifyWith( elem, [ animation, 1, 0 ] ); + } + + // Resolve the animation and report its conclusion + deferred.resolveWith( elem, [ animation ] ); + return false; + }, + animation = deferred.promise( { + elem: elem, + props: jQuery.extend( {}, properties ), + opts: jQuery.extend( true, { + specialEasing: {}, + easing: jQuery.easing._default + }, options ), + originalProperties: properties, + originalOptions: options, + startTime: fxNow || createFxNow(), + duration: options.duration, + tweens: [], + createTween: function( prop, end ) { + var tween = jQuery.Tween( elem, animation.opts, prop, end, + animation.opts.specialEasing[ prop ] || animation.opts.easing ); + animation.tweens.push( tween ); + return tween; + }, + stop: function( gotoEnd ) { + var index = 0, + + // If we are going to the end, we want to run all the tweens + // otherwise we skip this part + length = gotoEnd ? animation.tweens.length : 0; + if ( stopped ) { + return this; + } + stopped = true; + for ( ; index < length; index++ ) { + animation.tweens[ index ].run( 1 ); + } + + // Resolve when we played the last frame; otherwise, reject + if ( gotoEnd ) { + deferred.notifyWith( elem, [ animation, 1, 0 ] ); + deferred.resolveWith( elem, [ animation, gotoEnd ] ); + } else { + deferred.rejectWith( elem, [ animation, gotoEnd ] ); + } + return this; + } + } ), + props = animation.props; + + propFilter( props, animation.opts.specialEasing ); + + for ( ; index < length; index++ ) { + result = Animation.prefilters[ index ].call( animation, elem, props, animation.opts ); + if ( result ) { + if ( isFunction( result.stop ) ) { + jQuery._queueHooks( animation.elem, animation.opts.queue ).stop = + result.stop.bind( result ); + } + return result; + } + } + + jQuery.map( props, createTween, animation ); + + if ( isFunction( animation.opts.start ) ) { + animation.opts.start.call( elem, animation ); + } + + // Attach callbacks from options + animation + .progress( animation.opts.progress ) + .done( animation.opts.done, animation.opts.complete ) + .fail( animation.opts.fail ) + .always( animation.opts.always ); + + jQuery.fx.timer( + jQuery.extend( tick, { + elem: elem, + anim: animation, + queue: animation.opts.queue + } ) + ); + + return animation; +} + +jQuery.Animation = jQuery.extend( Animation, { + + tweeners: { + "*": [ function( prop, value ) { + var tween = this.createTween( prop, value ); + adjustCSS( tween.elem, prop, rcssNum.exec( value ), tween ); + return tween; + } ] + }, + + tweener: function( props, callback ) { + if ( isFunction( props ) ) { + callback = props; + props = [ "*" ]; + } else { + props = props.match( rnothtmlwhite ); + } + + var prop, + index = 0, + length = props.length; + + for ( ; index < length; index++ ) { + prop = props[ index ]; + Animation.tweeners[ prop ] = Animation.tweeners[ prop ] || []; + Animation.tweeners[ prop ].unshift( callback ); + } + }, + + prefilters: [ defaultPrefilter ], + + prefilter: function( callback, prepend ) { + if ( prepend ) { + Animation.prefilters.unshift( callback ); + } else { + Animation.prefilters.push( callback ); + } + } +} ); + +jQuery.speed = function( speed, easing, fn ) { + var opt = speed && typeof speed === "object" ? jQuery.extend( {}, speed ) : { + complete: fn || !fn && easing || + isFunction( speed ) && speed, + duration: speed, + easing: fn && easing || easing && !isFunction( easing ) && easing + }; + + // Go to the end state if fx are off + if ( jQuery.fx.off ) { + opt.duration = 0; + + } else { + if ( typeof opt.duration !== "number" ) { + if ( opt.duration in jQuery.fx.speeds ) { + opt.duration = jQuery.fx.speeds[ opt.duration ]; + + } else { + opt.duration = jQuery.fx.speeds._default; + } + } + } + + // Normalize opt.queue - true/undefined/null -> "fx" + if ( opt.queue == null || opt.queue === true ) { + opt.queue = "fx"; + } + + // Queueing + opt.old = opt.complete; + + opt.complete = function() { + if ( isFunction( opt.old ) ) { + opt.old.call( this ); + } + + if ( opt.queue ) { + jQuery.dequeue( this, opt.queue ); + } + }; + + return opt; +}; + +jQuery.fn.extend( { + fadeTo: function( speed, to, easing, callback ) { + + // Show any hidden elements after setting opacity to 0 + return this.filter( isHiddenWithinTree ).css( "opacity", 0 ).show() + + // Animate to the value specified + .end().animate( { opacity: to }, speed, easing, callback ); + }, + animate: function( prop, speed, easing, callback ) { + var empty = jQuery.isEmptyObject( prop ), + optall = jQuery.speed( speed, easing, callback ), + doAnimation = function() { + + // Operate on a copy of prop so per-property easing won't be lost + var anim = Animation( this, jQuery.extend( {}, prop ), optall ); + + // Empty animations, or finishing resolves immediately + if ( empty || dataPriv.get( this, "finish" ) ) { + anim.stop( true ); + } + }; + doAnimation.finish = doAnimation; + + return empty || optall.queue === false ? + this.each( doAnimation ) : + this.queue( optall.queue, doAnimation ); + }, + stop: function( type, clearQueue, gotoEnd ) { + var stopQueue = function( hooks ) { + var stop = hooks.stop; + delete hooks.stop; + stop( gotoEnd ); + }; + + if ( typeof type !== "string" ) { + gotoEnd = clearQueue; + clearQueue = type; + type = undefined; + } + if ( clearQueue ) { + this.queue( type || "fx", [] ); + } + + return this.each( function() { + var dequeue = true, + index = type != null && type + "queueHooks", + timers = jQuery.timers, + data = dataPriv.get( this ); + + if ( index ) { + if ( data[ index ] && data[ index ].stop ) { + stopQueue( data[ index ] ); + } + } else { + for ( index in data ) { + if ( data[ index ] && data[ index ].stop && rrun.test( index ) ) { + stopQueue( data[ index ] ); + } + } + } + + for ( index = timers.length; index--; ) { + if ( timers[ index ].elem === this && + ( type == null || timers[ index ].queue === type ) ) { + + timers[ index ].anim.stop( gotoEnd ); + dequeue = false; + timers.splice( index, 1 ); + } + } + + // Start the next in the queue if the last step wasn't forced. + // Timers currently will call their complete callbacks, which + // will dequeue but only if they were gotoEnd. + if ( dequeue || !gotoEnd ) { + jQuery.dequeue( this, type ); + } + } ); + }, + finish: function( type ) { + if ( type !== false ) { + type = type || "fx"; + } + return this.each( function() { + var index, + data = dataPriv.get( this ), + queue = data[ type + "queue" ], + hooks = data[ type + "queueHooks" ], + timers = jQuery.timers, + length = queue ? queue.length : 0; + + // Enable finishing flag on private data + data.finish = true; + + // Empty the queue first + jQuery.queue( this, type, [] ); + + if ( hooks && hooks.stop ) { + hooks.stop.call( this, true ); + } + + // Look for any active animations, and finish them + for ( index = timers.length; index--; ) { + if ( timers[ index ].elem === this && timers[ index ].queue === type ) { + timers[ index ].anim.stop( true ); + timers.splice( index, 1 ); + } + } + + // Look for any animations in the old queue and finish them + for ( index = 0; index < length; index++ ) { + if ( queue[ index ] && queue[ index ].finish ) { + queue[ index ].finish.call( this ); + } + } + + // Turn off finishing flag + delete data.finish; + } ); + } +} ); + +jQuery.each( [ "toggle", "show", "hide" ], function( _i, name ) { + var cssFn = jQuery.fn[ name ]; + jQuery.fn[ name ] = function( speed, easing, callback ) { + return speed == null || typeof speed === "boolean" ? + cssFn.apply( this, arguments ) : + this.animate( genFx( name, true ), speed, easing, callback ); + }; +} ); + +// Generate shortcuts for custom animations +jQuery.each( { + slideDown: genFx( "show" ), + slideUp: genFx( "hide" ), + slideToggle: genFx( "toggle" ), + fadeIn: { opacity: "show" }, + fadeOut: { opacity: "hide" }, + fadeToggle: { opacity: "toggle" } +}, function( name, props ) { + jQuery.fn[ name ] = function( speed, easing, callback ) { + return this.animate( props, speed, easing, callback ); + }; +} ); + +jQuery.timers = []; +jQuery.fx.tick = function() { + var timer, + i = 0, + timers = jQuery.timers; + + fxNow = Date.now(); + + for ( ; i < timers.length; i++ ) { + timer = timers[ i ]; + + // Run the timer and safely remove it when done (allowing for external removal) + if ( !timer() && timers[ i ] === timer ) { + timers.splice( i--, 1 ); + } + } + + if ( !timers.length ) { + jQuery.fx.stop(); + } + fxNow = undefined; +}; + +jQuery.fx.timer = function( timer ) { + jQuery.timers.push( timer ); + jQuery.fx.start(); +}; + +jQuery.fx.interval = 13; +jQuery.fx.start = function() { + if ( inProgress ) { + return; + } + + inProgress = true; + schedule(); +}; + +jQuery.fx.stop = function() { + inProgress = null; +}; + +jQuery.fx.speeds = { + slow: 600, + fast: 200, + + // Default speed + _default: 400 +}; + + +// Based off of the plugin by Clint Helfers, with permission. +// https://web.archive.org/web/20100324014747/http://blindsignals.com/index.php/2009/07/jquery-delay/ +jQuery.fn.delay = function( time, type ) { + time = jQuery.fx ? jQuery.fx.speeds[ time ] || time : time; + type = type || "fx"; + + return this.queue( type, function( next, hooks ) { + var timeout = window.setTimeout( next, time ); + hooks.stop = function() { + window.clearTimeout( timeout ); + }; + } ); +}; + + +( function() { + var input = document.createElement( "input" ), + select = document.createElement( "select" ), + opt = select.appendChild( document.createElement( "option" ) ); + + input.type = "checkbox"; + + // Support: Android <=4.3 only + // Default value for a checkbox should be "on" + support.checkOn = input.value !== ""; + + // Support: IE <=11 only + // Must access selectedIndex to make default options select + support.optSelected = opt.selected; + + // Support: IE <=11 only + // An input loses its value after becoming a radio + input = document.createElement( "input" ); + input.value = "t"; + input.type = "radio"; + support.radioValue = input.value === "t"; +} )(); + + +var boolHook, + attrHandle = jQuery.expr.attrHandle; + +jQuery.fn.extend( { + attr: function( name, value ) { + return access( this, jQuery.attr, name, value, arguments.length > 1 ); + }, + + removeAttr: function( name ) { + return this.each( function() { + jQuery.removeAttr( this, name ); + } ); + } +} ); + +jQuery.extend( { + attr: function( elem, name, value ) { + var ret, hooks, + nType = elem.nodeType; + + // Don't get/set attributes on text, comment and attribute nodes + if ( nType === 3 || nType === 8 || nType === 2 ) { + return; + } + + // Fallback to prop when attributes are not supported + if ( typeof elem.getAttribute === "undefined" ) { + return jQuery.prop( elem, name, value ); + } + + // Attribute hooks are determined by the lowercase version + // Grab necessary hook if one is defined + if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { + hooks = jQuery.attrHooks[ name.toLowerCase() ] || + ( jQuery.expr.match.bool.test( name ) ? boolHook : undefined ); + } + + if ( value !== undefined ) { + if ( value === null ) { + jQuery.removeAttr( elem, name ); + return; + } + + if ( hooks && "set" in hooks && + ( ret = hooks.set( elem, value, name ) ) !== undefined ) { + return ret; + } + + elem.setAttribute( name, value + "" ); + return value; + } + + if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { + return ret; + } + + ret = jQuery.find.attr( elem, name ); + + // Non-existent attributes return null, we normalize to undefined + return ret == null ? undefined : ret; + }, + + attrHooks: { + type: { + set: function( elem, value ) { + if ( !support.radioValue && value === "radio" && + nodeName( elem, "input" ) ) { + var val = elem.value; + elem.setAttribute( "type", value ); + if ( val ) { + elem.value = val; + } + return value; + } + } + } + }, + + removeAttr: function( elem, value ) { + var name, + i = 0, + + // Attribute names can contain non-HTML whitespace characters + // https://html.spec.whatwg.org/multipage/syntax.html#attributes-2 + attrNames = value && value.match( rnothtmlwhite ); + + if ( attrNames && elem.nodeType === 1 ) { + while ( ( name = attrNames[ i++ ] ) ) { + elem.removeAttribute( name ); + } + } + } +} ); + +// Hooks for boolean attributes +boolHook = { + set: function( elem, value, name ) { + if ( value === false ) { + + // Remove boolean attributes when set to false + jQuery.removeAttr( elem, name ); + } else { + elem.setAttribute( name, name ); + } + return name; + } +}; + +jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( _i, name ) { + var getter = attrHandle[ name ] || jQuery.find.attr; + + attrHandle[ name ] = function( elem, name, isXML ) { + var ret, handle, + lowercaseName = name.toLowerCase(); + + if ( !isXML ) { + + // Avoid an infinite loop by temporarily removing this function from the getter + handle = attrHandle[ lowercaseName ]; + attrHandle[ lowercaseName ] = ret; + ret = getter( elem, name, isXML ) != null ? + lowercaseName : + null; + attrHandle[ lowercaseName ] = handle; + } + return ret; + }; +} ); + + + + +var rfocusable = /^(?:input|select|textarea|button)$/i, + rclickable = /^(?:a|area)$/i; + +jQuery.fn.extend( { + prop: function( name, value ) { + return access( this, jQuery.prop, name, value, arguments.length > 1 ); + }, + + removeProp: function( name ) { + return this.each( function() { + delete this[ jQuery.propFix[ name ] || name ]; + } ); + } +} ); + +jQuery.extend( { + prop: function( elem, name, value ) { + var ret, hooks, + nType = elem.nodeType; + + // Don't get/set properties on text, comment and attribute nodes + if ( nType === 3 || nType === 8 || nType === 2 ) { + return; + } + + if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { + + // Fix name and attach hooks + name = jQuery.propFix[ name ] || name; + hooks = jQuery.propHooks[ name ]; + } + + if ( value !== undefined ) { + if ( hooks && "set" in hooks && + ( ret = hooks.set( elem, value, name ) ) !== undefined ) { + return ret; + } + + return ( elem[ name ] = value ); + } + + if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { + return ret; + } + + return elem[ name ]; + }, + + propHooks: { + tabIndex: { + get: function( elem ) { + + // Support: IE <=9 - 11 only + // elem.tabIndex doesn't always return the + // correct value when it hasn't been explicitly set + // https://web.archive.org/web/20141116233347/http://fluidproject.org/blog/2008/01/09/getting-setting-and-removing-tabindex-values-with-javascript/ + // Use proper attribute retrieval(#12072) + var tabindex = jQuery.find.attr( elem, "tabindex" ); + + if ( tabindex ) { + return parseInt( tabindex, 10 ); + } + + if ( + rfocusable.test( elem.nodeName ) || + rclickable.test( elem.nodeName ) && + elem.href + ) { + return 0; + } + + return -1; + } + } + }, + + propFix: { + "for": "htmlFor", + "class": "className" + } +} ); + +// Support: IE <=11 only +// Accessing the selectedIndex property +// forces the browser to respect setting selected +// on the option +// The getter ensures a default option is selected +// when in an optgroup +// eslint rule "no-unused-expressions" is disabled for this code +// since it considers such accessions noop +if ( !support.optSelected ) { + jQuery.propHooks.selected = { + get: function( elem ) { + + /* eslint no-unused-expressions: "off" */ + + var parent = elem.parentNode; + if ( parent && parent.parentNode ) { + parent.parentNode.selectedIndex; + } + return null; + }, + set: function( elem ) { + + /* eslint no-unused-expressions: "off" */ + + var parent = elem.parentNode; + if ( parent ) { + parent.selectedIndex; + + if ( parent.parentNode ) { + parent.parentNode.selectedIndex; + } + } + } + }; +} + +jQuery.each( [ + "tabIndex", + "readOnly", + "maxLength", + "cellSpacing", + "cellPadding", + "rowSpan", + "colSpan", + "useMap", + "frameBorder", + "contentEditable" +], function() { + jQuery.propFix[ this.toLowerCase() ] = this; +} ); + + + + + // Strip and collapse whitespace according to HTML spec + // https://infra.spec.whatwg.org/#strip-and-collapse-ascii-whitespace + function stripAndCollapse( value ) { + var tokens = value.match( rnothtmlwhite ) || []; + return tokens.join( " " ); + } + + +function getClass( elem ) { + return elem.getAttribute && elem.getAttribute( "class" ) || ""; +} + +function classesToArray( value ) { + if ( Array.isArray( value ) ) { + return value; + } + if ( typeof value === "string" ) { + return value.match( rnothtmlwhite ) || []; + } + return []; +} + +jQuery.fn.extend( { + addClass: function( value ) { + var classes, elem, cur, curValue, clazz, j, finalValue, + i = 0; + + if ( isFunction( value ) ) { + return this.each( function( j ) { + jQuery( this ).addClass( value.call( this, j, getClass( this ) ) ); + } ); + } + + classes = classesToArray( value ); + + if ( classes.length ) { + while ( ( elem = this[ i++ ] ) ) { + curValue = getClass( elem ); + cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); + + if ( cur ) { + j = 0; + while ( ( clazz = classes[ j++ ] ) ) { + if ( cur.indexOf( " " + clazz + " " ) < 0 ) { + cur += clazz + " "; + } + } + + // Only assign if different to avoid unneeded rendering. + finalValue = stripAndCollapse( cur ); + if ( curValue !== finalValue ) { + elem.setAttribute( "class", finalValue ); + } + } + } + } + + return this; + }, + + removeClass: function( value ) { + var classes, elem, cur, curValue, clazz, j, finalValue, + i = 0; + + if ( isFunction( value ) ) { + return this.each( function( j ) { + jQuery( this ).removeClass( value.call( this, j, getClass( this ) ) ); + } ); + } + + if ( !arguments.length ) { + return this.attr( "class", "" ); + } + + classes = classesToArray( value ); + + if ( classes.length ) { + while ( ( elem = this[ i++ ] ) ) { + curValue = getClass( elem ); + + // This expression is here for better compressibility (see addClass) + cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); + + if ( cur ) { + j = 0; + while ( ( clazz = classes[ j++ ] ) ) { + + // Remove *all* instances + while ( cur.indexOf( " " + clazz + " " ) > -1 ) { + cur = cur.replace( " " + clazz + " ", " " ); + } + } + + // Only assign if different to avoid unneeded rendering. + finalValue = stripAndCollapse( cur ); + if ( curValue !== finalValue ) { + elem.setAttribute( "class", finalValue ); + } + } + } + } + + return this; + }, + + toggleClass: function( value, stateVal ) { + var type = typeof value, + isValidValue = type === "string" || Array.isArray( value ); + + if ( typeof stateVal === "boolean" && isValidValue ) { + return stateVal ? this.addClass( value ) : this.removeClass( value ); + } + + if ( isFunction( value ) ) { + return this.each( function( i ) { + jQuery( this ).toggleClass( + value.call( this, i, getClass( this ), stateVal ), + stateVal + ); + } ); + } + + return this.each( function() { + var className, i, self, classNames; + + if ( isValidValue ) { + + // Toggle individual class names + i = 0; + self = jQuery( this ); + classNames = classesToArray( value ); + + while ( ( className = classNames[ i++ ] ) ) { + + // Check each className given, space separated list + if ( self.hasClass( className ) ) { + self.removeClass( className ); + } else { + self.addClass( className ); + } + } + + // Toggle whole class name + } else if ( value === undefined || type === "boolean" ) { + className = getClass( this ); + if ( className ) { + + // Store className if set + dataPriv.set( this, "__className__", className ); + } + + // If the element has a class name or if we're passed `false`, + // then remove the whole classname (if there was one, the above saved it). + // Otherwise bring back whatever was previously saved (if anything), + // falling back to the empty string if nothing was stored. + if ( this.setAttribute ) { + this.setAttribute( "class", + className || value === false ? + "" : + dataPriv.get( this, "__className__" ) || "" + ); + } + } + } ); + }, + + hasClass: function( selector ) { + var className, elem, + i = 0; + + className = " " + selector + " "; + while ( ( elem = this[ i++ ] ) ) { + if ( elem.nodeType === 1 && + ( " " + stripAndCollapse( getClass( elem ) ) + " " ).indexOf( className ) > -1 ) { + return true; + } + } + + return false; + } +} ); + + + + +var rreturn = /\r/g; + +jQuery.fn.extend( { + val: function( value ) { + var hooks, ret, valueIsFunction, + elem = this[ 0 ]; + + if ( !arguments.length ) { + if ( elem ) { + hooks = jQuery.valHooks[ elem.type ] || + jQuery.valHooks[ elem.nodeName.toLowerCase() ]; + + if ( hooks && + "get" in hooks && + ( ret = hooks.get( elem, "value" ) ) !== undefined + ) { + return ret; + } + + ret = elem.value; + + // Handle most common string cases + if ( typeof ret === "string" ) { + return ret.replace( rreturn, "" ); + } + + // Handle cases where value is null/undef or number + return ret == null ? "" : ret; + } + + return; + } + + valueIsFunction = isFunction( value ); + + return this.each( function( i ) { + var val; + + if ( this.nodeType !== 1 ) { + return; + } + + if ( valueIsFunction ) { + val = value.call( this, i, jQuery( this ).val() ); + } else { + val = value; + } + + // Treat null/undefined as ""; convert numbers to string + if ( val == null ) { + val = ""; + + } else if ( typeof val === "number" ) { + val += ""; + + } else if ( Array.isArray( val ) ) { + val = jQuery.map( val, function( value ) { + return value == null ? "" : value + ""; + } ); + } + + hooks = jQuery.valHooks[ this.type ] || jQuery.valHooks[ this.nodeName.toLowerCase() ]; + + // If set returns undefined, fall back to normal setting + if ( !hooks || !( "set" in hooks ) || hooks.set( this, val, "value" ) === undefined ) { + this.value = val; + } + } ); + } +} ); + +jQuery.extend( { + valHooks: { + option: { + get: function( elem ) { + + var val = jQuery.find.attr( elem, "value" ); + return val != null ? + val : + + // Support: IE <=10 - 11 only + // option.text throws exceptions (#14686, #14858) + // Strip and collapse whitespace + // https://html.spec.whatwg.org/#strip-and-collapse-whitespace + stripAndCollapse( jQuery.text( elem ) ); + } + }, + select: { + get: function( elem ) { + var value, option, i, + options = elem.options, + index = elem.selectedIndex, + one = elem.type === "select-one", + values = one ? null : [], + max = one ? index + 1 : options.length; + + if ( index < 0 ) { + i = max; + + } else { + i = one ? index : 0; + } + + // Loop through all the selected options + for ( ; i < max; i++ ) { + option = options[ i ]; + + // Support: IE <=9 only + // IE8-9 doesn't update selected after form reset (#2551) + if ( ( option.selected || i === index ) && + + // Don't return options that are disabled or in a disabled optgroup + !option.disabled && + ( !option.parentNode.disabled || + !nodeName( option.parentNode, "optgroup" ) ) ) { + + // Get the specific value for the option + value = jQuery( option ).val(); + + // We don't need an array for one selects + if ( one ) { + return value; + } + + // Multi-Selects return an array + values.push( value ); + } + } + + return values; + }, + + set: function( elem, value ) { + var optionSet, option, + options = elem.options, + values = jQuery.makeArray( value ), + i = options.length; + + while ( i-- ) { + option = options[ i ]; + + /* eslint-disable no-cond-assign */ + + if ( option.selected = + jQuery.inArray( jQuery.valHooks.option.get( option ), values ) > -1 + ) { + optionSet = true; + } + + /* eslint-enable no-cond-assign */ + } + + // Force browsers to behave consistently when non-matching value is set + if ( !optionSet ) { + elem.selectedIndex = -1; + } + return values; + } + } + } +} ); + +// Radios and checkboxes getter/setter +jQuery.each( [ "radio", "checkbox" ], function() { + jQuery.valHooks[ this ] = { + set: function( elem, value ) { + if ( Array.isArray( value ) ) { + return ( elem.checked = jQuery.inArray( jQuery( elem ).val(), value ) > -1 ); + } + } + }; + if ( !support.checkOn ) { + jQuery.valHooks[ this ].get = function( elem ) { + return elem.getAttribute( "value" ) === null ? "on" : elem.value; + }; + } +} ); + + + + +// Return jQuery for attributes-only inclusion + + +support.focusin = "onfocusin" in window; + + +var rfocusMorph = /^(?:focusinfocus|focusoutblur)$/, + stopPropagationCallback = function( e ) { + e.stopPropagation(); + }; + +jQuery.extend( jQuery.event, { + + trigger: function( event, data, elem, onlyHandlers ) { + + var i, cur, tmp, bubbleType, ontype, handle, special, lastElement, + eventPath = [ elem || document ], + type = hasOwn.call( event, "type" ) ? event.type : event, + namespaces = hasOwn.call( event, "namespace" ) ? event.namespace.split( "." ) : []; + + cur = lastElement = tmp = elem = elem || document; + + // Don't do events on text and comment nodes + if ( elem.nodeType === 3 || elem.nodeType === 8 ) { + return; + } + + // focus/blur morphs to focusin/out; ensure we're not firing them right now + if ( rfocusMorph.test( type + jQuery.event.triggered ) ) { + return; + } + + if ( type.indexOf( "." ) > -1 ) { + + // Namespaced trigger; create a regexp to match event type in handle() + namespaces = type.split( "." ); + type = namespaces.shift(); + namespaces.sort(); + } + ontype = type.indexOf( ":" ) < 0 && "on" + type; + + // Caller can pass in a jQuery.Event object, Object, or just an event type string + event = event[ jQuery.expando ] ? + event : + new jQuery.Event( type, typeof event === "object" && event ); + + // Trigger bitmask: & 1 for native handlers; & 2 for jQuery (always true) + event.isTrigger = onlyHandlers ? 2 : 3; + event.namespace = namespaces.join( "." ); + event.rnamespace = event.namespace ? + new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ) : + null; + + // Clean up the event in case it is being reused + event.result = undefined; + if ( !event.target ) { + event.target = elem; + } + + // Clone any incoming data and prepend the event, creating the handler arg list + data = data == null ? + [ event ] : + jQuery.makeArray( data, [ event ] ); + + // Allow special events to draw outside the lines + special = jQuery.event.special[ type ] || {}; + if ( !onlyHandlers && special.trigger && special.trigger.apply( elem, data ) === false ) { + return; + } + + // Determine event propagation path in advance, per W3C events spec (#9951) + // Bubble up to document, then to window; watch for a global ownerDocument var (#9724) + if ( !onlyHandlers && !special.noBubble && !isWindow( elem ) ) { + + bubbleType = special.delegateType || type; + if ( !rfocusMorph.test( bubbleType + type ) ) { + cur = cur.parentNode; + } + for ( ; cur; cur = cur.parentNode ) { + eventPath.push( cur ); + tmp = cur; + } + + // Only add window if we got to document (e.g., not plain obj or detached DOM) + if ( tmp === ( elem.ownerDocument || document ) ) { + eventPath.push( tmp.defaultView || tmp.parentWindow || window ); + } + } + + // Fire handlers on the event path + i = 0; + while ( ( cur = eventPath[ i++ ] ) && !event.isPropagationStopped() ) { + lastElement = cur; + event.type = i > 1 ? + bubbleType : + special.bindType || type; + + // jQuery handler + handle = ( + dataPriv.get( cur, "events" ) || Object.create( null ) + )[ event.type ] && + dataPriv.get( cur, "handle" ); + if ( handle ) { + handle.apply( cur, data ); + } + + // Native handler + handle = ontype && cur[ ontype ]; + if ( handle && handle.apply && acceptData( cur ) ) { + event.result = handle.apply( cur, data ); + if ( event.result === false ) { + event.preventDefault(); + } + } + } + event.type = type; + + // If nobody prevented the default action, do it now + if ( !onlyHandlers && !event.isDefaultPrevented() ) { + + if ( ( !special._default || + special._default.apply( eventPath.pop(), data ) === false ) && + acceptData( elem ) ) { + + // Call a native DOM method on the target with the same name as the event. + // Don't do default actions on window, that's where global variables be (#6170) + if ( ontype && isFunction( elem[ type ] ) && !isWindow( elem ) ) { + + // Don't re-trigger an onFOO event when we call its FOO() method + tmp = elem[ ontype ]; + + if ( tmp ) { + elem[ ontype ] = null; + } + + // Prevent re-triggering of the same event, since we already bubbled it above + jQuery.event.triggered = type; + + if ( event.isPropagationStopped() ) { + lastElement.addEventListener( type, stopPropagationCallback ); + } + + elem[ type ](); + + if ( event.isPropagationStopped() ) { + lastElement.removeEventListener( type, stopPropagationCallback ); + } + + jQuery.event.triggered = undefined; + + if ( tmp ) { + elem[ ontype ] = tmp; + } + } + } + } + + return event.result; + }, + + // Piggyback on a donor event to simulate a different one + // Used only for `focus(in | out)` events + simulate: function( type, elem, event ) { + var e = jQuery.extend( + new jQuery.Event(), + event, + { + type: type, + isSimulated: true + } + ); + + jQuery.event.trigger( e, null, elem ); + } + +} ); + +jQuery.fn.extend( { + + trigger: function( type, data ) { + return this.each( function() { + jQuery.event.trigger( type, data, this ); + } ); + }, + triggerHandler: function( type, data ) { + var elem = this[ 0 ]; + if ( elem ) { + return jQuery.event.trigger( type, data, elem, true ); + } + } +} ); + + +// Support: Firefox <=44 +// Firefox doesn't have focus(in | out) events +// Related ticket - https://bugzilla.mozilla.org/show_bug.cgi?id=687787 +// +// Support: Chrome <=48 - 49, Safari <=9.0 - 9.1 +// focus(in | out) events fire after focus & blur events, +// which is spec violation - http://www.w3.org/TR/DOM-Level-3-Events/#events-focusevent-event-order +// Related ticket - https://bugs.chromium.org/p/chromium/issues/detail?id=449857 +if ( !support.focusin ) { + jQuery.each( { focus: "focusin", blur: "focusout" }, function( orig, fix ) { + + // Attach a single capturing handler on the document while someone wants focusin/focusout + var handler = function( event ) { + jQuery.event.simulate( fix, event.target, jQuery.event.fix( event ) ); + }; + + jQuery.event.special[ fix ] = { + setup: function() { + + // Handle: regular nodes (via `this.ownerDocument`), window + // (via `this.document`) & document (via `this`). + var doc = this.ownerDocument || this.document || this, + attaches = dataPriv.access( doc, fix ); + + if ( !attaches ) { + doc.addEventListener( orig, handler, true ); + } + dataPriv.access( doc, fix, ( attaches || 0 ) + 1 ); + }, + teardown: function() { + var doc = this.ownerDocument || this.document || this, + attaches = dataPriv.access( doc, fix ) - 1; + + if ( !attaches ) { + doc.removeEventListener( orig, handler, true ); + dataPriv.remove( doc, fix ); + + } else { + dataPriv.access( doc, fix, attaches ); + } + } + }; + } ); +} +var location = window.location; + +var nonce = { guid: Date.now() }; + +var rquery = ( /\?/ ); + + + +// Cross-browser xml parsing +jQuery.parseXML = function( data ) { + var xml; + if ( !data || typeof data !== "string" ) { + return null; + } + + // Support: IE 9 - 11 only + // IE throws on parseFromString with invalid input. + try { + xml = ( new window.DOMParser() ).parseFromString( data, "text/xml" ); + } catch ( e ) { + xml = undefined; + } + + if ( !xml || xml.getElementsByTagName( "parsererror" ).length ) { + jQuery.error( "Invalid XML: " + data ); + } + return xml; +}; + + +var + rbracket = /\[\]$/, + rCRLF = /\r?\n/g, + rsubmitterTypes = /^(?:submit|button|image|reset|file)$/i, + rsubmittable = /^(?:input|select|textarea|keygen)/i; + +function buildParams( prefix, obj, traditional, add ) { + var name; + + if ( Array.isArray( obj ) ) { + + // Serialize array item. + jQuery.each( obj, function( i, v ) { + if ( traditional || rbracket.test( prefix ) ) { + + // Treat each array item as a scalar. + add( prefix, v ); + + } else { + + // Item is non-scalar (array or object), encode its numeric index. + buildParams( + prefix + "[" + ( typeof v === "object" && v != null ? i : "" ) + "]", + v, + traditional, + add + ); + } + } ); + + } else if ( !traditional && toType( obj ) === "object" ) { + + // Serialize object item. + for ( name in obj ) { + buildParams( prefix + "[" + name + "]", obj[ name ], traditional, add ); + } + + } else { + + // Serialize scalar item. + add( prefix, obj ); + } +} + +// Serialize an array of form elements or a set of +// key/values into a query string +jQuery.param = function( a, traditional ) { + var prefix, + s = [], + add = function( key, valueOrFunction ) { + + // If value is a function, invoke it and use its return value + var value = isFunction( valueOrFunction ) ? + valueOrFunction() : + valueOrFunction; + + s[ s.length ] = encodeURIComponent( key ) + "=" + + encodeURIComponent( value == null ? "" : value ); + }; + + if ( a == null ) { + return ""; + } + + // If an array was passed in, assume that it is an array of form elements. + if ( Array.isArray( a ) || ( a.jquery && !jQuery.isPlainObject( a ) ) ) { + + // Serialize the form elements + jQuery.each( a, function() { + add( this.name, this.value ); + } ); + + } else { + + // If traditional, encode the "old" way (the way 1.3.2 or older + // did it), otherwise encode params recursively. + for ( prefix in a ) { + buildParams( prefix, a[ prefix ], traditional, add ); + } + } + + // Return the resulting serialization + return s.join( "&" ); +}; + +jQuery.fn.extend( { + serialize: function() { + return jQuery.param( this.serializeArray() ); + }, + serializeArray: function() { + return this.map( function() { + + // Can add propHook for "elements" to filter or add form elements + var elements = jQuery.prop( this, "elements" ); + return elements ? jQuery.makeArray( elements ) : this; + } ) + .filter( function() { + var type = this.type; + + // Use .is( ":disabled" ) so that fieldset[disabled] works + return this.name && !jQuery( this ).is( ":disabled" ) && + rsubmittable.test( this.nodeName ) && !rsubmitterTypes.test( type ) && + ( this.checked || !rcheckableType.test( type ) ); + } ) + .map( function( _i, elem ) { + var val = jQuery( this ).val(); + + if ( val == null ) { + return null; + } + + if ( Array.isArray( val ) ) { + return jQuery.map( val, function( val ) { + return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; + } ); + } + + return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; + } ).get(); + } +} ); + + +var + r20 = /%20/g, + rhash = /#.*$/, + rantiCache = /([?&])_=[^&]*/, + rheaders = /^(.*?):[ \t]*([^\r\n]*)$/mg, + + // #7653, #8125, #8152: local protocol detection + rlocalProtocol = /^(?:about|app|app-storage|.+-extension|file|res|widget):$/, + rnoContent = /^(?:GET|HEAD)$/, + rprotocol = /^\/\//, + + /* Prefilters + * 1) They are useful to introduce custom dataTypes (see ajax/jsonp.js for an example) + * 2) These are called: + * - BEFORE asking for a transport + * - AFTER param serialization (s.data is a string if s.processData is true) + * 3) key is the dataType + * 4) the catchall symbol "*" can be used + * 5) execution will start with transport dataType and THEN continue down to "*" if needed + */ + prefilters = {}, + + /* Transports bindings + * 1) key is the dataType + * 2) the catchall symbol "*" can be used + * 3) selection will start with transport dataType and THEN go to "*" if needed + */ + transports = {}, + + // Avoid comment-prolog char sequence (#10098); must appease lint and evade compression + allTypes = "*/".concat( "*" ), + + // Anchor tag for parsing the document origin + originAnchor = document.createElement( "a" ); + originAnchor.href = location.href; + +// Base "constructor" for jQuery.ajaxPrefilter and jQuery.ajaxTransport +function addToPrefiltersOrTransports( structure ) { + + // dataTypeExpression is optional and defaults to "*" + return function( dataTypeExpression, func ) { + + if ( typeof dataTypeExpression !== "string" ) { + func = dataTypeExpression; + dataTypeExpression = "*"; + } + + var dataType, + i = 0, + dataTypes = dataTypeExpression.toLowerCase().match( rnothtmlwhite ) || []; + + if ( isFunction( func ) ) { + + // For each dataType in the dataTypeExpression + while ( ( dataType = dataTypes[ i++ ] ) ) { + + // Prepend if requested + if ( dataType[ 0 ] === "+" ) { + dataType = dataType.slice( 1 ) || "*"; + ( structure[ dataType ] = structure[ dataType ] || [] ).unshift( func ); + + // Otherwise append + } else { + ( structure[ dataType ] = structure[ dataType ] || [] ).push( func ); + } + } + } + }; +} + +// Base inspection function for prefilters and transports +function inspectPrefiltersOrTransports( structure, options, originalOptions, jqXHR ) { + + var inspected = {}, + seekingTransport = ( structure === transports ); + + function inspect( dataType ) { + var selected; + inspected[ dataType ] = true; + jQuery.each( structure[ dataType ] || [], function( _, prefilterOrFactory ) { + var dataTypeOrTransport = prefilterOrFactory( options, originalOptions, jqXHR ); + if ( typeof dataTypeOrTransport === "string" && + !seekingTransport && !inspected[ dataTypeOrTransport ] ) { + + options.dataTypes.unshift( dataTypeOrTransport ); + inspect( dataTypeOrTransport ); + return false; + } else if ( seekingTransport ) { + return !( selected = dataTypeOrTransport ); + } + } ); + return selected; + } + + return inspect( options.dataTypes[ 0 ] ) || !inspected[ "*" ] && inspect( "*" ); +} + +// A special extend for ajax options +// that takes "flat" options (not to be deep extended) +// Fixes #9887 +function ajaxExtend( target, src ) { + var key, deep, + flatOptions = jQuery.ajaxSettings.flatOptions || {}; + + for ( key in src ) { + if ( src[ key ] !== undefined ) { + ( flatOptions[ key ] ? target : ( deep || ( deep = {} ) ) )[ key ] = src[ key ]; + } + } + if ( deep ) { + jQuery.extend( true, target, deep ); + } + + return target; +} + +/* Handles responses to an ajax request: + * - finds the right dataType (mediates between content-type and expected dataType) + * - returns the corresponding response + */ +function ajaxHandleResponses( s, jqXHR, responses ) { + + var ct, type, finalDataType, firstDataType, + contents = s.contents, + dataTypes = s.dataTypes; + + // Remove auto dataType and get content-type in the process + while ( dataTypes[ 0 ] === "*" ) { + dataTypes.shift(); + if ( ct === undefined ) { + ct = s.mimeType || jqXHR.getResponseHeader( "Content-Type" ); + } + } + + // Check if we're dealing with a known content-type + if ( ct ) { + for ( type in contents ) { + if ( contents[ type ] && contents[ type ].test( ct ) ) { + dataTypes.unshift( type ); + break; + } + } + } + + // Check to see if we have a response for the expected dataType + if ( dataTypes[ 0 ] in responses ) { + finalDataType = dataTypes[ 0 ]; + } else { + + // Try convertible dataTypes + for ( type in responses ) { + if ( !dataTypes[ 0 ] || s.converters[ type + " " + dataTypes[ 0 ] ] ) { + finalDataType = type; + break; + } + if ( !firstDataType ) { + firstDataType = type; + } + } + + // Or just use first one + finalDataType = finalDataType || firstDataType; + } + + // If we found a dataType + // We add the dataType to the list if needed + // and return the corresponding response + if ( finalDataType ) { + if ( finalDataType !== dataTypes[ 0 ] ) { + dataTypes.unshift( finalDataType ); + } + return responses[ finalDataType ]; + } +} + +/* Chain conversions given the request and the original response + * Also sets the responseXXX fields on the jqXHR instance + */ +function ajaxConvert( s, response, jqXHR, isSuccess ) { + var conv2, current, conv, tmp, prev, + converters = {}, + + // Work with a copy of dataTypes in case we need to modify it for conversion + dataTypes = s.dataTypes.slice(); + + // Create converters map with lowercased keys + if ( dataTypes[ 1 ] ) { + for ( conv in s.converters ) { + converters[ conv.toLowerCase() ] = s.converters[ conv ]; + } + } + + current = dataTypes.shift(); + + // Convert to each sequential dataType + while ( current ) { + + if ( s.responseFields[ current ] ) { + jqXHR[ s.responseFields[ current ] ] = response; + } + + // Apply the dataFilter if provided + if ( !prev && isSuccess && s.dataFilter ) { + response = s.dataFilter( response, s.dataType ); + } + + prev = current; + current = dataTypes.shift(); + + if ( current ) { + + // There's only work to do if current dataType is non-auto + if ( current === "*" ) { + + current = prev; + + // Convert response if prev dataType is non-auto and differs from current + } else if ( prev !== "*" && prev !== current ) { + + // Seek a direct converter + conv = converters[ prev + " " + current ] || converters[ "* " + current ]; + + // If none found, seek a pair + if ( !conv ) { + for ( conv2 in converters ) { + + // If conv2 outputs current + tmp = conv2.split( " " ); + if ( tmp[ 1 ] === current ) { + + // If prev can be converted to accepted input + conv = converters[ prev + " " + tmp[ 0 ] ] || + converters[ "* " + tmp[ 0 ] ]; + if ( conv ) { + + // Condense equivalence converters + if ( conv === true ) { + conv = converters[ conv2 ]; + + // Otherwise, insert the intermediate dataType + } else if ( converters[ conv2 ] !== true ) { + current = tmp[ 0 ]; + dataTypes.unshift( tmp[ 1 ] ); + } + break; + } + } + } + } + + // Apply converter (if not an equivalence) + if ( conv !== true ) { + + // Unless errors are allowed to bubble, catch and return them + if ( conv && s.throws ) { + response = conv( response ); + } else { + try { + response = conv( response ); + } catch ( e ) { + return { + state: "parsererror", + error: conv ? e : "No conversion from " + prev + " to " + current + }; + } + } + } + } + } + } + + return { state: "success", data: response }; +} + +jQuery.extend( { + + // Counter for holding the number of active queries + active: 0, + + // Last-Modified header cache for next request + lastModified: {}, + etag: {}, + + ajaxSettings: { + url: location.href, + type: "GET", + isLocal: rlocalProtocol.test( location.protocol ), + global: true, + processData: true, + async: true, + contentType: "application/x-www-form-urlencoded; charset=UTF-8", + + /* + timeout: 0, + data: null, + dataType: null, + username: null, + password: null, + cache: null, + throws: false, + traditional: false, + headers: {}, + */ + + accepts: { + "*": allTypes, + text: "text/plain", + html: "text/html", + xml: "application/xml, text/xml", + json: "application/json, text/javascript" + }, + + contents: { + xml: /\bxml\b/, + html: /\bhtml/, + json: /\bjson\b/ + }, + + responseFields: { + xml: "responseXML", + text: "responseText", + json: "responseJSON" + }, + + // Data converters + // Keys separate source (or catchall "*") and destination types with a single space + converters: { + + // Convert anything to text + "* text": String, + + // Text to html (true = no transformation) + "text html": true, + + // Evaluate text as a json expression + "text json": JSON.parse, + + // Parse text as xml + "text xml": jQuery.parseXML + }, + + // For options that shouldn't be deep extended: + // you can add your own custom options here if + // and when you create one that shouldn't be + // deep extended (see ajaxExtend) + flatOptions: { + url: true, + context: true + } + }, + + // Creates a full fledged settings object into target + // with both ajaxSettings and settings fields. + // If target is omitted, writes into ajaxSettings. + ajaxSetup: function( target, settings ) { + return settings ? + + // Building a settings object + ajaxExtend( ajaxExtend( target, jQuery.ajaxSettings ), settings ) : + + // Extending ajaxSettings + ajaxExtend( jQuery.ajaxSettings, target ); + }, + + ajaxPrefilter: addToPrefiltersOrTransports( prefilters ), + ajaxTransport: addToPrefiltersOrTransports( transports ), + + // Main method + ajax: function( url, options ) { + + // If url is an object, simulate pre-1.5 signature + if ( typeof url === "object" ) { + options = url; + url = undefined; + } + + // Force options to be an object + options = options || {}; + + var transport, + + // URL without anti-cache param + cacheURL, + + // Response headers + responseHeadersString, + responseHeaders, + + // timeout handle + timeoutTimer, + + // Url cleanup var + urlAnchor, + + // Request state (becomes false upon send and true upon completion) + completed, + + // To know if global events are to be dispatched + fireGlobals, + + // Loop variable + i, + + // uncached part of the url + uncached, + + // Create the final options object + s = jQuery.ajaxSetup( {}, options ), + + // Callbacks context + callbackContext = s.context || s, + + // Context for global events is callbackContext if it is a DOM node or jQuery collection + globalEventContext = s.context && + ( callbackContext.nodeType || callbackContext.jquery ) ? + jQuery( callbackContext ) : + jQuery.event, + + // Deferreds + deferred = jQuery.Deferred(), + completeDeferred = jQuery.Callbacks( "once memory" ), + + // Status-dependent callbacks + statusCode = s.statusCode || {}, + + // Headers (they are sent all at once) + requestHeaders = {}, + requestHeadersNames = {}, + + // Default abort message + strAbort = "canceled", + + // Fake xhr + jqXHR = { + readyState: 0, + + // Builds headers hashtable if needed + getResponseHeader: function( key ) { + var match; + if ( completed ) { + if ( !responseHeaders ) { + responseHeaders = {}; + while ( ( match = rheaders.exec( responseHeadersString ) ) ) { + responseHeaders[ match[ 1 ].toLowerCase() + " " ] = + ( responseHeaders[ match[ 1 ].toLowerCase() + " " ] || [] ) + .concat( match[ 2 ] ); + } + } + match = responseHeaders[ key.toLowerCase() + " " ]; + } + return match == null ? null : match.join( ", " ); + }, + + // Raw string + getAllResponseHeaders: function() { + return completed ? responseHeadersString : null; + }, + + // Caches the header + setRequestHeader: function( name, value ) { + if ( completed == null ) { + name = requestHeadersNames[ name.toLowerCase() ] = + requestHeadersNames[ name.toLowerCase() ] || name; + requestHeaders[ name ] = value; + } + return this; + }, + + // Overrides response content-type header + overrideMimeType: function( type ) { + if ( completed == null ) { + s.mimeType = type; + } + return this; + }, + + // Status-dependent callbacks + statusCode: function( map ) { + var code; + if ( map ) { + if ( completed ) { + + // Execute the appropriate callbacks + jqXHR.always( map[ jqXHR.status ] ); + } else { + + // Lazy-add the new callbacks in a way that preserves old ones + for ( code in map ) { + statusCode[ code ] = [ statusCode[ code ], map[ code ] ]; + } + } + } + return this; + }, + + // Cancel the request + abort: function( statusText ) { + var finalText = statusText || strAbort; + if ( transport ) { + transport.abort( finalText ); + } + done( 0, finalText ); + return this; + } + }; + + // Attach deferreds + deferred.promise( jqXHR ); + + // Add protocol if not provided (prefilters might expect it) + // Handle falsy url in the settings object (#10093: consistency with old signature) + // We also use the url parameter if available + s.url = ( ( url || s.url || location.href ) + "" ) + .replace( rprotocol, location.protocol + "//" ); + + // Alias method option to type as per ticket #12004 + s.type = options.method || options.type || s.method || s.type; + + // Extract dataTypes list + s.dataTypes = ( s.dataType || "*" ).toLowerCase().match( rnothtmlwhite ) || [ "" ]; + + // A cross-domain request is in order when the origin doesn't match the current origin. + if ( s.crossDomain == null ) { + urlAnchor = document.createElement( "a" ); + + // Support: IE <=8 - 11, Edge 12 - 15 + // IE throws exception on accessing the href property if url is malformed, + // e.g. http://example.com:80x/ + try { + urlAnchor.href = s.url; + + // Support: IE <=8 - 11 only + // Anchor's host property isn't correctly set when s.url is relative + urlAnchor.href = urlAnchor.href; + s.crossDomain = originAnchor.protocol + "//" + originAnchor.host !== + urlAnchor.protocol + "//" + urlAnchor.host; + } catch ( e ) { + + // If there is an error parsing the URL, assume it is crossDomain, + // it can be rejected by the transport if it is invalid + s.crossDomain = true; + } + } + + // Convert data if not already a string + if ( s.data && s.processData && typeof s.data !== "string" ) { + s.data = jQuery.param( s.data, s.traditional ); + } + + // Apply prefilters + inspectPrefiltersOrTransports( prefilters, s, options, jqXHR ); + + // If request was aborted inside a prefilter, stop there + if ( completed ) { + return jqXHR; + } + + // We can fire global events as of now if asked to + // Don't fire events if jQuery.event is undefined in an AMD-usage scenario (#15118) + fireGlobals = jQuery.event && s.global; + + // Watch for a new set of requests + if ( fireGlobals && jQuery.active++ === 0 ) { + jQuery.event.trigger( "ajaxStart" ); + } + + // Uppercase the type + s.type = s.type.toUpperCase(); + + // Determine if request has content + s.hasContent = !rnoContent.test( s.type ); + + // Save the URL in case we're toying with the If-Modified-Since + // and/or If-None-Match header later on + // Remove hash to simplify url manipulation + cacheURL = s.url.replace( rhash, "" ); + + // More options handling for requests with no content + if ( !s.hasContent ) { + + // Remember the hash so we can put it back + uncached = s.url.slice( cacheURL.length ); + + // If data is available and should be processed, append data to url + if ( s.data && ( s.processData || typeof s.data === "string" ) ) { + cacheURL += ( rquery.test( cacheURL ) ? "&" : "?" ) + s.data; + + // #9682: remove data so that it's not used in an eventual retry + delete s.data; + } + + // Add or update anti-cache param if needed + if ( s.cache === false ) { + cacheURL = cacheURL.replace( rantiCache, "$1" ); + uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce.guid++ ) + + uncached; + } + + // Put hash and anti-cache on the URL that will be requested (gh-1732) + s.url = cacheURL + uncached; + + // Change '%20' to '+' if this is encoded form body content (gh-2658) + } else if ( s.data && s.processData && + ( s.contentType || "" ).indexOf( "application/x-www-form-urlencoded" ) === 0 ) { + s.data = s.data.replace( r20, "+" ); + } + + // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. + if ( s.ifModified ) { + if ( jQuery.lastModified[ cacheURL ] ) { + jqXHR.setRequestHeader( "If-Modified-Since", jQuery.lastModified[ cacheURL ] ); + } + if ( jQuery.etag[ cacheURL ] ) { + jqXHR.setRequestHeader( "If-None-Match", jQuery.etag[ cacheURL ] ); + } + } + + // Set the correct header, if data is being sent + if ( s.data && s.hasContent && s.contentType !== false || options.contentType ) { + jqXHR.setRequestHeader( "Content-Type", s.contentType ); + } + + // Set the Accepts header for the server, depending on the dataType + jqXHR.setRequestHeader( + "Accept", + s.dataTypes[ 0 ] && s.accepts[ s.dataTypes[ 0 ] ] ? + s.accepts[ s.dataTypes[ 0 ] ] + + ( s.dataTypes[ 0 ] !== "*" ? ", " + allTypes + "; q=0.01" : "" ) : + s.accepts[ "*" ] + ); + + // Check for headers option + for ( i in s.headers ) { + jqXHR.setRequestHeader( i, s.headers[ i ] ); + } + + // Allow custom headers/mimetypes and early abort + if ( s.beforeSend && + ( s.beforeSend.call( callbackContext, jqXHR, s ) === false || completed ) ) { + + // Abort if not done already and return + return jqXHR.abort(); + } + + // Aborting is no longer a cancellation + strAbort = "abort"; + + // Install callbacks on deferreds + completeDeferred.add( s.complete ); + jqXHR.done( s.success ); + jqXHR.fail( s.error ); + + // Get transport + transport = inspectPrefiltersOrTransports( transports, s, options, jqXHR ); + + // If no transport, we auto-abort + if ( !transport ) { + done( -1, "No Transport" ); + } else { + jqXHR.readyState = 1; + + // Send global event + if ( fireGlobals ) { + globalEventContext.trigger( "ajaxSend", [ jqXHR, s ] ); + } + + // If request was aborted inside ajaxSend, stop there + if ( completed ) { + return jqXHR; + } + + // Timeout + if ( s.async && s.timeout > 0 ) { + timeoutTimer = window.setTimeout( function() { + jqXHR.abort( "timeout" ); + }, s.timeout ); + } + + try { + completed = false; + transport.send( requestHeaders, done ); + } catch ( e ) { + + // Rethrow post-completion exceptions + if ( completed ) { + throw e; + } + + // Propagate others as results + done( -1, e ); + } + } + + // Callback for when everything is done + function done( status, nativeStatusText, responses, headers ) { + var isSuccess, success, error, response, modified, + statusText = nativeStatusText; + + // Ignore repeat invocations + if ( completed ) { + return; + } + + completed = true; + + // Clear timeout if it exists + if ( timeoutTimer ) { + window.clearTimeout( timeoutTimer ); + } + + // Dereference transport for early garbage collection + // (no matter how long the jqXHR object will be used) + transport = undefined; + + // Cache response headers + responseHeadersString = headers || ""; + + // Set readyState + jqXHR.readyState = status > 0 ? 4 : 0; + + // Determine if successful + isSuccess = status >= 200 && status < 300 || status === 304; + + // Get response data + if ( responses ) { + response = ajaxHandleResponses( s, jqXHR, responses ); + } + + // Use a noop converter for missing script + if ( !isSuccess && jQuery.inArray( "script", s.dataTypes ) > -1 ) { + s.converters[ "text script" ] = function() {}; + } + + // Convert no matter what (that way responseXXX fields are always set) + response = ajaxConvert( s, response, jqXHR, isSuccess ); + + // If successful, handle type chaining + if ( isSuccess ) { + + // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. + if ( s.ifModified ) { + modified = jqXHR.getResponseHeader( "Last-Modified" ); + if ( modified ) { + jQuery.lastModified[ cacheURL ] = modified; + } + modified = jqXHR.getResponseHeader( "etag" ); + if ( modified ) { + jQuery.etag[ cacheURL ] = modified; + } + } + + // if no content + if ( status === 204 || s.type === "HEAD" ) { + statusText = "nocontent"; + + // if not modified + } else if ( status === 304 ) { + statusText = "notmodified"; + + // If we have data, let's convert it + } else { + statusText = response.state; + success = response.data; + error = response.error; + isSuccess = !error; + } + } else { + + // Extract error from statusText and normalize for non-aborts + error = statusText; + if ( status || !statusText ) { + statusText = "error"; + if ( status < 0 ) { + status = 0; + } + } + } + + // Set data for the fake xhr object + jqXHR.status = status; + jqXHR.statusText = ( nativeStatusText || statusText ) + ""; + + // Success/Error + if ( isSuccess ) { + deferred.resolveWith( callbackContext, [ success, statusText, jqXHR ] ); + } else { + deferred.rejectWith( callbackContext, [ jqXHR, statusText, error ] ); + } + + // Status-dependent callbacks + jqXHR.statusCode( statusCode ); + statusCode = undefined; + + if ( fireGlobals ) { + globalEventContext.trigger( isSuccess ? "ajaxSuccess" : "ajaxError", + [ jqXHR, s, isSuccess ? success : error ] ); + } + + // Complete + completeDeferred.fireWith( callbackContext, [ jqXHR, statusText ] ); + + if ( fireGlobals ) { + globalEventContext.trigger( "ajaxComplete", [ jqXHR, s ] ); + + // Handle the global AJAX counter + if ( !( --jQuery.active ) ) { + jQuery.event.trigger( "ajaxStop" ); + } + } + } + + return jqXHR; + }, + + getJSON: function( url, data, callback ) { + return jQuery.get( url, data, callback, "json" ); + }, + + getScript: function( url, callback ) { + return jQuery.get( url, undefined, callback, "script" ); + } +} ); + +jQuery.each( [ "get", "post" ], function( _i, method ) { + jQuery[ method ] = function( url, data, callback, type ) { + + // Shift arguments if data argument was omitted + if ( isFunction( data ) ) { + type = type || callback; + callback = data; + data = undefined; + } + + // The url can be an options object (which then must have .url) + return jQuery.ajax( jQuery.extend( { + url: url, + type: method, + dataType: type, + data: data, + success: callback + }, jQuery.isPlainObject( url ) && url ) ); + }; +} ); + +jQuery.ajaxPrefilter( function( s ) { + var i; + for ( i in s.headers ) { + if ( i.toLowerCase() === "content-type" ) { + s.contentType = s.headers[ i ] || ""; + } + } +} ); + + +jQuery._evalUrl = function( url, options, doc ) { + return jQuery.ajax( { + url: url, + + // Make this explicit, since user can override this through ajaxSetup (#11264) + type: "GET", + dataType: "script", + cache: true, + async: false, + global: false, + + // Only evaluate the response if it is successful (gh-4126) + // dataFilter is not invoked for failure responses, so using it instead + // of the default converter is kludgy but it works. + converters: { + "text script": function() {} + }, + dataFilter: function( response ) { + jQuery.globalEval( response, options, doc ); + } + } ); +}; + + +jQuery.fn.extend( { + wrapAll: function( html ) { + var wrap; + + if ( this[ 0 ] ) { + if ( isFunction( html ) ) { + html = html.call( this[ 0 ] ); + } + + // The elements to wrap the target around + wrap = jQuery( html, this[ 0 ].ownerDocument ).eq( 0 ).clone( true ); + + if ( this[ 0 ].parentNode ) { + wrap.insertBefore( this[ 0 ] ); + } + + wrap.map( function() { + var elem = this; + + while ( elem.firstElementChild ) { + elem = elem.firstElementChild; + } + + return elem; + } ).append( this ); + } + + return this; + }, + + wrapInner: function( html ) { + if ( isFunction( html ) ) { + return this.each( function( i ) { + jQuery( this ).wrapInner( html.call( this, i ) ); + } ); + } + + return this.each( function() { + var self = jQuery( this ), + contents = self.contents(); + + if ( contents.length ) { + contents.wrapAll( html ); + + } else { + self.append( html ); + } + } ); + }, + + wrap: function( html ) { + var htmlIsFunction = isFunction( html ); + + return this.each( function( i ) { + jQuery( this ).wrapAll( htmlIsFunction ? html.call( this, i ) : html ); + } ); + }, + + unwrap: function( selector ) { + this.parent( selector ).not( "body" ).each( function() { + jQuery( this ).replaceWith( this.childNodes ); + } ); + return this; + } +} ); + + +jQuery.expr.pseudos.hidden = function( elem ) { + return !jQuery.expr.pseudos.visible( elem ); +}; +jQuery.expr.pseudos.visible = function( elem ) { + return !!( elem.offsetWidth || elem.offsetHeight || elem.getClientRects().length ); +}; + + + + +jQuery.ajaxSettings.xhr = function() { + try { + return new window.XMLHttpRequest(); + } catch ( e ) {} +}; + +var xhrSuccessStatus = { + + // File protocol always yields status code 0, assume 200 + 0: 200, + + // Support: IE <=9 only + // #1450: sometimes IE returns 1223 when it should be 204 + 1223: 204 + }, + xhrSupported = jQuery.ajaxSettings.xhr(); + +support.cors = !!xhrSupported && ( "withCredentials" in xhrSupported ); +support.ajax = xhrSupported = !!xhrSupported; + +jQuery.ajaxTransport( function( options ) { + var callback, errorCallback; + + // Cross domain only allowed if supported through XMLHttpRequest + if ( support.cors || xhrSupported && !options.crossDomain ) { + return { + send: function( headers, complete ) { + var i, + xhr = options.xhr(); + + xhr.open( + options.type, + options.url, + options.async, + options.username, + options.password + ); + + // Apply custom fields if provided + if ( options.xhrFields ) { + for ( i in options.xhrFields ) { + xhr[ i ] = options.xhrFields[ i ]; + } + } + + // Override mime type if needed + if ( options.mimeType && xhr.overrideMimeType ) { + xhr.overrideMimeType( options.mimeType ); + } + + // X-Requested-With header + // For cross-domain requests, seeing as conditions for a preflight are + // akin to a jigsaw puzzle, we simply never set it to be sure. + // (it can always be set on a per-request basis or even using ajaxSetup) + // For same-domain requests, won't change header if already provided. + if ( !options.crossDomain && !headers[ "X-Requested-With" ] ) { + headers[ "X-Requested-With" ] = "XMLHttpRequest"; + } + + // Set headers + for ( i in headers ) { + xhr.setRequestHeader( i, headers[ i ] ); + } + + // Callback + callback = function( type ) { + return function() { + if ( callback ) { + callback = errorCallback = xhr.onload = + xhr.onerror = xhr.onabort = xhr.ontimeout = + xhr.onreadystatechange = null; + + if ( type === "abort" ) { + xhr.abort(); + } else if ( type === "error" ) { + + // Support: IE <=9 only + // On a manual native abort, IE9 throws + // errors on any property access that is not readyState + if ( typeof xhr.status !== "number" ) { + complete( 0, "error" ); + } else { + complete( + + // File: protocol always yields status 0; see #8605, #14207 + xhr.status, + xhr.statusText + ); + } + } else { + complete( + xhrSuccessStatus[ xhr.status ] || xhr.status, + xhr.statusText, + + // Support: IE <=9 only + // IE9 has no XHR2 but throws on binary (trac-11426) + // For XHR2 non-text, let the caller handle it (gh-2498) + ( xhr.responseType || "text" ) !== "text" || + typeof xhr.responseText !== "string" ? + { binary: xhr.response } : + { text: xhr.responseText }, + xhr.getAllResponseHeaders() + ); + } + } + }; + }; + + // Listen to events + xhr.onload = callback(); + errorCallback = xhr.onerror = xhr.ontimeout = callback( "error" ); + + // Support: IE 9 only + // Use onreadystatechange to replace onabort + // to handle uncaught aborts + if ( xhr.onabort !== undefined ) { + xhr.onabort = errorCallback; + } else { + xhr.onreadystatechange = function() { + + // Check readyState before timeout as it changes + if ( xhr.readyState === 4 ) { + + // Allow onerror to be called first, + // but that will not handle a native abort + // Also, save errorCallback to a variable + // as xhr.onerror cannot be accessed + window.setTimeout( function() { + if ( callback ) { + errorCallback(); + } + } ); + } + }; + } + + // Create the abort callback + callback = callback( "abort" ); + + try { + + // Do send the request (this may raise an exception) + xhr.send( options.hasContent && options.data || null ); + } catch ( e ) { + + // #14683: Only rethrow if this hasn't been notified as an error yet + if ( callback ) { + throw e; + } + } + }, + + abort: function() { + if ( callback ) { + callback(); + } + } + }; + } +} ); + + + + +// Prevent auto-execution of scripts when no explicit dataType was provided (See gh-2432) +jQuery.ajaxPrefilter( function( s ) { + if ( s.crossDomain ) { + s.contents.script = false; + } +} ); + +// Install script dataType +jQuery.ajaxSetup( { + accepts: { + script: "text/javascript, application/javascript, " + + "application/ecmascript, application/x-ecmascript" + }, + contents: { + script: /\b(?:java|ecma)script\b/ + }, + converters: { + "text script": function( text ) { + jQuery.globalEval( text ); + return text; + } + } +} ); + +// Handle cache's special case and crossDomain +jQuery.ajaxPrefilter( "script", function( s ) { + if ( s.cache === undefined ) { + s.cache = false; + } + if ( s.crossDomain ) { + s.type = "GET"; + } +} ); + +// Bind script tag hack transport +jQuery.ajaxTransport( "script", function( s ) { + + // This transport only deals with cross domain or forced-by-attrs requests + if ( s.crossDomain || s.scriptAttrs ) { + var script, callback; + return { + send: function( _, complete ) { + script = jQuery( " + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+\[\begin{split}\newcommand{\as}{\kw{as}} +\newcommand{\case}{\kw{case}} +\newcommand{\cons}{\textsf{cons}} +\newcommand{\consf}{\textsf{consf}} +\newcommand{\emptyf}{\textsf{emptyf}} +\newcommand{\End}{\kw{End}} +\newcommand{\kwend}{\kw{end}} +\newcommand{\even}{\textsf{even}} +\newcommand{\evenO}{\textsf{even}_\textsf{O}} +\newcommand{\evenS}{\textsf{even}_\textsf{S}} +\newcommand{\Fix}{\kw{Fix}} +\newcommand{\fix}{\kw{fix}} +\newcommand{\for}{\textsf{for}} +\newcommand{\forest}{\textsf{forest}} +\newcommand{\Functor}{\kw{Functor}} +\newcommand{\In}{\kw{in}} +\newcommand{\ind}[3]{\kw{Ind}~[#1]\left(#2\mathrm{~:=~}#3\right)} +\newcommand{\Indp}[4]{\kw{Ind}_{#4}[#1](#2:=#3)} +\newcommand{\Indpstr}[5]{\kw{Ind}_{#4}[#1](#2:=#3)/{#5}} +\newcommand{\injective}{\kw{injective}} +\newcommand{\kw}[1]{\textsf{#1}} +\newcommand{\length}{\textsf{length}} +\newcommand{\letin}[3]{\kw{let}~#1:=#2~\kw{in}~#3} +\newcommand{\List}{\textsf{list}} +\newcommand{\lra}{\longrightarrow} +\newcommand{\Match}{\kw{match}} +\newcommand{\Mod}[3]{{\kw{Mod}}({#1}:{#2}\,\zeroone{:={#3}})} +\newcommand{\ModImp}[3]{{\kw{Mod}}({#1}:{#2}:={#3})} +\newcommand{\ModA}[2]{{\kw{ModA}}({#1}=={#2})} +\newcommand{\ModS}[2]{{\kw{Mod}}({#1}:{#2})} +\newcommand{\ModType}[2]{{\kw{ModType}}({#1}:={#2})} +\newcommand{\mto}{.\;} +\newcommand{\nat}{\textsf{nat}} +\newcommand{\Nil}{\textsf{nil}} +\newcommand{\nilhl}{\textsf{nil\_hl}} +\newcommand{\nO}{\textsf{O}} +\newcommand{\node}{\textsf{node}} +\newcommand{\nS}{\textsf{S}} +\newcommand{\odd}{\textsf{odd}} +\newcommand{\oddS}{\textsf{odd}_\textsf{S}} +\newcommand{\ovl}[1]{\overline{#1}} +\newcommand{\Pair}{\textsf{pair}} +\newcommand{\plus}{\mathsf{plus}} +\newcommand{\SProp}{\textsf{SProp}} +\newcommand{\Prop}{\textsf{Prop}} +\newcommand{\return}{\kw{return}} +\newcommand{\Set}{\textsf{Set}} +\newcommand{\Sort}{\mathcal{S}} +\newcommand{\Str}{\textsf{Stream}} +\newcommand{\Struct}{\kw{Struct}} +\newcommand{\subst}[3]{#1\{#2/#3\}} +\newcommand{\tl}{\textsf{tl}} +\newcommand{\tree}{\textsf{tree}} +\newcommand{\trii}{\triangleright_\iota} +\newcommand{\Type}{\textsf{Type}} +\newcommand{\WEV}[3]{\mbox{$#1[] \vdash #2 \lra #3$}} +\newcommand{\WEVT}[3]{\mbox{$#1[] \vdash #2 \lra$}\\ \mbox{$ #3$}} +\newcommand{\WF}[2]{{\mathcal{W\!F}}(#1)[#2]} +\newcommand{\WFE}[1]{\WF{E}{#1}} +\newcommand{\WFT}[2]{#1[] \vdash {\mathcal{W\!F}}(#2)} +\newcommand{\WFTWOLINES}[2]{{\mathcal{W\!F}}\begin{array}{l}(#1)\\\mbox{}[{#2}]\end{array}} +\newcommand{\with}{\kw{with}} +\newcommand{\WS}[3]{#1[] \vdash #2 <: #3} +\newcommand{\WSE}[2]{\WS{E}{#1}{#2}} +\newcommand{\WT}[4]{#1[#2] \vdash #3 : #4} +\newcommand{\WTE}[3]{\WT{E}{#1}{#2}{#3}} +\newcommand{\WTEG}[2]{\WTE{\Gamma}{#1}{#2}} +\newcommand{\WTM}[3]{\WT{#1}{}{#2}{#3}} +\newcommand{\zeroone}[1]{[{#1}]} +\end{split}\]
+
+

Recent changes

+
+

Unreleased changes

+ +
+

Added

+
    +

  • in NatInt.v

    +
      +

    • lemmas mul_reg_l and mul_reg_r +(#17560, +by Remzi Yang).

      • +
    +
    • +

  • file List_Extension.v in Wellfounded +(#18183, +by Andrej Dudenhefner).

    • +

  • in Inverse_Image.v in Wellfounded

    +
      +

    • lemmas Acc_simulation and wf_simulation +(#18183, +by Andrej Dudenhefner).

      • +
    +
    • +

  • in Operators_Properties.v in Relations

    +
      +

    • lemma clos_t_clos_rt +(#18183, +by Andrej Dudenhefner).

      • +
    +
    • +

  • in List_Extension.v

    +
      +

    • well-founded list extension list_ext of a well-founded relation, +including infrastructure lemmas. It can be used for +well-foundedness proofs such as wf_lex_exp in +Lexicographic_Exponentiation.v +(#18183, +by Andrej Dudenhefner).

      • +
    +
    • +

  • in VectorSpec.v

    +
      +

    • lemma Forall2_cons_iff +(#19269, +by Lucas Donati and Andrej Dudenhefner and Pierre Rousselin).

      • +
    +
    • +

  • in List.v

    +
      +

    • lemmas length_cons and length_nil +(#19479, +by Hugo Herbelin).

      • +
    +
    • +

  • in Eqdep_dec.v in Logic

    +
      +

    • lemmas UIP_None_l, UIP_None_r, UIP_None_None, +UIP_nil_l, UIP_nil_r, UIP_nil_nil +(#19483, +by Andres Erbsen).

      • +
    +
    • +

  • in List.v

    +
      +

    • Proper instance to enable setoid_rewrite to rewrite +inside the function argument of List.map +(#19515, +by Andres Erbsen).

      • +
    +
    • +

  • in Fin.v

    +
      +

    • lemmas case_L_R'_L, case_L_R'_R, case_L_R_L, case_L_R_R +(#19655, +by Andrej Dudenhefner).

      • +
    +
    • +

  • in List.v

    +
      +

    • lemmas length_tl, tl_map, filter_rev, +filter_map_swap, filter_true, filter_false, +list_prod_as_flat_map, skipn_seq, map_const, +fst_list_prod, snd_list_prod, Injective_map_NoDup_in, +and Permutation_map_same_l +(#19748, +by Andres Erbsen).

      • +
    +
    • +

  • in BinPos.v

    +
      +

    • lemma BinPos.iter_op_correct, relating Pos.iter_op for +associative operations to the more general Pos.iter +(#19749, +by Andres Erbsen).

      • +
    +
    • +

  • in Znat.v

    +
      +

    • lemmas N2Z.inj_lxor, N2Z.inj_land, N2Z.inj_lor, +N2Z.inj_ldiff, N2Z.inj_shiftl, and N2Z.inj_shiftr +relating bitwise operations on N to those on Z +(#19750, +by Andres Erbsen).

      • +
    +
    • +

  • file Zdiv_facts.v +(#19752, +by Andres Erbsen).

    • +

  • in file Zdiv_facts.v

    +
      +

    • lemmas Z.diveq_iff and Z.mod_diveq_iff that further +genralize the same concept as Z.mod_small to known quotients +other than 0. +(#19752, +by Andres Erbsen).

      • +

    • lemmas Z.eq_mod_opp and Z.eq_mod_abs +(#19752, +by Andres Erbsen).

      • +
    +
    • +

  • in file Zdiv.v

    +
      +

    • lemma Z.mod_id_iff generalizes Z.mod_small. +(#19752, +by Andres Erbsen).

      • +

    • lemmas Z.mod_opp_mod_opp, Z.mod_mod_opp_r, +Z.mod_opp_r_mod, Z.mod_mod_abs_r, Z.mod_abs_r_mod +combining Z.modulo with Z.opp or Z.abs +(#19752, +by Andres Erbsen).

      • +

    • Lemmas cong_iff_0 and cong_iff_ex can be used to reduce +congruence equalities to equations where only one side is headed +by Z.modulo. +(#19752, +by Andres Erbsen).

      • +

    • Lemmas Z.gcd_mod_l and Z.gcd_mod_r generalize +Z.gcd_mod. +(#19752, +by Andres Erbsen).

      • +

    • Lemma Z.mod_mod_divide generalizes Zmod_mod. +(#19752, +by Andres Erbsen).

      • +

    • Lemma Z.mod_pow_l allows pushing modulo inside exponentiation +(#19752, +by Andres Erbsen).

      • +
    +
    • +

  • Deprecated: module ZArith_Base, module Ztac, and Zeq_bool. +Use ZArith (or BinInt), Lia, and Z.eqb instead. +Reducing use of the deprecated modules in stdlib changed the transitive +dependencies of several stdlib files; you may now need to Require or +Import ZArith or Lia. +The definition of Zeq_bool was also changed to be an alias for +Z.eqb; this is expected to simplify simultaneous compatibility with 8.20 +and 9.0 +(#19801, +by Andres Erbsen).

    • +

  • Added: +Stdlib.All which does Require Export of all other files in the stdlib +(#19914, +by Gaëtan Gilbert).

    • +

  • in EquivDec.v in Classes +(#19949, +by Daniil Iaitskov).

    +
      +

    • EqDec instance for option

      • +
    +
    • +
+
+
+

Changed

+
    +

  • Changed the requirement prefix of the standard library from Coq +to Stdlib and made it mandatory. As a temporary measure, for +backward compatibility with older versions, Coq, or a missing +From Stdlib, is immediatly translated to Stdlib with a +warning. It is thus not recommended to name anything Coq or +Coq.*. The recommended transition path is to first potentially +silence the warnings, adding the lines +-arg -w -arg -deprecated-from-Coq, +-arg -w -arg -deprecated-dirpath-Coq and +-arg -w -arg -deprecated-missing-stdlib +or simply the more generic +-arg -compat -arg 8.20 to your _CoqProject. +Then, when droping support for Coq <= 8.20, replacing requirement of +Stdlib modules by From Stdlib Require {Import,Export,} <LibraryModules>.. +Beware that the Stdlib still has a handful redundant names, that is +for modules Byte, you still have to use From Stdlib.Strings or +From Stdlib.Init, for Tactics use From Stdlib.Program +or From Stdlib.Init, for Tauto use From Stdlib.micromega +or From Stdlib.Init and for Wf, use From Stdlib.Program +or From Stdlib.Init +(#19310 +and #19530, +the latter starting to implement +CEP#83 +by Pierre Roux).

    • +

  • in List.v

    +
      +

    • lemmas that were using the letter O in their name to refer to +zero now use instead the digit 0 +(#19479, +by Hugo Herbelin).

      • +
    +
    • +

  • in Fin.v

    +
      +

    • case_L_R' and case_L_R made transparent definitions +(#19655, +by Andrej Dudenhefner).

      • +
    +
    • +

  • in several files

    +
      +

    • remove transitive requirements or export of theories about Z, +you may need to add explicit Require or Import +of ZArith or Lia +(#19801, +by Andres Erbsen).

      • +
    +
    • +

  • in Zbool.v

    +
      +

    • definition of Zeq_bool is now an alias for Z.eqb, +this is expected to simplify simultaneous compatibility with 8.20 and 9.0 +(#19801, +by Andres Erbsen).

      • +
    +
    • +
+
+
+

Renamed

+
+
+

Deprecated

+
+
+

Changed

+
    +

  • modules ZArith_Base and Ztac, +use ZArith (or BinInt) or Lia instead +(#19801, +by Andres Erbsen).

    • +

  • in Zbool.v

    +
      +

    • definition Zeq_bool, use Z.eqb instead. +(#19801, +by Andres Erbsen).

      • +
    +
    • +
+
+
+
+

Previous versions

+

The standard library historically used to be distributed with Coq, +please look in Coq own changelog for details about older changes.

+
+
+ + +
+
+ +
+
+
+
+ + + + + +
+ + Other versions + v: 9.0 + + +
+
+
Versions
+ +
dev
+ +
stable
+ +
8.20
+ +
8.19
+ +
8.18
+ +
8.17
+ +
8.16
+ +
8.15
+ +
8.14
+ +
8.13
+ +
8.12
+ +
8.11
+ +
8.10
+ +
8.9
+ +
8.8
+ +
8.7
+ +
8.6
+ +
8.5
+ +
8.4
+ +
8.3
+ +
8.2
+ +
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+ +
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+
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+ + + + \ No newline at end of file diff --git a/master/refman-stdlib/coq-exnindex.html b/master/refman-stdlib/coq-exnindex.html new file mode 100644 index 0000000000..b989b1b861 --- /dev/null +++ b/master/refman-stdlib/coq-exnindex.html @@ -0,0 +1,214 @@ + + + + + + Errors and Warnings Index — The Rocq Standard Library 9.0+alpha documentation + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
  • »
    • +
  • Errors and Warnings Index
    • +
  • +
    • +
+
+
+
+ +
+
+ +
+ +
+

© Copyright 1999-2024, Inria, CNRS and contributors.

+
+ + Built with Sphinx using a + theme + provided by Read the Docs. + + +
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+ + Other versions + v: 9.0 + + +
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stable
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+ +
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+ +
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+ +
8.16
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+ +
8.14
+ +
8.13
+ +
8.12
+ +
8.11
+ +
8.10
+ +
8.9
+ +
8.8
+ +
8.7
+ +
8.6
+ +
8.5
+ +
8.4
+ +
8.3
+ +
8.2
+ +
8.1
+ +
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+ +
+
+
Downloads
+ +
+
+
+ + + + \ No newline at end of file diff --git a/master/refman-stdlib/coq-optindex.html b/master/refman-stdlib/coq-optindex.html new file mode 100644 index 0000000000..c36d079d88 --- /dev/null +++ b/master/refman-stdlib/coq-optindex.html @@ -0,0 +1,214 @@ + + + + + + Flags, options and Tables Index — The Rocq Standard Library 9.0+alpha documentation + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
  • »
    • +
  • Flags, options and Tables Index
    • +
  • +
    • +
+
+
+
+
+ + +

Flags, options and Tables Index

+ +
+ p +
+ + + + + + + +
 
+ p
+ Printing Float +
+ + +
+
+
+ +
+ +
+

© Copyright 1999-2024, Inria, CNRS and contributors.

+
+ + Built with Sphinx using a + theme + provided by Read the Docs. + + +
+
+
+
+
+ + + + + +
+ + Other versions + v: 9.0 + + +
+
+
Versions
+ +
dev
+ +
stable
+ +
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+ +
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+ +
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+ +
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+ +
8.16
+ +
8.15
+ +
8.14
+ +
8.13
+ +
8.12
+ +
8.11
+ +
8.10
+ +
8.9
+ +
8.8
+ +
8.7
+ +
8.6
+ +
8.5
+ +
8.4
+ +
8.3
+ +
8.2
+ +
8.1
+ +
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+ +
+
+
Downloads
+ +
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+
+ + + + \ No newline at end of file diff --git a/master/refman-stdlib/coq-tacindex.html b/master/refman-stdlib/coq-tacindex.html new file mode 100644 index 0000000000..abeaf0d37e --- /dev/null +++ b/master/refman-stdlib/coq-tacindex.html @@ -0,0 +1,228 @@ + + + + + + Tactic Index — The Rocq Standard Library 9.0+alpha documentation + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
  • »
    • +
  • Tactic Index
    • +
  • +
    • +
+
+
+
+
+ + +

Tactic Index

+ +
+ d | + s +
+ + + + + + + + + + + + + + + +
 
+ d
+ discrR +
 
+ s
+ split_Rabs +
+ split_Rmult +
+ + +
+
+
+ +
+ +
+

© Copyright 1999-2024, Inria, CNRS and contributors.

+
+ + Built with Sphinx using a + theme + provided by Read the Docs. + + +
+
+
+
+
+ + + + + +
+ + Other versions + v: 9.0 + + +
+
+
Versions
+ +
dev
+ +
stable
+ +
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+ +
8.19
+ +
8.18
+ +
8.17
+ +
8.16
+ +
8.15
+ +
8.14
+ +
8.13
+ +
8.12
+ +
8.11
+ +
8.10
+ +
8.9
+ +
8.8
+ +
8.7
+ +
8.6
+ +
8.5
+ +
8.4
+ +
8.3
+ +
8.2
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8.1
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+
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+ + + + \ No newline at end of file diff --git a/master/refman-stdlib/genindex.html b/master/refman-stdlib/genindex.html new file mode 100644 index 0000000000..14012f8102 --- /dev/null +++ b/master/refman-stdlib/genindex.html @@ -0,0 +1,359 @@ + + + + + + Index — The Rocq Standard Library 9.0+alpha documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ + +

Index

+ +
+ Symbols + | A + | D + | F + | H + | L + | M + | N + | P + | R + | S + | T + +
+

Symbols

+ + + +
+ +

A

+ + + +
+ +

D

+ + +
+ +

F

+ + + +
+ +

H

+ + +
+ +

L

+ + +
+ +

M

+ + + +
+ +

N

+ + + +
+ +

P

+ + + +
+ +

R

+ + +
+ +

S

+ + + +
+ +

T

+ + + +
+ + + +
+
+
+ +
+ +
+

© Copyright 1999-2024, Inria, CNRS and contributors.

+
+ + Built with Sphinx using a + theme + provided by Read the Docs. + + +
+
+
+
+
+ + + + + +
+ + Other versions + v: 9.0 + + +
+
+
Versions
+ +
dev
+ +
stable
+ +
8.20
+ +
8.19
+ +
8.18
+ +
8.17
+ +
8.16
+ +
8.15
+ +
8.14
+ +
8.13
+ +
8.12
+ +
8.11
+ +
8.10
+ +
8.9
+ +
8.8
+ +
8.7
+ +
8.6
+ +
8.5
+ +
8.4
+ +
8.3
+ +
8.2
+ +
8.1
+ +
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+ +
+
+
Downloads
+ +
+
+
+ + + + \ No newline at end of file diff --git a/master/refman-stdlib/index.html b/master/refman-stdlib/index.html new file mode 100644 index 0000000000..453a45a533 --- /dev/null +++ b/master/refman-stdlib/index.html @@ -0,0 +1,323 @@ + + + + + + + Introduction and Contents — The Rocq Standard Library 9.0+alpha documentation + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+\[\begin{split}\newcommand{\as}{\kw{as}} +\newcommand{\case}{\kw{case}} +\newcommand{\cons}{\textsf{cons}} +\newcommand{\consf}{\textsf{consf}} +\newcommand{\emptyf}{\textsf{emptyf}} +\newcommand{\End}{\kw{End}} +\newcommand{\kwend}{\kw{end}} +\newcommand{\even}{\textsf{even}} +\newcommand{\evenO}{\textsf{even}_\textsf{O}} +\newcommand{\evenS}{\textsf{even}_\textsf{S}} +\newcommand{\Fix}{\kw{Fix}} +\newcommand{\fix}{\kw{fix}} +\newcommand{\for}{\textsf{for}} +\newcommand{\forest}{\textsf{forest}} +\newcommand{\Functor}{\kw{Functor}} +\newcommand{\In}{\kw{in}} +\newcommand{\ind}[3]{\kw{Ind}~[#1]\left(#2\mathrm{~:=~}#3\right)} +\newcommand{\Indp}[4]{\kw{Ind}_{#4}[#1](#2:=#3)} +\newcommand{\Indpstr}[5]{\kw{Ind}_{#4}[#1](#2:=#3)/{#5}} +\newcommand{\injective}{\kw{injective}} +\newcommand{\kw}[1]{\textsf{#1}} +\newcommand{\length}{\textsf{length}} +\newcommand{\letin}[3]{\kw{let}~#1:=#2~\kw{in}~#3} +\newcommand{\List}{\textsf{list}} +\newcommand{\lra}{\longrightarrow} +\newcommand{\Match}{\kw{match}} +\newcommand{\Mod}[3]{{\kw{Mod}}({#1}:{#2}\,\zeroone{:={#3}})} +\newcommand{\ModImp}[3]{{\kw{Mod}}({#1}:{#2}:={#3})} +\newcommand{\ModA}[2]{{\kw{ModA}}({#1}=={#2})} +\newcommand{\ModS}[2]{{\kw{Mod}}({#1}:{#2})} +\newcommand{\ModType}[2]{{\kw{ModType}}({#1}:={#2})} +\newcommand{\mto}{.\;} +\newcommand{\nat}{\textsf{nat}} +\newcommand{\Nil}{\textsf{nil}} +\newcommand{\nilhl}{\textsf{nil\_hl}} +\newcommand{\nO}{\textsf{O}} +\newcommand{\node}{\textsf{node}} +\newcommand{\nS}{\textsf{S}} +\newcommand{\odd}{\textsf{odd}} +\newcommand{\oddS}{\textsf{odd}_\textsf{S}} +\newcommand{\ovl}[1]{\overline{#1}} +\newcommand{\Pair}{\textsf{pair}} +\newcommand{\plus}{\mathsf{plus}} +\newcommand{\SProp}{\textsf{SProp}} +\newcommand{\Prop}{\textsf{Prop}} +\newcommand{\return}{\kw{return}} +\newcommand{\Set}{\textsf{Set}} +\newcommand{\Sort}{\mathcal{S}} +\newcommand{\Str}{\textsf{Stream}} +\newcommand{\Struct}{\kw{Struct}} +\newcommand{\subst}[3]{#1\{#2/#3\}} +\newcommand{\tl}{\textsf{tl}} +\newcommand{\tree}{\textsf{tree}} +\newcommand{\trii}{\triangleright_\iota} +\newcommand{\Type}{\textsf{Type}} +\newcommand{\WEV}[3]{\mbox{$#1[] \vdash #2 \lra #3$}} +\newcommand{\WEVT}[3]{\mbox{$#1[] \vdash #2 \lra$}\\ \mbox{$ #3$}} +\newcommand{\WF}[2]{{\mathcal{W\!F}}(#1)[#2]} +\newcommand{\WFE}[1]{\WF{E}{#1}} +\newcommand{\WFT}[2]{#1[] \vdash {\mathcal{W\!F}}(#2)} +\newcommand{\WFTWOLINES}[2]{{\mathcal{W\!F}}\begin{array}{l}(#1)\\\mbox{}[{#2}]\end{array}} +\newcommand{\with}{\kw{with}} +\newcommand{\WS}[3]{#1[] \vdash #2 <: #3} +\newcommand{\WSE}[2]{\WS{E}{#1}{#2}} +\newcommand{\WT}[4]{#1[#2] \vdash #3 : #4} +\newcommand{\WTE}[3]{\WT{E}{#1}{#2}{#3}} +\newcommand{\WTEG}[2]{\WTE{\Gamma}{#1}{#2}} +\newcommand{\WTM}[3]{\WT{#1}{}{#2}{#3}} +\newcommand{\zeroone}[1]{[{#1}]} +\end{split}\]
+
+

Introduction and Contents

+

The is the reference manual of the Standard Library of Coq. +It mostly presents a few tactics.

+

The full table of contents is presented below:

+
+

Contents

+
+ +
+
+

Overview

+ +
+
+

Appendix

+ +
+
+

Note

+

License

+

This material (the Rocq Stdlib Reference Manual) may be distributed only +subject to the terms and conditions set forth in the Open +Publication License, v1.0 or later (the latest version is presently +available at http://www.opencontent.org/openpub). Options A and B +are not elected.

+
+
+
+ + +
+
+
+ +
+ +
+

© Copyright 1999-2024, Inria, CNRS and contributors.

+
+ + Built with Sphinx using a + theme + provided by Read the Docs. + + +
+
+
+
+
+ + + + + +
+ + Other versions + v: 9.0 + + +
+
+
Versions
+ +
dev
+ +
stable
+ +
8.20
+ +
8.19
+ +
8.18
+ +
8.17
+ +
8.16
+ +
8.15
+ +
8.14
+ +
8.13
+ +
8.12
+ +
8.11
+ +
8.10
+ +
8.9
+ +
8.8
+ +
8.7
+ +
8.6
+ +
8.5
+ +
8.4
+ +
8.3
+ +
8.2
+ +
8.1
+ +
8.0
+ +
+
+
Downloads
+ +
+
+
+ + + + \ No newline at end of file diff --git a/master/refman-stdlib/language/coq-library.html b/master/refman-stdlib/language/coq-library.html new file mode 100644 index 0000000000..52c238a32b --- /dev/null +++ b/master/refman-stdlib/language/coq-library.html @@ -0,0 +1,937 @@ + + + + + + + The standard library — The Rocq Standard Library 9.0+alpha documentation + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+\[\begin{split}\newcommand{\as}{\kw{as}} +\newcommand{\case}{\kw{case}} +\newcommand{\cons}{\textsf{cons}} +\newcommand{\consf}{\textsf{consf}} +\newcommand{\emptyf}{\textsf{emptyf}} +\newcommand{\End}{\kw{End}} +\newcommand{\kwend}{\kw{end}} +\newcommand{\even}{\textsf{even}} +\newcommand{\evenO}{\textsf{even}_\textsf{O}} +\newcommand{\evenS}{\textsf{even}_\textsf{S}} +\newcommand{\Fix}{\kw{Fix}} +\newcommand{\fix}{\kw{fix}} +\newcommand{\for}{\textsf{for}} +\newcommand{\forest}{\textsf{forest}} +\newcommand{\Functor}{\kw{Functor}} +\newcommand{\In}{\kw{in}} +\newcommand{\ind}[3]{\kw{Ind}~[#1]\left(#2\mathrm{~:=~}#3\right)} +\newcommand{\Indp}[4]{\kw{Ind}_{#4}[#1](#2:=#3)} +\newcommand{\Indpstr}[5]{\kw{Ind}_{#4}[#1](#2:=#3)/{#5}} +\newcommand{\injective}{\kw{injective}} +\newcommand{\kw}[1]{\textsf{#1}} +\newcommand{\length}{\textsf{length}} +\newcommand{\letin}[3]{\kw{let}~#1:=#2~\kw{in}~#3} +\newcommand{\List}{\textsf{list}} +\newcommand{\lra}{\longrightarrow} +\newcommand{\Match}{\kw{match}} +\newcommand{\Mod}[3]{{\kw{Mod}}({#1}:{#2}\,\zeroone{:={#3}})} +\newcommand{\ModImp}[3]{{\kw{Mod}}({#1}:{#2}:={#3})} +\newcommand{\ModA}[2]{{\kw{ModA}}({#1}=={#2})} +\newcommand{\ModS}[2]{{\kw{Mod}}({#1}:{#2})} +\newcommand{\ModType}[2]{{\kw{ModType}}({#1}:={#2})} +\newcommand{\mto}{.\;} +\newcommand{\nat}{\textsf{nat}} +\newcommand{\Nil}{\textsf{nil}} +\newcommand{\nilhl}{\textsf{nil\_hl}} +\newcommand{\nO}{\textsf{O}} +\newcommand{\node}{\textsf{node}} +\newcommand{\nS}{\textsf{S}} +\newcommand{\odd}{\textsf{odd}} +\newcommand{\oddS}{\textsf{odd}_\textsf{S}} +\newcommand{\ovl}[1]{\overline{#1}} +\newcommand{\Pair}{\textsf{pair}} +\newcommand{\plus}{\mathsf{plus}} +\newcommand{\SProp}{\textsf{SProp}} +\newcommand{\Prop}{\textsf{Prop}} +\newcommand{\return}{\kw{return}} +\newcommand{\Set}{\textsf{Set}} +\newcommand{\Sort}{\mathcal{S}} +\newcommand{\Str}{\textsf{Stream}} +\newcommand{\Struct}{\kw{Struct}} +\newcommand{\subst}[3]{#1\{#2/#3\}} +\newcommand{\tl}{\textsf{tl}} +\newcommand{\tree}{\textsf{tree}} +\newcommand{\trii}{\triangleright_\iota} +\newcommand{\Type}{\textsf{Type}} +\newcommand{\WEV}[3]{\mbox{$#1[] \vdash #2 \lra #3$}} +\newcommand{\WEVT}[3]{\mbox{$#1[] \vdash #2 \lra$}\\ \mbox{$ #3$}} +\newcommand{\WF}[2]{{\mathcal{W\!F}}(#1)[#2]} +\newcommand{\WFE}[1]{\WF{E}{#1}} +\newcommand{\WFT}[2]{#1[] \vdash {\mathcal{W\!F}}(#2)} +\newcommand{\WFTWOLINES}[2]{{\mathcal{W\!F}}\begin{array}{l}(#1)\\\mbox{}[{#2}]\end{array}} +\newcommand{\with}{\kw{with}} +\newcommand{\WS}[3]{#1[] \vdash #2 <: #3} +\newcommand{\WSE}[2]{\WS{E}{#1}{#2}} +\newcommand{\WT}[4]{#1[#2] \vdash #3 : #4} +\newcommand{\WTE}[3]{\WT{E}{#1}{#2}{#3}} +\newcommand{\WTEG}[2]{\WTE{\Gamma}{#1}{#2}} +\newcommand{\WTM}[3]{\WT{#1}{}{#2}{#3}} +\newcommand{\zeroone}[1]{[{#1}]} +\end{split}\]
+
+

The standard library

+
+

Survey

+

The standard library is structured into the following +subdirectories:

+
+
    +

  • Logic : Classical logic and dependent equality

    • +

  • Arith : Basic Peano arithmetic

    • +

  • PArith : Basic positive integer arithmetic

    • +

  • NArith : Basic binary natural number arithmetic

    • +

  • ZArith : Basic relative integer arithmetic

    • +

  • Numbers : Various approaches to natural, integer and cyclic numbers (currently axiomatically and on top of 2^31 binary words)

    • +

  • Bool : Booleans (basic functions and results)

    • +

  • Lists : Monomorphic and polymorphic lists (basic functions and results), Streams (infinite sequences defined with coinductive types)

    • +

  • Sets : Sets (classical, constructive, finite, infinite, power set, etc.)

    • +

  • FSets : Specification and implementations of finite sets and finite maps (by lists and by AVL trees)

    • +

  • Reals : Axiomatization of real numbers (classical, basic functions, integer part, fractional part, limit, derivative, Cauchy series, power series and results,...)

    • +

  • Floats : Machine implementation of floating-point arithmetic (for the binary64 format)

    • +

  • Relations : Relations (definitions and basic results)

    • +

  • Sorting : Sorted list (basic definitions and heapsort correctness)

    • +

  • Strings : 8-bits characters and strings

    • +

  • Wellfounded : Well-founded relations (basic results)

    • +
+
+

These directories belong to the initial load path of the system, and +the modules they provide are compiled at installation time. So they +are directly accessible with the command Require.

+

The different modules of the Coq standard library are documented +online at https://coq.inria.fr/stdlib/.

+
+
+

Peano’s arithmetic (nat)

+

While in the initial state, many operations and predicates of Peano's +arithmetic are defined, further operations and results belong to other +modules. For instance, the decidability of the basic predicates are +defined here. This is provided by requiring the module Arith.

+

The following table describes the notations available in scope +nat_scope :

+ ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

Notation

Interpretation

_ < _

lt

_ <= _

le

_ > _

gt

_ >= _

ge

x < y < z

x < y /\ y < z

x < y <= z

x < y /\ y <= z

x <= y < z

x <= y /\ y < z

x <= y <= z

x <= y /\ y <= z

_ + _

plus

_ - _

minus

_ * _

mult

+
+
+

Notations for integer arithmetic

+

The following table describes the syntax of expressions +for integer arithmetic. It is provided by requiring and opening the module ZArith and opening scope Z_scope. +It specifies how notations are interpreted and, when not +already reserved, the precedence and associativity.

+ ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

Notation

Interpretation

Precedence

Associativity

_ < _

Z.lt

_ <= _

Z.le

_ > _

Z.gt

_ >= _

Z.ge

x < y < z

x < y /\ y < z

x < y <= z

x < y /\ y <= z

x <= y < z

x <= y /\ y < z

x <= y <= z

x <= y /\ y <= z

_ ?= _

Z.compare

70

no

_ + _

Z.add

_ - _

Z.sub

_ * _

Z.mul

_ / _

Z.div

_ mod _

Z.modulo

40

no

- _

Z.opp

_ ^ _

Z.pow

+
+

Example

+
+
+
From Stdlib Require Import ZArith. +
[Loading ML file rocq-runtime.plugins.ring ... done] +[Loading ML file rocq-runtime.plugins.zify ... done] +[Loading ML file rocq-runtime.plugins.micromega_core ... done] +[Loading ML file rocq-runtime.plugins.micromega ... done] +[Loading ML file rocq-runtime.plugins.btauto ... done] +
+
Check (2 + 3)%Z. +
(2 + 3)%Z + : Z +
+
Open Scope Z_scope. +
Check 2 + 3. +
2 + 3 + : Z +
+
+
+
+
+
+

Real numbers library

+
+

Notations for real numbers

+

This is provided by requiring and opening the module Reals and +opening scope R_scope. This set of notations is very similar to +the notation for integer arithmetic. The inverse function was added.

+ ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

Notation

Interpretation

_ < _

Rlt

_ <= _

Rle

_ > _

Rgt

_ >= _

Rge

x < y < z

x < y /\ y < z

x < y <= z

x < y /\ y <= z

x <= y < z

x <= y /\ y < z

x <= y <= z

x <= y /\ y <= z

_ + _

Rplus

_ - _

Rminus

_ * _

Rmult

_ / _

Rdiv

- _

Ropp

/ _

Rinv

_ ^ _

pow

+
+

Example

+
+
+
From Stdlib Require Import Reals. +
Check (2 + 3)%R. +
(2 + 3)%R + : R +
+
Open Scope R_scope. +
Check 2 + 3. +
2 + 3 + : R +
+
+
+
+
+
+

Some tactics for real numbers

+

In addition to the powerful ring, field and lra +tactics (see Chapters ring and micromega), there are also:

+
+
+Tactic discrR
+

Proves that two real integer constants are different.

+
+ +
+

Example

+
+
+
From Stdlib Require Import DiscrR. +
Open Scope R_scope. +
Goal 5 <> 0. +
1 goal + + ============================ + 5 <> 0 +
+
discrR. +
+
+
+
+
+Tactic split_Rabs
+

Allows unfolding the Rabs constant and splits corresponding conjunctions.

+
+ +
+

Example

+
+
+
From Stdlib Require Import Reals. +
Open Scope R_scope. +
Goal forall x:R, x <= Rabs x. +
1 goal + + ============================ + forall x : R, x <= Rabs x +
+
intro; split_Rabs. +
2 goals + + x : R + Hlt : x < 0 + ============================ + x <= - x + +goal 2 is: + x <= x +
+
+
+
+
+
+Tactic split_Rmult
+

Splits a condition that a product is non-null into subgoals +corresponding to the condition on each operand of the product.

+
+ +
+

Example

+
+
+
From Stdlib Require Import Reals. +
Open Scope R_scope. +
Goal forall x y z:R, x * y * z <> 0. +
1 goal + + ============================ + forall x y z : R, x * y * z <> 0 +
+
intros; split_Rmult. +
3 goals + + x, y, z : R + ============================ + x <> 0 + +goal 2 is: + y <> 0 +goal 3 is: + z <> 0 +
+
+
+
+
+
+
+

List library

+

Some elementary operations on polymorphic lists are defined here. +They can be accessed by requiring module List.

+

It defines the following notions:

+
+
    +

  • length

    • +

  • head : first element (with default)

    • +

  • tail : all but first element

    • +

  • app : concatenation

    • +

  • rev : reverse

    • +

  • nth : accessing n-th element (with default)

    • +

  • map : applying a function

    • +

  • flat_map : applying a function returning lists

    • +

  • fold_left : iterator (from head to tail)

    • +

  • fold_right : iterator (from tail to head)

    • +
+
+

The following table shows notations available when opening scope list_scope.

+ ++++++ + + + + + + + + + + + + + + + + + + + +

Notation

Interpretation

Precedence

Associativity

_ ++ _

app

60

right

_ :: _

cons

60

right

+
+
+

Floats library

+

The standard library has a small Floats module for accessing +processor floating-point operations through the Coq kernel. +However, while this module supports computation and has a bit-level +specification, it doesn't include elaborate theorems, such as a link +to real arithmetic or various error bounds. To do proofs by +reflection, use Floats in conjunction with the complementary +Flocq library, which provides +many such theorems.

+

The library of primitive floating-point arithmetic can be loaded by +requiring module Floats:

+
+
+
From Stdlib Require Import Floats. +
+
+

It exports the module PrimFloat that provides a primitive type +named float, defined in the kernel +as well as two variant types float_comparison and float_class:

+
+
+
Print float. +
*** [ float : Set ] +
+
Print float_comparison. +
Variant float_comparison : Set := + FEq : float_comparison + | FLt : float_comparison + | FGt : float_comparison + | FNotComparable : float_comparison. +
+
Print float_class. +
Variant float_class : Set := + PNormal : float_class + | NNormal : float_class + | PSubn : float_class + | NSubn : float_class + | PZero : float_class + | NZero : float_class + | PInf : float_class + | NInf : float_class + | NaN : float_class. +
+
+
+

It then defines the primitive operators below, using the processor +floating-point operators for binary64 in rounding-to-nearest even:

+
    +

  • abs

    • +

  • opp

    • +

  • sub

    • +

  • add

    • +

  • mul

    • +

  • div

    • +

  • sqrt

    • +

  • compare : compare two floats and return a float_comparison

    • +

  • classify : analyze a float and return a float_class

    • +

  • of_int63 : round a primitive integer and convert it into a float

    • +

  • normfr_mantissa : take a float in [0.5; 1.0) and return its mantissa

    • +

  • frshiftexp : convert a float to fractional part in [0.5; 1.0) and integer part

    • +

  • ldshiftexp : multiply a float by an integral power of 2

    • +

  • next_up : return the next float towards positive infinity

    • +

  • next_down : return the next float towards negative infinity

    • +
+

For special floating-point values, the following constants are also +defined:

+
    +

  • zero

    • +

  • neg_zero

    • +

  • one

    • +

  • two

    • +

  • infinity

    • +

  • neg_infinity

    • +

  • nan : Not a Number (assumed to be unique: the "payload" of NaNs is ignored)

    • +
+

The following table shows the notations available when opening scope +float_scope.

+ ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

Notation

Interpretation

- _

opp

_ - _

sub

_ + _

add

_ * _

mul

_ / _

div

_ =? _

eqb

_ <? _

ltb

_ <=? _

leb

_ ?= _

compare

+

Floating-point constants are parsed and pretty-printed as (17-digit) +decimal constants. This ensures that the composition +\(\text{parse} \circ \text{print}\) amounts to the identity.

+
+
+Warning The constant number is not a binary64 floating-point value. A closest value number will be used and unambiguously printed number. [inexact-float,parsing]
+

Not all decimal constants are floating-point values. This warning +is generated when parsing such a constant (for instance 0.1).

+
+ +
+
+Flag Printing Float
+

Turn this flag off (it is on by default) to deactivate decimal +printing of floating-point constants. They will then be printed +with an hexadecimal representation.

+
+ +
+

Example

+
+
+
Open Scope float_scope. +
Eval compute in 1 + 0.5. +
= 1.5 + : float +
+
Eval compute in 1 / 0. +
= infinity + : float +
+
Eval compute in 1 / -0. +
= neg_infinity + : float +
+
Eval compute in 0 / 0. +
= nan + : float +
+
Eval compute in 0 ?= -0. +
= FEq + : float_comparison +
+
Eval compute in nan ?= nan. +
= FNotComparable + : float_comparison +
+
Eval compute in next_down (-1). +
= -1.0000000000000002 + : float +
+
+
+
+

The primitive operators are specified with respect to their Gallina +counterpart, using the variant type spec_float, and the injection +Prim2SF:

+
+
+
Print spec_float. +
Variant spec_float : Set := + S754_zero : bool -> spec_float + | S754_infinity : bool -> spec_float + | S754_nan : spec_float + | S754_finite : bool -> positive -> Z -> spec_float. + +Arguments S754_zero s%bool_scope +Arguments S754_infinity s%bool_scope +Arguments S754_finite s%bool_scope m%positive_scope e%Z_scope +
+
Check Prim2SF. +
Prim2SF + : float -> spec_float +
+
Check mul_spec. +
mul_spec + : forall x y : float, Prim2SF (x * y) = SF64mul (Prim2SF x) (Prim2SF y) +
+
+
+

For more details on the available definitions and lemmas, see the +online documentation of the Floats library.

+
+
+

Primitive strings library

+

The standard library provides a PrimString module declaring a primitive +string type PrimString.string (corresponding to the OCaml string type), +together with a small set of primitive functions:

+
    +

  • max_length : gives the maximum length of a string

    • +

  • make : builds a string of the given length conly containing the given byte

    • +

  • length : gives the lenght of the given string

    • +

  • get : gives the byte at a given index in the given string

    • +

  • sub : extracts the sub-string from the given string that starts at the given offset and with the given length

    • +

  • cat : concatenates the two given strings

    • +

  • compare : compares the two strings and returns a comparison

    • +
+

Bytes are represented using the PrimString.char63, which is defined as Uint63.int, +but primitive strings only store values fitting on 8 bits (i.e., values between 0 and 255).

+

Axiomatic specifications of these primitive string functions are provided in the +PrimStringAxioms module. Additional properties, and relations to equivalent +primitives defined in Gallina are provided in module PString (which exports +PrimString and PrimStringAxioms.

+

A custom string notation is provided for the string and char63 types, +in respective scopes pstring and char63.

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+\[\begin{split}\newcommand{\as}{\kw{as}} +\newcommand{\case}{\kw{case}} +\newcommand{\cons}{\textsf{cons}} +\newcommand{\consf}{\textsf{consf}} +\newcommand{\emptyf}{\textsf{emptyf}} +\newcommand{\End}{\kw{End}} +\newcommand{\kwend}{\kw{end}} +\newcommand{\even}{\textsf{even}} +\newcommand{\evenO}{\textsf{even}_\textsf{O}} +\newcommand{\evenS}{\textsf{even}_\textsf{S}} +\newcommand{\Fix}{\kw{Fix}} +\newcommand{\fix}{\kw{fix}} +\newcommand{\for}{\textsf{for}} +\newcommand{\forest}{\textsf{forest}} +\newcommand{\Functor}{\kw{Functor}} +\newcommand{\In}{\kw{in}} +\newcommand{\ind}[3]{\kw{Ind}~[#1]\left(#2\mathrm{~:=~}#3\right)} +\newcommand{\Indp}[4]{\kw{Ind}_{#4}[#1](#2:=#3)} +\newcommand{\Indpstr}[5]{\kw{Ind}_{#4}[#1](#2:=#3)/{#5}} +\newcommand{\injective}{\kw{injective}} +\newcommand{\kw}[1]{\textsf{#1}} +\newcommand{\length}{\textsf{length}} +\newcommand{\letin}[3]{\kw{let}~#1:=#2~\kw{in}~#3} +\newcommand{\List}{\textsf{list}} +\newcommand{\lra}{\longrightarrow} +\newcommand{\Match}{\kw{match}} +\newcommand{\Mod}[3]{{\kw{Mod}}({#1}:{#2}\,\zeroone{:={#3}})} +\newcommand{\ModImp}[3]{{\kw{Mod}}({#1}:{#2}:={#3})} +\newcommand{\ModA}[2]{{\kw{ModA}}({#1}=={#2})} +\newcommand{\ModS}[2]{{\kw{Mod}}({#1}:{#2})} +\newcommand{\ModType}[2]{{\kw{ModType}}({#1}:={#2})} +\newcommand{\mto}{.\;} +\newcommand{\nat}{\textsf{nat}} +\newcommand{\Nil}{\textsf{nil}} +\newcommand{\nilhl}{\textsf{nil\_hl}} +\newcommand{\nO}{\textsf{O}} +\newcommand{\node}{\textsf{node}} +\newcommand{\nS}{\textsf{S}} +\newcommand{\odd}{\textsf{odd}} +\newcommand{\oddS}{\textsf{odd}_\textsf{S}} +\newcommand{\ovl}[1]{\overline{#1}} +\newcommand{\Pair}{\textsf{pair}} +\newcommand{\plus}{\mathsf{plus}} +\newcommand{\SProp}{\textsf{SProp}} +\newcommand{\Prop}{\textsf{Prop}} +\newcommand{\return}{\kw{return}} +\newcommand{\Set}{\textsf{Set}} +\newcommand{\Sort}{\mathcal{S}} +\newcommand{\Str}{\textsf{Stream}} +\newcommand{\Struct}{\kw{Struct}} +\newcommand{\subst}[3]{#1\{#2/#3\}} +\newcommand{\tl}{\textsf{tl}} +\newcommand{\tree}{\textsf{tree}} +\newcommand{\trii}{\triangleright_\iota} +\newcommand{\Type}{\textsf{Type}} +\newcommand{\WEV}[3]{\mbox{$#1[] \vdash #2 \lra #3$}} +\newcommand{\WEVT}[3]{\mbox{$#1[] \vdash #2 \lra$}\\ \mbox{$ #3$}} +\newcommand{\WF}[2]{{\mathcal{W\!F}}(#1)[#2]} +\newcommand{\WFE}[1]{\WF{E}{#1}} +\newcommand{\WFT}[2]{#1[] \vdash {\mathcal{W\!F}}(#2)} +\newcommand{\WFTWOLINES}[2]{{\mathcal{W\!F}}\begin{array}{l}(#1)\\\mbox{}[{#2}]\end{array}} +\newcommand{\with}{\kw{with}} +\newcommand{\WS}[3]{#1[] \vdash #2 <: #3} +\newcommand{\WSE}[2]{\WS{E}{#1}{#2}} +\newcommand{\WT}[4]{#1[#2] \vdash #3 : #4} +\newcommand{\WTE}[3]{\WT{E}{#1}{#2}{#3}} +\newcommand{\WTEG}[2]{\WTE{\Gamma}{#1}{#2}} +\newcommand{\WTM}[3]{\WT{#1}{}{#2}{#3}} +\newcommand{\zeroone}[1]{[{#1}]} +\end{split}\]
+
+

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+

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+ + +
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+ +
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+
+ +
+\[\begin{split}\newcommand{\as}{\kw{as}} +\newcommand{\case}{\kw{case}} +\newcommand{\cons}{\textsf{cons}} +\newcommand{\consf}{\textsf{consf}} +\newcommand{\emptyf}{\textsf{emptyf}} +\newcommand{\End}{\kw{End}} +\newcommand{\kwend}{\kw{end}} +\newcommand{\even}{\textsf{even}} +\newcommand{\evenO}{\textsf{even}_\textsf{O}} +\newcommand{\evenS}{\textsf{even}_\textsf{S}} +\newcommand{\Fix}{\kw{Fix}} +\newcommand{\fix}{\kw{fix}} +\newcommand{\for}{\textsf{for}} +\newcommand{\forest}{\textsf{forest}} +\newcommand{\Functor}{\kw{Functor}} +\newcommand{\In}{\kw{in}} +\newcommand{\ind}[3]{\kw{Ind}~[#1]\left(#2\mathrm{~:=~}#3\right)} +\newcommand{\Indp}[4]{\kw{Ind}_{#4}[#1](#2:=#3)} +\newcommand{\Indpstr}[5]{\kw{Ind}_{#4}[#1](#2:=#3)/{#5}} +\newcommand{\injective}{\kw{injective}} +\newcommand{\kw}[1]{\textsf{#1}} +\newcommand{\length}{\textsf{length}} +\newcommand{\letin}[3]{\kw{let}~#1:=#2~\kw{in}~#3} +\newcommand{\List}{\textsf{list}} +\newcommand{\lra}{\longrightarrow} +\newcommand{\Match}{\kw{match}} +\newcommand{\Mod}[3]{{\kw{Mod}}({#1}:{#2}\,\zeroone{:={#3}})} +\newcommand{\ModImp}[3]{{\kw{Mod}}({#1}:{#2}:={#3})} +\newcommand{\ModA}[2]{{\kw{ModA}}({#1}=={#2})} +\newcommand{\ModS}[2]{{\kw{Mod}}({#1}:{#2})} +\newcommand{\ModType}[2]{{\kw{ModType}}({#1}:={#2})} +\newcommand{\mto}{.\;} +\newcommand{\nat}{\textsf{nat}} +\newcommand{\Nil}{\textsf{nil}} +\newcommand{\nilhl}{\textsf{nil\_hl}} +\newcommand{\nO}{\textsf{O}} +\newcommand{\node}{\textsf{node}} +\newcommand{\nS}{\textsf{S}} +\newcommand{\odd}{\textsf{odd}} +\newcommand{\oddS}{\textsf{odd}_\textsf{S}} +\newcommand{\ovl}[1]{\overline{#1}} +\newcommand{\Pair}{\textsf{pair}} +\newcommand{\plus}{\mathsf{plus}} +\newcommand{\SProp}{\textsf{SProp}} +\newcommand{\Prop}{\textsf{Prop}} +\newcommand{\return}{\kw{return}} +\newcommand{\Set}{\textsf{Set}} +\newcommand{\Sort}{\mathcal{S}} +\newcommand{\Str}{\textsf{Stream}} +\newcommand{\Struct}{\kw{Struct}} +\newcommand{\subst}[3]{#1\{#2/#3\}} +\newcommand{\tl}{\textsf{tl}} +\newcommand{\tree}{\textsf{tree}} +\newcommand{\trii}{\triangleright_\iota} +\newcommand{\Type}{\textsf{Type}} +\newcommand{\WEV}[3]{\mbox{$#1[] \vdash #2 \lra #3$}} +\newcommand{\WEVT}[3]{\mbox{$#1[] \vdash #2 \lra$}\\ \mbox{$ #3$}} +\newcommand{\WF}[2]{{\mathcal{W\!F}}(#1)[#2]} +\newcommand{\WFE}[1]{\WF{E}{#1}} +\newcommand{\WFT}[2]{#1[] \vdash {\mathcal{W\!F}}(#2)} +\newcommand{\WFTWOLINES}[2]{{\mathcal{W\!F}}\begin{array}{l}(#1)\\\mbox{}[{#2}]\end{array}} +\newcommand{\with}{\kw{with}} +\newcommand{\WS}[3]{#1[] \vdash #2 <: #3} +\newcommand{\WSE}[2]{\WS{E}{#1}{#2}} +\newcommand{\WT}[4]{#1[#2] \vdash #3 : #4} +\newcommand{\WTE}[3]{\WT{E}{#1}{#2}{#3}} +\newcommand{\WTEG}[2]{\WTE{\Gamma}{#1}{#2}} +\newcommand{\WTM}[3]{\WT{#1}{}{#2}{#3}} +\newcommand{\zeroone}[1]{[{#1}]} +\end{split}\]
+
+

Bibliography

+

+
+ + +
+
+ +
+
+
+
+ + + + + +
+ + Other versions + v: 9.0 + + +
+
+
Versions
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stable
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8.1
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+
+
Downloads
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+ + + + \ No newline at end of file diff --git a/master/refman/.buildinfo b/master/refman/.buildinfo index 11e70a30a4..6d150f694c 100644 --- a/master/refman/.buildinfo +++ b/master/refman/.buildinfo @@ -1,4 +1,4 @@ # Sphinx build info version 1 # This file hashes the configuration used when building these files. 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zify
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More about nsat
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Debugging \(\SProp\) issue
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Typeclasses eautodev +
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diff --git a/master/refman/addendum/universe-polymorphism.html b/master/refman/addendum/universe-polymorphism.html index 99185a41f5..9dd0c766ee 100644 --- a/master/refman/addendum/universe-polymorphism.html +++ b/master/refman/addendum/universe-polymorphism.html @@ -2284,7 +2284,7 @@

Polymorphic definitions
Check bar@{_ _}.
The command has indeed failed with message: -Universe instance length is 1 but should be 2. +Universe instance length for bar is 1 but should be 2.

@@ -2540,51 +2540,53 @@

Polymorphic definitions
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diff --git a/master/refman/appendix/history-and-changes/index.html b/master/refman/appendix/history-and-changes/index.html index 6166909364..427dfc73bc 100644 --- a/master/refman/appendix/history-and-changes/index.html +++ b/master/refman/appendix/history-and-changes/index.html @@ -1309,51 +1309,53 @@
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Details of changes in 8.0dev +
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diff --git a/master/refman/coq-attrindex.html b/master/refman/coq-attrindex.html index dfc0702392..48508005b6 100644 --- a/master/refman/coq-attrindex.html +++ b/master/refman/coq-attrindex.html @@ -1437,51 +1437,53 @@

Attribute Index

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Command Index

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Errors and Warnings Index

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Flags, options and Tables Index

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Tactic Index

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Gallina Index

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Z

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Details of changes in 7.4dev +
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coqrc
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diff --git a/master/refman/proof-engine/ltac.html b/master/refman/proof-engine/ltac.html index 576b0f70ab..d6fb701841 100644 --- a/master/refman/proof-engine/ltac.html +++ b/master/refman/proof-engine/ltac.html @@ -4286,42 +4286,42 @@

Profiling L
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Show Ltac Profile. -
total time: 1.235s +
total time: 0.954s tactic local total calls max ───────────────────────────────────────────┴──────┴──────┴───────┴─────────┘ -─tac -------------------------------------- 0.1% 100.0% 1 1.235s -─<Corelib.Init.Tauto.with_uniform_flags> -- 0.0% 92.7% 26 0.086s -─<Corelib.Init.Tauto.tauto_gen> ----------- 0.0% 92.7% 26 0.086s -─<Corelib.Init.Tauto.tauto_intuitionistic> 0.1% 92.6% 26 0.086s -─t_tauto_intuit --------------------------- 0.1% 92.5% 26 0.086s -─<Corelib.Init.Tauto.simplif> ------------- 61.4% 89.0% 26 0.085s -─<Corelib.Init.Tauto.is_conj> ------------- 20.9% 20.9% 28756 0.014s -─lia -------------------------------------- 0.1% 6.9% 28 0.056s -─Zify.zify -------------------------------- 4.8% 5.4% 54 0.056s -─<Corelib.Init.Tauto.axioms> -------------- 2.5% 3.5% 0 0.005s -─elim id ---------------------------------- 3.4% 3.4% 650 0.000s +─tac -------------------------------------- 0.1% 100.0% 1 0.954s +─<Corelib.Init.Tauto.with_uniform_flags> -- 0.0% 93.2% 26 0.056s +─<Corelib.Init.Tauto.tauto_gen> ----------- 0.0% 93.2% 26 0.056s +─<Corelib.Init.Tauto.tauto_intuitionistic> 0.0% 93.1% 26 0.056s +─t_tauto_intuit --------------------------- 0.1% 93.0% 26 0.056s +─<Corelib.Init.Tauto.simplif> ------------- 59.0% 89.5% 26 0.055s +─<Corelib.Init.Tauto.is_conj> ------------- 24.1% 24.1% 28756 0.008s +─lia -------------------------------------- 0.1% 6.5% 28 0.045s +─Zify.zify -------------------------------- 4.9% 5.4% 54 0.045s +─<Corelib.Init.Tauto.axioms> -------------- 2.3% 3.5% 0 0.002s +─elim id ---------------------------------- 3.0% 3.0% 650 0.000s tactic local total calls max ─────────────────────────────────────────────┴──────┴──────┴───────┴─────────┘ -─tac ---------------------------------------- 0.1% 100.0% 1 1.235s - ├─<Corelib.Init.Tauto.with_uniform_flags> -- 0.0% 92.7% 26 0.086s - │└<Corelib.Init.Tauto.tauto_gen> ----------- 0.0% 92.7% 26 0.086s - │└<Corelib.Init.Tauto.tauto_intuitionistic> 0.1% 92.6% 26 0.086s - │└t_tauto_intuit --------------------------- 0.1% 92.5% 26 0.086s - │ ├─<Corelib.Init.Tauto.simplif> ----------- 61.4% 89.0% 26 0.085s - │ │ ├─<Corelib.Init.Tauto.is_conj> --------- 20.9% 20.9% 28756 0.014s - │ │ └─elim id ------------------------------ 3.4% 3.4% 650 0.000s - │ └─<Corelib.Init.Tauto.axioms> ------------ 2.5% 3.5% 0 0.005s - └─lia -------------------------------------- 0.1% 6.9% 28 0.056s - └Zify.zify -------------------------------- 4.8% 5.4% 54 0.056s +─tac ---------------------------------------- 0.1% 100.0% 1 0.954s + ├─<Corelib.Init.Tauto.with_uniform_flags> -- 0.0% 93.2% 26 0.056s + │└<Corelib.Init.Tauto.tauto_gen> ----------- 0.0% 93.2% 26 0.056s + │└<Corelib.Init.Tauto.tauto_intuitionistic> 0.0% 93.1% 26 0.056s + │└t_tauto_intuit --------------------------- 0.1% 93.0% 26 0.056s + │ ├─<Corelib.Init.Tauto.simplif> ----------- 59.0% 89.5% 26 0.055s + │ │ ├─<Corelib.Init.Tauto.is_conj> --------- 24.1% 24.1% 28756 0.008s + │ │ └─elim id ------------------------------ 3.0% 3.0% 650 0.000s + │ └─<Corelib.Init.Tauto.axioms> ------------ 2.3% 3.5% 0 0.002s + └─lia -------------------------------------- 0.1% 6.5% 28 0.045s + └Zify.zify -------------------------------- 4.9% 5.4% 54 0.045s
Show Ltac Profile "lia". -
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total time: 0.954s tactic local total calls max ───────┴──────┴──────┴───────┴─────────┘ -─lia -- 0.1% 6.9% 28 0.056s +─lia -- 0.1% 6.5% 28 0.045s tactic local total calls max ───────┴──────┴──────┴───────┴─────────┘ @@ -4438,51 +4438,53 @@

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71, 72, 73, 74, 75, 76, 77], "wftwolin": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "begin": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "arrai": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "l": [0, 1, 2, 3, 4, 5, 6, 7, 8, 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26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "wteg": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "gamma": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "wtm": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "c": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "i": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "cic": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "\u03b2\u03b4\u03b9\u03b6": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "latex": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77], "tac": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "p": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "program": [0, 1, 3, 4, 5, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "ssreflect": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "t": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "m": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "x": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "author": [2, 3, 4, 5, 7, 8, 9, 11, 14, 17, 27, 29, 42, 46, 57, 73, 74], "jean": [2, 17, 24, 77], "christoph": [2, 17, 24, 77], "filli\u00e2tr": [2, 17, 24, 77], "pierr": [2, 17, 24, 77], "letouzei": [2, 17, 24, 77], "we": [2, 3, 4, 5, 9, 11, 12, 13, 14, 16, 17, 24, 26, 27, 28, 29, 30, 31, 33, 34, 35, 38, 39, 40, 42, 44, 45, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 72, 75], "present": [2, 3, 6, 9, 11, 13, 15, 17, 24, 25, 26, 29, 30, 32, 33, 34, 37, 41, 42, 44, 45, 46, 50, 53, 54, 55, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 71, 73, 74, 75, 76], "here": [2, 3, 4, 5, 9, 11, 13, 14, 16, 17, 24, 29, 31, 33, 34, 35, 37, 38, 41, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 75], "command": [2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 25, 26, 27, 28, 29, 30, 32, 34, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 53, 54, 55, 58, 60, 62, 63, 64, 72, 73, 74], "us": [2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 39, 40, 41, 42, 45, 55, 57, 59, 60, 61, 62, 63, 65, 72, 73, 74, 75, 77], "build": [2, 5, 9, 11, 14, 17, 24, 25, 26, 27, 32, 33, 34, 37, 42, 46, 51, 54, 55, 57, 59, 60, 63, 65, 66, 67, 72, 75, 76, 77], "certifi": [2, 9, 17, 24, 77], "rel": [2, 14, 17, 26, 35, 51, 53, 55, 59, 71], "effici": [2, 11, 12, 13, 17, 25, 29, 36, 57, 60, 64, 77], "function": [2, 3, 5, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 27, 31, 33, 35, 36, 37, 39, 42, 45, 46, 51, 52, 55, 57, 58, 59, 62, 64, 67, 71, 73, 77], "them": [2, 3, 8, 9, 10, 11, 13, 14, 17, 24, 26, 27, 28, 31, 34, 35, 37, 38, 40, 41, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 73, 75], "from": [2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 34, 36, 37, 38, 39, 40, 41, 42, 43, 46, 51, 52, 53, 54, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 72, 73, 75, 77], "either": [2, 5, 8, 11, 14, 17, 26, 28, 29, 31, 34, 35, 36, 37, 39, 40, 41, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 74, 75], "proof": [2, 3, 6, 7, 9, 11, 13, 17, 24, 26, 29, 30, 33, 34, 36, 37, 38, 39, 40, 42, 43, 44, 51, 52, 53, 55, 59, 61, 62, 64, 67, 72, 73, 74, 75, 76, 77], "specif": [2, 3, 5, 9, 11, 24, 28, 31, 32, 34, 35, 36, 39, 40, 42, 51, 52, 53, 55, 57, 58, 59, 60, 61, 64, 66, 67, 71, 77], "The": [2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 17, 24, 25, 28, 29, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 46, 52, 54, 55, 58, 59, 60, 62, 63, 64, 65, 66, 67, 72, 73, 74, 76, 77], "avail": [2, 9, 11, 12, 13, 17, 24, 25, 27, 30, 35, 36, 37, 38, 40, 42, 46, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 71, 72, 74, 75, 76, 77], "output": [2, 3, 4, 11, 14, 17, 24, 33, 42, 51, 52, 53, 54, 59, 60, 64, 66, 71, 75], "ar": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 50, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 63, 64, 65, 67, 71, 72, 73, 74, 75], "current": [2, 3, 4, 5, 8, 9, 10, 12, 14, 17, 24, 28, 29, 32, 34, 35, 36, 37, 38, 41, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 75], "ocaml": [2, 11, 17, 24, 25, 29, 32, 36, 51, 53, 54, 55, 63, 64, 66, 71, 73, 75], "haskel": [2, 13, 17, 24, 25, 57, 64, 77], "scheme": [2, 11, 17, 24, 25, 26, 27, 34, 37, 40, 46, 51, 57, 59, 62, 77], "follow": [2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74, 75], "abus": [2, 55], "refer": [2, 3, 4, 5, 8, 10, 13, 14, 16, 24, 25, 28, 29, 31, 32, 34, 35, 36, 37, 38, 39, 41, 42, 44, 46, 50, 51, 52, 53, 55, 57, 58, 60, 62, 64, 66, 67, 71, 72, 74, 75], "ani": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 26, 28, 29, 30, 31, 32, 34, 35, 37, 38, 39, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 75], "three": [2, 4, 9, 11, 17, 24, 25, 34, 40, 52, 53, 54, 57, 59, 60, 67, 71], "chang": [2, 4, 5, 8, 9, 11, 13, 14, 25, 26, 28, 29, 31, 34, 36, 37, 38, 41, 43, 51, 52, 53, 54, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 73, 74, 75], "version": [2, 3, 4, 7, 9, 13, 14, 15, 25, 29, 32, 35, 36, 37, 41, 46, 50, 51, 52, 57, 58, 59, 60, 62, 66, 73, 74, 75, 77], "8": [2, 3, 4, 13, 24, 25, 30, 35, 41, 51, 52, 53, 54, 57, 58, 59, 60, 64, 66, 71, 75], "11": [2, 24, 25, 34, 53, 57, 60], "befor": [2, 4, 5, 13, 14, 17, 28, 29, 32, 34, 37, 41, 42, 44, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 73, 74, 75], "describ": [2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 17, 24, 29, 31, 32, 34, 35, 37, 39, 40, 42, 43, 46, 51, 52, 53, 54, 55, 57, 58, 59, 64, 65, 66, 67, 71, 72, 75], "thi": [2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 71, 72, 73, 74, 75, 76], "chapter": [2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 24, 26, 27, 29, 31, 32, 33, 34, 38, 40, 42, 45, 52, 54, 55, 57, 58, 59, 61, 63, 65, 71, 72, 73, 75, 76], "framework": [2, 17, 24], "should": [2, 3, 9, 10, 11, 12, 13, 14, 17, 24, 26, 28, 29, 30, 32, 34, 35, 40, 41, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 74], "first": [2, 4, 5, 6, 8, 9, 11, 13, 14, 15, 17, 24, 25, 26, 27, 35, 37, 38, 40, 41, 42, 43, 44, 51, 52, 53, 55, 58, 59, 60, 62, 64, 65, 66, 67, 71, 72, 74, 75, 77], "load": [2, 3, 5, 6, 7, 11, 17, 24, 25, 27, 29, 34, 35, 54, 55, 57, 58, 60, 64, 66, 67, 71, 72, 73], "explicitli": [2, 4, 12, 13, 14, 17, 24, 27, 28, 29, 34, 38, 39, 43, 46, 51, 52, 53, 55, 57, 58, 59, 60, 64, 66, 67, 71, 74], "via": [2, 5, 8, 11, 17, 35, 51, 53, 54, 55, 57, 59, 71, 72], "corelib": [2, 6, 9, 35, 36, 51, 54, 57, 59, 64, 66], "requir": [2, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 17, 24, 27, 28, 29, 30, 31, 32, 34, 35, 36, 38, 42, 44, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 72, 73, 74, 75], "file": [2, 3, 5, 6, 7, 8, 9, 11, 17, 24, 25, 27, 29, 34, 35, 41, 54, 55, 57, 60, 64, 71, 72, 73, 76], "runtim": [2, 3, 5, 6, 11, 17, 29, 34, 51, 53, 54, 55, 57, 59, 60, 72, 73], "plugin": [2, 3, 5, 6, 11, 12, 17, 24, 25, 29, 33, 34, 35, 53, 54, 55, 57, 59, 60, 63, 66, 71, 72], "done": 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38, 39, 40, 41, 42, 44, 51, 53, 55, 57, 59, 64, 67, 71, 72], "constant": [2, 4, 5, 6, 9, 10, 11, 13, 14, 17, 24, 25, 26, 30, 31, 32, 34, 35, 36, 38, 41, 42, 44, 46, 51, 54, 55, 57, 58, 60, 64, 66, 67, 74], "constructor": [2, 4, 9, 10, 12, 13, 14, 17, 24, 25, 26, 27, 30, 31, 32, 35, 36, 37, 40, 41, 42, 43, 44, 46, 54, 55, 57, 58, 59, 60, 62, 64, 66, 71, 74], "modul": [2, 3, 5, 6, 7, 9, 10, 11, 13, 17, 24, 25, 27, 28, 29, 32, 33, 36, 37, 38, 40, 41, 42, 44, 51, 52, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 72, 75], "name": [2, 3, 4, 5, 6, 8, 9, 10, 11, 13, 14, 17, 25, 26, 27, 28, 29, 31, 32, 34, 36, 38, 39, 40, 41, 42, 43, 44, 46, 51, 52, 53, 55, 57, 58, 59, 60, 64, 67, 71, 72, 74, 75], "recurs": [2, 5, 9, 17, 24, 25, 31, 32, 33, 37, 40, 41, 44, 46, 51, 53, 54, 57, 58, 59, 60, 64, 66, 67, 75, 77], "string": [2, 11, 13, 14, 17, 25, 29, 40, 51, 53, 54, 55, 57, 59, 64, 66, 74, 75], "two": [2, 3, 4, 5, 8, 9, 10, 11, 13, 14, 15, 17, 24, 25, 26, 27, 29, 30, 31, 34, 36, 37, 38, 40, 41, 42, 44, 46, 51, 52, 53, 55, 57, 58, 59, 60, 63, 64, 66, 67, 71, 74, 75], "form": [2, 3, 4, 5, 6, 7, 9, 11, 13, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 35, 37, 38, 39, 40, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 75], "displai": [2, 9, 12, 14, 16, 17, 25, 35, 37, 41, 42, 46, 51, 53, 54, 55, 57, 58, 60, 64, 66], "term": [2, 3, 4, 9, 10, 11, 12, 13, 14, 17, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 50, 53, 57, 58, 59, 60, 62, 63, 66, 67, 72, 75], "conveni": [2, 4, 6, 12, 17, 24, 28, 29, 33, 34, 35, 44, 46, 52, 53, 54, 57, 66, 67, 71], "preview": [2, 52], "result": [2, 3, 4, 5, 8, 10, 11, 12, 13, 14, 17, 24, 26, 27, 31, 32, 34, 39, 40, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 75], "second": [2, 3, 4, 8, 9, 10, 11, 13, 15, 17, 24, 25, 26, 28, 35, 37, 38, 40, 42, 44, 51, 52, 53, 55, 57, 59, 60, 64, 66, 67, 71, 75], "all": [2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 26, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 73], "depend": [2, 3, 7, 8, 9, 12, 13, 14, 24, 25, 26, 27, 28, 29, 30, 32, 34, 35, 36, 37, 38, 40, 42, 43, 44, 51, 52, 54, 55, 57, 60, 62, 64, 66, 71, 72, 77], "third": [2, 3, 17, 25, 40, 41, 44, 51, 52, 53, 54, 57, 58, 75], "produc": [2, 5, 7, 8, 9, 11, 13, 14, 17, 24, 25, 29, 32, 34, 36, 38, 40, 41, 44, 52, 53, 54, 55, 57, 64, 66, 71, 72, 73, 74, 75], "singl": [2, 3, 4, 13, 14, 17, 24, 25, 28, 29, 30, 34, 35, 37, 40, 44, 46, 52, 53, 55, 57, 58, 59, 60, 64, 66, 67, 71, 75], "specifi": [2, 3, 4, 5, 6, 8, 9, 11, 13, 17, 24, 25, 28, 29, 32, 34, 35, 36, 37, 40, 41, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 75], "local": [2, 3, 4, 5, 9, 13, 17, 24, 25, 26, 28, 30, 31, 32, 34, 41, 42, 52, 55, 59, 62, 64, 66, 67, 75], "renam": [2, 17, 24, 25, 34, 37, 55, 57, 58, 59, 71, 74], "need": [2, 3, 5, 8, 9, 10, 11, 13, 14, 17, 24, 25, 28, 29, 31, 32, 34, 35, 38, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 73, 75, 76], "fulfil": [2, 17, 67], "syntact": [2, 3, 11, 17, 24, 25, 26, 27, 28, 29, 30, 31, 34, 35, 37, 39, 41, 57, 58, 59, 64, 66, 71, 74], "keep": [2, 3, 12, 14, 17, 24, 33, 34, 36, 42, 46, 52, 53, 55, 57, 64, 67], "origin": [2, 3, 4, 9, 11, 17, 24, 29, 31, 34, 38, 43, 44, 46, 53, 57, 58, 62, 64, 66, 67, 71], "much": [2, 11, 13, 17, 25, 33, 51, 53, 57, 59, 63, 64, 71], "possibl": [2, 3, 4, 5, 8, 9, 11, 13, 14, 17, 24, 27, 28, 31, 34, 35, 37, 41, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 74, 75], "also": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 72, 73, 74, 75, 77], "work": [2, 3, 4, 5, 9, 10, 12, 13, 17, 24, 25, 26, 27, 32, 35, 41, 42, 43, 46, 51, 52, 54, 55, 57, 58, 59, 64, 67, 71, 74, 77], "directori": [2, 14, 17, 24, 27, 35, 51, 52, 53, 59, 60, 71, 75], "It": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 27, 28, 29, 30, 31, 32, 34, 35, 37, 38, 40, 41, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74, 75], "inspect": [2, 17, 57, 59], "what": [2, 3, 5, 10, 13, 16, 17, 24, 25, 27, 29, 33, 34, 35, 41, 42, 46, 51, 53, 54, 55, 57, 59, 60, 64, 66, 67, 71], "pwd": [2, 14, 59], "cd": [2, 17, 53], "librari": [2, 5, 7, 8, 11, 25, 29, 35, 40, 41, 52, 54, 55, 57, 58, 64, 66, 67, 72, 75], "ident": [2, 3, 5, 6, 9, 10, 11, 12, 13, 14, 17, 24, 25, 27, 28, 29, 30, 31, 32, 34, 35, 37, 38, 40, 43, 44, 46, 51, 53, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 73, 74], "whole": [2, 3, 9, 11, 17, 29, 40, 46, 51, 52, 53, 55, 57, 59, 71, 75], "v": [2, 3, 7, 8, 11, 12, 13, 14, 17, 24, 25, 26, 27, 34, 35, 37, 42, 44, 46, 51, 52, 53, 54, 58, 59, 67, 71, 75], "an": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 58, 60, 62, 63, 64, 66, 71, 72, 74, 75, 77], "clash": [2, 17, 53, 54, 57], "prefix": [2, 3, 9, 11, 14, 17, 24, 27, 28, 34, 35, 38, 40, 41, 42, 44, 51, 52, 54, 57, 58, 59, 64, 66, 67, 71, 75], "coq_": 2, "ensur": [2, 10, 13, 14, 17, 24, 30, 34, 39, 52, 55, 59, 64, 71, 72], "session": [2, 14, 17, 51, 52, 59], "independ": [2, 13, 14, 17, 24, 34, 51, 52, 53, 54, 55, 57, 67], "other": [2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 41, 42, 43, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 67, 71, 72, 76], "separ": [2, 3, 10, 14, 17, 24, 25, 26, 29, 33, 34, 35, 40, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 67, 71, 74], "mention": [2, 3, 14, 17, 24, 26, 34, 39, 44, 46, 51, 54, 57, 58, 60, 64, 66, 71], "just": [2, 3, 4, 8, 9, 11, 13, 17, 24, 28, 31, 34, 35, 37, 41, 42, 46, 51, 52, 53, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 75], "instead": [2, 3, 4, 7, 8, 11, 12, 13, 14, 17, 24, 26, 28, 33, 34, 35, 36, 37, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74, 75], "one": [2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 15, 17, 24, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 40, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 72, 74, 75, 77], "monolith": [2, 17], "split": [2, 17, 25, 29, 34, 42, 51, 54, 57, 58, 60, 66, 67, 75], "per": [2, 3, 11, 17, 24, 52, 53, 57, 59, 71], "correspond": [2, 3, 8, 9, 11, 13, 14, 15, 17, 24, 26, 28, 33, 34, 35, 37, 38, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 72, 75], "henc": [2, 3, 4, 5, 8, 9, 13, 14, 17, 26, 34, 37, 42, 51, 53, 54, 57, 58, 64, 67, 71], "quit": [2, 3, 11, 13, 17, 25, 34, 42, 54, 55, 57, 60], "similar": [2, 3, 5, 9, 13, 17, 24, 26, 34, 35, 37, 38, 51, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 72, 74, 75], "except": [2, 3, 4, 11, 12, 13, 14, 17, 24, 25, 26, 27, 29, 31, 34, 35, 36, 38, 40, 43, 51, 52, 53, 54, 57, 58, 59, 60, 64, 66, 67, 71, 75], "onli": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 46, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 73, 74, 75], "part": [2, 3, 10, 11, 13, 15, 17, 24, 25, 27, 29, 34, 35, 37, 46, 51, 52, 53, 54, 55, 57, 58, 66, 67, 71, 72, 73, 74], "convent": [2, 17, 25, 33, 42, 51, 57, 59, 71], "same": [2, 3, 4, 6, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 28, 29, 30, 31, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 51, 52, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 75], "meant": [2, 3, 14, 17, 55, 59, 64], "help": [2, 3, 8, 13, 14, 15, 16, 17, 24, 25, 27, 29, 41, 46, 51, 52, 53, 54, 55, 57, 58, 60, 62, 67, 75], "automat": [2, 3, 5, 7, 9, 10, 13, 14, 17, 24, 25, 27, 28, 35, 37, 40, 42, 46, 52, 53, 54, 55, 57, 58, 60, 64, 65, 66, 71, 72, 75, 77], "test": [2, 3, 4, 9, 10, 11, 13, 17, 24, 25, 29, 30, 34, 42, 46, 55, 57, 59, 66], "see": [2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 14, 17, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74, 75], "instanc": [2, 4, 5, 10, 11, 12, 14, 17, 25, 26, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 46, 51, 52, 53, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 75], "suit": [2, 17, 53, 57, 58, 63], "sourc": [2, 4, 5, 14, 24, 25, 51, 52, 53, 55, 57, 71, 73], "testcompil": [2, 17], "temporari": [2, 14, 17, 24, 57], "Then": [2, 4, 5, 11, 14, 24, 26, 27, 29, 32, 34, 41, 42, 46, 51, 53, 54, 55, 57, 58, 59, 60, 64, 65, 66, 67, 71, 74, 75], "its": [2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 14, 17, 24, 25, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 72, 73, 74, 75, 77], "signatur": [2, 3, 11, 17, 24, 34, 35, 54, 55, 59], "compil": [2, 3, 8, 9, 10, 11, 12, 24, 25, 26, 27, 29, 32, 35, 36, 38, 46, 54, 55, 57, 64, 66, 73, 74, 75, 77], "built": [2, 4, 11, 17, 24, 25, 26, 31, 32, 34, 37, 41, 42, 52, 53, 54, 58, 60, 61, 62, 67, 71, 72], "succe": [2, 3, 13, 17, 25, 44, 46, 51, 55, 57, 58, 59, 60, 62, 64, 66], "fail": [2, 3, 4, 5, 8, 9, 10, 12, 13, 14, 17, 24, 25, 26, 29, 30, 34, 35, 40, 41, 42, 43, 44, 52, 53, 55, 58, 59, 60, 62, 64, 66, 67, 71, 72, 75], "show": [2, 3, 5, 7, 8, 9, 11, 13, 14, 17, 24, 25, 27, 34, 35, 37, 38, 42, 51, 52, 53, 54, 57, 58, 59, 60, 64, 67, 71], "where": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 26, 27, 29, 30, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 75], "deprec": [2, 4, 13, 17, 25, 28, 29, 32, 35, 41, 51, 55, 58, 59, 60, 64, 66, 71, 72], "sinc": [2, 3, 4, 5, 8, 10, 11, 12, 13, 14, 17, 24, 26, 28, 30, 34, 35, 37, 41, 42, 44, 46, 51, 52, 53, 54, 57, 58, 59, 60, 66, 67, 71, 74, 75], "20": [2, 3, 25, 46, 54, 57, 67, 77], "line": [2, 8, 10, 12, 14, 24, 25, 26, 29, 42, 52, 53, 54, 55, 57, 58, 59, 64, 66, 71], "If": [2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 17, 26, 28, 29, 30, 32, 34, 35, 37, 38, 39, 41, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 73, 74, 75], "accord": [2, 11, 17, 26, 34, 35, 41, 51, 53, 55, 57, 59, 60, 64, 71], "which": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 71, 72, 73, 75], "valid": [2, 3, 4, 5, 8, 10, 11, 14, 17, 25, 26, 29, 32, 34, 35, 40, 42, 51, 54, 55, 57, 58, 59, 66, 71, 72], "path": [2, 4, 5, 17, 24, 25, 35, 51, 52, 54, 60], "otherwis": [2, 3, 9, 13, 14, 17, 28, 29, 34, 41, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 73], "doe": [2, 3, 4, 5, 8, 9, 12, 13, 14, 17, 24, 25, 26, 27, 29, 30, 34, 35, 36, 38, 39, 41, 42, 44, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 75], "json": [2, 17, 51, 53, 59], "abil": [2, 3, 11, 12, 13, 17, 30, 52], "most": [2, 3, 4, 10, 12, 17, 24, 27, 29, 34, 38, 41, 45, 46, 51, 52, 53, 54, 55, 57, 58, 60, 63, 64, 66, 67, 71, 72, 73], "import": [2, 3, 4, 5, 7, 9, 11, 13, 17, 24, 25, 26, 28, 29, 31, 32, 34, 35, 36, 38, 40, 42, 44, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72], "default": [2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 27, 28, 29, 32, 34, 35, 37, 38, 43, 44, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 74, 75], "mostli": [2, 3, 17, 24, 52, 57, 60], "develop": [2, 3, 12, 13, 14, 17, 24, 25, 27, 32, 35, 42, 44, 51, 52, 53, 54, 57, 58, 59, 60, 64, 66, 67, 71, 74, 77], "debug": [2, 5, 9, 13, 14, 17, 24, 25, 28, 52, 53, 57, 58, 60, 62, 64, 66, 72], "contain": [2, 5, 7, 8, 10, 13, 14, 15, 17, 24, 27, 29, 30, 31, 34, 35, 38, 39, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 73, 74, 75], "raw": [2, 14, 17, 54, 55, 71], "intermediari": [2, 64], "strict": [2, 5, 13, 14, 17, 24, 25, 31, 39, 41, 42, 54, 57, 58, 59, 60, 66, 71], "ha": [2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 72, 73, 74], "order": [2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 15, 17, 24, 25, 26, 27, 29, 30, 32, 34, 35, 37, 40, 42, 43, 46, 51, 52, 53, 54, 55, 57, 60, 61, 62, 64, 66, 67, 71, 72, 75, 77], "when": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 24, 25, 27, 28, 29, 30, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 51, 52, 53, 54, 55, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74, 75], "principl": [2, 5, 17, 24, 25, 27, 30, 34, 37, 51, 57, 58, 63, 64, 71, 77], "do": [2, 3, 4, 7, 8, 10, 13, 14, 17, 24, 25, 29, 31, 32, 34, 35, 37, 38, 42, 46, 51, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 74, 75], "want": [2, 11, 13, 17, 34, 35, 36, 41, 42, 43, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 73, 74], "comput": [2, 3, 7, 8, 9, 11, 17, 24, 25, 29, 30, 32, 34, 35, 36, 37, 41, 42, 46, 52, 55, 57, 59, 67, 71, 72, 77], "call": [2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 39, 40, 42, 44, 45, 46, 51, 53, 54, 57, 58, 59, 60, 64, 66, 67, 71, 72], "ones": [2, 3, 4, 6, 8, 13, 14, 17, 25, 28, 34, 35, 37, 44, 46, 52, 53, 54, 57, 58, 59, 63, 66, 67, 71, 75], "so": [2, 3, 4, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 26, 29, 31, 32, 34, 35, 36, 37, 38, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 73, 74, 75], "mechan": [2, 3, 4, 9, 10, 13, 17, 24, 25, 29, 34, 38, 41, 46, 51, 52, 53, 55, 59, 64, 65, 66, 71, 72, 77], "provid": [2, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 24, 25, 26, 27, 29, 30, 32, 33, 34, 35, 36, 37, 41, 42, 43, 44, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 71, 72, 73, 74, 75], "routin": 2, "each": [2, 3, 5, 6, 8, 9, 10, 11, 13, 14, 17, 24, 26, 29, 30, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 72, 74, 75], "time": [2, 3, 5, 8, 9, 11, 12, 13, 14, 17, 24, 25, 27, 28, 29, 32, 34, 36, 37, 41, 42, 44, 46, 52, 55, 57, 58, 59, 64, 66, 67, 71], "group": [2, 4, 17, 24, 37, 42, 52, 53, 54, 57, 58, 60], "preserv": [2, 5, 14, 17, 24, 25, 29, 30, 34, 42, 55, 57, 64, 67, 71], "essenti": [2, 17, 25, 34, 55, 57, 67, 71], "reduct": [2, 3, 9, 10, 11, 12, 17, 25, 26, 30, 32, 36, 41, 44, 46, 51, 53, 57, 58, 67, 77], "non": [2, 3, 4, 6, 8, 9, 10, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 35, 37, 40, 41, 46, 51, 52, 53, 57, 59, 60, 62, 64, 66, 72, 75], "abstract": [2, 4, 5, 11, 13, 14, 17, 24, 25, 26, 27, 28, 29, 34, 35, 38, 42, 44, 54, 55, 58, 59, 64, 67, 71], "dummi": [2, 14, 17, 24, 55, 77], "remov": [2, 3, 4, 5, 11, 14, 17, 24, 29, 31, 37, 41, 46, 51, 52, 53, 55, 57, 58, 59, 60, 66, 67, 71, 72, 74, 75], "deem": [2, 51], "safe": [2, 11, 17, 34], "have": [2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 44, 46, 51, 52, 53, 55, 58, 59, 60, 62, 64, 66, 67, 71, 73, 75], "more": [2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 38, 40, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 72, 73, 74, 75], "eleg": [2, 55, 59], "therefor": [2, 17, 29, 31, 37, 52, 53, 57, 58, 62, 72, 73], "mai": [2, 3, 4, 5, 8, 9, 10, 12, 13, 14, 15, 17, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 40, 41, 42, 43, 44, 46, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 73, 74, 75, 77], "appear": [2, 6, 9, 10, 11, 13, 14, 17, 24, 28, 29, 31, 34, 35, 37, 38, 39, 41, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 74, 75], "modular": [2, 17, 24], "nevertheless": [2, 17], "print": [2, 5, 6, 8, 11, 12, 13, 17, 24, 25, 27, 29, 31, 34, 35, 36, 38, 39, 41, 42, 51, 52, 53, 57, 58, 60, 62, 64, 66, 67, 74], "concern": [2, 12, 17, 24, 26], "less": [2, 4, 8, 11, 14, 17, 24, 34, 46, 51, 53, 54, 55, 57, 59, 60, 64, 71, 77], "becaus": [2, 3, 4, 8, 11, 12, 14, 17, 24, 26, 28, 29, 31, 33, 34, 35, 37, 39, 40, 41, 43, 44, 45, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72], "lazi": [2, 8, 9, 12, 17, 24, 55, 64], "still": [2, 3, 7, 9, 10, 13, 17, 24, 29, 32, 34, 36, 37, 38, 42, 44, 46, 51, 53, 54, 57, 58, 59, 60, 64, 66, 67, 74], "make": [2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 28, 29, 30, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 51, 52, 53, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 75, 77], "readabl": [2, 17, 24, 29, 53, 57, 64, 71, 75], "control": [2, 3, 13, 14, 16, 17, 24, 25, 34, 37, 41, 51, 52, 53, 55, 60, 62, 67, 71, 75], "flag": [2, 4, 5, 8, 9, 10, 12, 13, 14, 16, 24, 25, 26, 32, 34, 35, 37, 38, 40, 41, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 60, 62, 64, 66, 67, 71], "made": [2, 3, 14, 17, 24, 29, 34, 35, 38, 41, 46, 51, 53, 54, 55, 57, 58, 64, 66, 71, 72, 75], "beta": [2, 11, 17, 24, 55, 57, 58, 64, 71, 77], "redex": [2, 17, 25, 31, 34, 64, 71], "simplif": [2, 11, 17, 24, 25, 41, 54, 67], "etc": [2, 4, 9, 14, 17, 24, 25, 26, 27, 33, 35, 42, 44, 45, 51, 52, 53, 54, 55, 57, 59, 71, 75], "turn": [2, 8, 10, 12, 13, 14, 17, 24, 27, 29, 32, 37, 41, 42, 44, 46, 51, 52, 54, 55, 57, 58, 59, 64, 66, 67, 71], "off": [2, 8, 10, 12, 13, 14, 17, 24, 29, 34, 35, 37, 43, 44, 46, 51, 52, 53, 54, 57, 59, 64, 66, 67, 71], "you": [2, 3, 4, 7, 8, 10, 11, 13, 14, 15, 16, 17, 24, 25, 27, 29, 32, 34, 35, 37, 41, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 73, 74, 75], "close": [2, 3, 4, 5, 7, 9, 11, 14, 17, 24, 28, 29, 32, 34, 35, 38, 44, 51, 52, 55, 57, 59, 60, 64, 66, 67, 71, 75], "conserv": [2, 17], "try": [2, 3, 11, 14, 17, 24, 25, 34, 35, 40, 41, 43, 46, 53, 55, 57, 60, 62, 64, 66, 67, 71], "sure": [2, 4, 17, 35, 52, 53, 58, 71], "impli": [2, 3, 10, 14, 17, 24, 30, 34, 57, 67, 71], "respect": [2, 3, 4, 5, 11, 13, 14, 17, 24, 26, 30, 34, 38, 40, 42, 44, 52, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 72, 74, 75], "keepsingleton": [2, 17], "normal": [2, 3, 4, 5, 11, 17, 24, 26, 29, 30, 31, 34, 35, 41, 44, 51, 52, 53, 54, 55, 57, 59, 64, 66, 67, 71, 72, 77], "singleton": [2, 13, 17, 24, 34, 54, 58], "structur": [2, 3, 4, 8, 9, 13, 17, 24, 25, 32, 34, 35, 36, 37, 38, 40, 44, 45, 53, 54, 58, 59, 66, 67, 71, 72, 77], "seen": [2, 4, 13, 14, 17, 24, 32, 34, 55, 57, 67, 71], "alia": [2, 17, 24, 29, 35, 46, 55, 58], "inner": [2, 14, 17, 35, 42, 43, 54, 55, 57, 59, 62, 64, 66, 67, 71, 75], "typic": [2, 4, 6, 12, 14, 17, 24, 28, 29, 30, 34, 35, 44, 46, 51, 53, 55, 57, 58, 59, 60, 64, 67, 71], "sig": [2, 17, 27, 28, 35, 67, 71], "allow": [2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 37, 38, 40, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 72], "disabl": [2, 8, 9, 12, 13, 14, 17, 25, 28, 32, 34, 35, 37, 44, 51, 52, 54, 57, 59, 64, 66], "wish": [2, 5, 17, 53], "autoinlin": [2, 17], "enabl": [2, 4, 7, 8, 9, 10, 11, 12, 13, 14, 17, 25, 29, 34, 37, 42, 51, 52, 53, 54, 57, 58, 59, 60, 67, 75], "bodi": [2, 4, 6, 13, 14, 17, 24, 32, 35, 37, 38, 41, 42, 44, 51, 55, 57, 58, 59, 64, 72, 75], "defin": [2, 3, 4, 5, 6, 7, 9, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 36, 38, 39, 40, 41, 42, 43, 44, 46, 51, 52, 53, 57, 58, 59, 62, 64, 66, 67, 71, 72, 74, 77], "heurist": [2, 5, 14, 17, 55, 57, 58, 66], "like": [2, 4, 8, 9, 10, 11, 13, 14, 17, 24, 26, 27, 29, 32, 34, 35, 38, 39, 41, 42, 43, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 73, 75], "size": [2, 3, 9, 13, 17, 24, 34, 37, 51, 52, 55, 57, 59, 64, 71, 72], "recursor": [2, 17], "_rect": [2, 17, 34, 35, 40, 71, 72], "_rec": [2, 34, 35, 40, 71, 72], "nat_rect": [2, 27, 34, 59], "project": [2, 3, 9, 10, 12, 13, 14, 15, 17, 24, 25, 27, 29, 30, 34, 40, 41, 42, 51, 52, 54, 55, 57, 59, 60, 64, 72, 73, 74, 76], "few": [2, 3, 17, 24, 27, 29, 34, 35, 36, 37, 51, 52, 53, 55, 57, 58, 71, 73, 75], "andb": [2, 13, 17, 27, 62], "orb": [2, 27, 57, 62], "behaviour": [2, 17, 38, 53], "well": [2, 3, 4, 8, 9, 10, 11, 13, 14, 17, 24, 25, 26, 29, 30, 31, 32, 33, 35, 37, 39, 43, 45, 46, 51, 52, 53, 54, 55, 57, 58, 59, 63, 64, 66, 67, 71, 72, 74, 75], "found": [2, 4, 5, 9, 11, 13, 17, 25, 29, 30, 34, 35, 36, 38, 39, 42, 46, 51, 54, 55, 57, 58, 59, 62, 64, 67, 71, 72, 75], "combin": [2, 3, 5, 9, 12, 14, 17, 24, 25, 26, 27, 29, 34, 37, 40, 42, 46, 52, 53, 54, 55, 57, 59, 63, 64, 75], "featur": [2, 3, 8, 11, 17, 24, 25, 29, 32, 33, 35, 36, 44, 46, 51, 52, 53, 54, 55, 57, 59, 66, 71, 72, 73, 74, 76], "alwai": [2, 3, 4, 6, 9, 10, 11, 12, 13, 14, 17, 24, 26, 34, 35, 37, 41, 42, 44, 51, 52, 53, 54, 55, 57, 58, 60, 66, 67, 71, 74, 75], "dure": [2, 9, 11, 13, 14, 17, 24, 25, 37, 42, 46, 51, 53, 54, 55, 57, 58, 60, 64, 66, 67, 71, 72], "noinlin": 2, "convers": [2, 3, 7, 8, 9, 11, 12, 13, 17, 24, 25, 26, 30, 32, 33, 34, 35, 37, 54, 55, 57, 58, 60, 66, 71, 75], "never": [2, 13, 14, 17, 24, 35, 41, 42, 44, 51, 54, 55, 57, 58, 60, 64], "state": [2, 3, 5, 7, 8, 11, 13, 17, 24, 25, 27, 29, 31, 32, 37, 51, 52, 54, 55, 57, 58, 59, 62, 64, 67, 71], "tabl": [2, 3, 4, 16, 17, 24, 25, 27, 35, 37, 38, 46, 51, 53, 54, 55, 57, 59, 67, 71, 75], "record": [2, 3, 8, 10, 11, 12, 13, 14, 17, 24, 25, 30, 33, 34, 42, 54, 55, 57, 59, 60, 62, 67, 71], "custom": [2, 3, 11, 13, 17, 24, 25, 29, 36, 53, 54, 57], "declar": [2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 43, 46, 51, 53, 54, 58, 59, 60, 64, 71, 72, 75], "previou": [2, 3, 4, 8, 9, 11, 13, 15, 17, 24, 27, 29, 31, 34, 37, 40, 41, 42, 45, 46, 51, 52, 54, 55, 57, 59, 60, 62, 64, 66, 67, 71, 74], "reset": [2, 17, 24, 29, 30, 34, 40, 41, 46, 51, 52, 54, 59, 72], "empti": [2, 3, 5, 7, 12, 13, 17, 24, 26, 34, 40, 43, 51, 53, 55, 57, 58, 59, 60, 67, 71, 72], "ask": [2, 3, 17, 25, 42, 43, 53], "mean": [2, 3, 5, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 31, 32, 34, 35, 38, 40, 42, 43, 44, 46, 51, 52, 53, 54, 57, 58, 59, 64, 65, 66, 71], "both": [2, 3, 4, 11, 14, 17, 24, 25, 26, 27, 28, 29, 31, 34, 37, 38, 40, 42, 43, 44, 46, 51, 52, 53, 54, 57, 58, 60, 61, 64, 66, 67, 73, 74], "But": [2, 11, 17, 34, 39, 41, 46, 51, 53, 54, 64, 75], "For": [2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 14, 16, 17, 24, 26, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 75], "reason": [2, 3, 5, 9, 10, 11, 17, 24, 25, 34, 44, 51, 53, 54, 55, 57, 59, 62, 65, 71, 72, 75, 77], "decis": [2, 17, 24, 25, 58, 62, 64, 77], "taken": [2, 9, 13, 17, 24, 34, 36, 42, 44, 53, 57, 64, 67, 71], "whether": [2, 3, 9, 10, 12, 13, 14, 17, 29, 34, 35, 41, 44, 51, 52, 53, 54, 55, 57, 59, 60, 62, 64, 66, 71, 75], "occurr": [2, 3, 11, 14, 17, 24, 25, 26, 43, 44, 46, 52, 54, 55, 59, 60, 64, 71], "replac": [2, 3, 4, 7, 9, 10, 11, 17, 24, 25, 28, 31, 32, 34, 37, 41, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 62, 64, 66, 67, 71, 74, 75], "manual": [2, 11, 24, 25, 29, 50, 52, 53, 57, 60, 66, 67, 71], "perform": [2, 3, 5, 7, 8, 11, 13, 17, 24, 25, 26, 34, 41, 42, 46, 51, 54, 55, 57, 60, 62, 64, 66, 67, 71, 72], "wai": [2, 3, 5, 11, 12, 13, 14, 17, 24, 25, 26, 27, 29, 30, 31, 32, 34, 35, 37, 42, 43, 44, 46, 51, 52, 53, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 72, 73, 75], "complementari": [2, 17, 24, 42, 57], "main": [2, 8, 9, 11, 13, 17, 25, 27, 29, 34, 40, 41, 51, 52, 53, 54, 55, 57, 60, 64, 71], "logic": [2, 3, 9, 12, 13, 14, 17, 24, 25, 26, 28, 29, 30, 34, 35, 39, 51, 57, 58, 59, 61, 66, 67, 75, 77], "implicit": [2, 3, 5, 9, 13, 17, 24, 25, 28, 33, 34, 37, 38, 42, 43, 45, 51, 53, 55, 57, 58, 59, 66, 67, 75], "integ": [2, 3, 7, 11, 14, 17, 24, 25, 29, 34, 39, 52, 53, 54, 55, 57, 59, 60, 64, 66], "thei": [2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 72, 73, 74, 75], "omit": [2, 3, 8, 14, 17, 27, 28, 29, 30, 32, 34, 37, 38, 40, 41, 42, 44, 45, 46, 53, 54, 55, 57, 58, 59, 60, 66, 67, 71, 75], "position": [2, 58], "start": [2, 3, 6, 8, 9, 13, 17, 24, 25, 26, 27, 29, 32, 34, 35, 37, 40, 41, 42, 44, 46, 52, 53, 54, 55, 58, 59, 60, 64, 66, 67, 71, 74, 75], "actual": [2, 3, 5, 8, 11, 14, 17, 24, 34, 37, 42, 43, 44, 46, 54, 55, 57, 60, 64, 67, 71, 72], "take": [2, 3, 5, 8, 11, 12, 13, 17, 24, 26, 28, 29, 31, 32, 37, 40, 41, 42, 46, 51, 52, 53, 54, 55, 57, 58, 60, 62, 64, 66, 67, 71, 75], "place": [2, 3, 17, 32, 40, 43, 51, 53, 57, 58, 59, 64, 66, 67, 71, 75], "error": [2, 3, 4, 9, 10, 11, 12, 13, 14, 16, 17, 24, 25, 27, 28, 29, 32, 34, 35, 37, 38, 39, 40, 41, 42, 44, 46, 51, 52, 53, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 75], "rais": [2, 3, 10, 13, 17, 29, 35, 54, 55, 64, 72], "cannot": [2, 3, 4, 8, 9, 10, 11, 12, 13, 14, 17, 26, 28, 29, 32, 34, 35, 36, 37, 40, 41, 44, 46, 51, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 75], "honor": [2, 8, 17, 51, 57, 71], "occur": [2, 3, 4, 8, 17, 24, 26, 28, 30, 34, 37, 38, 41, 42, 44, 46, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71], "final": [2, 3, 4, 5, 6, 8, 9, 10, 11, 13, 14, 17, 24, 25, 27, 29, 35, 40, 51, 52, 53, 54, 57, 59, 64, 66, 67, 71, 75], "behavior": [2, 3, 4, 11, 13, 14, 17, 24, 29, 30, 32, 34, 41, 43, 44, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 73, 75], "relax": [2, 17, 30, 44, 53, 57, 60], "safeimplicit": 2, "warn": [2, 3, 4, 10, 12, 13, 16, 17, 24, 25, 27, 28, 29, 32, 34, 35, 37, 41, 42, 44, 46, 51, 52, 54, 55, 57, 59, 60, 62, 66, 71, 72], "emit": [2, 10, 12, 13, 17, 34, 53, 71, 74], "obtain": [2, 3, 4, 5, 17, 34, 36, 54, 55, 57, 58, 64, 67, 72, 75], "nonetheless": [2, 17, 30, 32, 36, 51, 66], "review": [2, 17, 27], "locat": [2, 17, 24, 25, 35, 51, 52, 53, 54, 55], "issu": [2, 3, 24, 25, 46, 52, 54, 55, 58, 64, 66, 71, 73], "comment": [2, 5, 17, 24, 25, 29, 52, 54, 57, 60, 66, 75], "mark": [2, 12, 17, 24, 31, 35, 37, 38, 41, 44, 51, 52, 53, 54, 55, 57, 59, 60, 64, 66, 71], "remain": [2, 3, 9, 11, 13, 14, 17, 24, 34, 36, 39, 41, 42, 44, 46, 52, 57, 58, 64, 66], "note": [2, 3, 4, 5, 7, 8, 10, 11, 12, 13, 14, 15, 17, 24, 26, 27, 28, 29, 34, 35, 37, 40, 41, 42, 43, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74, 77], "might": [2, 3, 5, 13, 17, 46, 51, 53, 55, 57, 62, 64, 67, 71, 72, 75], "run": [2, 5, 8, 9, 13, 14, 17, 24, 25, 29, 51, 53, 57, 59, 60, 64, 66, 71, 73], "properli": [2, 8, 9, 10, 17, 29, 52, 53, 57, 59, 66], "encount": [2, 11, 17, 52, 53, 54, 64], "inform": [2, 3, 4, 10, 12, 13, 14, 17, 24, 25, 26, 27, 29, 30, 34, 37, 39, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 67, 72, 75, 77], "remind": [2, 3, 57], "inconsist": [2, 8, 10, 12, 14, 17, 24, 26, 34, 39, 44, 51, 59, 66, 67, 71], "lead": [2, 10, 14, 17, 24, 26, 29, 34, 39, 57, 58, 60, 64, 71, 74, 75], "incorrect": [2, 8, 12, 14, 17, 25, 34, 37, 46, 52, 57, 66], "termin": [2, 8, 9, 17, 24, 25, 27, 29, 30, 32, 34, 35, 38, 52, 55, 59, 60, 66, 71, 72], "assum": [2, 3, 5, 11, 13, 17, 26, 27, 28, 32, 34, 35, 36, 38, 39, 42, 44, 46, 51, 53, 54, 55, 57, 58, 59, 64, 66, 71, 75], "while": [2, 3, 4, 9, 10, 12, 13, 14, 17, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 36, 37, 40, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 73], "proposit": [2, 3, 5, 10, 17, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 39, 40, 51, 57, 58, 62, 64, 66, 67, 77], "perfectli": 2, "content": [2, 17, 24, 27, 32, 35, 42, 51, 52, 53, 54, 57, 59, 66, 71, 75], "must": [2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 27, 29, 30, 34, 35, 36, 37, 39, 40, 41, 44, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74, 75], "cours": [2, 14, 17, 24, 42, 51, 52, 57, 64, 71], "guess": [2, 4, 11, 17, 32, 43, 53, 57, 67], "tell": [2, 3, 11, 17, 24, 34, 41, 42, 44, 46, 51, 55, 57, 60, 64, 67, 71, 75], "given": [2, 3, 4, 5, 9, 10, 11, 13, 14, 17, 24, 25, 27, 28, 29, 32, 35, 36, 37, 40, 41, 42, 43, 44, 46, 51, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74, 75], "tv": 2, "give": [2, 3, 4, 5, 7, 8, 9, 11, 13, 14, 17, 24, 25, 26, 27, 28, 29, 31, 32, 34, 35, 37, 40, 41, 42, 45, 46, 51, 52, 53, 54, 55, 57, 58, 59, 64, 66, 67, 71, 75], "ariti": [2, 17, 24, 25, 46, 55], "sequenc": [2, 3, 5, 17, 24, 25, 28, 29, 30, 46, 51, 57, 58, 59, 60, 64, 66, 71, 75], "product": [2, 3, 5, 10, 11, 13, 14, 17, 24, 26, 27, 28, 34, 36, 39, 40, 46, 54, 55, 57, 59, 60, 64, 66, 67, 71], "variabl": [2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 31, 32, 34, 35, 37, 38, 39, 40, 41, 42, 45, 53, 54, 57, 58, 59, 60, 62, 64, 67, 71, 72, 75], "quot": [2, 5, 13, 17, 24, 25, 28, 29, 44, 51, 55, 59, 66, 71, 75], "number": [2, 3, 4, 5, 7, 11, 13, 14, 17, 24, 25, 26, 27, 29, 30, 34, 36, 37, 39, 40, 41, 42, 43, 44, 46, 52, 53, 55, 57, 58, 59, 62, 64, 66, 67, 72, 74, 77], "check": [2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 30, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 46, 51, 52, 53, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74, 75], "y": [2, 3, 4, 5, 9, 11, 12, 13, 14, 17, 24, 26, 27, 28, 31, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 46, 52, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 77], "b": [2, 3, 4, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 27, 28, 31, 34, 35, 37, 38, 40, 41, 42, 44, 46, 50, 51, 52, 53, 54, 55, 57, 59, 60, 62, 64, 66, 67, 71, 72, 77], "recogn": [2, 4, 5, 8, 11, 17, 24, 29, 34, 46, 51, 52, 55, 62, 67, 71, 75], "becom": [2, 8, 11, 17, 24, 26, 28, 34, 35, 40, 44, 46, 52, 53, 55, 57, 58, 59, 64, 66, 67, 71], "int": [2, 3, 17, 36, 55, 71, 75], "0": [2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 25, 26, 27, 28, 29, 30, 31, 34, 35, 36, 37, 41, 43, 44, 46, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74, 75, 77], "respons": [2, 10, 17, 52, 55, 75], "expect": [2, 3, 4, 11, 12, 14, 17, 24, 26, 29, 31, 32, 33, 34, 40, 41, 42, 43, 44, 46, 51, 52, 54, 55, 57, 58, 60, 64, 67, 71], "fact": [2, 5, 11, 14, 17, 24, 28, 32, 34, 39, 41, 42, 46, 54, 55, 57, 58, 62, 64, 66, 67, 71, 75], "copi": [2, 17, 36, 46, 52, 53, 54, 57, 75], "everywher": [2, 17, 55, 58, 64], "being": [2, 3, 9, 11, 12, 13, 14, 17, 24, 32, 33, 34, 35, 37, 38, 40, 42, 46, 51, 52, 53, 54, 55, 57, 60, 64, 66, 67, 71, 72, 75], "sugar": [2, 7, 17, 28, 54, 55, 59, 77], "effect": [2, 3, 9, 11, 13, 14, 17, 24, 25, 29, 30, 34, 35, 38, 43, 51, 52, 53, 54, 57, 59, 64, 66, 71, 75], "alreadi": [2, 4, 13, 17, 24, 27, 28, 32, 37, 41, 42, 44, 51, 52, 53, 54, 55, 57, 58, 59, 60, 66, 67, 71, 73], "foreign": [2, 17], "wa": [2, 3, 10, 11, 12, 17, 24, 27, 28, 29, 32, 34, 35, 37, 38, 41, 42, 43, 44, 51, 52, 53, 54, 55, 57, 58, 59, 60, 63, 64, 66, 67, 71, 72], "previous": [2, 13, 17, 28, 34, 38, 52, 54, 57, 59, 71], "would": [2, 3, 4, 11, 14, 17, 28, 29, 30, 31, 32, 34, 37, 41, 42, 43, 44, 46, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 75], "overrid": [2, 14, 17, 37, 51, 53, 57, 66, 67, 71], "been": [2, 3, 8, 9, 10, 11, 13, 14, 17, 24, 25, 27, 28, 29, 32, 34, 35, 41, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 63, 64, 66, 67, 71, 72, 73, 74], "definit": [2, 4, 8, 10, 11, 13, 17, 24, 25, 26, 27, 28, 29, 31, 33, 35, 36, 38, 41, 42, 43, 44, 51, 53, 58, 59, 60, 62, 66, 67, 72, 73, 74, 75, 77], "fill": [2, 9, 13, 17, 25, 52, 55, 57, 62, 71], "label": [2, 8, 14, 17, 29, 54, 59], "TO": 2, "BE": 2, "search": [2, 4, 5, 7, 13, 17, 24, 25, 42, 44, 51, 52, 53, 61, 62, 64], "insid": [2, 3, 4, 8, 9, 13, 14, 17, 24, 25, 28, 29, 34, 35, 38, 46, 52, 55, 57, 58, 59, 60, 64, 66, 67, 71, 74], "real": [2, 3, 7, 11, 24, 25, 34, 46, 53, 55, 66, 67, 71], "nativ": [2, 5, 10, 12, 24, 25, 36, 51, 55, 58, 59, 64], "boolean": [2, 5, 9, 11, 13, 14, 17, 24, 25, 27, 29, 34, 37, 39, 40, 42, 55, 59, 60, 62, 64, 67, 71], "syntax": [2, 4, 5, 6, 8, 9, 11, 13, 14, 25, 26, 27, 30, 32, 34, 35, 37, 39, 40, 41, 42, 43, 45, 51, 52, 53, 58, 59, 60, 63, 64, 66, 75, 77], "itself": [2, 3, 8, 9, 11, 12, 13, 14, 17, 30, 34, 39, 40, 41, 42, 43, 44, 51, 53, 54, 55, 57, 58, 60, 63, 64, 67, 71], "initi": [2, 6, 7, 11, 13, 17, 24, 27, 29, 38, 46, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 74, 75], "datatyp": [2, 17, 24, 25, 26, 35, 44, 46, 54, 55, 57, 59, 60, 67, 71], "pattern": [2, 9, 13, 17, 24, 25, 27, 28, 30, 32, 34, 40, 41, 42, 45, 60, 64, 67, 72, 77], "charact": [2, 8, 10, 13, 14, 17, 24, 25, 27, 29, 35, 36, 40, 44, 46, 53, 54, 55, 57, 58, 59, 64, 66, 71, 72, 74, 75], "char": [2, 17, 53], "prelud": [2, 17, 25, 29, 51, 59, 66], "liter": [2, 5, 17, 29, 36, 42, 54, 55, 57, 71], "handl": [2, 3, 8, 9, 11, 17, 24, 26, 37, 43, 46, 53, 55, 57, 58, 59, 61, 62, 66, 67, 71], "special": [2, 3, 4, 9, 12, 13, 16, 17, 24, 25, 27, 28, 29, 34, 51, 52, 53, 54, 55, 59, 60, 64, 66, 67, 71, 75], "design": [2, 8, 11, 17, 24, 25, 37, 44, 57, 64, 71, 77], "regist": [2, 3, 4, 5, 7, 9, 11, 13, 17, 25, 32, 42, 57, 64, 67, 71, 72], "standard": [2, 3, 5, 9, 14, 25, 27, 29, 35, 36, 40, 51, 52, 53, 54, 58, 59, 62, 64, 65, 66, 67, 72, 73, 74, 75], "indic": [2, 8, 11, 12, 13, 14, 17, 24, 26, 31, 34, 35, 39, 40, 41, 42, 43, 46, 51, 52, 53, 54, 57, 58, 59, 62, 64, 66, 67, 71], "how": [2, 7, 8, 13, 17, 24, 25, 27, 29, 30, 34, 35, 37, 42, 43, 45, 51, 53, 54, 57, 58, 59, 60, 62, 64, 67, 71, 72, 74, 77], "over": [2, 3, 11, 14, 17, 24, 25, 26, 27, 28, 30, 32, 34, 37, 38, 39, 40, 41, 42, 44, 46, 52, 53, 54, 58, 59, 60, 61, 62, 64, 66, 67], "could": [2, 3, 4, 5, 6, 11, 12, 17, 24, 29, 31, 34, 37, 42, 46, 51, 52, 55, 57, 58, 60, 62, 66, 71, 72, 73], "arbitrari": [2, 3, 5, 10, 11, 14, 17, 24, 31, 44, 46, 53, 57, 60, 62, 71], "k": [2, 3, 6, 14, 17, 24, 26, 34, 42, 54, 57, 67, 72, 77], "emul": [2, 12, 17, 40, 57], "branch": [2, 5, 9, 17, 25, 34, 40, 45, 46, 55, 59, 60, 66, 67, 72], "element": [2, 3, 11, 12, 17, 25, 26, 27, 34, 35, 36, 46, 57, 59, 60, 71], "destruct": [2, 13, 17, 24, 25, 34, 54, 55, 57, 58, 64, 71], "foo": [2, 11, 14, 17, 29, 35, 38, 40, 43, 51, 52, 53, 55, 57, 58, 59, 64, 66, 71, 74, 75], "fun": [2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 14, 17, 25, 26, 27, 29, 30, 31, 32, 34, 35, 37, 38, 40, 41, 42, 43, 44, 46, 54, 55, 57, 58, 59, 64, 66, 67, 71, 72, 75], "consid": [2, 3, 4, 5, 9, 11, 12, 13, 14, 17, 24, 26, 28, 29, 30, 31, 34, 37, 41, 42, 44, 46, 52, 53, 54, 55, 57, 58, 59, 60, 64, 67, 71, 73, 75], "unit": [2, 12, 13, 14, 17, 27, 34, 40, 46, 53, 54, 55, 57, 62, 64, 71], "block": [2, 9, 10, 14, 17, 25, 29, 30, 34, 37, 38, 44, 46, 54, 64, 65, 67], "earli": [2, 15, 17, 25, 26, 54, 64], "evalu": [2, 3, 9, 11, 17, 24, 25, 28, 30, 34, 35, 41, 53, 57, 60, 64, 71], "bar": [2, 8, 14, 17, 29, 35, 51, 52, 53, 55, 57, 64, 66, 71, 74], "As": [2, 3, 5, 6, 9, 10, 11, 13, 14, 17, 26, 28, 30, 34, 36, 37, 38, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 66, 67, 71, 72], "care": [2, 13, 14, 17, 46, 53, 54, 64, 67, 71, 75], "pre": [2, 17, 25, 53, 60], "sound": [2, 17, 34], "ad": [2, 4, 9, 13, 14, 17, 24, 25, 29, 34, 37, 42, 44, 51, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 73, 75, 77], "hoc": [2, 3, 17, 71, 77], "often": [2, 3, 10, 13, 14, 17, 25, 28, 43, 46, 52, 53, 54, 55, 57, 58, 66], "fulli": [2, 3, 8, 17, 24, 26, 28, 31, 32, 35, 38, 44, 51, 52, 53, 54, 55, 58, 59, 64, 66, 71, 72], "rigor": [2, 24], "correct": [2, 8, 9, 11, 17, 24, 25, 28, 32, 35, 46, 51, 53, 57, 59, 64, 66, 67, 71], "theoret": [2, 17, 24, 31, 39, 77], "valu": [2, 4, 5, 6, 9, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 31, 32, 34, 36, 37, 38, 40, 42, 43, 51, 52, 53, 57, 58, 59, 60, 62, 64, 66, 67, 71, 74], "larger": [2, 13, 14, 17, 25, 51, 52, 57, 60, 71, 75], "than": [2, 3, 5, 8, 11, 12, 13, 14, 17, 24, 29, 30, 31, 34, 35, 37, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 73, 75], "max_int": 2, "overflow": [2, 17, 59, 66, 71], "bad": [2, 11, 12, 14, 17, 34, 59, 64], "event": [2, 17, 51], "practic": [2, 3, 5, 17, 24, 25, 32, 34, 39, 42, 53, 55, 57, 58, 64, 66, 71, 74, 77], "translat": [2, 3, 17, 24, 25, 33, 41, 45, 57, 71, 75], "magic": [2, 17, 24, 55, 59], "improv": [2, 3, 8, 11, 17, 24, 29, 52, 54, 57, 67], "asymptot": [2, 59], "complex": [2, 11, 17, 24, 25, 29, 33, 35, 52, 54, 55, 57, 59, 61, 63, 66, 67], "represent": [2, 3, 5, 11, 12, 17, 24, 29, 34, 37, 51, 53, 57, 64, 71], "mul": [2, 5, 17, 36, 52, 57, 59, 71], "stai": [2, 27], "quadrat": [2, 17], "interest": [2, 4, 5, 11, 17, 24, 31, 42, 54, 57, 67], "associ": [2, 3, 11, 13, 14, 17, 24, 25, 26, 27, 28, 29, 31, 32, 34, 35, 36, 37, 38, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67], "primit": [2, 10, 12, 13, 14, 17, 24, 25, 27, 30, 33, 34, 41, 46, 54, 55, 57, 64, 67], "counterpart": [2, 3, 9, 11, 17, 30, 34, 57], "bool": [2, 3, 4, 5, 12, 13, 17, 24, 27, 30, 35, 36, 37, 40, 41, 42, 44, 46, 55, 57, 58, 59, 60, 71], "true": [2, 3, 4, 5, 7, 9, 11, 12, 13, 14, 17, 24, 26, 27, 34, 35, 36, 37, 40, 41, 44, 46, 51, 53, 54, 55, 57, 58, 59, 62, 64, 67, 71, 74], "fals": [2, 4, 5, 9, 10, 12, 13, 17, 24, 27, 34, 37, 40, 41, 46, 51, 54, 55, 57, 58, 59, 62, 64, 66, 67, 71], "sumbool": [2, 27, 46, 71], "enclos": [2, 29, 41, 53, 54, 55, 66, 71, 75], "parenthes": [2, 3, 8, 17, 24, 28, 29, 35, 37, 46, 54, 55, 57, 58, 67, 71], "meet": [2, 9, 71], "lexic": [2, 17, 25, 51, 59, 71, 75], "criteria": [2, 17, 72], "infix": [2, 14, 17, 24, 25, 27, 42, 57, 58, 64, 74], "symbol": [2, 3, 11, 14, 17, 24, 25, 27, 28, 29, 31, 41, 42, 43, 46, 57, 59, 60, 62, 64, 67, 71, 75, 77], "rest": [2, 3, 13, 17, 26, 29, 36, 42, 52, 57, 66], "prod": [2, 17, 26, 27, 34, 46, 62, 67], "caveat": [2, 17, 25, 55, 57, 60], "abov": [2, 3, 5, 11, 13, 14, 17, 24, 28, 30, 34, 37, 38, 42, 44, 51, 52, 53, 54, 55, 57, 58, 59, 64, 66, 71, 72, 75], "succ": [2, 24, 54, 59, 64], "fo": 2, "els": [2, 4, 9, 11, 12, 13, 17, 29, 30, 35, 40, 41, 46, 52, 54, 55, 57, 59, 62, 67, 71, 75], "interfac": [2, 17, 24, 25, 35, 52, 53, 66, 74, 75, 76], "link": [2, 16, 17, 24, 27, 46, 53, 57, 72, 75], "linker": [2, 24], "know": [2, 8, 17, 24, 27, 32, 34, 42, 46, 52, 53, 54, 55, 57, 59, 60, 62, 64, 67, 71], "extern": [2, 5, 11, 13, 17, 29, 33, 52, 54, 55, 59, 60, 63, 66, 73, 74, 75], "shall": [2, 17, 24, 26, 31, 34, 39, 42, 57, 71], "access": [2, 5, 14, 17, 24, 25, 28, 32, 33, 34, 35, 36, 38, 44, 51, 52, 53, 55, 57, 59, 71], "callback": [2, 17], "referenc": [2, 17, 53, 71], "stdlib": [2, 3, 5, 7, 9, 11, 12, 14, 17, 27, 28, 29, 35, 51, 53, 54, 55, 57, 59, 60, 64, 67, 72, 75], "f_impl": 2, "compat": [2, 3, 4, 13, 14, 24, 25, 29, 34, 42, 51, 52, 53, 58, 62, 63, 64, 71], "support": [2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 17, 24, 25, 30, 32, 34, 35, 36, 37, 40, 41, 42, 44, 51, 53, 54, 55, 57, 59, 60, 62, 63, 64, 66, 71, 72, 74, 75, 76], "thrown": 2, "after": [2, 4, 5, 7, 8, 9, 11, 13, 17, 24, 29, 32, 34, 35, 38, 41, 42, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72], "callabl": 2, "express": [2, 3, 4, 5, 9, 10, 11, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 39, 40, 41, 43, 44, 57, 58, 59, 60, 64, 66, 67, 75], "signal": [2, 8, 17, 57], "alias": [2, 17, 24, 25, 29, 35, 55], "uniqu": [2, 3, 12, 13, 17, 24, 31, 35, 38, 57, 59, 67, 71], "multipl": [2, 3, 4, 9, 14, 17, 24, 25, 27, 29, 34, 35, 40, 44, 52, 58, 59, 60, 64, 66, 67, 71], "expos": [2, 17, 25, 40, 41, 57, 71], "share": [2, 11, 13, 14, 17, 24, 28, 29, 34, 46, 51, 52, 53, 57, 59, 60, 64, 67, 71], "impact": [2, 17, 53, 66, 71], "synthesis": 2, "thu": [2, 3, 4, 5, 10, 12, 17, 24, 32, 34, 42, 43, 46, 51, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 72, 75], "safeti": 2, "registr": [2, 17, 25], "usabl": [2, 17, 24, 38, 52, 66, 67, 71], "togeth": [2, 3, 9, 17, 24, 25, 27, 31, 34, 35, 43, 53, 54, 55, 57, 66, 71, 75], "map": [2, 3, 5, 13, 17, 24, 25, 26, 34, 35, 36, 39, 41, 44, 51, 53, 57, 58, 59, 60, 71, 72, 75], "directli": [2, 3, 4, 9, 13, 14, 17, 24, 27, 28, 34, 43, 51, 52, 53, 55, 57, 58, 60, 64, 67, 72, 75], "happen": [2, 4, 9, 10, 13, 17, 34, 38, 46, 52, 54, 55, 57, 58, 64, 71, 72], "instruct": [2, 5, 17, 53, 58, 59], "particular": [2, 3, 6, 9, 10, 12, 13, 17, 29, 30, 31, 32, 33, 34, 37, 38, 40, 42, 52, 53, 54, 55, 57, 59, 60, 64, 66, 71, 75], "blacklist": [2, 17, 59], "includ": [2, 3, 5, 8, 9, 12, 13, 14, 17, 24, 25, 27, 28, 29, 34, 35, 36, 38, 39, 40, 41, 43, 44, 51, 52, 53, 54, 55, 57, 59, 60, 62, 64, 66, 67, 71, 73, 75], "natur": [2, 5, 7, 9, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 34, 35, 37, 39, 40, 42, 44, 46, 52, 53, 57, 58, 59, 62, 64, 66, 71, 72], "finer": [2, 17, 34, 57], "grain": [2, 17, 41], "bit": [2, 5, 17, 29, 30, 34, 36, 51, 53, 66, 71, 75, 77], "mask": [2, 35], "unless": [2, 3, 13, 14, 17, 29, 40, 41, 42, 44, 51, 52, 57, 58, 64, 71, 72, 75], "treatment": [2, 9, 17, 40], "fixpoint": [2, 3, 10, 13, 17, 24, 25, 27, 29, 30, 31, 32, 37, 38, 41, 44, 46, 52, 57, 59, 64, 66, 67, 71, 72], "simplifi": [2, 11, 17, 24, 41, 54, 57, 64, 67], "redux": 2, "factor": [2, 5, 11, 17, 25, 34, 45], "16": [2, 25, 53, 54, 57, 71], "32": [2, 17, 36, 51, 53, 66], "6": [2, 9, 25, 29, 35, 53, 54, 55, 57, 58, 71, 74, 77], "64": [2, 36, 51, 66], "swap": [2, 17, 54, 57, 58], "lambda": [2, 3, 10, 11, 17, 31, 52, 55, 64, 67, 71, 77], "7": [2, 11, 25, 54, 57, 64, 71, 74, 75, 77], "128": 2, "256": 2, "push": [2, 17, 57, 71], "9": [2, 24, 25, 29, 30, 35, 53, 54, 57, 64, 71, 74, 77], "512": 2, "linear": [2, 3, 11, 14, 17, 24, 25, 46, 51, 54, 55, 57, 64], "10": [2, 5, 24, 25, 29, 31, 52, 54, 57, 59, 60, 64, 71, 74, 77], "1024": 2, "typeexpand": 2, "expand": [2, 13, 14, 17, 28, 29, 30, 31, 35, 37, 41, 46, 52, 54, 55, 57, 58, 64, 67, 71], "learn": [2, 17, 25, 54, 72], "written": [2, 3, 5, 11, 13, 17, 24, 26, 28, 29, 34, 35, 36, 37, 42, 43, 44, 46, 52, 53, 54, 55, 57, 59, 64, 71, 73, 74], "due": [2, 3, 13, 14, 17, 24, 27, 30, 34, 46, 52, 54, 55, 59, 64, 66, 67, 71, 72, 73], "typabl": [2, 4, 34], "now": [2, 3, 4, 11, 13, 14, 17, 24, 26, 27, 30, 34, 35, 41, 42, 46, 51, 52, 53, 54, 55, 57, 59, 60, 64, 67, 71, 72, 74], "solv": [2, 3, 5, 7, 11, 13, 17, 24, 25, 39, 42, 44, 57, 60, 61, 62, 64, 67], "problem": [2, 4, 7, 9, 13, 17, 24, 29, 34, 42, 44, 46, 51, 52, 53, 54, 58, 62, 66, 67], "least": [2, 3, 12, 13, 17, 25, 28, 29, 30, 34, 41, 46, 52, 53, 57, 58, 64, 66, 67, 71, 72, 74, 75], "unsaf": [2, 17, 55, 66], "cast": [2, 12, 17, 25, 40, 46, 54, 55, 57, 58, 60, 64, 71], "obj": [2, 24, 42], "veri": [2, 8, 9, 11, 13, 17, 24, 25, 27, 29, 34, 42, 46, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67], "polymorph": [2, 3, 13, 17, 24, 25, 26, 29, 30, 31, 32, 33, 37, 39, 40, 41, 44, 46, 51, 59, 66, 67, 71], "alright": 2, "refus": [2, 3, 64], "checker": [2, 9, 11, 17, 24, 25, 26, 29, 33, 73], "known": [2, 8, 10, 12, 13, 17, 24, 27, 30, 33, 34, 39, 41, 44, 51, 55, 57, 66, 71], "distr": 2, "dp": [2, 17], "foral": [2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 25, 26, 27, 29, 30, 31, 32, 34, 36, 37, 41, 42, 43, 44, 46, 52, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 75], "direct": [2, 9, 12, 16, 17, 24, 31, 34, 42, 46, 52, 53, 57, 58, 71], "restrict": [2, 3, 12, 14, 17, 24, 26, 34, 35, 40, 51, 54, 57, 58, 59, 60, 62, 67, 71], "secondli": [2, 17], "quantif": [2, 3, 4, 13, 14, 17, 24, 26, 27, 28, 60, 67], "anyth": [2, 13, 17, 35, 44, 46, 51, 55, 57, 58, 64, 75], "anything_rect": 2, "anything_ind": 2, "anything_rec": 2, "anything_sind": 2, "dynam": [2, 11, 13, 17, 25, 36, 59, 71], "gadt": 2, "yet": [2, 17, 42, 43, 46, 51, 52, 54, 55, 57, 58, 60, 66, 71, 72], "those": [2, 3, 5, 10, 11, 12, 17, 24, 26, 33, 34, 35, 37, 43, 46, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72], "get": [2, 5, 9, 11, 13, 14, 17, 24, 25, 28, 29, 34, 36, 42, 51, 52, 53, 55, 58, 59, 60, 64, 66, 67], "segment": [2, 17, 24, 52, 59, 71], "fault": [2, 24, 71], "your": [2, 3, 8, 11, 14, 15, 17, 25, 29, 51, 52, 54, 55, 57, 58, 59, 60, 62, 66, 71, 73, 74, 75], "seem": [2, 5, 17, 71], "ill": [2, 4, 9, 10, 17, 24, 26, 30, 34, 51, 55, 64, 71, 72], "go": [2, 5, 9, 17, 24, 30, 42, 51, 52, 54, 55, 57, 59, 60, 64, 67, 71, 75], "wrong": [2, 3, 17, 24, 44, 51, 54, 66, 72], "come": [2, 6, 8, 13, 17, 24, 27, 34, 43, 51, 52, 54, 55, 57, 59, 60, 64, 71], "Of": [2, 14, 42, 51, 57], "launch": [2, 13, 17, 25, 52, 53], "appli": [2, 3, 4, 5, 9, 10, 11, 13, 14, 17, 24, 25, 26, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 40, 41, 42, 44, 46, 51, 53, 54, 55, 59, 60, 62, 66, 71, 72, 75], "shape": [2, 3, 57], "point": [2, 3, 11, 13, 17, 24, 25, 26, 32, 34, 35, 36, 39, 51, 52, 53, 54, 55, 57, 66, 71], "view": [2, 11, 17, 25, 26, 29, 32, 34, 39, 41, 52, 55, 60, 66], "about": [2, 3, 5, 11, 13, 14, 15, 17, 24, 25, 29, 30, 34, 37, 39, 41, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 72], "let02": [2, 77], "sai": [2, 3, 4, 17, 24, 26, 27, 28, 29, 31, 34, 42, 52, 53, 54, 55, 57, 58, 64, 71, 74], "though": [2, 8, 9, 17, 24, 29, 35, 37, 46, 51, 53, 54, 55, 64, 67, 71], "realist": [2, 42], "accept": [2, 3, 8, 13, 17, 24, 28, 29, 30, 32, 34, 40, 44, 45, 46, 51, 52, 53, 54, 55, 57, 58, 60, 64, 66, 71, 72], "without": [2, 3, 5, 8, 9, 11, 13, 14, 17, 24, 26, 29, 32, 33, 34, 35, 37, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 63, 64, 66, 67, 71, 74, 75, 77], "below": [2, 4, 5, 8, 9, 10, 11, 13, 14, 17, 25, 26, 27, 31, 34, 35, 38, 40, 41, 43, 51, 52, 53, 54, 55, 57, 64, 66, 71, 72, 74, 75], "choos": [2, 3, 17, 32, 34, 42, 43, 52, 53, 54, 57, 58, 67, 71, 72, 75], "everyth": [2, 17, 52, 53], "slight": [2, 17, 24, 58], "modif": [2, 4, 11, 17, 36, 41, 58, 71], "find": [2, 3, 4, 5, 7, 11, 13, 14, 16, 17, 25, 27, 29, 34, 42, 43, 51, 52, 53, 54, 55, 57, 58, 59, 62, 64, 66, 67, 71, 72, 77], "Its": [2, 3, 11, 17, 24, 52, 55, 57, 60, 67, 74], "euclid": [2, 17, 24], "unari": [2, 3, 26, 29, 34, 64], "repres": [2, 3, 5, 11, 13, 14, 17, 24, 26, 27, 28, 29, 31, 32, 34, 36, 37, 39, 40, 42, 43, 51, 52, 53, 54, 55, 57, 58, 59, 64, 65, 66, 67, 71], "theorem": [2, 5, 7, 8, 11, 12, 17, 24, 25, 27, 29, 32, 33, 35, 37, 38, 42, 43, 51, 52, 57, 59, 60, 62, 65, 66, 71, 73, 74, 75, 77], "eucl_dev": 2, "whose": [2, 3, 4, 5, 11, 13, 14, 17, 24, 26, 30, 31, 33, 34, 35, 37, 39, 41, 42, 44, 46, 53, 54, 55, 57, 58, 59, 60, 64, 67, 71, 75], "diveucl": 2, "quotient": [2, 5, 17, 40, 57, 64], "modulo": [2, 4, 5, 11, 17, 24, 34, 54, 57, 58, 59, 71], "assert": [2, 17, 24, 25, 26, 28, 34, 41, 54, 55, 57, 58, 62, 64, 66, 67, 71], "disappear": [2, 17, 24, 34, 55, 60, 67, 71], "wf_nat": [2, 17, 24], "gt_wf_rec": 2, "lt_wf_rec": [2, 24], "induction_ltof2": 2, "val": [2, 34, 55, 57], "sub": [2, 4, 8, 17, 36, 41, 46, 51, 53, 54, 57, 59, 60, 67, 71], "rec": [2, 17, 24, 35, 54, 55, 75], "le_lt_dec": [2, 17, 24], "n0": [2, 9, 31, 46, 57, 58, 67, 72], "n1": [2, 9, 34, 53, 57, 72], "le_gt_dec": 2, "divex": 2, "d": [2, 4, 5, 11, 14, 17, 24, 26, 34, 46, 51, 52, 53, 54, 57, 58, 62, 67, 75, 77], "q": [2, 3, 5, 7, 10, 11, 12, 17, 24, 27, 34, 35, 46, 51, 53, 54, 55, 57, 58, 59, 67, 71, 75], "r": [2, 3, 5, 7, 9, 11, 13, 14, 17, 24, 27, 28, 34, 35, 37, 41, 44, 51, 53, 54, 57, 58, 59, 60, 64, 67, 71, 72, 75, 77], "mandatori": [2, 8, 17, 32, 57, 66, 71], "enhanc": [2, 17, 52, 57], "past": [2, 17, 52, 64], "u": [2, 3, 4, 9, 10, 11, 14, 17, 24, 26, 27, 31, 34, 35, 38, 39, 41, 42, 46, 51, 53, 54, 55, 57, 58, 62, 64, 67, 71], "plai": [2, 17, 26, 42, 64, 66], "toplevel": [2, 10, 13, 14, 17, 24, 25, 27, 29, 35, 44, 46, 51, 52, 53, 55, 57, 58, 59, 60, 64, 71, 72, 74], "easier": [2, 10, 17, 24, 45, 52, 57, 58, 67, 71], "nat_of_int": 2, "int_of_nat": 2, "div": [2, 3, 5, 11, 17, 59], "173": [2, 14], "15": [2, 13, 25, 52, 53, 57, 66], "mere": [2, 17, 55, 57, 64, 71], "extrocamlintconv": 2, "concret": [2, 13, 14, 17, 25, 26, 29, 34, 42, 46, 51, 57, 64, 71], "patholog": 2, "success": [2, 3, 4, 5, 13, 17, 24, 25, 34, 51, 52, 55, 57, 59, 60, 62, 64, 66, 67, 74], "sever": [2, 3, 4, 5, 11, 17, 24, 25, 26, 28, 29, 30, 31, 32, 34, 40, 42, 44, 46, 51, 52, 54, 55, 57, 59, 60, 64, 65, 67, 71, 72, 75, 76], "chain": [2, 17, 25, 51, 64, 71, 74], "http": [2, 5, 17, 24, 25, 27, 50, 51, 52, 53, 59, 64, 75, 77], "github": [2, 5, 17, 51, 52], "com": [2, 5, 17, 51, 52, 54], "coq": [2, 8, 9, 11, 13, 15, 17, 25, 26, 29, 30, 46, 51, 53, 54, 55, 57, 58, 59, 63, 66, 71, 72, 73, 75, 76, 77], "commun": [2, 17, 24, 27, 29, 51], "hydra": 2, "battl": 2, "bdd": 2, "contrib": [2, 17, 24, 53, 55], "canon": [2, 4, 5, 11, 13, 17, 24, 25, 30, 32, 34, 35, 37, 38, 44, 45, 53, 57, 59, 71, 77], "chines": [2, 24], "continu": [2, 17, 24, 52, 53, 54, 55, 57, 71, 73], "fire": [2, 14, 17], "squad": 2, "founifi": 2, "graph": [2, 14, 17, 24, 25, 39, 54, 72], "higman": 2, "cf": [2, 9, 17, 24, 29, 34, 40, 42, 46, 59, 67], "nw": 2, "hardwar": [2, 8, 24], "multipli": [2, 57], "stalmarck": [2, 24], "probabl": [2, 17, 32, 44, 51, 54, 57, 58, 59, 75], "heavi": 2, "impred": [2, 12, 14, 17, 24, 25, 34, 51, 53, 77], "thank": [2, 5, 12, 17, 24, 34, 42, 55, 57, 64, 71], "matthieu": [3, 9, 14, 17, 77], "sozeau": [3, 9, 14, 17, 77], "equal": [3, 5, 8, 10, 11, 12, 13, 14, 17, 24, 25, 26, 30, 31, 32, 34, 35, 36, 39, 40, 42, 44, 46, 52, 54, 55, 57, 58, 60, 61, 65, 71, 72, 77], "equip": [3, 4, 17, 24, 27, 36, 42, 64], "equival": [3, 9, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 32, 34, 35, 36, 37, 38, 41, 42, 46, 51, 52, 53, 54, 55, 59, 60, 62, 64, 66, 67, 71, 75], "behav": [3, 11, 17, 24, 28, 29, 31, 34, 35, 43, 53, 54, 55, 57, 58, 60, 62, 64, 67, 71], "weaker": [3, 17, 24, 60], "g": [3, 4, 5, 8, 9, 10, 13, 14, 17, 24, 27, 28, 29, 30, 31, 34, 35, 36, 41, 43, 44, 46, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 75, 77], "system": [3, 8, 9, 11, 17, 24, 25, 26, 27, 28, 29, 32, 33, 34, 38, 39, 46, 51, 52, 53, 54, 55, 57, 59, 60, 62, 71, 73, 77], "toolbox": [3, 17], "extend": [3, 4, 5, 9, 10, 11, 14, 17, 24, 25, 26, 27, 28, 29, 32, 34, 35, 37, 40, 41, 42, 45, 51, 52, 53, 55, 59, 60, 71, 77], "capabl": [3, 17, 51, 53, 54, 55, 64], "document": [3, 8, 9, 11, 12, 16, 17, 24, 25, 42, 51, 52, 54, 55, 57, 59, 64, 65, 66, 67, 71, 72, 74, 76], "adapt": [3, 7, 17, 24, 51, 57, 63], "claudio": [3, 17, 24], "sacerdoti": [3, 17, 24], "coen": [3, 17, 24], "base": [3, 5, 10, 11, 12, 13, 14, 17, 24, 25, 29, 33, 35, 39, 42, 43, 44, 51, 52, 53, 54, 55, 57, 58, 60, 62, 63, 64, 66, 67, 71, 73, 74, 75, 77], "cl\u00e9ment": [3, 17], "renard": [3, 24], "implement": [3, 8, 11, 12, 13, 17, 24, 25, 29, 34, 35, 36, 37, 39, 43, 46, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 77], "drop": [3, 17, 51, 54, 59, 71], "old": [3, 11, 24, 25, 51, 53, 55, 58, 60, 66, 67], "complet": [3, 4, 5, 6, 7, 8, 9, 10, 11, 17, 24, 29, 30, 32, 34, 36, 40, 42, 51, 52, 53, 54, 57, 58, 59, 60, 62, 66, 67, 71], "typeclass": [3, 4, 5, 7, 17, 25, 35, 37, 38, 44, 45, 58, 60, 64, 66, 71], "infrastructur": [3, 25, 42, 53], "algorithm": [3, 7, 9, 11, 13, 17, 24, 25, 41, 51, 54, 57, 59, 62, 66, 77], "constraint": [3, 5, 8, 9, 10, 13, 17, 24, 25, 34, 35, 39, 43, 44, 51, 53, 54, 55, 58, 67, 71], "ml": [3, 5, 6, 8, 11, 17, 24, 25, 26, 29, 34, 36, 46, 51, 52, 53, 54, 57, 59, 60, 63, 64, 72, 77], "resolut": [3, 13, 17, 24, 25, 58, 60, 66, 71, 75], "anoth": [3, 4, 9, 11, 13, 14, 17, 24, 27, 31, 32, 34, 35, 40, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 62, 63, 64, 66, 67, 71], "pure": [3, 7, 11, 17, 55, 57, 64, 71, 72, 75], "again": [3, 13, 17, 24, 34, 42, 52, 53, 55, 57, 60, 64, 66, 71], "ordinari": [3, 17, 26, 37, 39, 71], "rocq": [3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 17, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 41, 42, 43, 44, 45, 46, 50, 52, 54, 55, 58, 59, 62, 63, 64, 65, 66, 67, 72, 73, 76], "manipul": [3, 9, 10, 17, 24, 25, 34, 37, 39, 55, 57, 63, 77], "put": [3, 5, 13, 14, 17, 34, 35, 43, 51, 53, 54, 57, 58, 59, 60, 66, 67, 71, 72, 75], "lemma": [3, 5, 11, 13, 14, 17, 24, 25, 32, 34, 35, 36, 38, 42, 44, 46, 54, 57, 58, 59, 60, 62, 64, 67, 72], "prove": [3, 5, 7, 8, 9, 11, 17, 24, 25, 27, 30, 32, 34, 35, 42, 43, 57, 58, 60, 62, 64, 72, 77], "higher": [3, 14, 17, 24, 25, 27, 40, 51, 54, 57, 58, 59, 60, 64, 67, 71, 73, 77], "depth": [3, 5, 13, 17, 29, 54, 57, 58, 59, 60, 62, 64, 71, 75], "solut": [3, 5, 13, 17, 42, 44, 58, 59, 63, 67], "fast": [3, 17, 24, 25, 53], "besid": [3, 17, 24, 34, 57], "necessari": [3, 4, 9, 13, 17, 24, 29, 31, 33, 37, 53, 55, 57, 59, 62, 64, 67, 71], "nicola": [3, 17, 77], "tabareau": [3, 17, 77], "glu": 3, "A": [3, 4, 5, 7, 9, 10, 11, 12, 13, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 50, 51, 52, 53, 54, 55, 57, 59, 60, 62, 63, 64, 66, 71, 72, 74, 75, 76, 77], "x1": [3, 9, 13, 17, 27, 42, 54, 57, 59, 60, 72], "t1": [3, 13, 17, 34, 42, 46, 57], "xn": [3, 9, 17, 57], "tn": [3, 13, 17, 57], "carrier": [3, 11, 14, 42, 57], "said": [3, 4, 17, 26, 34, 36, 42, 44, 55, 59, 71], "possibli": [3, 4, 17, 24, 34, 35, 42, 43, 51, 53, 54, 57, 59, 64, 67, 71, 73], "paramet": [3, 4, 5, 7, 8, 13, 14, 17, 24, 25, 28, 29, 34, 37, 40, 41, 42, 43, 44, 53, 54, 55, 58, 59, 60, 64, 66, 67, 71, 72], "finit": [3, 5, 17, 24, 30, 34], "unord": [3, 17, 57], "set_eq": 3, "satisfi": [3, 4, 5, 11, 13, 14, 17, 30, 34, 35, 54, 55, 59, 64, 67, 71], "convert": [3, 4, 12, 13, 14, 17, 25, 26, 34, 37, 41, 44, 54, 55, 57, 58, 64, 67], "reflex": [3, 5, 6, 11, 13, 17, 24, 27, 34, 36, 51, 54, 57, 59, 60, 62, 64, 66, 67, 71], "symmetri": [3, 17, 24, 34, 44, 57, 60, 64], "transit": [3, 7, 8, 13, 14, 17, 24, 25, 26, 35, 41, 44, 51, 54, 57, 58, 59, 60, 64, 66, 74], "symmetr": [3, 17, 24, 31, 59, 64, 71], "a1": [3, 27, 34, 46, 57, 58, 71], "a2": [3, 27, 34, 58], "covariantli": 3, "r1": [3, 5, 17, 27, 41, 44, 57, 59], "r2": [3, 17, 27, 41, 44, 57, 59], "whenev": [3, 7, 14, 17, 27, 29, 42, 55, 57, 62, 64, 67, 71], "imag": [3, 11, 17, 24, 51, 52, 66], "input": [3, 4, 9, 10, 13, 14, 17, 25, 27, 29, 35, 44, 46, 51, 54, 57, 58, 60, 64, 71, 72, 74, 75], "monoton": [3, 4, 17], "i_": [3, 34, 57], "r_1": 3, "r_2": 3, "notic": [3, 4, 5, 17, 26, 34, 35, 38, 46, 51, 52, 54, 57, 58, 64, 66, 71, 72, 74], "arrow": [3, 4, 14, 17, 52, 57, 60, 64, 67], "reader": [3, 11, 24, 29, 31, 42, 57], "between": [3, 4, 10, 11, 13, 14, 17, 24, 25, 26, 27, 29, 33, 34, 38, 39, 43, 44, 46, 51, 52, 53, 54, 57, 58, 60, 64, 65, 67, 71, 72, 75], "introduc": [3, 5, 8, 10, 11, 13, 14, 17, 24, 25, 28, 30, 31, 34, 35, 37, 38, 43, 44, 46, 51, 52, 55, 57, 58, 59, 60, 62, 66, 67, 71, 72, 75], "straightforwardli": 3, "ari": [3, 17, 34], "simultan": [3, 17, 24, 25, 26, 30, 32, 34, 42, 53, 57, 58], "everi": [3, 9, 11, 12, 13, 14, 17, 28, 29, 34, 40, 51, 52, 54, 55, 57, 58, 64, 71], "argument": [3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 17, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 38, 40, 42, 43, 45, 51, 52, 54, 55, 58, 59, 60, 62, 64, 66, 72, 75], "invers": [3, 11, 17, 24, 25, 31, 58, 60, 64, 72, 77], "t_1": [3, 26, 31, 34, 35], "ldot": [3, 7, 34], "t_n": [3, 26, 34, 66], "union": [3, 13, 17, 54, 59, 66, 77], "append": [3, 17, 29, 35, 43, 53, 54, 66, 75], "binari": [3, 5, 7, 11, 14, 17, 24, 29, 37, 42, 51, 53, 57, 58, 60, 64, 71], "latter": [3, 11, 17, 28, 34, 35, 42, 51, 54, 55, 57, 58, 64, 66, 67, 75], "condit": [3, 4, 9, 11, 17, 24, 25, 30, 50, 53, 59, 60, 63, 64, 66, 67], "s1": [3, 30, 38, 57], "s2": [3, 30], "divis": [3, 11, 17, 24, 25, 57], "rdiv": [3, 5], "le": [3, 5, 13, 14, 17, 24, 27, 42, 46, 52, 55, 57, 64, 67, 77], "usual": [3, 8, 9, 12, 17, 25, 26, 27, 28, 30, 34, 35, 37, 40, 43, 44, 46, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 74, 75], "leibniz": [3, 5, 7, 11, 13, 17, 24, 25, 27, 35, 40, 57, 58, 67], "unfortun": [3, 5, 17, 42, 46, 57], "intend": [3, 17, 24, 28, 32, 39, 51, 57, 64, 66, 71], "next": [3, 9, 13, 17, 24, 27, 29, 33, 34, 42, 44, 46, 51, 52, 54, 55, 57, 60, 64, 65, 66, 67, 71], "section": [3, 5, 6, 7, 8, 9, 10, 11, 12, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 40, 41, 42, 43, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 65, 67, 71, 74], "deal": [3, 5, 8, 13, 17, 24, 25, 42, 46, 57, 60, 64, 71, 72], "exact": [3, 12, 14, 17, 24, 25, 35, 40, 43, 53, 54, 55, 58, 59, 60, 64, 66, 67, 71], "goal": [3, 6, 7, 8, 9, 12, 13, 14, 17, 24, 25, 27, 29, 31, 34, 35, 36, 37, 38, 42, 43, 44, 52, 53, 59, 60, 61, 62, 64, 71, 72, 74], "howev": [3, 4, 5, 9, 12, 13, 14, 17, 24, 27, 29, 34, 36, 37, 41, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 64, 66, 67, 71, 72], "verifi": [3, 7, 9, 11, 14, 17, 24, 25, 29, 31, 32, 33, 35, 51, 60, 66], "verif": [3, 24, 25, 32, 66, 67, 77], "consist": [3, 4, 5, 11, 13, 14, 17, 24, 27, 30, 31, 34, 35, 52, 55, 57, 58, 59, 64, 65, 66, 71], "composit": [3, 71], "some": [3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 37, 38, 40, 41, 42, 44, 45, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 71, 72, 73, 75], "obviou": [3, 34, 57, 71], "suppos": [3, 9, 17, 55, 57, 64], "hypothesi": [3, 9, 11, 17, 24, 25, 27, 28, 29, 34, 38, 55, 57, 59, 60, 62, 64, 66, 67, 71, 72, 75], "h": [3, 4, 6, 9, 11, 12, 13, 14, 17, 24, 27, 34, 40, 44, 46, 51, 54, 55, 57, 58, 62, 64, 66, 67, 72, 75, 77], "These": [3, 11, 13, 14, 17, 24, 25, 27, 28, 29, 31, 32, 34, 36, 37, 38, 40, 52, 53, 54, 55, 57, 58, 60, 64, 66, 67, 71, 72, 73], "attribut": [3, 5, 9, 13, 14, 16, 25, 28, 30, 32, 34, 37, 40, 41, 42, 44, 51, 54, 55, 59, 60, 62, 64, 66, 71, 74], "univers": [3, 4, 8, 9, 12, 13, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 37, 39, 40, 44, 46, 51, 54, 57, 59, 62, 66, 67, 71, 77], "add": [3, 4, 5, 8, 9, 10, 11, 13, 14, 17, 24, 25, 29, 31, 32, 34, 37, 41, 42, 44, 46, 51, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 73, 75], "one_term": [3, 5, 7, 11, 13, 29, 34, 54, 58, 60, 62, 64, 67, 71, 72], "aeq": 3, "\u03b1": [3, 14, 25, 54, 55, 57], "typeabl": 3, "fresh": [3, 14, 17, 24, 25, 31, 34, 53, 57, 58, 64, 66, 67, 71], "intern": [3, 5, 11, 14, 17, 24, 25, 31, 34, 37, 44, 51, 53, 54, 55, 58, 60, 62, 66, 67, 71, 72, 73, 74, 77], "although": [3, 5, 9, 17, 35, 37, 53, 55, 57, 58, 60, 64, 66], "depart": 3, "To": [3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 17, 24, 25, 27, 29, 30, 32, 34, 37, 39, 41, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 64, 66, 67, 71, 72, 74, 75], "eq": [3, 5, 11, 14, 17, 27, 35, 40, 42, 54, 57, 58, 59, 64, 67, 71], "refl_equ": [3, 17, 57], "properti": [3, 4, 6, 9, 11, 12, 13, 17, 24, 25, 26, 27, 30, 31, 32, 34, 38, 39, 42, 45, 46, 57, 58, 67, 72, 77], "deriv": [3, 5, 9, 13, 17, 24, 25, 26, 30, 34, 38, 40, 54, 64, 66, 73], "autorewrit": [3, 17, 24, 60], "abl": [3, 8, 11, 13, 14, 17, 24, 25, 34, 42, 44, 46, 51, 53, 55, 57, 58, 59, 61, 62, 67], "defined": 3, "interact": [3, 6, 10, 13, 17, 24, 25, 32, 33, 37, 38, 40, 42, 43, 52, 59, 65, 66, 67, 71, 75, 76, 77], "denot": [3, 4, 11, 17, 24, 26, 28, 29, 30, 34, 35, 39, 40, 42, 43, 52, 54, 57, 58, 67, 71], "small": [3, 5, 8, 11, 14, 17, 25, 26, 33, 34, 39, 42, 44, 52, 53, 57, 64], "theori": [3, 4, 5, 11, 17, 24, 25, 26, 27, 28, 29, 39, 42, 46, 51, 53, 57, 58, 60, 62, 67, 71, 77], "homogen": [3, 17], "export": [3, 5, 8, 9, 11, 13, 17, 24, 29, 35, 38, 51, 52, 54, 55, 59, 60, 71], "relation_definit": [3, 13, 17, 42, 59], "eq_set": 3, "axiom": [3, 6, 7, 9, 10, 11, 12, 14, 17, 24, 25, 27, 28, 29, 30, 31, 32, 34, 35, 36, 38, 42, 44, 51, 52, 54, 57, 58, 59, 60, 64, 66, 67, 71, 72, 74], "eq_set_refl": 3, "eq_set_sym": 3, "eq_set_tran": 3, "empty_neutr": 3, "union_compat": 3, "eq_set_rel": 3, "eq_set_rel_rel": 3, "eq_set_rel_reflex": 3, "eq_set_rel_symmetr": 3, "eq_set_rel_transit": 3, "union_mor": 3, "x0": [3, 13, 17, 37, 43, 44, 54, 66, 71], "y0": [3, 13, 43], "No": [3, 5, 6, 9, 11, 12, 13, 14, 17, 24, 25, 26, 30, 34, 35, 36, 40, 42, 44, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74], "qed": [3, 5, 6, 8, 9, 12, 13, 14, 17, 24, 29, 32, 34, 36, 38, 40, 42, 51, 52, 54, 57, 58, 59, 60, 62, 64, 66, 67, 72], "reduc": [3, 7, 8, 10, 11, 12, 13, 17, 24, 26, 31, 32, 34, 36, 37, 40, 41, 44, 51, 53, 57, 58, 59, 60, 64, 66, 67, 71], "burden": [3, 63], "maxim": [3, 13, 17, 25, 41, 51, 57, 71, 77], "insert": [3, 4, 9, 12, 13, 17, 24, 25, 29, 41, 46, 52, 53, 55, 57, 66, 71, 75], "write": [3, 4, 8, 11, 13, 14, 17, 24, 25, 26, 27, 29, 31, 32, 33, 34, 38, 39, 43, 51, 53, 54, 55, 57, 58, 59, 63, 66, 67, 71, 73, 75], "proce": [3, 11, 13, 52, 57, 71], "simpl": [3, 4, 10, 11, 17, 24, 25, 29, 37, 41, 42, 43, 46, 52, 53, 54, 57, 58, 59, 60, 62, 67, 72], "step": [3, 5, 7, 11, 13, 17, 24, 25, 26, 29, 41, 51, 52, 53, 54, 58, 60, 64, 65, 67], "applic": [3, 5, 10, 11, 13, 14, 17, 24, 25, 26, 29, 30, 35, 36, 37, 41, 46, 52, 55, 57, 59, 60, 64, 66, 67, 71, 72, 77], "establish": [3, 17, 57], "intro": [3, 5, 11, 12, 13, 17, 24, 25, 34, 42, 43, 44, 52, 54, 55, 60, 62, 64, 66, 67, 71, 72], "manag": [3, 13, 17, 24, 25, 32, 38, 51, 53, 57, 59, 60, 62, 73], "hypothes": [3, 5, 9, 13, 17, 24, 25, 28, 32, 34, 51, 57, 60, 62, 64, 67, 71], "One": [3, 8, 9, 13, 14, 17, 25, 31, 32, 34, 37, 38, 39, 44, 51, 53, 54, 55, 59, 60, 64, 66, 67, 71, 75], "cmd": [3, 17, 38, 51, 52, 54], "exist": [3, 4, 5, 9, 11, 13, 14, 17, 25, 26, 27, 28, 29, 31, 32, 34, 36, 37, 39, 41, 42, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 63, 64, 66, 67, 71, 74], "outsid": [3, 5, 9, 11, 12, 13, 14, 17, 28, 29, 35, 38, 40, 41, 42, 43, 53, 54, 59, 60, 66, 71], "suffix": [3, 17, 35, 51, 52, 53, 54, 57, 59, 71, 75], "_morphism": 3, "modifi": [3, 4, 8, 11, 13, 14, 17, 24, 25, 29, 36, 38, 41, 51, 52, 54, 55, 57, 58, 64, 66, 67, 71], "themselv": [3, 13, 14, 17, 26, 35, 37, 39, 41, 42, 53, 57, 59, 64, 71], "exploit": [3, 17, 24, 57, 67], "monotoni": 3, "hand": [3, 10, 12, 13, 17, 25, 27, 29, 33, 35, 52, 53, 54, 55, 57, 58, 64, 67, 71, 72], "partial": [3, 13, 17, 24, 34, 35, 37, 44, 51, 53, 54, 57, 59, 62, 66, 71, 72], "domain": [3, 5, 11, 14, 17, 24, 25, 26, 34, 42, 61, 64, 71], "compris": [3, 24], "eqo": 3, "smallest": [3, 5, 27, 34, 67], "nonzero": [3, 11, 37, 54], "eq0": 3, "open": [3, 5, 6, 11, 13, 17, 25, 27, 35, 36, 38, 50, 52, 54, 55, 57, 59, 60, 64, 66], "addit": [3, 4, 5, 8, 9, 13, 17, 24, 25, 27, 29, 31, 34, 35, 39, 51, 52, 53, 54, 55, 58, 59, 62, 64, 65, 66, 67, 71, 72, 73], "up": [3, 8, 13, 17, 24, 25, 26, 31, 34, 35, 38, 42, 43, 52, 53, 54, 55, 57, 58, 64, 66, 67, 71, 75], "longer": [3, 9, 17, 24, 31, 34, 38, 44, 52, 53, 58, 66, 67, 71], "posit": [3, 4, 5, 7, 9, 10, 11, 14, 17, 24, 25, 30, 36, 37, 39, 41, 44, 46, 51, 52, 54, 55, 57, 58, 59, 64, 66, 67, 71], "z": [3, 5, 7, 11, 13, 14, 17, 24, 26, 27, 28, 29, 34, 35, 37, 40, 41, 42, 43, 44, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71], "lt": [3, 9, 13, 17, 27, 42, 71, 72], "increas": [3, 5, 8, 17, 24, 53, 57, 62], "decreas": [3, 7, 9, 17, 30, 34, 55, 59, 72], "dualli": [3, 44, 57], "hold": [3, 4, 17, 30, 34, 35, 40, 42, 55, 58, 75], "On": [3, 10, 12, 17, 24, 27, 30, 32, 37, 40, 44, 46, 51, 52, 53, 54, 57, 58, 64, 71], "contrari": [3, 4, 9, 13, 17, 30, 40, 44, 57, 67], "messag": [3, 4, 8, 11, 12, 13, 14, 16, 17, 24, 26, 28, 29, 30, 34, 35, 37, 40, 41, 42, 43, 44, 46, 51, 52, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 74], "rewritten": [3, 9, 11, 24, 30, 46, 57, 58, 64], "compos": [3, 4, 34, 44, 57, 67, 71], "propag": [3, 11, 17, 41], "varianc": [3, 17], "annot": [3, 9, 14, 17, 24, 25, 27, 34, 41, 42, 45, 51, 53, 55, 57, 66], "switch": [3, 8, 13, 14, 17, 24, 25, 51, 53, 66], "travers": [3, 17, 57, 58, 67], "detail": [3, 5, 7, 14, 25, 31, 36, 37, 41, 42, 51, 52, 55, 57, 58, 59, 64, 66, 71, 72, 74, 75], "contravariantli": 3, "differ": [3, 4, 9, 11, 13, 14, 15, 17, 24, 25, 26, 29, 31, 34, 35, 37, 38, 41, 43, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 67, 71, 72, 73, 75, 77], "duplic": [3, 11, 17, 43, 57, 67, 71], "multiset_eq": 3, "repeat": [3, 17, 25, 43, 44, 52, 55, 57, 58, 59, 66, 67], "request": [3, 14, 17, 25, 43, 51, 64], "unclear": [3, 10, 54], "analog": [3, 17, 34, 54, 57, 58, 66], "crelat": 3, "cmorphism": [3, 17], "cequival": 3, "rewriterel": [3, 17, 57], "index": [3, 13, 17, 24, 25, 26, 27, 29, 39, 40, 44, 52, 58, 60, 64, 66, 67, 73, 75], "iff": [3, 17, 26, 27, 31, 57, 59, 71], "impl": [3, 5, 59], "flip": [3, 17], "pointwis": 3, "simpli": [3, 4, 11, 13, 14, 17, 24, 31, 39, 54, 55, 57, 59, 62, 67, 71, 75], "machineri": [3, 17, 57], "infer": [3, 4, 9, 10, 13, 14, 24, 25, 26, 34, 37, 40, 41, 42, 45, 46, 51, 57, 58, 60, 62, 67, 71], "face": [3, 17, 75], "situat": [3, 4, 11, 17, 46, 54, 57, 71], "instanti": [3, 10, 13, 14, 17, 24, 34, 35, 43, 44, 54, 55, 57, 58, 60, 62, 67, 71], "discharg": [3, 14, 17, 24, 25, 28, 38, 72], "That": [3, 27, 29, 30, 34, 36, 52, 54, 55, 58, 64, 66], "variou": [3, 16, 17, 24, 25, 28, 29, 34, 44, 51, 52, 53, 55, 57, 58, 59, 60, 64, 66, 71], "hint": [3, 13, 14, 17, 24, 25, 27, 35, 38, 54, 62, 64, 75], "databas": [3, 13, 17, 25, 54, 57, 62, 64], "refl": [3, 17], "sym": [3, 17, 44], "tran": [3, 17], "id": [3, 4, 9, 10, 14, 17, 24, 26, 34, 35, 42, 44, 51, 52, 53, 54, 55, 57, 58, 64, 66, 71, 75], "equivalence_reflex": [3, 59], "equivalence_symmetr": [3, 59], "equivalence_transit": 3, "amount": [3, 5, 8, 14, 17, 51, 54, 58], "relationclass": [3, 17, 64], "further": [3, 17, 30, 35, 41, 51, 52, 54, 55, 57, 64, 66, 67, 71], "explan": [3, 13, 37, 45, 51, 58, 59, 67], "encod": [3, 13, 17, 24, 25, 27, 34, 53, 71, 75], "car": 3, "eq_rel": 3, "eq_rel_rel": 3, "eq_rel_reflex": 3, "eq_rel_symmetr": 3, "eq_rel_transit": 3, "x2": [3, 27, 42, 59, 60, 72], "apply_mor": 3, "setoid_": [3, 17], "moreov": [3, 5, 17, 28, 44, 46, 51, 52, 57, 62, 71], "unprefix": 3, "fall": [3, 9, 10, 13, 24, 53], "back": [3, 9, 14, 17, 24, 51, 52, 54, 57, 59, 66, 67], "involv": [3, 4, 9, 12, 17, 24, 25, 26, 34, 41, 42, 51, 52, 53, 54, 57, 59, 60, 62, 64, 67], "pass": [3, 5, 8, 10, 12, 17, 24, 37, 38, 42, 51, 52, 53, 54, 55, 57, 60, 64, 66, 67, 71, 75], "etransit": [3, 17, 43, 64], "one_term_with_bind": [3, 58, 64, 67, 72], "rewrite_occ": [3, 64], "int_or_var": [3, 54, 66, 71], "ltac_expr3": [3, 29, 54, 58, 64, 66], "defaultrel": 3, "By": [3, 4, 5, 11, 12, 13, 14, 17, 29, 37, 44, 46, 51, 53, 54, 55, 57, 60, 64, 66, 67, 71], "recent": [3, 24, 25, 53, 71], "environ": [3, 8, 9, 11, 12, 13, 14, 17, 24, 25, 26, 28, 30, 31, 32, 34, 35, 38, 42, 43, 52, 53, 55, 57, 60, 62, 64, 66, 67, 71, 72, 75], "simul": [3, 17, 24, 57, 66], "understand": [3, 5, 10, 12, 15, 17, 24, 25, 29, 33, 51, 53, 54, 55, 59, 60], "congruenc": [3, 12, 17, 24, 25, 34, 54, 62, 64, 67], "pack": [3, 42, 53], "slightli": [3, 17, 24, 35, 51, 52, 54, 55, 57, 58, 67], "permut": [3, 17, 25, 55, 57], "bi": 3, "implic": [3, 17, 26, 27, 28, 42, 54, 57, 60, 66, 67, 71], "port": [3, 17, 24, 55, 72], "semant": [3, 11, 13, 14, 17, 24, 25, 26, 29, 35, 36, 39, 41, 44, 53, 54, 57, 58, 71, 77], "limit": [3, 5, 9, 10, 13, 14, 17, 24, 25, 29, 35, 41, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 63, 64, 66, 71, 72], "lift": [3, 12, 14, 17], "were": [3, 11, 13, 17, 24, 34, 35, 36, 38, 42, 44, 51, 53, 54, 55, 59, 60, 66, 71, 72, 75], "discuss": [3, 17, 24, 25, 54], "setoid_rewrit": [3, 17, 24, 60, 64], "head": [3, 10, 13, 14, 17, 24, 26, 30, 35, 41, 42, 44, 53, 54, 55, 57, 58, 59, 60, 64, 67, 71], "constr": [3, 5, 14, 17, 24, 34, 42, 54, 55, 57, 71], "bind": [3, 9, 10, 14, 17, 24, 25, 28, 32, 34, 35, 37, 40, 43, 44, 46, 51, 54, 57, 64, 66, 67, 72], "construct": [3, 4, 5, 8, 9, 10, 11, 13, 14, 17, 25, 27, 28, 29, 30, 31, 33, 35, 41, 42, 43, 46, 52, 53, 55, 57, 58, 62, 63, 64, 65, 66, 67, 71, 77], "ex": [3, 17, 24, 27, 44, 58, 67, 71], "existenti": [3, 6, 9, 10, 13, 17, 24, 25, 26, 34, 41, 45, 54, 58, 59, 60, 64, 66, 67], "morphisms_prop": [3, 17], "all_iff_morph": 3, "pointwise_rel": 3, "simpl_rel": [3, 17], "predic": [3, 9, 17, 24, 25, 26, 27, 30, 34, 40, 42, 54, 60, 64, 77], "onc": [3, 8, 9, 10, 11, 13, 14, 17, 24, 25, 27, 32, 34, 41, 42, 44, 46, 51, 53, 55, 57, 58, 59, 60, 64, 66, 67, 71, 72], "implicitli": [3, 13, 14, 17, 24, 34, 51, 55, 59, 60, 64], "inde": [3, 4, 11, 12, 13, 14, 17, 25, 26, 29, 30, 34, 35, 40, 41, 42, 43, 44, 46, 53, 54, 55, 57, 58, 60, 64, 66, 67, 71, 72], "surround": [3, 17, 44, 57, 59, 71], "whatev": [3, 44, 64, 75], "map_morph": 3, "eqa": [3, 13], "eqb": [3, 5, 13, 17, 36, 59], "list_equiv": 3, "parameter": [3, 5, 11, 14, 17, 24, 25, 28, 37, 40, 54], "captur": [3, 17, 34, 44, 57, 64, 71], "bound": [3, 5, 6, 7, 10, 14, 17, 24, 25, 26, 28, 31, 32, 34, 39, 41, 42, 44, 46, 52, 54, 55, 57, 58, 59, 60, 62, 64, 72], "With": [3, 4, 13, 14, 17, 46, 53, 57, 58, 67, 71], "subterm": [3, 9, 10, 11, 17, 24, 25, 31, 34, 41, 54, 55, 57, 58, 59, 64, 66, 67, 71, 72], "almost": [3, 17, 57, 67, 75], "recov": [3, 8, 14, 17, 30, 46, 51, 54, 67], "smaller": [3, 11, 14, 17, 32, 33, 34, 53, 58, 62, 67, 72], "dual": [3, 9, 24, 55], "why": [3, 11, 17, 34, 37, 43, 55], "conjunct": [3, 5, 11, 17, 24, 34, 57, 59, 60, 67, 71], "suffici": [3, 5, 11, 13, 53], "aris": [3, 9, 13, 17, 30, 67, 71], "through": [3, 4, 12, 17, 24, 28, 29, 30, 32, 34, 35, 36, 37, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 65, 66, 67, 71, 72, 73, 74], "prime": [3, 17, 29, 34, 57], "space": [3, 17, 29, 52, 53, 57, 59, 66, 71, 74, 75], "rewrite_strat": [3, 17], "rule": [3, 4, 5, 11, 12, 13, 14, 17, 24, 25, 29, 32, 33, 35, 36, 37, 39, 41, 42, 44, 46, 51, 53, 54, 55, 58, 59, 60, 62, 66, 67, 77], "slow": [3, 11, 17, 53, 54, 55], "down": [3, 14, 24, 25, 45, 51, 52, 54, 55, 57, 59], "wherea": [3, 17, 29, 54, 55, 57, 58, 62, 74], "opaqu": [3, 6, 8, 9, 14, 17, 24, 25, 31, 32, 35, 38, 51, 57, 59, 60, 64, 66, 67, 71, 75], "caus": [3, 8, 12, 14, 17, 32, 51, 52, 53, 54, 55, 57, 58, 59, 63, 64, 66, 71, 75], "miss": [3, 5, 10, 13, 17, 24, 35, 43, 51, 52, 55, 57, 58, 62, 64, 71, 75], "configur": [3, 8, 17, 24, 25, 29, 40, 51, 52, 59, 64, 66, 73], "transpar": [3, 4, 6, 9, 14, 17, 24, 25, 31, 32, 35, 37, 41, 51, 54, 55, 57, 59, 60, 64, 66, 67, 75], "unif": [3, 10, 13, 17, 24, 25, 37, 40, 42, 43, 54, 60, 64, 71], "eauto": [3, 17, 25, 43, 54, 57, 60], "individu": [3, 17, 53, 55, 64, 67, 71], "double_f": 3, "unifi": [3, 12, 13, 14, 17, 34, 41, 42, 43, 54, 57, 58, 64, 66], "assert_succe": [3, 17, 25], "bottomup": 3, "hide": [3, 17, 25, 34, 41, 44, 57, 58, 66, 71], "side": [3, 10, 13, 14, 17, 24, 25, 27, 32, 34, 35, 38, 43, 52, 54, 55, 57, 58, 60, 62, 64, 67, 71], "behind": [3, 4, 17, 28, 34, 57], "assert_fail": [3, 17, 25], "disallow": [3, 12, 14, 17, 37, 51], "substitut": [3, 10, 11, 17, 24, 25, 26, 34, 38, 46, 51, 55, 57, 58, 64, 67, 71], "distinct": [3, 9, 13, 17, 26, 34, 42, 44, 46, 53, 54, 55, 57, 60, 64, 67, 71], "eq_refl": [3, 5, 9, 11, 12, 13, 14, 17, 27, 40, 64, 66, 67, 71], "resolv": [3, 9, 13, 14, 17, 35, 43, 52, 55, 57, 58, 59, 60, 64, 66, 67, 71], "treat": [3, 9, 12, 13, 17, 29, 46, 53, 54, 57, 59, 60, 62, 64, 67, 71, 72], "lot": [3, 11, 17, 24, 52, 55], "tri": [3, 4, 5, 9, 13, 14, 17, 34, 35, 41, 46, 52, 53, 54, 55, 57, 58, 59, 60, 62, 66, 67], "speed": [3, 13, 17, 24, 34, 64], "abbrevi": [3, 4, 5, 13, 14, 17, 24, 25, 27, 32, 35, 38, 59, 74], "typeclass_inst": [3, 13, 17, 60], "strat": 3, "rewstrategi": [3, 17], "conclus": [3, 11, 13, 17, 24, 28, 34, 54, 55, 57, 58, 60, 64, 66, 67, 71], "noth": [3, 17, 38, 41, 51, 54, 55, 57, 58, 60, 62, 64, 66, 67], "didn": [3, 17, 51, 53], "progress": [3, 17, 24, 25, 51, 52, 55, 60, 66, 77], "succeed": [3, 17, 54, 59, 72], "unabl": [3, 14, 34, 43, 46, 53, 57, 58, 59, 66, 67], "basic": [3, 9, 11, 17, 24, 25, 32, 33, 34, 35, 37, 40, 42, 44, 46, 51, 58, 59, 60, 63, 66, 67, 73], "db": [3, 17], "topdown": 3, "creat": [3, 8, 9, 13, 17, 24, 25, 29, 34, 38, 40, 42, 51, 52, 53, 54, 57, 58, 59, 64, 66, 67, 72, 75], "procedur": [3, 4, 11, 17, 24, 25, 54, 57, 60, 62, 64, 77], "programm": [3, 24, 25, 65], "visser": [3, 77], "et": [3, 24, 77], "al": [3, 57], "lv97": [3, 77], "vbt98": [3, 77], "core": [3, 13, 17, 24, 25, 27, 29, 41, 45, 51, 57, 59, 60, 62, 65, 71], "stratego": [3, 77], "transform": [3, 4, 11, 17, 29, 57, 58, 66, 67, 77], "languag": [3, 9, 11, 14, 26, 29, 36, 37, 39, 40, 41, 46, 53, 54, 63, 64, 65, 66, 74, 75, 77], "vis01": [3, 77], "rewstrategy1": [3, 17], "choic": [3, 17, 27, 34, 51, 52, 55, 62, 71, 75], "rewstrategy0": 3, "eval": [3, 5, 12, 14, 17, 24, 25, 29, 30, 31, 32, 35, 37, 42, 51, 52, 53, 55, 59], "red_expr": [3, 17, 32, 54, 64], "fold": [3, 17, 37, 57], "failur": [3, 8, 13, 14, 17, 24, 25, 46, 53, 55, 57, 59, 60, 62, 64, 71, 77], "catch": [3, 17, 25, 42, 46, 57], "zero": [3, 7, 11, 17, 26, 27, 37, 42, 46, 53, 54, 55, 58, 59, 60, 64], "nest": [3, 9, 17, 24, 25, 29, 32, 35, 38, 40, 54, 57, 58, 59, 64, 66, 71, 75], "andbc": [3, 57], "bottom": [3, 17, 37, 46, 52, 54, 55, 58, 64, 71], "top": [3, 8, 10, 12, 13, 14, 17, 24, 25, 29, 35, 37, 46, 51, 52, 53, 54, 55, 57, 58, 59, 64, 67, 71, 73, 75], "oper": [3, 5, 9, 10, 11, 14, 17, 24, 25, 27, 32, 34, 36, 51, 52, 54, 55, 57, 60, 64, 66, 67, 71], "texttt": 3, "conceptu": [3, 34], "straightforward": [3, 55], "root": [3, 17, 25, 27, 46, 51], "iter": [3, 5, 13, 17, 25, 26, 28, 30, 71], "consider": [3, 9, 17, 37, 39, 46, 64, 67, 71], "stop": [3, 5, 12, 17, 24, 32, 38, 52, 54, 57, 71], "Their": [3, 17, 32, 34, 39, 55, 57, 59, 71], "mani": [3, 8, 11, 13, 14, 17, 24, 25, 27, 29, 33, 34, 35, 39, 42, 51, 52, 53, 54, 55, 57, 58, 60, 64, 66, 71, 73], "stronger": [3, 12, 17, 34], "interpret": [3, 5, 9, 11, 13, 17, 24, 25, 27, 29, 32, 34, 35, 41, 44, 51, 52, 53, 54, 55, 59, 75], "ssrbool": [3, 17, 57], "ssrmatch": [3, 17, 57], "scope": [3, 5, 11, 17, 24, 25, 27, 29, 32, 36, 38, 43, 45, 52, 54, 55, 57, 59, 60, 64, 66], "bool_scop": [3, 17, 41, 71], "abort": [3, 11, 17, 34, 42, 44, 54, 55, 57, 64, 66, 67], "amokran": [4, 24], "sa\u00efbi": [4, 24], "prover": [4, 5, 15, 17, 24, 26, 29, 31, 33, 52, 55, 59, 65, 73, 75, 76], "power": [4, 5, 11, 17, 24, 54, 57, 67, 71, 72], "our": [4, 5, 7, 11, 17, 24, 34, 35, 54], "determin": [4, 13, 17, 31, 34, 36, 40, 41, 43, 53, 54, 57, 58, 64, 66, 67, 71, 72, 75], "appropri": [4, 13, 14, 17, 29, 53, 55, 57, 59, 62, 64, 66, 67, 75], "sens": [4, 24, 26, 30, 54, 55, 57, 71], "subtyp": [4, 9, 14, 17, 25, 31, 35, 39, 77], "certain": [4, 11, 17, 24, 29, 44, 46, 51, 54, 57, 58, 59, 64, 67, 71], "categori": [4, 8, 13, 17, 35, 51, 59, 61, 74, 75], "biject": [4, 17], "morphism": [4, 11, 17, 25, 59, 71], "famili": [4, 14, 17, 24, 25, 34, 40, 54, 55, 63, 67, 71], "coercion_class": [4, 71], "user": [4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 17, 25, 29, 32, 33, 34, 35, 36, 37, 39, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 57, 58, 59, 61, 62, 64, 65, 66, 67, 71, 72, 73, 74, 75, 76, 77], "sortclass": [4, 17, 57, 71], "funclass": [4, 17, 41, 71], "formal": [4, 6, 10, 17, 24, 25, 26, 29, 31, 32, 34, 37, 39, 41, 51, 55, 57, 67, 77], "don": [4, 10, 13, 14, 17, 28, 34, 35, 37, 46, 52, 53, 54, 57, 58, 60, 62, 64, 66], "confus": [4, 10, 13, 17, 24, 26, 29, 34, 44, 46, 52, 55, 57, 71], "target": [4, 11, 17, 25, 51, 58, 71], "x\u2081": 4, "a\u2081": 4, "x\u2096": 4, "a\u2096": 4, "v\u2081": 4, "v\u2099": [4, 55], "u\u2081": 4, "u\u2098": 4, "new": [4, 5, 6, 8, 10, 13, 14, 15, 25, 27, 29, 31, 32, 34, 36, 37, 39, 42, 43, 46, 51, 52, 54, 55, 58, 59, 60, 61, 64, 66, 67, 71, 72, 73, 75, 77], "ignor": [4, 13, 14, 17, 24, 29, 31, 34, 35, 44, 51, 52, 53, 54, 57, 58, 60, 64, 66, 71], "exactli": [4, 10, 11, 13, 17, 26, 27, 34, 40, 42, 44, 46, 51, 52, 54, 55, 57, 59, 66, 67, 71], "uniform": [4, 17, 24, 34, 40, 44, 54, 55], "recommend": [4, 8, 13, 14, 15, 17, 32, 35, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 72, 74, 75], "guarante": [4, 14, 17, 51, 52, 53, 55], "spuriou": [4, 17, 57, 71], "coerc": [4, 41, 57, 60, 64], "t\u2081": 4, "t\u2099": 4, "toward": [4, 17, 53], "intuit": [4, 11, 17, 24, 29, 55, 58, 62], "synthes": [4, 17, 24, 27, 28, 42, 46, 77], "precis": [4, 8, 13, 17, 24, 26, 29, 31, 33, 34, 35, 37, 39, 46, 51, 57, 64, 71], "doesn": [4, 14, 17, 29, 31, 35, 46, 51, 52, 53, 54, 55, 57, 58, 59, 62, 66, 67, 71, 73], "look": [4, 8, 9, 11, 13, 14, 16, 17, 25, 51, 53, 54, 55, 57, 58, 59, 60, 66, 67, 71, 72, 75], "incom": [4, 17], "necessarili": [4, 46, 67, 72], "semi": [4, 11, 17], "lattic": 4, "forget": [4, 11, 37, 55, 59, 60, 67], "harder": [4, 17, 58], "There": [4, 9, 10, 11, 14, 17, 24, 25, 26, 27, 28, 29, 34, 37, 38, 39, 40, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 63, 64, 66, 67, 71, 72, 75], "subclass": [4, 10, 13, 27, 39, 42, 59], "oldest": [4, 17], "notat": [4, 5, 9, 10, 11, 14, 24, 25, 26, 28, 29, 31, 33, 34, 35, 36, 37, 38, 40, 41, 45, 46, 51, 52, 53, 57, 58, 60, 64, 67, 73, 74, 75, 77], "f\u2081": 4, "f\u2096": 4, "ident_decl": [4, 9, 13, 28, 30, 32, 34, 37, 38, 40, 42, 59], "def_bodi": [4, 32, 38, 42], "unspecifi": [4, 14, 17, 43, 55, 62, 67], "ye": [4, 9, 11, 14, 17, 29, 34, 37, 42, 51, 53, 59, 67], "field": [4, 5, 7, 12, 13, 14, 17, 24, 25, 42, 51, 53, 55, 59, 61, 74], "nonuniform": [4, 17], "silenc": [4, 17, 24, 41, 46, 57, 62, 74], "18": [4, 13, 25, 57, 58, 59, 60, 64], "futur": [4, 9, 10, 13, 14, 17, 32, 41, 51, 52, 53, 57, 62, 66, 71, 77], "ambigu": [4, 17, 25, 46, 53, 57, 59, 60, 66, 71], "yield": [4, 11, 17, 24, 31, 46, 54, 55, 58, 67, 71], "f\u2099": 4, "report": [4, 8, 12, 17, 24, 29, 52, 54, 55, 59, 64, 72, 77], "definition": [4, 12, 17, 31, 32, 35, 37, 64], "circular": [4, 17, 57], "assumpt": [4, 10, 17, 24, 25, 26, 32, 33, 34, 35, 36, 44, 51, 52, 53, 54, 58, 59, 60, 66, 67, 77], "induct": [4, 5, 9, 10, 11, 12, 13, 14, 17, 24, 25, 27, 29, 30, 31, 32, 33, 35, 37, 41, 42, 44, 52, 54, 55, 57, 58, 59, 60, 62, 64, 65, 66, 73, 75, 77], "of_typ": [4, 17, 28], "src": [4, 53], "dest": [4, 17], "x\u2099": [4, 55], "t\u2098": 4, "word": [4, 14, 17, 30, 42, 51, 52, 53, 55, 58, 66], "context": [4, 5, 9, 10, 11, 14, 17, 24, 25, 26, 29, 30, 31, 32, 34, 35, 38, 41, 43, 44, 51, 52, 59, 60, 62, 64, 66, 67, 71], "forc": [4, 8, 11, 17, 24, 34, 42, 44, 52, 53, 54, 57, 60, 64, 66, 67, 71], "updat": [4, 8, 15, 17, 24, 36, 37, 46, 52, 53, 58, 59, 67, 71], "last": [4, 5, 9, 17, 24, 32, 34, 35, 37, 38, 42, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 65, 66, 67, 71, 72], "record_definit": [4, 13, 30, 34, 37], "redefin": [4, 17, 54, 55, 57, 66, 71, 75], "forgotten": 4, "atom": [4, 5, 8, 14, 17, 26, 60, 62, 67, 71], "bool_in_nat": 4, "unset": [4, 5, 12, 14, 17, 24, 25, 34, 35, 37, 38, 42, 44, 46, 51, 54, 55, 57, 59, 66, 67, 71], "none": [4, 5, 13, 17, 24, 27, 34, 40, 42, 46, 51, 54, 55, 57, 66, 71], "remark": [4, 17, 24, 25, 32, 34], "co": [4, 10, 11, 17, 24, 25, 42, 44, 54, 57, 59, 64, 67, 71, 77], "fg": 4, "bij": 4, "ap": [4, 11], "ssort": 4, "sstuff": 4, "s_nat": 4, "compar": [4, 5, 11, 14, 17, 24, 25, 37, 42, 53, 54, 55, 57, 58, 64, 66, 67, 73], "fct": 4, "incr_fct": 4, "fct_of_incr_fct": 4, "illeg": 4, "id_fct_funclass": 4, "reverse_coercion": [4, 17], "reversecoercionsourc": 4, "reversecoerciontarget": 4, "fr\u00e9d\u00e9ric": [5, 17, 57], "besson": [5, 17], "evgeni": [5, 17], "makarov": [5, 17], "mathbb": [5, 7, 17], "lqa": 5, "incomplet": [5, 8, 10, 17, 24, 46, 58, 66, 67, 71], "option": [5, 8, 9, 10, 11, 13, 14, 16, 24, 25, 26, 27, 34, 35, 38, 40, 42, 44, 46, 50, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 67, 71, 74], "john": [5, 77], "harrison": 5, "hol": 5, "light": [5, 17, 24, 52, 66, 75], "driver": 5, "csdp": 5, "gener": [5, 7, 8, 9, 12, 13, 17, 24, 25, 27, 28, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 43, 46, 51, 52, 53, 58, 59, 60, 61, 62, 64, 66, 75, 77], "cach": [5, 12, 17], "rerun": 5, "script": [5, 8, 17, 24, 25, 35, 42, 43, 53, 54, 55, 57, 58, 59, 60, 63, 64, 66, 73], "info": [5, 17, 54, 60], "dump": [5, 17, 24, 51, 75], "arith": [5, 11, 17, 24, 53, 59, 60, 72], "profil": [5, 17, 25, 53, 59, 64], "statist": [5, 17, 66], "pivot": 5, "detect": [5, 8, 17, 25, 41, 44, 52, 53, 57, 66], "ineffici": [5, 17, 24, 57], "formula": [5, 7, 26, 57, 58, 62, 77], "numer": [5, 11, 17, 24, 27, 29, 59, 71], "subtract": [5, 57], "exponenti": [5, 17, 29], "implb": [5, 17, 27], "negb": [5, 13, 27, 62, 71], "comparison": [5, 14, 17, 24, 42], "gtb": 5, "ltb": [5, 17, 59], "geb": 5, "leb": [5, 9, 17, 57, 59], "rather": [5, 11, 13, 17, 24, 29, 30, 34, 35, 53, 54, 55, 57, 58, 59, 64, 67, 71], "resp": [5, 17, 34, 36, 46, 57], "rang": [5, 17, 26, 29, 52, 55, 58, 71], "r0": [5, 17], "rmult": [5, 11], "rplu": 5, "rminu": 5, "izr": [5, 17, 71], "q2r": [5, 57], "rinv": 5, "decim": [5, 17, 27, 29, 59, 71], "hilbert": [5, 7, 17], "nullstellensatz": [5, 7, 17], "reli": [5, 17, 24, 30, 32, 33, 34, 38, 46, 51, 52, 53, 54, 55, 57, 58, 59, 64, 66, 67, 71], "notion": [5, 11, 17, 24, 25, 26, 27, 33, 34, 46, 51, 54, 55, 58, 64, 71, 77], "cone": [5, 17], "polynomi": [5, 7, 17, 24, 25, 61], "mathit": [5, 26, 34], "under": [5, 9, 11, 17, 25, 32, 40, 44, 46, 52, 53, 54, 55, 59, 64, 66, 67], "dfrac": 5, "quad": 5, "p_1": [5, 7, 34, 35], "p_2": [5, 35], "join": [5, 24], "inequ": [5, 17, 24, 60], "belong": [5, 8, 11, 26, 29, 34, 37, 39, 53, 54, 57, 59, 60, 63, 67, 71, 75], "bigwedge_": 5, "ge": [5, 17, 27], "unsatisfi": [5, 60], "neg": [5, 17, 29, 30, 37, 64, 66, 71], "absurd": [5, 27, 34, 51, 58], "squar": [5, 17, 24, 44, 54, 59, 71, 75], "bigwedge_i": 5, "c_i": [5, 34, 35], "j": [5, 6, 8, 14, 17, 24, 25, 26, 34, 36, 39, 43, 51, 54, 57, 64, 72, 77], "s_i": [5, 7, 34], "p_j": [5, 34], "oracl": 5, "within": [5, 17, 24, 28, 29, 31, 33, 35, 37, 38, 41, 42, 44, 51, 52, 54, 55, 58, 59, 60, 64, 66, 71], "upon": [5, 11, 36, 43, 51], "equat": [5, 6, 14, 17, 24, 25, 27, 34, 40, 42, 46, 53, 55, 58, 60, 61, 64, 67, 72], "explor": [5, 17, 59], "subset": [5, 9, 17, 24, 25, 34, 39, 44, 55, 57, 58, 66, 71, 77], "lincon": 5, "sum_": [5, 7, 57], "alpha_p": 5, "deduct": [5, 24, 57], "overlap": [5, 17, 42, 46, 53, 57, 59, 66], "xlra": 5, "ltac_expr": [5, 9, 11, 29, 54, 55, 60, 62, 64, 66, 71], "wlra": 5, "advanc": [5, 17, 25, 33, 34, 42, 53, 54, 58, 64, 71, 74], "coq_micromega": 5, "mli": [5, 17, 53], "decid": [5, 8, 11, 17, 24, 25, 29, 34, 51, 53, 55, 57, 60, 71], "mathtt": 5, "remedi": [5, 17], "weak": [5, 17, 25, 27, 35, 55, 64, 67, 71], "account": [5, 9, 13, 14, 17, 24, 26, 34, 37, 41, 44, 54, 57, 60, 67, 71], "discret": 5, "round": [5, 17, 53], "ceil": 5, "rightarrow": [5, 7, 26, 75], "lceil": 5, "rceil": 5, "deduc": [5, 17, 44, 51, 57, 58, 67], "lfloor": 5, "rfloor": 5, "conclud": [5, 13, 17, 34, 54, 57, 64, 67], "exhibit": 5, "equiv": [5, 34, 39], "enumer": [5, 17, 34, 40], "c_1": [5, 26, 34, 35], "c_2": 5, "bigvee_": 5, "subgoal": [5, 11, 13, 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64, 67, 71], "wellfound": [9, 17], "drawback": [9, 17, 67, 71], "underli": [9, 11, 17, 24, 26, 54, 57, 67, 71], "isn": [9, 10, 17, 28, 52, 57, 58, 60, 64, 66, 67], "anymor": [9, 17, 55, 59], "highli": [10, 43, 60, 63], "mistyp": 10, "anomali": [10, 17, 24, 59], "unlik": [10, 13, 17, 24, 30, 39, 52, 54, 55, 57, 58, 59, 60, 64, 67, 71], "pplu": 10, "rewrite_rul": 10, "univ_decl": [10, 14, 28, 35], "rw_pattern": 10, "namespac": [10, 14, 17, 35, 42, 53, 59], "against": [10, 13, 17, 44, 54, 57, 58, 59, 60, 62], "align": [10, 59, 71], "collect": [10, 17, 27, 51, 53, 60, 66, 72], "pplus_rewrit": 10, "rigid": [10, 13, 14, 17, 24, 60, 72], "enough": [10, 11, 14, 17, 34, 44, 57, 58, 67, 71], "discrimine": [10, 12, 46], "furthermor": [10, 17, 24, 25, 26, 29, 31, 33, 34, 51, 52, 55, 57, 63, 66], "grammar": [10, 17, 25, 28, 29, 54, 55, 57, 58, 62, 71], "rw_head_pattern": 10, "elimin": [10, 12, 14, 17, 24, 25, 26, 27, 30, 31, 34, 35, 37, 40, 54, 55, 58, 67, 71, 72, 77], "rw_pattern_arg": 10, 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24, 26, 31, 32, 34, 40, 52, 54, 55, 57, 60, 64, 66, 67, 72], "reach": [13, 52, 58], "breadth": 13, "deepen": 13, "best_effort": [13, 17], "couldn": 13, "unbound": [13, 14, 17, 54, 55, 58], "count": [13, 17, 25, 51, 57, 58, 59, 64, 66, 67], "faithfulli": 13, "mimic": [13, 37, 57], "move": [13, 17, 24, 25, 43, 52, 53, 55, 66, 67, 71], "autoappli": [13, 17], "shortcut": [13, 17, 25, 52, 55, 64, 71], "prevent": [13, 17, 29, 34, 41, 42, 51, 53, 54, 57, 64, 71], "releas": [13, 15, 17, 24, 25, 52, 53, 57, 63, 74], "filter": [13, 17, 30, 51, 53, 59, 60], "eta": [13, 17, 25, 31, 37], "expens": [13, 17, 54, 66], "rebuild": [13, 17], "benefit": [13, 17, 51, 57], "invert": [13, 17, 57, 67, 72], "elabor": [13, 14, 17, 25, 33, 37, 41, 44, 45, 51, 55, 58], "stricter": [13, 14, 17], "freez": 13, "verbos": [13, 17, 42, 51, 59], "successfulli": [13, 51, 52, 54, 57, 62, 63], "reus": [14, 17, 41, 57, 58, 59, 63, 64, 66], "sometim": [14, 17, 24, 25, 31, 34, 46, 53, 54, 55, 57, 59, 60, 66, 67, 71], 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31, 34, 35, 38, 55], "\u03b2\u03b4\u03b9\u03b6\u03b7": [14, 26, 31, 34, 35], "packtyp": 14, "pk": [14, 57], "1604": 14, "1612": 14, "lower": [14, 17, 25, 52, 54, 55, 57, 60, 64, 71], "monad": [14, 17, 55], "build_monad": 14, "dummy_rect": 14, "dummy_ind": 14, "dummy_rec": 14, "dummy_sind": 14, "2170": 14, "2175": 14, "insuffici": [14, 17, 51], "101": 14, "invariant_rect": 14, "invariant_ind": 14, "invariant_rec": 14, "invariant_sind": 14, "covariant_rect": 14, "covariant_ind": 14, "covariant_rec": 14, "covariant_sind": 14, "irrelevant_rect": 14, "irrelevant_ind": 14, "irrelevant_rec": 14, "irrelevant_sind": 14, "low": [14, 17, 25], "high": [14, 17, 24, 25, 35, 59, 60, 66, 72], "inv_low": 14, "inv_high": 14, "co_low": 14, "co_high": 14, "irr_low": 14, "irr_high": 14, "eq_rect": [14, 17, 27, 34, 40, 67], "eq_ind": [14, 27, 40], "eq_rec": [14, 27, 34, 40], "eq_sind": [14, 27, 40], "inhabit": [14, 29, 31, 32, 34, 37, 40, 43, 46, 51], "fit": [14, 17, 29, 34, 52, 55, 57, 71], "funext_typ": 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"coq:exn.\"All\"-is-a-predefined-collection-containing-all-variables.-It-can't-be-redefined", " It can't be redefined"]], "": [[71, 0, 1, "coq:exn.'via'-and-'abstract'-cannot-be-used-together", "'via' and 'abstract' cannot be used together"], [54, 1, 1, "coq:tacn.+-(backtracking-branching)", "+ (backtracking branching)"], [57, 1, 1, "coq:tacn.=>", "=>"], [66, 3, 1, "coq:cmd.Abort", "Abort"], [59, 3, 1, "coq:cmd.About", "About"], [71, 2, 1, "coq:warn.Activation-of-abbreviations-does-not-expect-mentioning-a-grammar-entry", "Activation of abbreviations does not expect mentioning a grammar entry"], [71, 2, 1, "coq:warn.Activation-of-abbreviations-does-not-expect-mentioning-a-scope", "Activation of abbreviations does not expect mentioning a scope"], [29, 3, 1, "coq:cmd.Add", "Add"], [11, 3, 1, "coq:cmd.Add-Field", "Add Field"], [3, 3, 1, "coq:cmd.Add-Morphism", "Add Morphism"], [3, 3, 1, "coq:cmd.Add-Parametric-Morphism", "Add Parametric Morphism"], [3, 3, 1, "coq:cmd.Add-Parametric-Relation", "Add Parametric Relation"], [3, 3, 1, "coq:cmd.Add-Parametric-Setoid", "Add Parametric Setoid"], [3, 3, 1, "coq:cmd.Add-Relation", "Add Relation"], [11, 3, 1, "coq:cmd.Add-Ring", "Add Ring"], [3, 3, 1, "coq:cmd.Add-Setoid", "Add Setoid"], [5, 3, 1, "coq:cmd.Add-Zify", "Add Zify"], [9, 3, 1, "coq:cmd.Admit-Obligations", "Admit Obligations"], [66, 3, 1, "coq:cmd.Admitted", "Admitted"], [12, 4, 1, "coq:flag.Allow-StrictProp", "Allow StrictProp"], [44, 0, 1, "coq:exn.Argument-at-position-\u2018natural\u2019-is-mentioned-more-than-once", "Argument at position \u2018natural\u2019 is mentioned more than once"], [54, 0, 1, "coq:exn.Argument-of-match-does-not-evaluate-to-a-term", "Argument of match does not evaluate to a term"], [41, 3, 1, "coq:cmd.Arguments", "Arguments"], [44, 0, 1, "coq:exn.Arguments-given-by-name-or-position-not-supported-in-explicit-mode", "Arguments given by name or position not supported in explicit mode"], [11, 0, 1, "coq:exn.Arguments-of-ring_simplify-do-not-have-all-the-same-type", "Arguments of ring_simplify do not have all the same type"], [41, 0, 1, "coq:exn.Arguments-of-section-variables-such-as-\u2018name\u2019-may-not-be-renamed", "Arguments of section variables such as \u2018name\u2019 may not be renamed"], [46, 4, 1, "coq:flag.Asymmetric-Patterns", "Asymmetric Patterns"], [66, 0, 1, "coq:exn.Attempt-to-save-an-incomplete-proof", "Attempt to save an incomplete proof"], [29, 3, 1, "coq:cmd.Attributes", "Attributes"], [34, 4, 1, "coq:flag.Auto-Template-Polymorphism", "Auto Template Polymorphism"], [34, 2, 1, "coq:warn.Automatically-declaring-\u2018ident\u2019-as-template-polymorphic", "Automatically declaring \u2018ident\u2019 as template polymorphic"], [28, 3, 1, "coq:cmd.Axiom", "Axiom"], [28, 3, 1, "coq:cmd.Axioms", "Axioms"], [59, 3, 1, "coq:cmd.Back", "Back"], [59, 3, 1, "coq:cmd.BackTo", "BackTo"], [11, 0, 1, "coq:exn.Bad-lemma-for-decidability-of-equality", "Bad lemma for decidability of equality"], [59, 0, 1, "coq:exn.Bad-magic-number", "Bad magic number"], [64, 0, 1, "coq:exn.Bad-occurrence-number-of-\u2018qualid\u2019", "Bad occurrence number of \u2018qualid\u2019"], [12, 2, 1, "coq:warn.Bad-relevance", "Bad relevance"], [11, 0, 1, "coq:exn.Bad-ring-structure", "Bad ring structure"], [71, 3, 1, "coq:cmd.Bind-Scope", "Bind Scope"], [67, 4, 1, "coq:flag.Boolean-Equality-Schemes", "Boolean Equality Schemes"], [5, 5, 1, "coq:thm.Bound-on-the-ceiling-function", "Bound on the ceiling function"], [66, 0, 1, "coq:exn.Brackets-do-not-support-multi-goal-selectors", "Brackets do not support multi-goal selectors"], [66, 6, 1, "coq:opt.Bullet-Behavior", "Bullet Behavior"], [72, 2, 1, "coq:warn.Cannot-build-functional-inversion-principle", "Cannot build functional inversion principle"], [58, 0, 1, "coq:exn.Cannot-change-\u2018ident\u2019,-it-is-used-in-conclusion", "Cannot change \u2018ident\u2019, it is used in conclusion"], [58, 0, 1, "coq:exn.Cannot-change-\u2018ident\u2019,-it-is-used-in-hypothesis-\u2018ident\u2019", "Cannot change \u2018ident\u2019, it is used in hypothesis \u2018ident\u2019"], [60, 0, 1, "coq:exn.Cannot-coerce-\u2018qualid\u2019-to-an-evaluable-reference", "Cannot coerce \u2018qualid\u2019 to an evaluable reference"], [72, 2, 1, "coq:warn.Cannot-define-graph-for-\u2018ident\u2019", "Cannot define graph for \u2018ident\u2019"], [72, 2, 1, "coq:warn.Cannot-define-principle(s)-for-\u2018ident\u2019", "Cannot define principle(s) for \u2018ident\u2019"], [11, 0, 1, "coq:exn.Cannot-find-a-declared-ring-structure-for-equality-\u2018term\u2019", "Cannot find a declared ring structure for equality \u2018term\u2019"], [11, 0, 1, "coq:exn.Cannot-find-a-declared-ring-structure-over-\u2018term\u2019", "Cannot find a declared ring structure over \u2018term\u2019"], [64, 0, 1, "coq:exn.Cannot-find-a-relation-to-rewrite", "Cannot find a relation to rewrite"], [64, 0, 1, "coq:exn.Cannot-find-any-non-recursive-equality-over-\u2018ident\u2019", "Cannot find any non-recursive equality over \u2018ident\u2019"], [72, 0, 1, "coq:exn.Cannot-find-induction-information-on-\u2018qualid\u2019", "Cannot find induction information on \u2018qualid\u2019"], [72, 0, 1, "coq:exn.Cannot-find-inversion-information-for-hypothesis-\u2018ident\u2019", "Cannot find inversion information for hypothesis \u2018ident\u2019"], [59, 0, 1, "coq:exn.Cannot-find-library-foo-in-loadpath", "Cannot find library foo in loadpath"], [4, 0, 1, "coq:exn.Cannot-find-the-source-class-of-\u2018qualid\u2019", "Cannot find the source class of \u2018qualid\u2019"], [4, 0, 1, "coq:exn.Cannot-find-the-target-class", "Cannot find the target class"], [35, 2, 1, "coq:warn.Cannot-import-local-constant,-it-will-be-ignored", "Cannot import local constant, it will be ignored"], [71, 0, 1, "coq:exn.Cannot-interpret-in-\u2018scope_name\u2019-because-\u2018qualid\u2019-could-not-be-found-in-the-current-environment", "Cannot interpret in \u2018scope_name\u2019 because \u2018qualid\u2019 could not be found in the current environment"], [71, 0, 1, "coq:exn.Cannot-interpret-this-number-as-a-value-of-type-\u2018type\u2019", "Cannot interpret this number as a value of type \u2018type\u2019"], [71, 0, 1, "coq:exn.Cannot-interpret-this-string-as-a-value-of-type-\u2018type\u2019", "Cannot interpret this string as a value of type \u2018type\u2019"], [59, 0, 1, "coq:exn.Cannot-load-\u2018qualid\u2019:-no-physical-path-bound-to-\u2018dirpath\u2019", "Cannot load \u2018qualid\u2019: no physical path bound to \u2018dirpath\u2019"], [58, 0, 1, "coq:exn.Cannot-move-\u2018ident\u2019-after-\u2018ident\u2019:-it-depends-on-\u2018ident\u2019", "Cannot move \u2018ident\u2019 after \u2018ident\u2019: it depends on \u2018ident\u2019"], [58, 0, 1, "coq:exn.Cannot-move-\u2018ident\u2019-after-\u2018ident\u2019:-it-occurs-in-the-type-of-\u2018ident\u2019", "Cannot move \u2018ident\u2019 after \u2018ident\u2019: it occurs in the type of \u2018ident\u2019"], [62, 0, 1, "coq:exn.Cannot-recognize-a-boolean-equality", "Cannot recognize a boolean equality"], [67, 0, 1, "coq:exn.Cannot-recognize-a-statement-based-on-\u2018reference\u2019", "Cannot recognize a statement based on \u2018reference\u2019"], [4, 0, 1, "coq:exn.Cannot-recognize-\u2018coercion_class\u2019-as-a-source-class-of-\u2018qualid\u2019", "Cannot recognize \u2018coercion_class\u2019 as a source class of \u2018qualid\u2019"], [64, 0, 1, "coq:exn.Cannot-turn-[inductive|constructor]-into-an-evaluable-reference", "Cannot turn [inductive|constructor] into an evaluable reference"], [72, 0, 1, "coq:exn.Cannot-use-mutual-definition-with-well-founded-recursion-or-measure", "Cannot use mutual definition with well-founded recursion or measure"], [42, 3, 1, "coq:cmd.Canonical-Structure", "Canonical Structure"], [59, 0, 1, "coq:exn.Can\u2019t-find-file-\u2018ident\u2019-on-loadpath", "Can\u2019t find file \u2018ident\u2019 on loadpath"], [67, 4, 1, "coq:flag.Case-Analysis-Schemes", "Case Analysis Schemes"], [5, 5, 1, "coq:thm.Case-split", "Case split"], [40, 0, 1, "coq:exn.Casts-are-not-supported-in-this-pattern", "Casts are not supported in this pattern"], [2, 3, 1, "coq:cmd.Cd", "Cd"], [59, 3, 1, "coq:cmd.Check", "Check"], [13, 3, 1, "coq:cmd.Class", "Class"], [71, 3, 1, "coq:cmd.Close-Scope", "Close Scope"], [30, 3, 1, "coq:cmd.CoFixpoint", "CoFixpoint"], [30, 3, 1, "coq:cmd.CoInductive", "CoInductive"], [4, 3, 1, "coq:cmd.Coercion", "Coercion"], [66, 3, 1, "coq:cmd.Collection", "Collection"], [67, 3, 1, "coq:cmd.Combined-Scheme", "Combined Scheme"], [29, 3, 1, "coq:cmd.Comments", "Comments"], [64, 3, 1, "coq:cmd.Compute", "Compute"], [54, 0, 1, "coq:exn.Condition-not-satisfied", "Condition not satisfied"], [28, 3, 1, "coq:cmd.Conjecture", "Conjecture"], [28, 3, 1, "coq:cmd.Conjectures", "Conjectures"], [14, 3, 1, "coq:cmd.Constraint", "Constraint"], [38, 3, 1, "coq:cmd.Context", "Context"], [44, 4, 1, "coq:flag.Contextual-Implicit", "Contextual Implicit"], [51, 4, 1, "coq:flag.Coqtop-Exit-On-Error", "Coqtop Exit On Error"], [32, 3, 1, "coq:cmd.Corollary", "Corollary"], [60, 3, 1, "coq:cmd.Create-HintDb", "Create HintDb"], [14, 7, 1, "coq:attr.Cumulative", "Cumulative"], [14, 4, 1, "coq:flag.Cumulativity-Weak-Constraints", "Cumulativity Weak Constraints"], [54, 3, 1, "coq:cmd.Debug", "Debug"], [59, 6, 1, "coq:opt.Debug", "Debug"], [60, 4, 1, "coq:flag.Debug-Auto", "Debug Auto"], [60, 4, 1, "coq:flag.Debug-Eauto", "Debug Eauto"], [57, 4, 1, "coq:flag.Debug-SsrMatching", "Debug SsrMatching"], [57, 4, 1, "coq:flag.Debug-Ssreflect", "Debug Ssreflect"], [60, 4, 1, "coq:flag.Debug-Trivial", "Debug Trivial"], [54, 0, 1, "coq:exn.Debug-mode-not-available-in-the-IDE", "Debug mode not available in the IDE"], [67, 4, 1, "coq:flag.Decidable-Equality-Schemes", "Decidable Equality Schemes"], [71, 3, 1, "coq:cmd.Declare-Custom-Entry", "Declare Custom Entry"], [64, 3, 1, "coq:cmd.Declare-Equivalent-Keys", "Declare Equivalent Keys"], [13, 3, 1, "coq:cmd.Declare-Instance", "Declare Instance"], [64, 3, 1, "coq:cmd.Declare-Left-Step", "Declare Left Step"], [59, 3, 1, "coq:cmd.Declare-ML-Module", "Declare ML Module"], [35, 3, 1, "coq:cmd.Declare-Module", "Declare Module"], [3, 3, 1, "coq:cmd.Declare-Morphism", "Declare Morphism"], [64, 3, 1, "coq:cmd.Declare-Reduction", "Declare Reduction"], [64, 3, 1, "coq:cmd.Declare-Right-Step", "Declare Right Step"], [71, 3, 1, "coq:cmd.Declare-Scope", "Declare Scope"], [60, 2, 1, "coq:warn.Declaring-arbitrary-terms-as-hints-is-fragile-and-deprecated;-it-is-recommended-to-declare-a-toplevel-constant-instead", "Declaring arbitrary terms as hints is fragile and deprecated; it is recommended to declare a toplevel constant instead"], [58, 6, 1, "coq:opt.Default-Goal-Selector", "Default Goal Selector"], [66, 6, 1, "coq:opt.Default-Proof-Mode", "Default Proof Mode"], [66, 6, 1, "coq:opt.Default-Proof-Using", "Default Proof Using"], [59, 6, 1, "coq:opt.Default-Timeout", "Default Timeout"], [66, 3, 1, "coq:cmd.Defined", "Defined"], [32, 3, 1, "coq:cmd.Definition", "Definition"], [12, 4, 1, "coq:flag.Definitional-UIP", "Definitional UIP"], [71, 3, 1, "coq:cmd.Delimit-Scope", "Delimit Scope"], [34, 4, 1, "coq:flag.Dependent-Proposition-Eliminators", "Dependent Proposition Eliminators"], [6, 3, 1, "coq:cmd.Derive", "Derive"], [67, 3, 1, "coq:cmd.Derive-Dependent-Inversion", "Derive Dependent Inversion"], [67, 3, 1, "coq:cmd.Derive-Dependent-Inversion_clear", "Derive Dependent Inversion_clear"], [67, 3, 1, "coq:cmd.Derive-Inversion", "Derive Inversion"], [67, 3, 1, "coq:cmd.Derive-Inversion_clear", "Derive Inversion_clear"], [66, 6, 1, "coq:opt.Diffs", "Diffs"], [71, 3, 1, "coq:cmd.Disable-Notation", "Disable Notation"], [59, 3, 1, "coq:cmd.Drop", "Drop"], [5, 6, 1, "coq:opt.Dump-Arith", "Dump Arith"], [59, 0, 1, "coq:exn.Dynlink-error:-execution-of-module-initializers-in-the", "Dynlink error: execution of module initializers in the"], [46, 0, 1, "coq:exn.Either-there-is-a-type-incompatibility-or-the-problem-involves-dependencies", "Either there is a type incompatibility or the problem involves dependencies"], [67, 4, 1, "coq:flag.Elimination-Schemes", "Elimination Schemes"], [71, 3, 1, "coq:cmd.Enable-Notation", "Enable Notation"], [38, 3, 1, "coq:cmd.End", "End"], [71, 0, 1, "coq:exn.End-of-quoted-string-not-followed-by-a-space-in-notation", "End of quoted string not followed by a space in notation"], [64, 3, 1, "coq:cmd.Eval", "Eval"], [32, 3, 1, "coq:cmd.Example", "Example"], [13, 3, 1, "coq:cmd.Existing-Class", "Existing Class"], [13, 3, 1, "coq:cmd.Existing-Instance", "Existing Instance"], [13, 3, 1, "coq:cmd.Existing-Instances", "Existing Instances"], [35, 3, 1, "coq:cmd.Export", "Export"], [54, 0, 1, "coq:exn.Expression-does-not-evaluate-to-a-tactic", "Expression does not evaluate to a tactic"], [2, 3, 1, "coq:cmd.Extract-Callback", "Extract Callback"], [2, 0, 1, "coq:exn.Extract-Callback-is-supported-only-for-OCaml-extraction", "Extract Callback is supported only for OCaml extraction"], [2, 3, 1, "coq:cmd.Extract-Constant", "Extract Constant"], [2, 3, 1, "coq:cmd.Extract-Foreign-Constant", "Extract Foreign Constant"], [2, 0, 1, "coq:exn.Extract-Foreign-Constant-is-supported-only-for-OCaml-extraction", "Extract Foreign Constant is supported only for OCaml extraction"], [2, 0, 1, "coq:exn.Extract-Foreign-Constant-is-supported-only-for-functions", "Extract Foreign Constant is supported only for functions"], [2, 3, 1, "coq:cmd.Extract-Inductive", "Extract Inductive"], [2, 3, 1, "coq:cmd.Extract-Inlined-Constant", "Extract Inlined Constant"], [2, 3, 1, "coq:cmd.Extraction", "Extraction"], [2, 4, 1, "coq:flag.Extraction-AutoInline", "Extraction AutoInline"], [2, 3, 1, "coq:cmd.Extraction-Blacklist", "Extraction Blacklist"], [2, 4, 1, "coq:flag.Extraction-Conservative-Types", "Extraction Conservative Types"], [2, 6, 1, "coq:opt.Extraction-File-Comment", "Extraction File Comment"], [2, 6, 1, "coq:opt.Extraction-Flag", "Extraction Flag"], [2, 3, 1, "coq:cmd.Extraction-Implicit", "Extraction Implicit"], [2, 3, 1, "coq:cmd.Extraction-Inline", "Extraction Inline"], [2, 4, 1, "coq:flag.Extraction-KeepSingleton", "Extraction KeepSingleton"], [2, 3, 1, "coq:cmd.Extraction-Language", "Extraction Language"], [2, 3, 1, "coq:cmd.Extraction-Library", "Extraction Library"], [2, 3, 1, "coq:cmd.Extraction-NoInline", "Extraction NoInline"], [2, 4, 1, "coq:flag.Extraction-Optimize", "Extraction Optimize"], [2, 6, 1, "coq:opt.Extraction-Output-Directory", "Extraction Output Directory"], [2, 4, 1, "coq:flag.Extraction-SafeImplicits", "Extraction SafeImplicits"], [2, 3, 1, "coq:cmd.Extraction-TestCompile", "Extraction TestCompile"], [2, 4, 1, "coq:flag.Extraction-TypeExpand", "Extraction TypeExpand"], [32, 3, 1, "coq:cmd.Fact", "Fact"], [59, 3, 1, "coq:cmd.Fail", "Fail"], [54, 0, 1, "coq:exn.Failed-to-progress", "Failed to progress"], [59, 4, 1, "coq:flag.Fast-Name-Printing", "Fast Name Printing"], [59, 0, 1, "coq:exn.File-not-found-on-loadpath:-\u2018string\u2019", "File not found on loadpath: \u2018string\u2019"], [59, 0, 1, "coq:exn.Files-processed-by-Load-cannot-leave-open-proofs", "Files processed by Load cannot leave open proofs"], [9, 3, 1, "coq:cmd.Final-Obligation", "Final Obligation"], [62, 6, 1, "coq:opt.Firstorder-Depth", "Firstorder Depth"], [62, 6, 1, "coq:opt.Firstorder-Solver", "Firstorder Solver"], [34, 3, 1, "coq:cmd.Fixpoint", "Fixpoint"], [41, 0, 1, "coq:exn.Flag-'rename'-expected-to-rename-\u2018name\u2019-into-\u2018name\u2019", "Flag 'rename' expected to rename \u2018name\u2019 into \u2018name\u2019"], [66, 3, 1, "coq:cmd.Focus", "Focus"], [46, 0, 1, "coq:exn.Found-a-constructor-of-inductive-type-term-while-a-constructor-of-term-is-expected", "Found a constructor of inductive type term while a constructor of term is expected"], [64, 0, 1, "coq:exn.Found-an-\"at\"-clause-without-\"with\"-clause", "Found an "at" clause without "with" clause"], [71, 2, 1, "coq:warn.Found-no-matching-notation-to-enable-or-disable", "Found no matching notation to enable or disable"], [64, 0, 1, "coq:exn.Found-no-subterm-matching-\u2018term\u2019-in-the-current-goal", "Found no subterm matching \u2018term\u2019 in the current goal"], [64, 0, 1, "coq:exn.Found-no-subterm-matching-\u2018term\u2019-in-\u2018ident\u2019", "Found no subterm matching \u2018term\u2019 in \u2018ident\u2019"], [4, 0, 1, "coq:exn.Found-target-class-\u2018coercion_class\u2019-instead-of-\u2018coercion_class\u2019", "Found target class \u2018coercion_class\u2019 instead of \u2018coercion_class\u2019"], [59, 3, 1, "coq:cmd.From-\u2026-Dependency", "From \u2026 Dependency"], [59, 3, 1, "coq:cmd.From-\u2026-Require", "From \u2026 Require"], [4, 0, 1, "coq:exn.Funclass-cannot-be-a-source-class", "Funclass cannot be a source class"], [72, 3, 1, "coq:cmd.Function", "Function"], [72, 3, 1, "coq:cmd.Functional-Case", "Functional Case"], [72, 3, 1, "coq:cmd.Functional-Scheme", "Functional Scheme"], [44, 3, 1, "coq:cmd.Generalizable", "Generalizable"], [72, 3, 1, "coq:cmd.Generate-graph-for", "Generate graph for"], [66, 3, 1, "coq:cmd.Goal", "Goal"], [59, 4, 1, "coq:flag.Guard-Checking", "Guard Checking"], [66, 3, 1, "coq:cmd.Guarded", "Guarded"], [60, 3, 1, "coq:cmd.Hint-Constants", "Hint Constants"], [60, 3, 1, "coq:cmd.Hint-Constructors", "Hint Constructors"], [60, 3, 1, "coq:cmd.Hint-Cut", "Hint Cut"], [60, 3, 1, "coq:cmd.Hint-Extern", "Hint Extern"], [60, 3, 1, "coq:cmd.Hint-Immediate", "Hint Immediate"], [60, 3, 1, "coq:cmd.Hint-Mode", "Hint Mode"], [60, 3, 1, "coq:cmd.Hint-Opaque", "Hint Opaque"], [60, 3, 1, "coq:cmd.Hint-Projections", "Hint Projections"], [60, 3, 1, "coq:cmd.Hint-Resolve", "Hint Resolve"], [60, 3, 1, "coq:cmd.Hint-Rewrite", "Hint Rewrite"], [60, 3, 1, "coq:cmd.Hint-Transparent", "Hint Transparent"], [60, 3, 1, "coq:cmd.Hint-Unfold", "Hint Unfold"], [60, 3, 1, "coq:cmd.Hint-Variables", "Hint Variables"], [57, 3, 1, "coq:cmd.Hint-View-for", "Hint View for"], [57, 3, 1, "coq:cmd.Hint-View-for-apply", "Hint View for apply"], [57, 3, 1, "coq:cmd.Hint-View-for-move", "Hint View for move"], [28, 3, 1, "coq:cmd.Hypotheses", "Hypotheses"], [28, 3, 1, "coq:cmd.Hypothesis", "Hypothesis"], [72, 0, 1, "coq:exn.Hypothesis-\u2018ident\u2019-must-contain-at-least-one-Function", "Hypothesis \u2018ident\u2019 must contain at least one Function"], [66, 6, 1, "coq:opt.Hyps-Limit", "Hyps Limit"], [62, 0, 1, "coq:exn.I-don\u2019t-know-how-to-handle-dependent-equality", "I don\u2019t know how to handle dependent equality"], [4, 3, 1, "coq:cmd.Identity-Coercion", "Identity Coercion"], [13, 2, 1, "coq:warn.Ignored-instance-declaration-for-\u201c\u2018ident\u2019\u201d:-\u201c\u2018term\u2019\u201d-is-not-a-class", "Ignored instance declaration for \u201c\u2018ident\u2019\u201d: \u201c\u2018term\u2019\u201d is not a class"], [44, 2, 1, "coq:warn.Ignoring-implicit-binder-declaration-in-unexpected-position", "Ignoring implicit binder declaration in unexpected position"], [9, 0, 1, "coq:exn.Ill-formed-recursive-definition", "Ill-formed recursive definition"], [34, 0, 1, "coq:exn.Ill-formed-template-inductive-declaration:-not-polymorphic-on-any-universe", "Ill-formed template inductive declaration: not polymorphic on any universe"], [44, 4, 1, "coq:flag.Implicit-Arguments", "Implicit Arguments"], [44, 3, 1, "coq:cmd.Implicit-Type", "Implicit Type"], [44, 3, 1, "coq:cmd.Implicit-Types", "Implicit Types"], [35, 3, 1, "coq:cmd.Import", "Import"], [35, 3, 1, "coq:cmd.Include", "Include"], [35, 3, 1, "coq:cmd.Include-Type", "Include Type"], [57, 0, 1, "coq:exn.Incorrect-number-of-tactics-(expected-N-tactics,-was-given-M)", "Incorrect number of tactics (expected N tactics, was given M)"], [34, 3, 1, "coq:cmd.Inductive", "Inductive"], [71, 3, 1, "coq:cmd.Infix", "Infix"], [54, 3, 1, "coq:cmd.Info", "Info"], [60, 4, 1, "coq:flag.Info-Auto", "Info Auto"], [60, 4, 1, "coq:flag.Info-Eauto", "Info Eauto"], [54, 6, 1, "coq:opt.Info-Level", "Info Level"], [5, 4, 1, "coq:flag.Info-Micromega", "Info Micromega"], [60, 4, 1, "coq:flag.Info-Trivial", "Info Trivial"], [59, 3, 1, "coq:cmd.Inspect", "Inspect"], [13, 3, 1, "coq:cmd.Instance", "Instance"], [59, 3, 1, "coq:cmd.Instructions", "Instructions"], [62, 4, 1, "coq:flag.Intuition-Negation-Unfolding", "Intuition Negation Unfolding"], [59, 0, 1, "coq:exn.Invalid-backtrack", "Invalid backtrack"], [67, 8, 1, "coq:table.Keep-Equalities", "Keep Equalities"], [67, 4, 1, "coq:flag.Keep-Proof-Equalities", "Keep Proof Equalities"], [64, 4, 1, "coq:flag.Kernel-Term-Sharing", "Kernel Term Sharing"], [64, 4, 1, "coq:flag.Keyed-Unification", "Keyed Unification"], [38, 0, 1, "coq:exn.Last-block-to-end-has-name-\u2018ident\u2019", "Last block to end has name \u2018ident\u2019"], [32, 3, 1, "coq:cmd.Lemma", "Lemma"], [38, 3, 1, "coq:cmd.Let", "Let"], [38, 3, 1, "coq:cmd.Let-CoFixpoint", "Let CoFixpoint"], [38, 3, 1, "coq:cmd.Let-Fixpoint", "Let Fixpoint"], [5, 4, 1, "coq:flag.Lia-Cache", "Lia Cache"], [59, 3, 1, "coq:cmd.Load", "Load"], [59, 0, 1, "coq:exn.Load-is-not-supported-inside-proofs", "Load is not supported inside proofs"], [59, 3, 1, "coq:cmd.Locate", "Locate"], [59, 3, 1, "coq:cmd.Locate-File", "Locate File"], [59, 3, 1, "coq:cmd.Locate-Library", "Locate Library"], [59, 3, 1, "coq:cmd.Locate-Ltac", "Locate Ltac"], [59, 3, 1, "coq:cmd.Locate-Ltac2", "Locate Ltac2"], [59, 3, 1, "coq:cmd.Locate-Module", "Locate Module"], [59, 3, 1, "coq:cmd.Locate-Term", "Locate Term"], [60, 6, 1, "coq:opt.Loose-Hint-Behavior", "Loose Hint Behavior"], [54, 3, 1, "coq:cmd.Ltac", "Ltac"], [54, 4, 1, "coq:flag.Ltac-Backtrace", "Ltac Backtrace"], [54, 4, 1, "coq:flag.Ltac-Batch-Debug", "Ltac Batch Debug"], [54, 4, 1, "coq:flag.Ltac-Debug", "Ltac Debug"], [54, 4, 1, "coq:flag.Ltac-Profiling", "Ltac Profiling"], [55, 3, 1, "coq:cmd.Ltac2", "Ltac2"], [55, 4, 1, "coq:flag.Ltac2-Backtrace", "Ltac2 Backtrace"], [55, 3, 1, "coq:cmd.Ltac2-Check", "Ltac2 Check"], [55, 3, 1, "coq:cmd.Ltac2-Eval", "Ltac2 Eval"], [55, 3, 1, "coq:cmd.Ltac2-Globalize", "Ltac2 Globalize"], [55, 4, 1, "coq:flag.Ltac2-In-Ltac1-Profiling", "Ltac2 In Ltac1 Profiling"], [55, 3, 1, "coq:cmd.Ltac2-Notation", "Ltac2 Notation"], [55, 3, 1, "coq:cmd.Ltac2-Notation-(abbreviation)", "Ltac2 Notation (abbreviation)"], [55, 3, 1, "coq:cmd.Ltac2-Set", "Ltac2 Set"], [55, 3, 1, "coq:cmd.Ltac2-Type", "Ltac2 Type"], [55, 4, 1, "coq:flag.Ltac2-Typed-Notations", "Ltac2 Typed Notations"], [55, 3, 1, "coq:cmd.Ltac2-external", "Ltac2 external"], [44, 2, 1, "coq:warn.Making-shadowed-name-of-implicit-argument-accessible-by-position", "Making shadowed name of implicit argument accessible by position"], [66, 4, 1, "coq:flag.Mangle-Names", "Mangle Names"], [66, 4, 1, "coq:flag.Mangle-Names-Light", "Mangle Names Light"], [66, 6, 1, "coq:opt.Mangle-Names-Prefix", "Mangle Names Prefix"], [44, 4, 1, "coq:flag.Maximal-Implicit-Insertion", "Maximal Implicit Insertion"], [71, 0, 1, "coq:exn.Missing-mapping-for-constructor-\u2018qualid\u2019", "Missing mapping for constructor \u2018qualid\u2019"], [35, 3, 1, "coq:cmd.Module", "Module"], [35, 3, 1, "coq:cmd.Module-Type", "Module Type"], [59, 0, 1, "coq:exn.Module/section-\u2018qualid\u2019-not-found", "Module/section \u2018qualid\u2019 not found"], [14, 7, 1, "coq:attr.Monomorphic", "Monomorphic"], [71, 0, 1, "coq:exn.More-than-one-interpretation-bound-to-this-notation,-confirm-with-the-\"all\"-modifier", "More than one interpretation bound to this notation, confirm with the "all" modifier"], [71, 0, 1, "coq:exn.Multiple-'via'-options", "Multiple 'via' options"], [71, 0, 1, "coq:exn.Multiple-'warning-after'-or-'abstract-after'-options", "Multiple 'warning after' or 'abstract after' options"], [64, 6, 1, "coq:opt.NativeCompute-Profile-Filename", "NativeCompute Profile Filename"], [64, 4, 1, "coq:flag.NativeCompute-Profiling", "NativeCompute Profiling"], [64, 4, 1, "coq:flag.NativeCompute-Timing", "NativeCompute Timing"], [66, 4, 1, "coq:flag.Nested-Proofs-Allowed", "Nested Proofs Allowed"], [66, 2, 1, "coq:warn.New-Collection-definition-of-\u2018ident\u2019-shadows-the-previous-one", "New Collection definition of \u2018ident\u2019 shadows the previous one"], [9, 3, 1, "coq:cmd.Next-Obligation", "Next Obligation"], [5, 4, 1, "coq:flag.Nia-Cache", "Nia Cache"], [54, 0, 1, "coq:exn.No-applicable-tactic", "No applicable tactic"], [72, 0, 1, "coq:exn.No-argument-name-\u2018ident\u2019", "No argument name \u2018ident\u2019"], [54, 0, 1, "coq:exn.No-evars", "No evars"], [35, 0, 1, "coq:exn.No-field-named-\u2018ident\u2019-in-\u2018qualid\u2019", "No field named \u2018ident\u2019 in \u2018qualid\u2019"], [66, 0, 1, "coq:exn.No-focused-proof", "No focused proof"], [66, 0, 1, "coq:exn.No-focused-proof-(No-proof-editing-in-progress)", "No focused proof (No proof-editing in progress)"], [66, 0, 1, "coq:exn.No-focused-proof-to-restart", "No focused proof to restart"], [64, 0, 1, "coq:exn.No-head-constant-to-reduce", "No head constant to reduce"], [54, 0, 1, "coq:exn.No-matching-clauses-for-match", "No matching clauses for match"], [54, 0, 1, "coq:exn.No-matching-clauses-for-match-goal", "No matching clauses for match goal"], [71, 0, 1, "coq:exn.No-notation-provided", "No notation provided"], [67, 0, 1, "coq:exn.No-primitive-equality-found", "No primitive equality found"], [58, 0, 1, "coq:exn.No-product-even-after-head-reduction", "No product even after head-reduction"], [3, 0, 1, "coq:exn.No-progress-made", "No progress made"], [58, 0, 1, "coq:exn.No-quantified-hypothesis-named-\u2018ident\u2019-in-current-goal-even-after-head-reduction", "No quantified hypothesis named \u2018ident\u2019 in current goal even after head-reduction"], [58, 0, 1, "coq:exn.No-such-assumption", "No such assumption"], [58, 0, 1, "coq:exn.No-such-binder", "No such binder"], [58, 0, 1, "coq:exn.No-such-bound-variable-\u2018ident\u2019-(no-bound-variables-at-all-in-the-expression)", "No such bound variable \u2018ident\u2019 (no bound variables at all in the expression)"], [66, 0, 1, "coq:exn.No-such-goal", "No such goal"], [66, 0, 1, "coq:exn.No-such-goal-(\u2018ident\u2019)", "No such goal (\u2018ident\u2019)"], [66, 0, 1, "coq:exn.No-such-goal-(\u2018natural\u2019)", "No such goal (\u2018natural\u2019)"], [58, 0, 1, "coq:exn.No-such-hypothesis:-\u2018ident\u2019", "No such hypothesis: \u2018ident\u2019"], [58, 0, 1, "coq:exn.No-\u2018natural\u2019-th-non-dependent-hypothesis-in-current-goal-even-after-head-reduction", "No \u2018natural\u2019-th non dependent hypothesis in current goal even after head-reduction"], [46, 0, 1, "coq:exn.Non-exhaustive-pattern-matching", "Non exhaustive pattern matching"], [9, 0, 1, "coq:exn.Non-extensible-universe-declaration-not-supported-with-monomorphic-Program-Definition", "Non extensible universe declaration not supported with monomorphic Program Definition"], [34, 0, 1, "coq:exn.Non-strictly-positive-occurrence-of-\u2018ident\u2019-in-\u2018type\u2019", "Non strictly positive occurrence of \u2018ident\u2019 in \u2018type\u2019"], [14, 7, 1, "coq:attr.NonCumulative", "NonCumulative"], [67, 4, 1, "coq:flag.Nonrecursive-Elimination-Schemes", "Nonrecursive Elimination Schemes"], [54, 0, 1, "coq:exn.Not-a-context-variable", "Not a context variable"], [67, 0, 1, "coq:exn.Not-a-discriminable-equality", "Not a discriminable equality"], [67, 0, 1, "coq:exn.Not-a-negated-primitive-equality", "Not a negated primitive equality"], [11, 0, 1, "coq:exn.Not-a-valid-ring-equation", "Not a valid ring equation"], [54, 0, 1, "coq:exn.Not-a-variable-or-hypothesis", "Not a variable or hypothesis"], [54, 0, 1, "coq:exn.Not-an-evar", "Not an evar"], [58, 0, 1, "coq:exn.Not-an-exact-proof", "Not an exact proof"], [67, 0, 1, "coq:exn.Not-an-inductive-goal-with-1-constructor", "Not an inductive goal with 1 constructor"], [67, 0, 1, "coq:exn.Not-an-inductive-goal-with-2-constructors", "Not an inductive goal with 2 constructors"], [67, 0, 1, "coq:exn.Not-an-inductive-product", "Not an inductive product"], [64, 0, 1, "coq:exn.Not-convertible", "Not convertible"], [67, 0, 1, "coq:exn.Not-enough-constructors", "Not enough constructors"], [44, 0, 1, "coq:exn.Not-enough-non-implicit-arguments-to-accept-the-argument-bound-to-\u2018ident\u2019", "Not enough non implicit arguments to accept the argument bound to \u2018ident\u2019"], [44, 0, 1, "coq:exn.Not-enough-non-implicit-arguments-to-accept-the-argument-bound-to-\u2018natural\u2019", "Not enough non implicit arguments to accept the argument bound to \u2018natural\u2019"], [54, 0, 1, "coq:exn.Not-equal", "Not equal"], [54, 0, 1, "coq:exn.Not-equal-(due-to-universes)", "Not equal (due to universes)"], [54, 0, 1, "coq:exn.Not-ground", "Not ground"], [72, 0, 1, "coq:exn.Not-the-right-number-of-induction-arguments", "Not the right number of induction arguments"], [58, 0, 1, "coq:exn.Not-the-right-number-of-missing-arguments-(expected-\u2018natural\u2019)", "Not the right number of missing arguments (expected \u2018natural\u2019)"], [71, 3, 1, "coq:cmd.Notation", "Notation"], [71, 3, 1, "coq:cmd.Notation-(abbreviation)", "Notation (abbreviation)"], [55, 0, 1, "coq:exn.Notation-levels-must-range-between-0-and-6", "Notation levels must range between 0 and 6"], [67, 0, 1, "coq:exn.Nothing-to-inject", "Nothing to inject"], [3, 0, 1, "coq:exn.Nothing-to-rewrite", "Nothing to rewrite"], [5, 4, 1, "coq:flag.Nra-Cache", "Nra Cache"], [71, 3, 1, "coq:cmd.Number-Notation", "Number Notation"], [9, 3, 1, "coq:cmd.Obligation", "Obligation"], [9, 3, 1, "coq:cmd.Obligation-Tactic", "Obligation Tactic"], [9, 3, 1, "coq:cmd.Obligations", "Obligations"], [64, 3, 1, "coq:cmd.Opaque", "Opaque"], [71, 3, 1, "coq:cmd.Open-Scope", "Open Scope"], [66, 3, 1, "coq:cmd.Optimize-Heap", "Optimize Heap"], [66, 3, 1, "coq:cmd.Optimize-Proof", "Optimize Proof"], [28, 3, 1, "coq:cmd.Parameter", "Parameter"], [28, 3, 1, "coq:cmd.Parameters", "Parameters"], [44, 4, 1, "coq:flag.Parsing-Explicit", "Parsing Explicit"], [14, 7, 1, "coq:attr.Polymorphic", "Polymorphic"], [14, 4, 1, "coq:flag.Polymorphic-Inductive-Cumulativity", "Polymorphic Inductive Cumulativity"], [14, 0, 1, "coq:exn.Polymorphic-universe-constraints-can-only-be-declared-inside-sections,-use-Monomorphic-Constraint-instead", "Polymorphic universe constraints can only be declared inside sections, use Monomorphic Constraint instead"], [14, 0, 1, "coq:exn.Polymorphic-universes-can-only-be-declared-inside-sections,-use-Monomorphic-Universe-instead", "Polymorphic universes can only be declared inside sections, use Monomorphic Universe instead"], [59, 4, 1, "coq:flag.Positivity-Checking", "Positivity Checking"], [57, 3, 1, "coq:cmd.Prenex-Implicits", "Prenex Implicits"], [9, 3, 1, "coq:cmd.Preterm", "Preterm"], [59, 3, 1, "coq:cmd.Primitive", "Primitive"], [37, 4, 1, "coq:flag.Primitive-Projections", "Primitive Projections"], [59, 3, 1, "coq:cmd.Print", "Print"], [59, 3, 1, "coq:cmd.Print-All", "Print All"], [59, 3, 1, "coq:cmd.Print-All-Dependencies", "Print All Dependencies"], [59, 3, 1, "coq:cmd.Print-Assumptions", "Print Assumptions"], [42, 3, 1, "coq:cmd.Print-Canonical-Projections", "Print Canonical Projections"], [4, 3, 1, "coq:cmd.Print-Classes", "Print Classes"], [4, 3, 1, "coq:cmd.Print-Coercion-Paths", "Print Coercion Paths"], [4, 3, 1, "coq:cmd.Print-Coercions", "Print Coercions"], [71, 3, 1, "coq:cmd.Print-Custom-Grammar", "Print Custom Grammar"], [66, 3, 1, "coq:cmd.Print-Debug-GC", "Print Debug GC"], [64, 3, 1, "coq:cmd.Print-Equivalent-Keys", "Print Equivalent Keys"], [2, 3, 1, "coq:cmd.Print-Extraction-Blacklist", "Print Extraction Blacklist"], [2, 3, 1, "coq:cmd.Print-Extraction-Callback", "Print Extraction Callback"], [2, 3, 1, "coq:cmd.Print-Extraction-Foreign", "Print Extraction Foreign"], [2, 3, 1, "coq:cmd.Print-Extraction-Inline", "Print Extraction Inline"], [11, 3, 1, "coq:cmd.Print-Fields", "Print Fields"], [62, 3, 1, "coq:cmd.Print-Firstorder-Solver", "Print Firstorder Solver"], [71, 3, 1, "coq:cmd.Print-Grammar", "Print Grammar"], [4, 3, 1, "coq:cmd.Print-Graph", "Print Graph"], [60, 3, 1, "coq:cmd.Print-Hint", "Print Hint"], [60, 3, 1, "coq:cmd.Print-HintDb", "Print HintDb"], [44, 3, 1, "coq:cmd.Print-Implicit", "Print Implicit"], [13, 3, 1, "coq:cmd.Print-Instances", "Print Instances"], [71, 3, 1, "coq:cmd.Print-Keywords", "Print Keywords"], [59, 3, 1, "coq:cmd.Print-Libraries", "Print Libraries"], [59, 3, 1, "coq:cmd.Print-LoadPath", "Print LoadPath"], [54, 3, 1, "coq:cmd.Print-Ltac", "Print Ltac"], [54, 3, 1, "coq:cmd.Print-Ltac-Signatures", "Print Ltac Signatures"], [55, 3, 1, "coq:cmd.Print-Ltac2", "Print Ltac2"], [55, 3, 1, "coq:cmd.Print-Ltac2-Signatures", "Print Ltac2 Signatures"], [55, 3, 1, "coq:cmd.Print-Ltac2-Type", "Print Ltac2 Type"], [59, 3, 1, "coq:cmd.Print-ML-Modules", "Print ML Modules"], [59, 3, 1, "coq:cmd.Print-ML-Path", "Print ML Path"], [35, 3, 1, "coq:cmd.Print-Module", "Print Module"], [35, 3, 1, "coq:cmd.Print-Module-Type", "Print Module Type"], [35, 3, 1, "coq:cmd.Print-Namespace", "Print Namespace"], [71, 3, 1, "coq:cmd.Print-Notation", "Print Notation"], [59, 3, 1, "coq:cmd.Print-Opaque-Dependencies", "Print Opaque Dependencies"], [29, 3, 1, "coq:cmd.Print-Options", "Print Options"], [59, 3, 1, "coq:cmd.Print-Registered", "Print Registered"], [59, 3, 1, "coq:cmd.Print-Registered-Schemes", "Print Registered Schemes"], [60, 3, 1, "coq:cmd.Print-Rewrite-HintDb", "Print Rewrite HintDb"], [11, 3, 1, "coq:cmd.Print-Rings", "Print Rings"], [71, 3, 1, "coq:cmd.Print-Scope", "Print Scope"], [71, 3, 1, "coq:cmd.Print-Scopes", "Print Scopes"], [59, 3, 1, "coq:cmd.Print-Section", "Print Section"], [64, 3, 1, "coq:cmd.Print-Strategies", "Print Strategies"], [64, 3, 1, "coq:cmd.Print-Strategy", "Print Strategy"], [29, 3, 1, "coq:cmd.Print-Table", "Print Table"], [29, 3, 1, "coq:cmd.Print-Tables", "Print Tables"], [59, 3, 1, "coq:cmd.Print-Transparent-Dependencies", "Print Transparent Dependencies"], [13, 3, 1, "coq:cmd.Print-Typeclasses", "Print Typeclasses"], [59, 3, 1, "coq:cmd.Print-Typing-Flags", "Print Typing Flags"], [14, 3, 1, "coq:cmd.Print-Universes", "Print Universes"], [71, 3, 1, "coq:cmd.Print-Visibility", "Print Visibility"], [59, 4, 1, "coq:flag.Printing-All", "Printing All"], [46, 4, 1, "coq:flag.Printing-Allow-Match-Default-Clause", "Printing Allow Match Default Clause"], [4, 8, 1, "coq:table.Printing-Coercion", "Printing Coercion"], [4, 4, 1, "coq:flag.Printing-Coercions", "Printing Coercions"], [59, 4, 1, "coq:flag.Printing-Compact-Contexts", "Printing Compact Contexts"], [37, 8, 1, "coq:table.Printing-Constructor", "Printing Constructor"], [59, 4, 1, "coq:flag.Printing-Dependent-Evars-Line", "Printing Dependent Evars Line"], [59, 6, 1, "coq:opt.Printing-Depth", "Printing Depth"], [43, 4, 1, "coq:flag.Printing-Existential-Instances", "Printing Existential Instances"], [46, 4, 1, "coq:flag.Printing-Factorizable-Match-Patterns", "Printing Factorizable Match Patterns"], [66, 4, 1, "coq:flag.Printing-Goal-Names", "Printing Goal Names"], [66, 4, 1, "coq:flag.Printing-Goal-Tags", "Printing Goal Tags"], [46, 8, 1, "coq:table.Printing-If", "Printing If"], [44, 4, 1, "coq:flag.Printing-Implicit", "Printing Implicit"], [44, 4, 1, "coq:flag.Printing-Implicit-Defensive", "Printing Implicit Defensive"], [46, 8, 1, "coq:table.Printing-Let", "Printing Let"], [46, 4, 1, "coq:flag.Printing-Match-All-Subterms", "Printing Match All Subterms"], [46, 4, 1, "coq:flag.Printing-Matching", "Printing Matching"], [71, 4, 1, "coq:flag.Printing-Notations", "Printing Notations"], [71, 4, 1, "coq:flag.Printing-Parentheses", "Printing Parentheses"], [37, 4, 1, "coq:flag.Printing-Primitive-Projection-Parameters", "Printing Primitive Projection Parameters"], [37, 4, 1, "coq:flag.Printing-Projections", "Printing Projections"], [71, 4, 1, "coq:flag.Printing-Raw-Literals", "Printing Raw Literals"], [37, 8, 1, "coq:table.Printing-Record", "Printing Record"], [37, 4, 1, "coq:flag.Printing-Records", "Printing Records"], [12, 4, 1, "coq:flag.Printing-Relevance-Marks", "Printing Relevance Marks"], [46, 4, 1, "coq:flag.Printing-Synth", "Printing Synth"], [59, 4, 1, "coq:flag.Printing-Unfocused", "Printing Unfocused"], [37, 4, 1, "coq:flag.Printing-Unfolded-Projection-As-Match", "Printing Unfolded Projection As Match"], [14, 4, 1, "coq:flag.Printing-Universes", "Printing Universes"], [44, 4, 1, "coq:flag.Printing-Use-Implicit-Types", "Printing Use Implicit Types"], [59, 6, 1, "coq:opt.Printing-Width", "Printing Width"], [46, 4, 1, "coq:flag.Printing-Wildcard", "Printing Wildcard"], [40, 7, 1, "coq:attr.Private", "Private"], [14, 4, 1, "coq:flag.Private-Polymorphic-Universes", "Private Polymorphic Universes"], [59, 3, 1, "coq:cmd.Profile", "Profile"], [9, 7, 1, "coq:attr.Program", "Program"], [9, 4, 1, "coq:flag.Program-Cases", "Program Cases"], [9, 4, 1, "coq:flag.Program-Generalized-Coercion", "Program Generalized Coercion"], [9, 4, 1, "coq:flag.Program-Mode", "Program Mode"], [66, 3, 1, "coq:cmd.Proof", "Proof"], [66, 3, 1, "coq:cmd.Proof-Mode", "Proof Mode"], [66, 3, 1, "coq:cmd.Proof-`term`", "Proof `term`"], [66, 3, 1, "coq:cmd.Proof-using", "Proof using"], [60, 3, 1, "coq:cmd.Proof-with", "Proof with"], [32, 3, 1, "coq:cmd.Property", "Property"], [32, 3, 1, "coq:cmd.Proposition", "Proposition"], [5, 5, 1, "coq:thm.Psatz", "Psatz"], [2, 3, 1, "coq:cmd.Pwd", "Pwd"], [66, 3, 1, "coq:cmd.Qed", "Qed"], [59, 3, 1, "coq:cmd.Quit", "Quit"], [37, 3, 1, "coq:cmd.Record", "Record"], [37, 0, 1, "coq:exn.Records-declared-with-the-keyword-Record-or-Structure-cannot-be-recursive", "Records declared with the keyword Record or Structure cannot be recursive"], [2, 3, 1, "coq:cmd.Recursive-Extraction", "Recursive Extraction"], [2, 3, 1, "coq:cmd.Recursive-Extraction-Library", "Recursive Extraction Library"], [59, 3, 1, "coq:cmd.Redirect", "Redirect"], [59, 3, 1, "coq:cmd.Register", "Register"], [59, 3, 1, "coq:cmd.Register-Inline", "Register Inline"], [59, 3, 1, "coq:cmd.Register-Scheme", "Register Scheme"], [64, 4, 1, "coq:flag.Regular-Subst-Tactic", "Regular Subst Tactic"], [32, 3, 1, "coq:cmd.Remark", "Remark"], [29, 3, 1, "coq:cmd.Remove", "Remove"], [60, 3, 1, "coq:cmd.Remove-Hints", "Remove Hints"], [59, 3, 1, "coq:cmd.Require", "Require"], [59, 3, 1, "coq:cmd.Require-Export", "Require Export"], [59, 3, 1, "coq:cmd.Require-Import", "Require Import"], [71, 3, 1, "coq:cmd.Reserved-Infix", "Reserved Infix"], [71, 3, 1, "coq:cmd.Reserved-Notation", "Reserved Notation"], [59, 3, 1, "coq:cmd.Reset", "Reset"], [2, 3, 1, "coq:cmd.Reset-Extraction-Blacklist", "Reset Extraction Blacklist"], [2, 3, 1, "coq:cmd.Reset-Extraction-Callback", "Reset Extraction Callback"], [2, 3, 1, "coq:cmd.Reset-Extraction-Inline", "Reset Extraction Inline"], [59, 3, 1, "coq:cmd.Reset-Initial", "Reset Initial"], [54, 3, 1, "coq:cmd.Reset-Ltac-Profile", "Reset Ltac Profile"], [66, 3, 1, "coq:cmd.Restart", "Restart"], [44, 4, 1, "coq:flag.Reversible-Pattern-Implicit", "Reversible Pattern Implicit"], [10, 3, 1, "coq:cmd.Rewrite-Rule", "Rewrite Rule"], [10, 3, 1, "coq:cmd.Rewrite-Rules", "Rewrite Rules"], [10, 0, 1, "coq:exn.Rewrite-rule-declaration-requires-passing-the-flag-\"-allow-rewrite-rules\"", "Rewrite rule declaration requires passing the flag "-allow-rewrite-rules""], [67, 4, 1, "coq:flag.Rewriting-Schemes", "Rewriting Schemes"], [11, 0, 1, "coq:exn.Ring-operation-should-be-declared-as-a-morphism", "Ring operation should be declared as a morphism"], [12, 0, 1, "coq:exn.SProp-is-disallowed-because-the-\"Allow-StrictProp\"-flag-is-off", "SProp is disallowed because the "Allow StrictProp" flag is off"], [66, 3, 1, "coq:cmd.Save", "Save"], [67, 3, 1, "coq:cmd.Scheme", "Scheme"], [67, 3, 1, "coq:cmd.Scheme-Boolean-Equality", "Scheme Boolean Equality"], [67, 3, 1, "coq:cmd.Scheme-Equality", "Scheme Equality"], [71, 0, 1, "coq:exn.Scope-delimiters-should-not-start-with-an-underscore", "Scope delimiters should not start with an underscore"], [71, 0, 1, "coq:exn.Scope-names-should-not-start-with-an-underscore", "Scope names should not start with an underscore"], [59, 3, 1, "coq:cmd.Search", "Search"], [59, 8, 1, "coq:table.Search-Blacklist", "Search Blacklist"], [59, 4, 1, "coq:flag.Search-Output-Name-Only", "Search Output Name Only"], [59, 3, 1, "coq:cmd.SearchPattern", "SearchPattern"], [59, 3, 1, "coq:cmd.SearchRewrite", "SearchRewrite"], [38, 3, 1, "coq:cmd.Section", "Section"], [64, 0, 1, "coq:exn.Section-variable-\u2018ident\u2019-occurs-implicitly-in-global-declaration-\u2018qualid\u2019-present-in-hypothesis-\u2018ident\u2019", "Section variable \u2018ident\u2019 occurs implicitly in global declaration \u2018qualid\u2019 present in hypothesis \u2018ident\u2019"], [64, 0, 1, "coq:exn.Section-variable-\u2018ident\u2019-occurs-implicitly-in-global-declaration-\u2018qualid\u2019-present-in-the-conclusion", "Section variable \u2018ident\u2019 occurs implicitly in global declaration \u2018qualid\u2019 present in the conclusion"], [2, 3, 1, "coq:cmd.Separate-Extraction", "Separate Extraction"], [29, 3, 1, "coq:cmd.Set", "Set"], [35, 4, 1, "coq:flag.Short-Module-Printing", "Short Module Printing"], [66, 3, 1, "coq:cmd.Show", "Show"], [66, 3, 1, "coq:cmd.Show-Conjectures", "Show Conjectures"], [66, 3, 1, "coq:cmd.Show-Existentials", "Show Existentials"], [2, 3, 1, "coq:cmd.Show-Extraction", "Show Extraction"], [66, 3, 1, "coq:cmd.Show-Goal", "Show Goal"], [66, 3, 1, "coq:cmd.Show-Intro", "Show Intro"], [66, 3, 1, "coq:cmd.Show-Intros", "Show Intros"], [5, 3, 1, "coq:cmd.Show-Lia-Profile", "Show Lia Profile"], [54, 3, 1, "coq:cmd.Show-Ltac-Profile", "Show Ltac Profile"], [66, 3, 1, "coq:cmd.Show-Match", "Show Match"], [9, 3, 1, "coq:cmd.Show-Obligation-Tactic", "Show Obligation Tactic"], [66, 3, 1, "coq:cmd.Show-Proof", "Show Proof"], [66, 3, 1, "coq:cmd.Show-Universes", "Show Universes"], [5, 3, 1, "coq:cmd.Show-Zify", "Show Zify"], [35, 0, 1, "coq:exn.Signature-components-for-field-\u2018ident\u2019-do-not-match", "Signature components for field \u2018ident\u2019 do not match"], [59, 4, 1, "coq:flag.Silent", "Silent"], [9, 3, 1, "coq:cmd.Solve-All-Obligations", "Solve All Obligations"], [9, 3, 1, "coq:cmd.Solve-Obligations", "Solve Obligations"], [66, 4, 1, "coq:flag.Solve-Unification-Constraints", "Solve Unification Constraints"], [57, 4, 1, "coq:flag.SsrHave-NoTCResolution", "SsrHave NoTCResolution"], [57, 4, 1, "coq:flag.SsrIdents", "SsrIdents"], [57, 4, 1, "coq:flag.SsrOldRewriteGoalsOrder", "SsrOldRewriteGoalsOrder"], [57, 4, 1, "coq:flag.SsrRewrite", "SsrRewrite"], [71, 2, 1, "coq:warn.Stack-overflow-or-segmentation-fault-happens-when-working-with-large-numbers-in-\u2018type\u2019-(threshold-may-vary-depending-on-your-system-limits-and-on-the-command-executed)", "Stack overflow or segmentation fault happens when working with large numbers in \u2018type\u2019 (threshold may vary depending on your system limits and on the command executed)"], [64, 3, 1, "coq:cmd.Strategy", "Strategy"], [44, 4, 1, "coq:flag.Strict-Implicit", "Strict Implicit"], [14, 4, 1, "coq:flag.Strict-Universe-Declaration", "Strict Universe Declaration"], [71, 3, 1, "coq:cmd.String-Notation", "String Notation"], [44, 4, 1, "coq:flag.Strongly-Strict-Implicit", "Strongly Strict Implicit"], [67, 4, 1, "coq:flag.Structural-Injection", "Structural Injection"], [37, 3, 1, "coq:cmd.Structure", "Structure"], [4, 3, 1, "coq:cmd.SubClass", "SubClass"], [59, 3, 1, "coq:cmd.Succeed", "Succeed"], [66, 4, 1, "coq:flag.Suggest-Proof-Using", "Suggest Proof Using"], [10, 3, 1, "coq:cmd.Symbol", "Symbol"], [10, 3, 1, "coq:cmd.Symbols", "Symbols"], [71, 0, 1, "coq:exn.Syntax-error:-[prim:reference]-expected-after-'Notation'-(in-[vernac:command])", "Syntax error: [prim:reference] expected after 'Notation' (in [vernac:command])"], [71, 0, 1, "coq:exn.Syntax-error:-[prim:reference]-expected-after-[prim:reference]-(in-[vernac:command])", "Syntax error: [prim:reference] expected after [prim:reference] (in [vernac:command])"], [71, 3, 1, "coq:cmd.Tactic-Notation", "Tactic Notation"], [54, 0, 1, "coq:exn.Tactic-failure", "Tactic failure"], [54, 0, 1, "coq:exn.Tactic-failure-(level-\u2018natural\u2019)", "Tactic failure (level \u2018natural\u2019)"], [54, 0, 1, "coq:exn.Tactic-failure:--succeeds", "Tactic failure: <tactic closure> succeeds"], [64, 0, 1, "coq:exn.Tactic-failure:-Setoid-library-not-loaded", "Tactic failure: Setoid library not loaded"], [64, 0, 1, "coq:exn.Tactic-generated-a-subgoal-identical-to-the-original-goal", "Tactic generated a subgoal identical to the original goal"], [64, 0, 1, "coq:exn.Terms-do-not-have-convertible-types", "Terms do not have convertible types"], [29, 3, 1, "coq:cmd.Test", "Test"], [60, 0, 1, "coq:exn.The-\"at\"-syntax-isn't-available-yet-for-the-autorewrite-tactic", "The "at" syntax isn't available yet for the autorewrite tactic"], [41, 0, 1, "coq:exn.The-&-modifier-may-only-occur-once", "The & modifier may only occur once"], [71, 2, 1, "coq:warn.The-'abstract-after'-directive-has-no-effect-when-the-parsing-function-(\u2018qualid\u2019)-targets-an-option-type", "The 'abstract after' directive has no effect when the parsing function (\u2018qualid\u2019) targets an option type"], [41, 0, 1, "coq:exn.The-'clear-implicits'-flag-must-be-omitted-if-implicit-annotations-are-given", "The 'clear implicits' flag must be omitted if implicit annotations are given"], [41, 0, 1, "coq:exn.The-'default-implicits'-flag-is-incompatible-with-implicit-annotations", "The 'default implicits' flag is incompatible with implicit annotations"], [41, 0, 1, "coq:exn.The-/-modifier-may-only-occur-once", "The / modifier may only occur once"], [59, 0, 1, "coq:exn.The-command-has-not-failed!", "The command has not failed!"], [34, 0, 1, "coq:exn.The-conclusion-of-\u2018type\u2019-is-not-valid;-it-must-be-built-from-\u2018ident\u2019", "The conclusion of \u2018type\u2019 is not valid; it must be built from \u2018ident\u2019"], [46, 0, 1, "coq:exn.The-constructor-\u2018ident\u2019-expects-\u2018natural\u2019-arguments", "The constructor \u2018ident\u2019 expects \u2018natural\u2019 arguments"], [14, 0, 1, "coq:exn.The-cumulative-attribute-can-only-be-used-in-a-polymorphic-context", "The cumulative attribute can only be used in a polymorphic context"], [46, 0, 1, "coq:exn.The-elimination-predicate-term-should-be-of-arity-\u2018natural\u2019-(for-non-dependent-case)-or-\u2018natural\u2019-(for-dependent-case)", "The elimination predicate term should be of arity \u2018natural\u2019 (for non dependent case) or \u2018natural\u2019 (for dependent case)"], [35, 0, 1, "coq:exn.The-field-\u2018ident\u2019-is-missing-in-\u2018qualid\u2019", "The field \u2018ident\u2019 is missing in \u2018qualid\u2019"], [72, 0, 1, "coq:exn.The-recursive-argument-must-be-specified", "The recursive argument must be specified"], [55, 0, 1, "coq:exn.The-reference-X-was-not-found-in-the-current-environment", "The reference X was not found in the current environment"], [64, 0, 1, "coq:exn.The-reference-is-not-unfoldable", "The reference is not unfoldable"], [64, 0, 1, "coq:exn.The-reference-\u2018qualid\u2019-was-not-found-in-the-current-environment", "The reference \u2018qualid\u2019 was not found in the current environment"], [58, 0, 1, "coq:exn.The-term-\"\u2018type\u2019\"-has-type-\"\u2018type\u2019\"-which-should-be-Set,-Prop-or-Type", "The term "\u2018type\u2019" has type "\u2018type\u2019" which should be Set, Prop or Type"], [2, 0, 1, "coq:exn.The-term-\u2018qualid\u2019-is-already-defined-as-foreign-custom-constant", "The term \u2018qualid\u2019 is already defined as foreign custom constant"], [2, 0, 1, "coq:exn.The-term-\u2018qualid\u2019-is-already-defined-as-inline-custom-constant", "The term \u2018qualid\u2019 is already defined as inline custom constant"], [32, 0, 1, "coq:exn.The-term-\u2018term\u2019-has-type-\u2018type\u2019-which-should-be-Set,-Prop-or-Type", "The term \u2018term\u2019 has type \u2018type\u2019 which should be Set, Prop or Type"], [32, 0, 1, "coq:exn.The-term-\u2018term\u2019-has-type-\u2018type\u2019-while-it-is-expected-to-have-type-\u2018type\u2019'", "The term \u2018term\u2019 has type \u2018type\u2019 while it is expected to have type \u2018type\u2019'"], [67, 0, 1, "coq:exn.The-type-has-no-constructors", "The type has no constructors"], [59, 0, 1, "coq:exn.The-type-\u2018ident\u2019-must-be-registered-before-this-construction-can-be-typechecked", "The type \u2018ident\u2019 must be registered before this construction can be typechecked"], [46, 0, 1, "coq:exn.The-variable-ident-is-bound-several-times-in-pattern-term", "The variable ident is bound several times in pattern term"], [58, 0, 1, "coq:exn.The-variable-\u2018ident\u2019-is-already-declared", "The variable \u2018ident\u2019 is already declared"], [40, 0, 1, "coq:exn.The-\u2018natural\u2019-th-argument-of-\u2018ident\u2019-must-be-\u2018ident\u2019-in-\u2018type\u2019", "The \u2018natural\u2019 th argument of \u2018ident\u2019 must be \u2018ident\u2019 in \u2018type\u2019"], [32, 3, 1, "coq:cmd.Theorem", "Theorem"], [54, 0, 1, "coq:exn.There-is-already-an-Ltac-named-\u2018qualid\u2019", "There is already an Ltac named \u2018qualid\u2019"], [54, 0, 1, "coq:exn.There-is-no-Ltac-named-\u2018qualid\u2019", "There is no Ltac named \u2018qualid\u2019"], [29, 2, 1, "coq:warn.There-is-no-flag-or-option-with-this-name:-\"\u2018setting_name\u2019\"", "There is no flag or option with this name: "\u2018setting_name\u2019""], [29, 0, 1, "coq:exn.There-is-no-flag,-option-or-table-with-this-name:-\"\u2018setting_name\u2019\"", "There is no flag, option or table with this name: "\u2018setting_name\u2019""], [29, 0, 1, "coq:exn.There-is-no-qualid-valued-table-with-this-name:-\"\u2018setting_name\u2019\"", "There is no qualid-valued table with this name: "\u2018setting_name\u2019""], [29, 0, 1, "coq:exn.There-is-no-string-valued-table-with-this-name:-\"\u2018setting_name\u2019\"", "There is no string-valued table with this name: "\u2018setting_name\u2019""], [38, 0, 1, "coq:exn.There-is-nothing-to-end", "There is nothing to end"], [29, 2, 1, "coq:warn.This-command-does-not-support-this-attribute", "This command does not support this attribute"], [59, 0, 1, "coq:exn.This-object-does-not-support-universe-names", "This object does not support universe names"], [66, 0, 1, "coq:exn.This-proof-is-focused,-but-cannot-be-unfocused-this-way", "This proof is focused, but cannot be unfocused this way"], [54, 0, 1, "coq:exn.This-tactic-has-more-than-one-success", "This tactic has more than one success"], [59, 3, 1, "coq:cmd.Time", "Time"], [59, 3, 1, "coq:cmd.Timeout", "Timeout"], [71, 2, 1, "coq:warn.To-avoid-stack-overflow,-large-numbers-in-\u2018type\u2019-are-interpreted-as-applications-of-\u2018qualid\u2019", "To avoid stack overflow, large numbers in \u2018type\u2019 are interpreted as applications of \u2018qualid\u2019"], [41, 0, 1, "coq:exn.To-rename-arguments-the-'rename'-flag-must-be-specified", "To rename arguments the 'rename' flag must be specified"], [64, 3, 1, "coq:cmd.Transparent", "Transparent"], [9, 4, 1, "coq:flag.Transparent-Obligations", "Transparent Obligations"], [35, 2, 1, "coq:warn.Trying-to-mask-the-absolute-name-\u2018qualid\u2019!", "Trying to mask the absolute name \u2018qualid\u2019!"], [59, 3, 1, "coq:cmd.Type", "Type"], [67, 0, 1, "coq:exn.Type-of-\u2018ident\u2019-is-not-an-equality-of-recognized-\u03a3-types:-expected-one-of-sig-sig2-sigT-sigT2-sigT2-ex-or-ex2-but-got-\u2018term\u2019", "Type of \u2018ident\u2019 is not an equality of recognized \u03a3 types: expected one of sig sig2 sigT sigT2 sigT2 ex or ex2 but got \u2018term\u2019"], [13, 4, 1, "coq:flag.Typeclass-Resolution-For-Conversion", "Typeclass Resolution For Conversion"], [13, 4, 1, "coq:flag.Typeclasses-Debug", "Typeclasses Debug"], [13, 6, 1, "coq:opt.Typeclasses-Debug-Verbosity", "Typeclasses Debug Verbosity"], [13, 6, 1, "coq:opt.Typeclasses-Default-Mode", "Typeclasses Default Mode"], [13, 4, 1, "coq:flag.Typeclasses-Dependency-Order", "Typeclasses Dependency Order"], [13, 6, 1, "coq:opt.Typeclasses-Depth", "Typeclasses Depth"], [13, 4, 1, "coq:flag.Typeclasses-Iterative-Deepening", "Typeclasses Iterative Deepening"], [13, 4, 1, "coq:flag.Typeclasses-Limit-Intros", "Typeclasses Limit Intros"], [13, 3, 1, "coq:cmd.Typeclasses-Opaque", "Typeclasses Opaque"], [13, 4, 1, "coq:flag.Typeclasses-Strict-Resolution", "Typeclasses Strict Resolution"], [13, 3, 1, "coq:cmd.Typeclasses-Transparent", "Typeclasses Transparent"], [13, 4, 1, "coq:flag.Typeclasses-Unique-Instances", "Typeclasses Unique Instances"], [13, 4, 1, "coq:flag.Typeclasses-Unique-Solutions", "Typeclasses Unique Solutions"], [13, 3, 1, "coq:cmd.Typeclasses-eauto", "Typeclasses eauto"], [67, 0, 1, "coq:exn.Unable-to-find-an-instance-for-the-variables-\u2018ident\u2019-\u2026-\u2018ident\u2019", "Unable to find an instance for the variables \u2018ident\u2019 \u2026 \u2018ident\u2019"], [58, 0, 1, "coq:exn.Unable-to-find-an-instance-for-the-variables-\u2018ident\u2019\u2026\u2018ident\u2019", "Unable to find an instance for the variables \u2018ident\u2019\u2026\u2018ident\u2019"], [46, 0, 1, "coq:exn.Unable-to-infer-a-match-predicate", "Unable to infer a match predicate"], [3, 0, 1, "coq:exn.Unable-to-satisfy-the-rewriting-constraints", "Unable to satisfy the rewriting constraints"], [58, 0, 1, "coq:exn.Unable-to-unify-\u2018one_term\u2019-with-\u2018one_term\u2019", "Unable to unify \u2018one_term\u2019 with \u2018one_term\u2019"], [55, 0, 1, "coq:exn.Unbound-[value|constructor]-X", "Unbound [value|constructor] X"], [54, 0, 1, "coq:exn.Unbound-context-identifier-\u2018ident\u2019", "Unbound context identifier \u2018ident\u2019"], [14, 0, 1, "coq:exn.Undeclared-universe-\u2018ident\u2019", "Undeclared universe \u2018ident\u2019"], [71, 3, 1, "coq:cmd.Undelimit-Scope", "Undelimit Scope"], [66, 3, 1, "coq:cmd.Undo", "Undo"], [71, 0, 1, "coq:exn.Unexpected-non-option-term-\u2018term\u2019-while-parsing-a-number-notation", "Unexpected non-option term \u2018term\u2019 while parsing a number notation"], [71, 0, 1, "coq:exn.Unexpected-non-option-term-\u2018term\u2019-while-parsing-a-string-notation", "Unexpected non-option term \u2018term\u2019 while parsing a string notation"], [71, 0, 1, "coq:exn.Unexpected-only-parsing-for-an-only-printing-notation", "Unexpected only parsing for an only printing notation"], [71, 0, 1, "coq:exn.Unexpected-only-printing-for-an-only-parsing-notation", "Unexpected only printing for an only parsing notation"], [71, 0, 1, "coq:exn.Unexpected-term-\u2018term\u2019-while-parsing-a-number-notation", "Unexpected term \u2018term\u2019 while parsing a number notation"], [71, 0, 1, "coq:exn.Unexpected-term-\u2018term\u2019-while-parsing-a-string-notation", "Unexpected term \u2018term\u2019 while parsing a string notation"], [66, 3, 1, "coq:cmd.Unfocus", "Unfocus"], [66, 3, 1, "coq:cmd.Unfocused", "Unfocused"], [34, 4, 1, "coq:flag.Uniform-Inductive-Parameters", "Uniform Inductive Parameters"], [14, 3, 1, "coq:cmd.Universe", "Universe"], [59, 4, 1, "coq:flag.Universe-Checking", "Universe Checking"], [14, 4, 1, "coq:flag.Universe-Minimization-ToSet", "Universe Minimization ToSet"], [14, 4, 1, "coq:flag.Universe-Polymorphism", "Universe Polymorphism"], [14, 0, 1, "coq:exn.Universe-inconsistency", "Universe inconsistency"], [59, 0, 1, "coq:exn.Universe-instance-length-is-\u2018natural\u2019-but-should-be-\u2018natural\u2019", "Universe instance length is \u2018natural\u2019 but should be \u2018natural\u2019"], [14, 3, 1, "coq:cmd.Universes", "Universes"], [71, 0, 1, "coq:exn.Unknown-custom-entry", "Unknown custom entry"], [71, 0, 1, "coq:exn.Unknown-custom-entry:-\u2018ident\u2019", "Unknown custom entry: \u2018ident\u2019"], [66, 0, 1, "coq:exn.Unknown-inductive-type", "Unknown inductive type"], [29, 3, 1, "coq:cmd.Unset", "Unset"], [66, 3, 1, "coq:cmd.Unshelve", "Unshelve"], [71, 0, 1, "coq:exn.Unterminated-string-in-notation", "Unterminated string in notation"], [28, 2, 1, "coq:warn.Use-of-\"Variable\"-or-\"Hypothesis\"-outside-sections-behaves-as-\"#[local]-Parameter\"-or-\"#[local]-Axiom\"", "Use of "Variable" or "Hypothesis" outside sections behaves as "#[local] Parameter" or "#[local] Axiom""], [71, 2, 1, "coq:warn.Use-of-\u2018string\u2019-Notation-is-deprecated-as-it-is-inconsistent-with-pattern-syntax", "Use of \u2018string\u2019 Notation is deprecated as it is inconsistent with pattern syntax"], [13, 2, 1, "coq:warn.Using-inferred-default-mode:-\u201cmode\u201d-for-\u201c\u2018ident\u2019\u201d", "Using inferred default mode: \u201cmode\u201d for \u201c\u2018ident\u2019\u201d"], [66, 3, 1, "coq:cmd.Validate-Proof", "Validate Proof"], [28, 3, 1, "coq:cmd.Variable", "Variable"], [66, 2, 1, "coq:warn.Variable-All-is-shadowed-by-Collection-named-All-containing-all-variables", "Variable All is shadowed by Collection named All containing all variables"], [28, 3, 1, "coq:cmd.Variables", "Variables"], [40, 3, 1, "coq:cmd.Variant", "Variant"], [59, 6, 1, "coq:opt.Warnings", "Warnings"], [44, 0, 1, "coq:exn.Wrong-argument-name", "Wrong argument name"], [44, 0, 1, "coq:exn.Wrong-argument-position", "Wrong argument position"], [66, 0, 1, "coq:exn.Wrong-bullet-\u2018bullet\u2019:-Bullet-\u2018bullet\u2019-is-mandatory-here", "Wrong bullet \u2018bullet\u2019: Bullet \u2018bullet\u2019 is mandatory here"], [66, 0, 1, "coq:exn.Wrong-bullet-\u2018bullet\u2019:-Current-bullet-\u2018bullet\u2019-is-not-finished", "Wrong bullet \u2018bullet\u2019: Current bullet \u2018bullet\u2019 is not finished"], [54, 1, 1, "coq:tacn.[-\u2026-|-\u2026-|-\u2026-]-(dispatch)", "[ \u2026 | \u2026 | \u2026 ] (dispatch)"], [54, 1, 1, "coq:tacn.[>-\u2026-|-\u2026-|-\u2026-]-(dispatch)", "[> \u2026 | \u2026 | \u2026 ] (dispatch)"], [55, 7, 1, "coq:attr.abstract", "abstract"], [66, 1, 1, "coq:tacn.abstract", "abstract"], [57, 1, 1, "coq:tacn.abstract-(ssreflect)", "abstract (ssreflect)"], [58, 1, 1, "coq:tacn.absurd", "absurd"], [71, 7, 1, "coq:attr.add_bottom", "add_bottom"], [71, 7, 1, "coq:attr.add_top", "add_top"], [66, 1, 1, "coq:tacn.admit", "admit"], [58, 1, 1, "coq:tacn.apply", "apply"], [57, 1, 1, "coq:tacn.apply-(ssreflect)", "apply (ssreflect)"], [58, 1, 1, "coq:tacn.assert", "assert"], [54, 1, 1, "coq:tacn.assert_fails", "assert_fails"], [54, 1, 1, "coq:tacn.assert_succeeds", "assert_succeeds"], [58, 1, 1, "coq:tacn.assumption", "assumption"], [60, 1, 1, "coq:tacn.auto", "auto"], [13, 1, 1, "coq:tacn.autoapply", "autoapply"], [60, 1, 1, "coq:tacn.autorewrite", "autorewrite"], [60, 1, 1, "coq:tacn.autounfold", "autounfold"], [60, 1, 1, "coq:tacn.autounfold_one", "autounfold_one"], [62, 1, 1, "coq:tacn.btauto", "btauto"], [66, 1, 1, "coq:tacn.bullet-(--+-*)", "bullet (- + *)"], [57, 1, 1, "coq:tacn.by", "by"], [59, 7, 1, "coq:attr.bypass_check(guard)", "bypass_check(guard)"], [59, 7, 1, "coq:attr.bypass_check(positivity)", "bypass_check(positivity)"], [59, 7, 1, "coq:attr.bypass_check(universes)", "bypass_check(universes)"], [42, 7, 1, "coq:attr.canonical", "canonical"], [67, 1, 1, "coq:tacn.case", "case"], [57, 1, 1, "coq:tacn.case-(ssreflect)", "case (ssreflect)"], [67, 1, 1, "coq:tacn.case_eq", "case_eq"], [64, 1, 1, "coq:tacn.cbn", "cbn"], [64, 1, 1, "coq:tacn.cbv", "cbv"], [64, 1, 1, "coq:tacn.change", "change"], [64, 1, 1, "coq:tacn.change_no_check", "change_no_check"], [58, 1, 1, "coq:tacn.classical_left", "classical_left"], [58, 1, 1, "coq:tacn.classical_right", "classical_right"], [58, 1, 1, "coq:tacn.clear", "clear"], [58, 1, 1, "coq:tacn.clear-dependent", "clear dependent"], [38, 7, 1, "coq:attr.clearbody", "clearbody"], [58, 1, 1, "coq:tacn.clearbody", "clearbody"], [71, 2, 1, "coq:warn.closed-notation-not-level-0", "closed-notation-not-level-0"], [67, 1, 1, "coq:tacn.cofix", "cofix"], [67, 1, 1, "coq:tacn.compare", "compare"], [64, 1, 1, "coq:tacn.compute", "compute"], [57, 1, 1, "coq:tacn.congr", "congr"], [62, 1, 1, "coq:tacn.congruence", "congruence"], [54, 1, 1, "coq:tacn.constr_eq", "constr_eq"], [54, 1, 1, "coq:tacn.constr_eq_nounivs", "constr_eq_nounivs"], [54, 1, 1, "coq:tacn.constr_eq_strict", "constr_eq_strict"], [67, 1, 1, "coq:tacn.constructor", "constructor"], [54, 1, 1, "coq:tacn.context", "context"], [58, 1, 1, "coq:tacn.contradict", "contradict"], [58, 1, 1, "coq:tacn.contradiction", "contradiction"], [54, 1, 1, "coq:tacn.convert", "convert"], [58, 1, 1, "coq:tacn.cut", "cut"], [66, 1, 1, "coq:tacn.cycle", "cycle"], [60, 1, 1, "coq:tacn.debug-auto", "debug auto"], [60, 1, 1, "coq:tacn.debug-eauto", "debug eauto"], [60, 1, 1, "coq:tacn.debug-trivial", "debug trivial"], [67, 1, 1, "coq:tacn.decide", "decide"], [67, 1, 1, "coq:tacn.decide-equality", "decide equality"], [67, 1, 1, "coq:tacn.decompose", "decompose"], [67, 1, 1, "coq:tacn.decompose-record", "decompose record"], [67, 1, 1, "coq:tacn.decompose-sum", "decompose sum"], [67, 1, 1, "coq:tacn.dependent-destruction", "dependent destruction"], [58, 1, 1, "coq:tacn.dependent-generalize_eqs", "dependent generalize_eqs"], [58, 1, 1, "coq:tacn.dependent-generalize_eqs_vars", "dependent generalize_eqs_vars"], [67, 1, 1, "coq:tacn.dependent-induction", "dependent induction"], [67, 1, 1, "coq:tacn.dependent-inversion", "dependent inversion"], [67, 1, 1, "coq:tacn.dependent-inversion_clear", "dependent inversion_clear"], [67, 1, 1, "coq:tacn.dependent-rewrite", "dependent rewrite"], [67, 1, 1, "coq:tacn.dependent-simple-inversion", "dependent simple inversion"], [74, 7, 1, "coq:attr.deprecated", "deprecated"], [67, 1, 1, "coq:tacn.destauto", "destauto"], [67, 1, 1, "coq:tacn.destruct", "destruct"], [62, 1, 1, "coq:tacn.dintuition", "dintuition"], [67, 1, 1, "coq:tacn.discriminate", "discriminate"], [54, 1, 1, "coq:tacn.do", "do"], [57, 1, 1, "coq:tacn.do-(ssreflect)", "do (ssreflect)"], [57, 1, 1, "coq:tacn.done", "done"], [62, 1, 1, "coq:tacn.dtauto", "dtauto"], [58, 1, 1, "coq:tacn.eapply", "eapply"], [58, 1, 1, "coq:tacn.eassert", "eassert"], [58, 1, 1, "coq:tacn.eassumption", "eassumption"], [60, 1, 1, "coq:tacn.easy", "easy"], [60, 1, 1, "coq:tacn.eauto", "eauto"], [67, 1, 1, "coq:tacn.ecase", "ecase"], [67, 1, 1, "coq:tacn.econstructor", "econstructor"], [67, 1, 1, "coq:tacn.edestruct", "edestruct"], [67, 1, 1, "coq:tacn.ediscriminate", "ediscriminate"], [67, 1, 1, "coq:tacn.eelim", "eelim"], [58, 1, 1, "coq:tacn.eenough", "eenough"], [58, 1, 1, "coq:tacn.eexact", "eexact"], [67, 1, 1, "coq:tacn.eexists", "eexists"], [67, 1, 1, "coq:tacn.einduction", "einduction"], [67, 1, 1, "coq:tacn.einjection", "einjection"], [58, 1, 1, "coq:tacn.eintros", "eintros"], [67, 1, 1, "coq:tacn.eleft", "eleft"], [67, 1, 1, "coq:tacn.elim", "elim"], [57, 1, 1, "coq:tacn.elim-(ssreflect)", "elim (ssreflect)"], [58, 1, 1, "coq:tacn.enough", "enough"], [58, 1, 1, "coq:tacn.epose", "epose"], [58, 1, 1, "coq:tacn.epose-proof", "epose proof"], [58, 1, 1, "coq:tacn.eremember", "eremember"], [64, 1, 1, "coq:tacn.erewrite", "erewrite"], [67, 1, 1, "coq:tacn.eright", "eright"], [58, 1, 1, "coq:tacn.eset", "eset"], [67, 1, 1, "coq:tacn.esimplify_eq", "esimplify_eq"], [67, 1, 1, "coq:tacn.esplit", "esplit"], [64, 1, 1, "coq:tacn.etransitivity", "etransitivity"], [64, 1, 1, "coq:tacn.eval", "eval"], [58, 1, 1, "coq:tacn.evar", "evar"], [58, 1, 1, "coq:tacn.exact", "exact"], [57, 1, 1, "coq:tacn.exact-(ssreflect)", "exact (ssreflect)"], [58, 1, 1, "coq:tacn.exact_no_check", "exact_no_check"], [54, 1, 1, "coq:tacn.exactly_once", "exactly_once"], [58, 1, 1, "coq:tacn.exfalso", "exfalso"], [67, 1, 1, "coq:tacn.exists", "exists"], [35, 7, 1, "coq:attr.export", "export"], [64, 1, 1, "coq:tacn.f_equal", "f_equal"], [54, 1, 1, "coq:tacn.fail", "fail"], [11, 1, 1, "coq:tacn.field", "field"], [11, 1, 1, "coq:tacn.field_lookup", "field_lookup"], [11, 1, 1, "coq:tacn.field_simplify", "field_simplify"], [11, 1, 1, "coq:tacn.field_simplify_eq", "field_simplify_eq"], [54, 1, 1, "coq:tacn.finish_timing", "finish_timing"], [54, 1, 1, "coq:tacn.first", "first"], [57, 1, 1, "coq:tacn.first-(ssreflect)", "first (ssreflect)"], [57, 9, 1, "coq:tacv.first-last", "first last"], [62, 1, 1, "coq:tacn.firstorder", "firstorder"], [67, 1, 1, "coq:tacn.fix", "fix"], [64, 1, 1, "coq:tacn.fold", "fold"], [54, 1, 1, "coq:tacn.fresh", "fresh"], [54, 1, 1, "coq:tacn.fun", "fun"], [72, 1, 1, "coq:tacn.functional-induction", "functional induction"], [72, 1, 1, "coq:tacn.functional-inversion", "functional inversion"], [58, 1, 1, "coq:tacn.generalize", "generalize"], [58, 1, 1, "coq:tacn.generalize-dependent", "generalize dependent"], [58, 1, 1, "coq:tacn.generalize_eqs", "generalize_eqs"], [58, 1, 1, "coq:tacn.generalize_eqs_vars", "generalize_eqs_vars"], [57, 1, 1, "coq:tacn.generally-have", "generally have"], [54, 1, 1, "coq:tacn.gfail", "gfail"], [66, 1, 1, "coq:tacn.give_up", "give_up"], [35, 7, 1, "coq:attr.global", "global"], [54, 1, 1, "coq:tacn.guard", "guard"], [54, 1, 1, "coq:tacn.has_evar", "has_evar"], [57, 1, 1, "coq:tacn.have", "have"], [3, 1, 1, "coq:tacn.head_of_constr", "head_of_constr"], [64, 1, 1, "coq:tacn.hnf", "hnf"], [54, 1, 1, "coq:tacn.idtac", "idtac"], [55, 1, 1, "coq:tacn.if-then-else-(Ltac2)", "if-then-else (Ltac2)"], [57, 1, 1, "coq:tacn.in", "in"], [67, 1, 1, "coq:tacn.induction", "induction"], [54, 3, 1, "coq:cmd.infoH", "infoH"], [60, 1, 1, "coq:tacn.info_auto", "info_auto"], [60, 1, 1, "coq:tacn.info_eauto", "info_eauto"], [60, 1, 1, "coq:tacn.info_trivial", "info_trivial"], [67, 1, 1, "coq:tacn.injection", "injection"], [58, 1, 1, "coq:tacn.instantiate", "instantiate"], [58, 1, 1, "coq:tacn.intro", "intro"], [58, 1, 1, "coq:tacn.intros", "intros"], [58, 1, 1, "coq:tacn.intros-until", "intros until"], [62, 1, 1, "coq:tacn.intuition", "intuition"], [67, 1, 1, "coq:tacn.inversion", "inversion"], [67, 1, 1, "coq:tacn.inversion_clear", "inversion_clear"], [67, 1, 1, "coq:tacn.inversion_sigma", "inversion_sigma"], [54, 1, 1, "coq:tacn.is_cofix", "is_cofix"], [54, 1, 1, "coq:tacn.is_const", "is_const"], [54, 1, 1, "coq:tacn.is_constructor", "is_constructor"], [54, 1, 1, "coq:tacn.is_evar", "is_evar"], [54, 1, 1, "coq:tacn.is_fix", "is_fix"], [54, 1, 1, "coq:tacn.is_ground", "is_ground"], [54, 1, 1, "coq:tacn.is_ind", "is_ind"], [54, 1, 1, "coq:tacn.is_proj", "is_proj"], [54, 1, 1, "coq:tacn.is_var", "is_var"], [58, 1, 1, "coq:tacn.lapply", "lapply"], [58, 0, 1, "coq:exn.lapply-needs-a-non-dependent-product", "lapply needs a non-dependent product"], [57, 1, 1, "coq:tacn.last", "last"], [57, 9, 1, "coq:tacv.last-first", "last first"], [64, 1, 1, "coq:tacn.lazy", "lazy"], [55, 1, 1, "coq:tacn.lazy_match!", "lazy_match!"], [55, 1, 1, "coq:tacn.lazy_match!-goal", "lazy_match! goal"], [54, 1, 1, "coq:tacn.lazymatch", "lazymatch"], [54, 1, 1, "coq:tacn.lazymatch-goal", "lazymatch goal"], [67, 1, 1, "coq:tacn.left", "left"], [54, 1, 1, "coq:tacn.let", "let"], [5, 1, 1, "coq:tacn.lia", "lia"], [35, 7, 1, "coq:attr.local", "local"], [5, 1, 1, "coq:tacn.lra", "lra"], [54, 1, 1, "coq:tacn.ltac-seq", "ltac-seq"], [54, 1, 1, "coq:tacn.match", "match"], [55, 1, 1, "coq:tacn.match-(Ltac2)", "match (Ltac2)"], [54, 1, 1, "coq:tacn.match-goal", "match goal"], [55, 1, 1, "coq:tacn.match!", "match!"], [55, 1, 1, "coq:tacn.match!-goal", "match! goal"], [60, 2, 1, "coq:warn.mismatched-hint-db", "mismatched-hint-db"], [13, 7, 1, "coq:attr.mode", "mode"], [58, 1, 1, "coq:tacn.move", "move"], [57, 1, 1, "coq:tacn.move-(ssreflect)", "move (ssreflect)"], [55, 1, 1, "coq:tacn.multi_match!", "multi_match!"], [55, 1, 1, "coq:tacn.multi_match!-goal", "multi_match! goal"], [54, 1, 1, "coq:tacn.multimatch", "multimatch"], [54, 1, 1, "coq:tacn.multimatch-goal", "multimatch goal"], [58, 1, 1, "coq:tacn.native_cast_no_check", "native_cast_no_check"], [64, 1, 1, "coq:tacn.native_compute", "native_compute"], [5, 1, 1, "coq:tacn.nia", "nia"], [4, 7, 1, "coq:attr.nonuniform", "nonuniform"], [54, 0, 1, "coq:exn.not-a-cofix-definition", "not a cofix definition"], [54, 0, 1, "coq:exn.not-a-constant", "not a constant"], [54, 0, 1, "coq:exn.not-a-constructor", "not a constructor"], [54, 0, 1, "coq:exn.not-a-fix-definition", "not a fix definition"], [54, 0, 1, "coq:exn.not-a-primitive-projection", "not a primitive projection"], [54, 0, 1, "coq:exn.not-an-(co)inductive-datatype", "not an (co)inductive datatype"], [54, 1, 1, "coq:tacn.not_evar", "not_evar"], [71, 2, 1, "coq:warn.notation-incompatible-prefix", "notation-incompatible-prefix"], [60, 1, 1, "coq:tacn.now", "now"], [64, 1, 1, "coq:tacn.now_show", "now_show"], [5, 1, 1, "coq:tacn.nra", "nra"], [7, 1, 1, "coq:tacn.nsatz", "nsatz"], [7, 1, 1, "coq:tacn.nsatz_compute", "nsatz_compute"], [54, 1, 1, "coq:tacn.numgoals", "numgoals"], [54, 1, 1, "coq:tacn.once", "once"], [54, 1, 1, "coq:tacn.only", "only"], [54, 1, 1, "coq:tacn.optimize_heap", "optimize_heap"], [57, 1, 1, "coq:tacn.over", "over"], [71, 0, 1, "coq:exn.overflow-in-int63-literal-\u2018bigint\u2019", "overflow in int63 literal \u2018bigint\u2019"], [64, 1, 1, "coq:tacn.pattern", "pattern"], [58, 1, 1, "coq:tacn.pose", "pose"], [57, 1, 1, "coq:tacn.pose-(ssreflect)", "pose (ssreflect)"], [58, 1, 1, "coq:tacn.pose-proof", "pose proof"], [71, 2, 1, "coq:warn.postfix-notation-not-level-1", "postfix-notation-not-level-1"], [40, 7, 1, "coq:attr.private(matching)", "private(matching)"], [9, 7, 1, "coq:attr.program", "program"], [54, 1, 1, "coq:tacn.progress", "progress"], [37, 7, 1, "coq:attr.projections(primitive)", "projections(primitive)"], [11, 1, 1, "coq:tacn.protect_fv", "protect_fv"], [5, 1, 1, "coq:tacn.psatz", "psatz"], [59, 0, 1, "coq:exn.public-name-according-to-findlib,-for-example", "public name according to findlib, for example"], [58, 1, 1, "coq:tacn.rapply", "rapply"], [64, 1, 1, "coq:tacn.red", "red"], [13, 7, 1, "coq:attr.refine", "refine"], [58, 1, 1, "coq:tacn.refine", "refine"], [64, 1, 1, "coq:tacn.reflexivity", "reflexivity"], [58, 1, 1, "coq:tacn.remember", "remember"], [58, 1, 1, "coq:tacn.rename", "rename"], [54, 1, 1, "coq:tacn.repeat", "repeat"], [64, 1, 1, "coq:tacn.replace", "replace"], [54, 1, 1, "coq:tacn.reset-ltac-profile", "reset ltac profile"], [54, 1, 1, "coq:tacn.restart_timer", "restart_timer"], [4, 7, 1, "coq:attr.reversible", "reversible"], [58, 1, 1, "coq:tacn.revert", "revert"], [58, 1, 1, "coq:tacn.revert-dependent", "revert dependent"], [66, 1, 1, "coq:tacn.revgoals", "revgoals"], [64, 1, 1, "coq:tacn.rewrite", "rewrite"], [57, 1, 1, "coq:tacn.rewrite-(ssreflect)", "rewrite (ssreflect)"], [64, 1, 1, "coq:tacn.rewrite-*", "rewrite *"], [3, 1, 1, "coq:tacn.rewrite_db", "rewrite_db"], [3, 1, 1, "coq:tacn.rewrite_strat", "rewrite_strat"], [67, 1, 1, "coq:tacn.right", "right"], [11, 1, 1, "coq:tacn.ring", "ring"], [11, 1, 1, "coq:tacn.ring_lookup", "ring_lookup"], [11, 1, 1, "coq:tacn.ring_simplify", "ring_simplify"], [62, 1, 1, "coq:tacn.rtauto", "rtauto"], [58, 1, 1, "coq:tacn.set", "set"], [57, 1, 1, "coq:tacn.set-(ssreflect)", "set (ssreflect)"], [3, 1, 1, "coq:tacn.setoid_etransitivity", "setoid_etransitivity"], [3, 1, 1, "coq:tacn.setoid_reflexivity", "setoid_reflexivity"], [3, 1, 1, "coq:tacn.setoid_replace", "setoid_replace"], [3, 1, 1, "coq:tacn.setoid_rewrite", "setoid_rewrite"], [3, 1, 1, "coq:tacn.setoid_symmetry", "setoid_symmetry"], [3, 1, 1, "coq:tacn.setoid_transitivity", "setoid_transitivity"], [59, 0, 1, "coq:exn.shared-library-failed:-Coq-Error:-\u2018string\u2019-is-not-a-valid", "shared library failed: Coq Error: \u2018string\u2019 is not a valid"], [66, 1, 1, "coq:tacn.shelve", "shelve"], [66, 1, 1, "coq:tacn.shelve_unifiable", "shelve_unifiable"], [54, 1, 1, "coq:tacn.show-ltac-profile", "show ltac profile"], [64, 1, 1, "coq:tacn.simpl", "simpl"], [58, 1, 1, "coq:tacn.simple-apply", "simple apply"], [62, 1, 1, "coq:tacn.simple-congruence", "simple congruence"], [67, 1, 1, "coq:tacn.simple-destruct", "simple destruct"], [58, 1, 1, "coq:tacn.simple-eapply", "simple eapply"], [67, 1, 1, "coq:tacn.simple-induction", "simple induction"], [67, 1, 1, "coq:tacn.simple-injection", "simple injection"], [67, 1, 1, "coq:tacn.simple-inversion", "simple inversion"], [64, 1, 1, "coq:tacn.simple-subst", "simple subst"], [67, 1, 1, "coq:tacn.simplify_eq", "simplify_eq"], [72, 1, 1, "coq:tacn.soft-functional-induction", "soft functional induction"], [54, 1, 1, "coq:tacn.solve", "solve"], [66, 1, 1, "coq:tacn.solve_constraints", "solve_constraints"], [58, 1, 1, "coq:tacn.specialize", "specialize"], [58, 1, 1, "coq:tacn.specialize_eqs", "specialize_eqs"], [67, 1, 1, "coq:tacn.split", "split"], [54, 1, 1, "coq:tacn.start-ltac-profiling", "start ltac profiling"], [64, 1, 1, "coq:tacn.stepl", "stepl"], [64, 1, 1, "coq:tacn.stepr", "stepr"], [54, 1, 1, "coq:tacn.stop-ltac-profiling", "stop ltac profiling"], [64, 1, 1, "coq:tacn.subst", "subst"], [64, 1, 1, "coq:tacn.substitute", "substitute"], [57, 1, 1, "coq:tacn.suff", "suff"], [57, 1, 1, "coq:tacn.suffices", "suffices"], [66, 1, 1, "coq:tacn.swap", "swap"], [64, 1, 1, "coq:tacn.symmetry", "symmetry"], [62, 1, 1, "coq:tacn.tauto", "tauto"], [34, 0, 1, "coq:exn.template-and-polymorphism-not-compatible", "template and polymorphism not compatible"], [54, 1, 1, "coq:tacn.time", "time"], [54, 1, 1, "coq:tacn.time_constr", "time_constr"], [54, 1, 1, "coq:tacn.timeout", "timeout"], [64, 1, 1, "coq:tacn.transitivity", "transitivity"], [66, 1, 1, "coq:tacn.transparent_abstract", "transparent_abstract"], [60, 1, 1, "coq:tacn.trivial", "trivial"], [54, 1, 1, "coq:tacn.try", "try"], [54, 1, 1, "coq:tacn.tryif", "tryif"], [54, 1, 1, "coq:tacn.type-of", "type of"], [54, 1, 1, "coq:tacn.type_term", "type_term"], [13, 1, 1, "coq:tacn.typeclasses-eauto", "typeclasses eauto"], [57, 1, 1, "coq:tacn.under", "under"], [64, 1, 1, "coq:tacn.unfold", "unfold"], [54, 1, 1, "coq:tacn.unify", "unify"], [14, 7, 1, "coq:attr.universes(cumulative)", "universes(cumulative)"], [14, 7, 1, "coq:attr.universes(polymorphic)", "universes(polymorphic)"], [34, 7, 1, "coq:attr.universes(template)", "universes(template)"], [57, 1, 1, "coq:tacn.unlock", "unlock"], [66, 1, 1, "coq:tacn.unshelve", "unshelve"], [66, 7, 1, "coq:attr.using", "using"], [58, 1, 1, "coq:tacn.vm_cast_no_check", "vm_cast_no_check"], [64, 1, 1, "coq:tacn.vm_compute", "vm_compute"], [74, 7, 1, "coq:attr.warn", "warn"], [29, 7, 1, "coq:attr.warning", "warning"], [29, 7, 1, "coq:attr.warnings", "warnings"], [64, 1, 1, "coq:tacn.with_strategy", "with_strategy"], [57, 1, 1, "coq:tacn.without-loss", "without loss"], [5, 1, 1, "coq:tacn.wlia", "wlia"], [57, 1, 1, "coq:tacn.wlog", "wlog"], [5, 1, 1, "coq:tacn.wlra_Q", "wlra_Q"], [5, 1, 1, "coq:tacn.wnia", "wnia"], [5, 1, 1, "coq:tacn.wnra_Q", "wnra_Q"], [5, 1, 1, "coq:tacn.wpsatz_Q", "wpsatz_Q"], [5, 1, 1, "coq:tacn.wpsatz_Z", "wpsatz_Z"], [5, 1, 1, "coq:tacn.wsos_Q", "wsos_Q"], [5, 1, 1, "coq:tacn.wsos_Z", "wsos_Z"], [5, 1, 1, "coq:tacn.xlia", "xlia"], [5, 1, 1, "coq:tacn.xlra_Q", "xlra_Q"], [5, 1, 1, "coq:tacn.xlra_R", "xlra_R"], [5, 1, 1, "coq:tacn.xnia", "xnia"], [5, 1, 1, "coq:tacn.xnra_Q", "xnra_Q"], [5, 1, 1, "coq:tacn.xnra_R", "xnra_R"], [5, 1, 1, "coq:tacn.xpsatz_Q", "xpsatz_Q"], [5, 1, 1, "coq:tacn.xpsatz_R", "xpsatz_R"], [5, 1, 1, "coq:tacn.xpsatz_Z", "xpsatz_Z"], [5, 1, 1, "coq:tacn.xsos_Q", "xsos_Q"], [5, 1, 1, "coq:tacn.xsos_R", "xsos_R"], [5, 1, 1, "coq:tacn.xsos_Z", "xsos_Z"], [5, 1, 1, "coq:tacn.zify", "zify"], [5, 1, 1, "coq:tacn.zify_elim_let", "zify_elim_let"], [5, 1, 1, "coq:tacn.zify_iter_let", "zify_iter_let"], [5, 1, 1, "coq:tacn.zify_iter_specs", "zify_iter_specs"], [5, 1, 1, "coq:tacn.zify_op", "zify_op"], [5, 1, 1, "coq:tacn.zify_saturate", "zify_saturate"], [66, 1, 1, "coq:tacn.{", "{"], [54, 1, 1, "coq:tacn.||-(first-tactic-making-progress)", "|| (first tactic making progress)"], [66, 1, 1, "coq:tacn.}", "}"], [4, 0, 1, "coq:exn.\u2018coercion_class\u2019-must-be-a-transparent-constant", "\u2018coercion_class\u2019 must be a transparent constant"], [37, 0, 1, "coq:exn.\u2018ident\u2019-already-exists", "\u2018ident\u2019 already exists"], [37, 2, 1, "coq:warn.\u2018ident\u2019-cannot-be-defined", "\u2018ident\u2019 cannot be defined"], [37, 2, 1, "coq:warn.\u2018ident\u2019-cannot-be-defined-because-it-is-informative-and-\u2018ident\u2019-is-not", "\u2018ident\u2019 cannot be defined because it is informative and \u2018ident\u2019 is not"], [37, 2, 1, "coq:warn.\u2018ident\u2019-cannot-be-defined-because-the-projection-\u2018ident\u2019-was-not-defined", "\u2018ident\u2019 cannot be defined because the projection \u2018ident\u2019 was not defined"], [13, 2, 1, "coq:warn.\u2018ident\u2019-is-already-declared-as-a-typeclass", "\u2018ident\u2019 is already declared as a typeclass"], [58, 0, 1, "coq:exn.\u2018ident\u2019-is-already-used", "\u2018ident\u2019 is already used"], [66, 2, 1, "coq:warn.\u2018ident\u2019-is-both-name-of-a-Collection-and-Variable,-Collection-\u2018ident\u2019-takes-precedence-over-Variable", "\u2018ident\u2019 is both name of a Collection and Variable, Collection \u2018ident\u2019 takes precedence over Variable"], [58, 0, 1, "coq:exn.\u2018ident\u2019-is-not-a-local-definition", "\u2018ident\u2019 is not a local definition"], [67, 0, 1, "coq:exn.\u2018ident\u2019-is-not-an-equality-of-\u03a3-types", "\u2018ident\u2019 is not an equality of \u03a3 types"], [64, 0, 1, "coq:exn.\u2018ident\u2019-is-opaque", "\u2018ident\u2019 is opaque"], [58, 0, 1, "coq:exn.\u2018ident\u2019-is-used-in-the-conclusion", "\u2018ident\u2019 is used in the conclusion"], [58, 0, 1, "coq:exn.\u2018ident\u2019-is-used-in-the-hypothesis-\u2018ident\u2019", "\u2018ident\u2019 is used in the hypothesis \u2018ident\u2019"], [66, 2, 1, "coq:warn.\u2018ident\u2019-was-already-a-defined-Variable,-the-name-\u2018ident\u2019-will-refer-to-Collection-when-executing-\"Proof-using\"-command", "\u2018ident\u2019 was already a defined Variable, the name \u2018ident\u2019 will refer to Collection when executing "Proof using" command"], [60, 0, 1, "coq:exn.\u2018qualid\u2019-cannot-be-used-as-a-hint", "\u2018qualid\u2019 cannot be used as a hint"], [64, 0, 1, "coq:exn.\u2018qualid\u2019-does-not-occur", "\u2018qualid\u2019 does not occur"], [4, 2, 1, "coq:warn.\u2018qualid\u2019-does-not-respect-the-uniform-inheritance-condition", "\u2018qualid\u2019 does not respect the uniform inheritance condition"], [4, 0, 1, "coq:exn.\u2018qualid\u2019-is-already-a-coercion", "\u2018qualid\u2019 is already a coercion"], [71, 0, 1, "coq:exn.\u2018qualid\u2019-is-bound-to-a-notation-that-does-not-denote-a-reference", "\u2018qualid\u2019 is bound to a notation that does not denote a reference"], [4, 0, 1, "coq:exn.\u2018qualid\u2019-is-not-a-function", "\u2018qualid\u2019 is not a function"], [35, 0, 1, "coq:exn.\u2018qualid\u2019-is-not-a-module", "\u2018qualid\u2019 is not a module"], [60, 0, 1, "coq:exn.\u2018qualid\u2019-is-not-an-inductive-type", "\u2018qualid\u2019 is not an inductive type"], [59, 0, 1, "coq:exn.\u2018qualid\u2019-not-a-defined-object", "\u2018qualid\u2019 not a defined object"], [4, 0, 1, "coq:exn.\u2018qualid\u2019-not-declared", "\u2018qualid\u2019 not declared"], [71, 0, 1, "coq:exn.\u2018qualid\u2019-was-already-mapped-to-\u2018qualid\u2019-and-cannot-be-remapped-to-\u2018qualid\u2019", "\u2018qualid\u2019 was already mapped to \u2018qualid\u2019 and cannot be remapped to \u2018qualid\u2019"], [74, 2, 1, "coq:warn.\u2018string\u2019", "\u2018string\u2019"], [71, 0, 1, "coq:exn.\u2018type\u2019-is-not-an-inductive-type", "\u2018type\u2019 is not an inductive type"], [71, 2, 1, "coq:warn.\u2018type\u2019-was-already-mapped-to-\u2018type\u2019,-mapping-it-also-to-\u2018type\u2019-might-yield-ill-typed-terms-when-using-the-notation", "\u2018type\u2019 was already mapped to \u2018type\u2019, mapping it also to \u2018type\u2019 might yield ill typed terms when using the notation"], [54, 1, 1, "coq:tacn.\u2026-:-\u2026-(goal-selector)", "\u2026 : \u2026 (goal selector)"], [57, 1, 1, "coq:tacn.\u2026-:-\u2026-(ssreflect)", "\u2026 : \u2026 (ssreflect)"]], "..": [[4, 2, 1, "coq:warn....-is-not-definitionally-an-identity-function", " is not definitionally an identity function"]], "Argument \u2018name\u2019 is a trailing implicit, so it can't be declared non maximal": [[44, 0, 1, "coq:exn.Argument-\u2018name\u2019-is-a-trailing-implicit,-so-it-can't-be-declared-non-maximal.-Please-use-{-}-instead-of-[-]", " Please use { } instead of [ ]"]], "Cannot infer a term for this placeholder": [[44, 0, 1, "coq:exn.Cannot-infer-a-term-for-this-placeholder.-(Casual-use-of-implicit-arguments)", " (Casual use of implicit arguments)"], [58, 0, 1, "coq:exn.Cannot-infer-a-term-for-this-placeholder.-(refine)", " (refine)"]], "Compiled library \u2018ident\u2019": [[59, 0, 1, "coq:exn.Compiled-library-\u2018ident\u2019.vo-makes-inconsistent-assumptions-over-library-\u2018qualid\u2019", "vo makes inconsistent assumptions over library \u2018qualid\u2019"]], "Duplicate clear of H": [[57, 2, 1, "coq:warn.Duplicate-clear-of-H.-Use-{-}H-instead-of-{-H-}H", " Use { }H instead of { H }H"]], "File ... found twice in ..": [[59, 2, 1, "coq:warn.File-...-found-twice-in-...", ""]], "Goal is solvable by congruence but some arguments are missing": [[62, 0, 1, "coq:exn.Goal-is-solvable-by-congruence-but-some-arguments-are-missing.-Try-congruence-with-\u2018term\u2019\u2026\u2018term\u2019,-replacing-metavariables-by-arbitrary-terms", " Try congruence with \u2018term\u2019\u2026\u2018term\u2019, replacing metavariables by arbitrary terms"]], "Library File (transitively required) \u2018qualid\u2019 is deprecated since \u2018string\u2019. \u2018string\u2019": [[74, 2, 1, "coq:warn.Library-File-(transitively-required)-\u2018qualid\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019.-Use-\u2018qualid\u2019-instead", " Use \u2018qualid\u2019 instead"]], "Library File \u2018qualid\u2019 is deprecated since \u2018string\u2019. \u2018string\u2019": [[74, 2, 1, "coq:warn.Library-File-\u2018qualid\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019.-Use-\u2018qualid\u2019-instead", " Use \u2018qualid\u2019 instead"]], "Ltac Profiler encountered an invalid stack (no self node)": [[54, 2, 1, "coq:warn.Ltac-Profiler-encountered-an-invalid-stack-(no-self-node).-This-can-happen-if-you-reset-the-profile-during-tactic-execution", " This can happen if you reset the profile during tactic execution"]], "Ltac2 alias \u2018qualid\u2019 is deprecated since \u2018string\u2019": [[74, 2, 1, "coq:warn.Ltac2-alias-\u2018qualid\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019", " \u2018string\u2019"]], "Ltac2 constructor \u2018qualid\u2019 is deprecated since \u2018string\u2019": [[74, 2, 1, "coq:warn.Ltac2-constructor-\u2018qualid\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019", " \u2018string\u2019"]], "Ltac2 definition \u2018qualid\u2019 is deprecated since \u2018string\u2019": [[74, 2, 1, "coq:warn.Ltac2-definition-\u2018qualid\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019", " \u2018string\u2019"]], "Ltac2 notation \u2018ltac2_scope\u2019\u2026\u2018ltac2_scope\u2019 is deprecated since \u2018string\u2019": [[74, 2, 1, "coq:warn.Ltac2-notation-\u2018ltac2_scope\u2019\u2026\u2018ltac2_scope\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019", " \u2018string\u2019"]], "Nested proofs are discouraged and not allowed by default. This error probably means that you forgot to close the last "Proof." with "Qed." or "Defined."": [[32, 0, 1, "coq:exn.Nested-proofs-are-discouraged-and-not-allowed-by-default.-This-error-probably-means-that-you-forgot-to-close-the-last-\"Proof.\"-with-\"Qed.\"-or-\"Defined.\".-If-you-really-intended-to-use-nested-proofs,-you-can-do-so-by-turning-the-\"Nested-Proofs-Allowed\"-flag-on", " If you really intended to use nested proofs, you can do so by turning the "Nested Proofs Allowed" flag on"]], "New coercion path ... is ambiguous with existing ..": [[4, 2, 1, "coq:warn.New-coercion-path-...-is-ambiguous-with-existing-...", ""]], "No information can be deduced from this equality and the injectivity of constructors. This may be because the terms are convertible, or due to pattern matching restrictions in the sort Prop": [[67, 0, 1, "coq:exn.No-information-can-be-deduced-from-this-equality-and-the-injectivity-of-constructors.-This-may-be-because-the-terms-are-convertible,-or-due-to-pattern-matching-restrictions-in-the-sort-Prop.-You-can-try-to-use-option-Set-Keep-Proof-Equalities", " You can try to use option Set Keep Proof Equalities"]], "No such bound variable \u2018ident\u2019 (possible names are: \u2018ident\u2019 ..": [[58, 0, 1, "coq:exn.No-such-bound-variable-\u2018ident\u2019-(possible-names-are:-\u2018ident\u2019-...)", ")"]], "No such goal": [[54, 0, 1, "coq:exn.No-such-goal.-(Goal-selector)", " (Goal selector)"], [54, 0, 1, "coq:exn.No-such-goal.-(fail)", " (fail)"], [66, 0, 1, "coq:exn.No-such-goal.-Focus-next-goal-with-bullet-\u2018bullet\u2019", " Focus next goal with bullet \u2018bullet\u2019"], [66, 0, 1, "coq:exn.No-such-goal.-Try-unfocusing-with-}", " Try unfocusing with }"]], "Notation \u2018string\u2019 is deprecated since \u2018string\u2019. \u2018string\u2019": [[74, 2, 1, "coq:warn.Notation-\u2018string\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019.-Use-\u2018qualid\u2019-instead", " Use \u2018qualid\u2019 instead"]], "Proof is not complete": [[66, 0, 1, "coq:exn.Proof-is-not-complete.-(abstract)", " (abstract)"], [58, 0, 1, "coq:exn.Proof-is-not-complete.-(assert)", " (assert)"]], "Require inside a module is deprecated and strongly discouraged": [[59, 2, 1, "coq:warn.Require-inside-a-module-is-deprecated-and-strongly-discouraged.-You-can-Require-a-module-at-toplevel-and-optionally-Import-it-inside-another-one", " You can Require a module at toplevel and optionally Import it inside another one"]], "Required library \u2018qualid\u2019 matches several files in path (found file.vo, file.vo, ..": [[59, 0, 1, "coq:exn.Required-library-\u2018qualid\u2019-matches-several-files-in-path-(found-file.vo,-file.vo,-...)", ")"]], "SSReflect: cannot obtain new equations out of ..": [[57, 2, 1, "coq:warn.SSReflect:-cannot-obtain-new-equations-out-of-...", ""]], "Tactic Notation \u2018qualid\u2019 is deprecated since \u2018string\u2019": [[74, 2, 1, "coq:warn.Tactic-Notation-\u2018qualid\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019", " \u2018string\u2019"]], "Tactic \u2018qualid\u2019 is deprecated since \u2018string\u2019": [[74, 2, 1, "coq:warn.Tactic-\u2018qualid\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019", " \u2018string\u2019"]], "The file \u2018ident\u2019": [[59, 0, 1, "coq:exn.The-file-\u2018ident\u2019.vo-contains-library-\u2018qualid\u2019-and-not-library-\u2018qualid\u2019", "vo contains library \u2018qualid\u2019 and not library \u2018qualid\u2019"]], "The relation \u2018ident\u2019 is not a declared reflexive relation. Maybe you need to require the Stdlib.Classes": [[64, 0, 1, "coq:exn.The-relation-\u2018ident\u2019-is-not-a-declared-reflexive-relation.-Maybe-you-need-to-require-the-Stdlib.Classes.RelationClasses-library", "RelationClasses library"]], "The relation \u2018ident\u2019 is not a declared symmetric relation. Maybe you need to require the Stdlib.Classes": [[64, 0, 1, "coq:exn.The-relation-\u2018ident\u2019-is-not-a-declared-symmetric-relation.-Maybe-you-need-to-require-the-Stdlib.Classes.RelationClasses-library", "RelationClasses library"]], "The relation \u2018ident\u2019 is not a declared transitive relation. Maybe you need to require the Stdlib.Classes": [[64, 0, 1, "coq:exn.The-relation-\u2018ident\u2019-is-not-a-declared-transitive-relation.-Maybe-you-need-to-require-the-Stdlib.Classes.RelationClasses-library", "RelationClasses library"]], "This command is just asserting the names of arguments of \u2018qualid\u2019. If this is what you want, add ': assert' to silence the warning. If you want to clear implicit arguments, add ': clear implicits'": [[41, 2, 1, "coq:warn.This-command-is-just-asserting-the-names-of-arguments-of-\u2018qualid\u2019.-If-this-is-what-you-want,-add-':-assert'-to-silence-the-warning.-If-you-want-to-clear-implicit-arguments,-add-':-clear-implicits'.-If-you-want-to-clear-notation-scopes,-add-':-clear-scopes'", " If you want to clear notation scopes, add ': clear scopes'"]], "This hint is not local but depends on a section variable": [[60, 2, 1, "coq:warn.This-hint-is-not-local-but-depends-on-a-section-variable.-It-will-disappear-when-the-section-is-closed", " It will disappear when the section is closed"]], "Type of \u2018qualid\u2019 seems incompatible with the type of \u2018qualid\u2019. Expected type is: \u2018type\u2019 instead of \u2018type\u2019": [[71, 2, 1, "coq:warn.Type-of-\u2018qualid\u2019-seems-incompatible-with-the-type-of-\u2018qualid\u2019.-Expected-type-is:-\u2018type\u2019-instead-of-\u2018type\u2019.-This-might-yield-ill-typed-terms-when-using-the-notation", " This might yield ill typed terms when using the notation"]], "Unable to apply lemma of type "..." on hypothesis of type "..": [[58, 0, 1, "coq:exn.Unable-to-apply-lemma-of-type-\"...\"-on-hypothesis-of-type-\"...\"", """]], "Unused variable \u2018ident\u2019 might be a misspelled constructor. Use _ or _\u2018ident\u2019 to silence this warning": [[46, 2, 1, "coq:warn.Unused-variable-\u2018ident\u2019-might-be-a-misspelled-constructor.-Use-_-or-_\u2018ident\u2019-to-silence-this-warning.", ""]], "package-name": [[59, 0, 1, "coq:exn.package-name.foo-and-not-foo_plugin", "foo and not foo_plugin"]], "plugin name anymore": [[59, 0, 1, "coq:exn.plugin-name-anymore.-Plugins-should-be-loaded-using-their", " Plugins should be loaded using their"]], "\u2018ident\u2019 already exists": [[28, 0, 1, "coq:exn.\u2018ident\u2019-already-exists.-(Axiom)", " (Axiom)"], [32, 0, 1, "coq:exn.\u2018ident\u2019-already-exists.-(Definition)", " (Definition)"], [32, 0, 1, "coq:exn.\u2018ident\u2019-already-exists.-(Theorem)", " (Theorem)"]], "\u2018qualid\u2019 should go from Byte.byte, (list Byte.byte), or PrimString": [[71, 0, 1, "coq:exn.\u2018qualid\u2019-should-go-from-Byte.byte,-(list-Byte.byte),-or-PrimString.string-to-\u2018type\u2019-or-(option-\u2018type\u2019)", "string to \u2018type\u2019 or (option \u2018type\u2019)"]], "\u2018qualid\u2019 should go from Number.int to \u2018type\u2019 or (option \u2018type\u2019). Instead of Number.int, the types Number.uint or Z or PrimInt63.pos_neg_int63 or PrimFloat.float or Number": [[71, 0, 1, "coq:exn.\u2018qualid\u2019-should-go-from-Number.int-to-\u2018type\u2019-or-(option-\u2018type\u2019).-Instead-of-Number.int,-the-types-Number.uint-or-Z-or-PrimInt63.pos_neg_int63-or-PrimFloat.float-or-Number.number-could-be-used-(you-may-need-to-require-BinNums-or-Number-or-PrimInt63-or-PrimFloat-first)", "number could be used (you may need to require BinNums or Number or PrimInt63 or PrimFloat first)"]], "\u2018qualid\u2019 should go from \u2018type\u2019 to Number.int or (option Number.int). Instead of Number.int, the types Number.uint or Z or PrimInt63.pos_neg_int63 or Number": [[71, 0, 1, "coq:exn.\u2018qualid\u2019-should-go-from-\u2018type\u2019-to-Number.int-or-(option-Number.int).-Instead-of-Number.int,-the-types-Number.uint-or-Z-or-PrimInt63.pos_neg_int63-or-Number.number-could-be-used-(you-may-need-to-require-BinNums-or-Number-or-PrimInt63-first)", "number could be used (you may need to require BinNums or Number or PrimInt63 first)"]], "\u2018qualid\u2019 should go from \u2018type\u2019 to T or (option T), where T is either Byte.byte, (list Byte.byte), or PrimString": [[71, 0, 1, "coq:exn.\u2018qualid\u2019-should-go-from-\u2018type\u2019-to-T-or-(option-T),-where-T-is-either-Byte.byte,-(list-Byte.byte),-or-PrimString.string", "string"]], "\u2018string\u2019 cannot be interpreted as a known notation in \u2018ident\u2019 entry": [[71, 0, 1, "coq:exn.\u2018string\u2019-cannot-be-interpreted-as-a-known-notation-in-\u2018ident\u2019-entry.-Make-sure-that-symbols-are-surrounded-by-spaces-and-that-holes-are-explicitly-denoted-by-\"_\"", " Make sure that symbols are surrounded by spaces and that holes are explicitly denoted by "_""]], "\u2018string\u2019 cannot be interpreted as a known notation": [[71, 0, 1, "coq:exn.\u2018string\u2019-cannot-be-interpreted-as-a-known-notation.-Make-sure-that-symbols-are-surrounded-by-spaces-and-that-holes-are-explicitly-denoted-by-\"_\"", " Make sure that symbols are surrounded by spaces and that holes are explicitly denoted by "_""]]}, "objtypes": {"0": "coq:exn", "1": "coq:tacn", "2": "coq:warn", "3": "coq:cmd", "4": "coq:flag", "5": "coq:thm", "6": "coq:opt", "7": "coq:attr", "8": "coq:table", "9": "coq:tacv"}, "objnames": {"0": ["coq", "exn", "Coq exn"], "1": ["coq", "tacn", "Coq tacn"], "2": ["coq", "warn", "Coq warn"], "3": ["coq", "cmd", "Coq cmd"], "4": ["coq", "flag", "Coq flag"], "5": ["coq", "thm", "Coq thm"], "6": ["coq", "opt", "Coq opt"], "7": ["coq", "attr", "Coq attr"], "8": ["coq", "table", "Coq table"], "9": ["coq", "tacv", "Coq tacv"]}, "titleterms": {"program": [2, 6, 9, 27, 55, 60], "extract": [2, 17, 24], "gener": [2, 3, 4, 11, 14, 23, 29, 44, 54, 55, 57, 67, 71, 72], "ml": [2, 55], "code": 2, "option": [2, 17, 21, 29, 51, 66, 75], "set": [2, 13, 26, 29, 37, 41, 57, 58, 60, 66], "target": [2, 53], "languag": [2, 17, 24, 25, 33, 45, 55, 57], "inlin": [2, 59], "optim": [2, 54], "extra": [2, 59], "elimin": [2, 46, 57], "useless": 2, "argument": [2, 37, 41, 44, 46, 53, 57, 67, 71], "realiz": 2, "axiom": 2, "induct": [2, 26, 34, 40, 46, 67, 71, 72], "type": [2, 3, 4, 10, 17, 26, 28, 30, 32, 34, 35, 37, 38, 40, 44, 46, 54, 55, 57, 59, 67, 71], "ffi": 2, "avoid": 2, "conflict": 2, "exist": [2, 24, 35], "filenam": [2, 53], "addit": [2, 57, 60], "differ": [2, 44, 66], "between": [2, 55, 59, 66], "rocq": [2, 25, 51, 53, 57, 60, 71, 74, 75], "system": [2, 35], "some": [2, 35], "exampl": [2, 3, 4, 5, 6, 11, 14, 17, 26, 27, 28, 29, 30, 31, 34, 35, 37, 38, 40, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74, 75], "A": [2, 14, 35, 58, 67], "detail": [2, 17, 24, 53], "euclidean": 2, "divis": 2, "": [2, 41, 67], "horror": 2, "museum": 2, "user": [2, 3, 10, 24, 27], "contribut": [2, 24, 27], "rewrit": [3, 10, 57, 64, 67], "introduct": [3, 25, 57], "relat": 3, "morphism": 3, "parametr": [3, 46, 57], "continu": [3, 41, 44], "contravari": 3, "ad": [3, 11, 52], "new": [3, 11, 17, 24, 35, 53, 57, 63], "nonreflex": 3, "nonsymmetr": 3, "covari": 3, "ambigu": 3, "setoid": [3, 64], "context": [3, 13, 54, 55, 57, 58], "valu": [3, 46, 54, 55], "declar": [3, 13, 38, 41, 42, 44, 55, 57, 66, 67], "command": [3, 13, 17, 19, 24, 35, 51, 52, 57, 59, 66, 67, 71, 75, 76], "tactic": [3, 5, 11, 17, 22, 24, 27, 43, 54, 55, 57, 58, 60, 61, 63, 64, 67, 71, 72, 74], "first": [3, 34, 46, 54, 57], "class": [3, 4, 37, 55, 71], "enabl": [3, 66, 71], "provid": [3, 46], "print": [3, 4, 14, 37, 43, 44, 46, 54, 55, 59, 71, 75], "deprec": [3, 74], "syntax": [3, 10, 17, 24, 29, 44, 46, 54, 55, 57, 71], "backward": [3, 58], "incompat": [3, 17], "extens": [3, 24, 45, 46, 57, 71], "under": [3, 57], "binder": [3, 28, 44, 57, 71], "subrel": 3, "constant": [3, 37, 59, 71], "unfold": [3, 41, 64], "dure": 3, "proper": 3, "instanc": [3, 13, 43], "search": [3, 59, 60], "strategi": [3, 46, 64], "usag": [3, 11, 57, 66, 75], "definit": [3, 9, 12, 14, 30, 32, 34, 37, 40, 46, 54, 55, 57, 64, 71], "innermost": 3, "outermost": 3, "implicit": [4, 41, 44, 46, 60, 71], "coercion": [4, 46, 71], "present": [4, 14], "revers": [4, 44, 54, 55, 64], "ident": [4, 54], "inherit": [4, 71], "graph": 4, "displai": [4, 43, 44, 52, 59, 71], "avail": 4, "activ": 4, "record": [4, 37], "section": [4, 13, 14, 38, 66, 75], "modul": [4, 35, 53], "function": [4, 28, 30, 34, 41, 44, 54, 60, 72], "applic": [4, 28, 44, 54, 58], "us": [4, 14, 25, 35, 37, 38, 43, 44, 46, 51, 52, 53, 54, 58, 64, 66, 67, 71], "attribut": [4, 17, 18, 29, 35, 38], "micromega": 5, "solver": [5, 7, 11, 61, 62], "arithmet": [5, 27], "goal": [5, 11, 54, 55, 57, 58, 66, 67], "over": [5, 9, 55, 57], "order": [5, 10, 58], "ring": [5, 11], "short": 5, "descript": 5, "positivstellensatz": 5, "refut": 5, "lra": 5, "decis": 5, "procedur": 5, "linear": 5, "real": [5, 17], "ration": [5, 11], "lia": 5, "integ": [5, 36, 71], "high": 5, "level": [5, 10, 29, 30, 32, 34, 55], "view": [5, 57], "cut": [5, 54], "plane": 5, "proof": [5, 8, 12, 14, 25, 31, 32, 46, 54, 57, 58, 60, 65, 66], "case": [5, 24, 40, 52, 57, 58, 67], "split": [5, 53], "nra": 5, "non": [5, 12, 34, 44, 54, 55, 58, 67, 71], "nia": 5, "psatz": 5, "zifi": 5, "pre": 5, "process": [5, 8, 54], "deriv": [6, 42, 67], "nsatz": 7, "equal": [7, 9, 27, 62, 64, 67], "integr": 7, "domain": 7, "more": 7, "about": [7, 46, 71], "asynchron": [8, 52], "parallel": 8, "annot": 8, "automat": [8, 11, 34, 41, 43, 44, 61, 67], "suggest": 8, "block": [8, 57], "error": [8, 20, 54, 55], "resili": 8, "caveat": [8, 30], "interact": [8, 35, 44, 51, 54, 55, 57], "mode": [8, 44, 52, 55, 57, 66], "limit": [8, 67], "number": [8, 54, 60, 71], "worker": 8, "elabor": 9, "syntact": [9, 54, 55], "control": [9, 35, 44, 46, 54, 57, 58, 59, 64, 66], "fixpoint": [9, 34], "lemma": [9, 27, 66], "solv": [9, 43, 54, 66], "oblig": 9, "frequent": 9, "ask": 9, "question": 9, "defin": [10, 34, 35, 37, 54, 55, 60], "rule": [10, 26, 31, 34, 38, 57, 64, 71, 75], "symbol": [10, 52, 54], "pattern": [10, 44, 46, 54, 55, 57, 58, 59, 71], "higher": 10, "hole": [10, 54], "univers": [10, 14], "polymorph": [10, 14, 34, 57], "preserv": 10, "confluenc": 10, "termin": [10, 12, 57], "compat": [10, 17, 37, 55, 57, 74], "eta": 10, "law": 10, "support": [10, 29, 52], "field": [11, 35, 37], "polynomi": 11, "equat": [11, 57], "what": 11, "doe": [11, 46], "thi": 11, "do": [11, 54], "The": [11, 26, 27, 34, 35, 44, 51, 53, 57, 71, 75], "variabl": [11, 43, 44, 46, 51, 52, 55, 66], "map": 11, "i": [11, 54, 58], "concret": [11, 24], "structur": [11, 42, 57], "how": [11, 66], "work": [11, 53, 66], "deal": 11, "side": [11, 46], "histori": [11, 15, 24], "discuss": 11, "sprop": 12, "irrelev": [12, 31], "proposit": [12, 27, 54], "basic": [12, 27, 29, 52, 53, 54, 57, 65, 71], "construct": [12, 24, 26, 34, 37, 40, 54, 59], "encod": [12, 52], "strict": [12, 34, 44, 55], "uip": 12, "debug": [12, 54, 55, 59], "issu": [12, 17, 57], "typeclass": [13, 57], "bind": [13, 41, 52, 55, 58, 71], "parameter": [13, 34, 71], "build": [13, 53], "hierarchi": [13, 42], "superclass": 13, "substructur": 13, "summari": [13, 17, 24, 35, 38], "transpar": 13, "opaqu": 13, "eauto": 13, "monomorph": 14, "cumul": 14, "noncumul": 14, "specifi": 14, "demonstr": 14, "varianc": 14, "weak": 14, "constraint": [14, 66], "global": [14, 54, 71], "local": [14, 29, 35, 38, 46, 53, 54, 57, 58, 60, 71], "convers": [14, 31, 64], "unif": [14, 58, 66], "minim": 14, "explicit": [14, 43, 44, 57], "sort": [14, 34, 39], "recent": [15, 17], "chang": [15, 17, 24, 55], "index": [16, 18, 19, 20, 21, 22, 23, 34, 57, 69], "unreleas": 17, "kernel": 17, "specif": [17, 25, 27], "infer": [17, 43, 44], "notat": [17, 27, 42, 54, 55, 59, 71], "ltac": [17, 54, 55], "ltac2": [17, 55], "ssreflect": [17, 57], "line": [17, 51, 75, 76], "tool": [17, 24, 76], "rocqid": [17, 52], "standard": [17, 24, 55, 57, 60, 71], "librari": [17, 24, 27, 51, 53, 59, 60, 71, 73, 74], "infrastructur": 17, "depend": [17, 46, 53, 58, 59, 67], "miscellan": [17, 24], "version": [17, 24, 53], "8": 17, "20": 17, "0": [17, 24], "coqid": 17, "19": 17, "1": [17, 24, 37, 67], "2": [17, 24, 37, 67], "18": 17, "17": 17, "16": 17, "15": 17, "14": 17, "nativ": [17, 53], "compil": [17, 51, 52, 53, 59], "13": 17, "beta1": 17, "12": 17, "flag": [17, 21, 29, 59], "refer": [17, 54, 59], "manual": [17, 41, 44], "11": 17, "10": 17, "other": [17, 44, 66], "beta2": 17, "beta3": 17, "9": 17, "7": [17, 24], "potenti": 17, "6": [17, 24], "sourc": 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"open": 71, "type_scop": 71, "function_scop": 71, "radix": 71, "plugin": [73, 74], "trigger": 74, "introduc": 74, "alia": 74, "doc": 75, "materi": 75, "emphasi": 75, "escap": 75, "html": 75, "verbatim": 75, "hyperlink": 75, "hide": 75, "style": 75, "graphic": 76, "bibliographi": 77}, "envversion": {"sphinx.domains.c": 2, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 8, "sphinx.domains.index": 1, "sphinx.domains.javascript": 2, "sphinx.domains.math": 2, "sphinx.domains.python": 3, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx.ext.todo": 2, "sphinxcontrib.bibtex": 9, "coqrst.coqdomain": 2, "sphinx": 57}, "alltitles": {"Program extraction": [[2, "program-extraction"]], "Generating ML Code": [[2, "generating-ml-code"]], "Extraction Options": [[2, "extraction-options"]], "Setting the target language": [[2, "setting-the-target-language"]], "Inlining and optimizations": [[2, "inlining-and-optimizations"]], "Extra elimination of useless arguments": [[2, "extra-elimination-of-useless-arguments"]], "Realizing axioms": [[2, "realizing-axioms"]], "Realizing inductive types": [[2, "realizing-inductive-types"]], "Generating FFI Code": [[2, "generating-ffi-code"]], "Avoiding conflicts with existing filenames": [[2, "avoiding-conflicts-with-existing-filenames"]], "Additional settings": [[2, "additional-settings"]], "Differences between Rocq and ML type systems": [[2, "differences-between-rocq-and-ml-type-systems"]], "Some examples": [[2, "some-examples"]], "A detailed example: Euclidean division": [[2, "a-detailed-example-euclidean-division"]], "Extraction's horror museum": [[2, "extraction-s-horror-museum"]], "Users' Contributions": [[2, "users-contributions"]], "Generalized rewriting": [[3, "generalized-rewriting"]], "Introduction to generalized rewriting": [[3, "introduction-to-generalized-rewriting"]], "Relations and morphisms": [[3, "relations-and-morphisms"]], "Example: Parametric relation": [[3, null], [3, null]], "Example: Parametric relation (continued)": [[3, null]], "Example: Morphisms": [[3, null]], "Example: Contravariant morphisms": [[3, null]], "Example: Rewriting": [[3, null]], "Adding new relations and morphisms": [[3, "adding-new-relations-and-morphisms"]], "Example": [[3, null], [3, null], [3, null], [3, null], [3, null], [3, null], [6, null], [11, null], [11, null], [11, null], [17, null], [26, null], [27, null], [30, null], [30, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [35, null], [35, null], [35, null], [35, null], [35, null], [37, null], [37, null], [40, null], [40, null], [41, null], [41, null], [41, null], [41, null], [41, null], [41, null], [42, null], [42, null], [42, null], [44, null], [44, 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relations": [[3, "rewriting-and-nonsymmetric-relations"]], "Example: Covariance and contravariance": [[3, null]], "Rewriting in ambiguous setoid contexts": [[3, "rewriting-in-ambiguous-setoid-contexts"]], "Rewriting with Type valued relations": [[3, "rewriting-with-type-valued-relations"]], "Declaring rewrite relations": [[3, "declaring-rewrite-relations"]], "Commands and tactics": [[3, "commands-and-tactics"]], "First class setoids and morphisms": [[3, "first-class-setoids-and-morphisms"]], "Example: First class setoids": [[3, null]], "Tactics enabled on user provided relations": [[3, "tactics-enabled-on-user-provided-relations"]], "Printing relations and morphisms": [[3, "printing-relations-and-morphisms"]], "Deprecated syntax and backward incompatibilities": [[3, "deprecated-syntax-and-backward-incompatibilities"]], "Extensions": [[3, "extensions"]], "Rewriting under binders": [[3, "rewriting-under-binders"], [57, "rewriting-under-binders"]], "Subrelations": [[3, "subrelations"]], "Constant unfolding during rewriting": [[3, "constant-unfolding-during-rewriting"]], "Constant unfolding during Proper-instance search": [[3, "constant-unfolding-during-proper-instance-search"]], "Strategies for rewriting": [[3, "strategies-for-rewriting"]], "Usage": [[3, "usage"], [57, "usage"], [75, "usage"]], "Definitions": [[3, "definitions"], [32, "definitions"], [57, "definitions"]], "Example: innermost and outermost": [[3, "rewrite-strat-innermost-outermost"]], "Implicit Coercions": [[4, "implicit-coercions"]], "General Presentation": [[4, "general-presentation"], [14, "general-presentation"]], "Coercion Classes": [[4, "coercion-classes"], [4, "id2"]], "Coercions": [[4, "id1"]], "Reversible Coercions": [[4, "reversible-coercions"]], "Identity Coercions": [[4, "identity-coercions"]], "Inheritance Graph": [[4, "inheritance-graph"]], "Displaying Available Coercions": [[4, "displaying-available-coercions"]], "Activating the Printing of Coercions": [[4, "activating-the-printing-of-coercions"]], "Classes as Records": [[4, "classes-as-records"]], "Coercions and Sections": [[4, "coercions-and-sections"]], "Coercions and Modules": [[4, "coercions-and-modules"]], "Examples": [[4, "examples"], [31, "examples"], [35, "examples"], [57, "examples"]], "Example: Coercion at function application": [[4, null]], "Example: Coercion to a type": [[4, null]], "Example: Coercion to a function": [[4, null]], "Example: Reversible coercions": [[4, "example-reversible-coercion"]], "Example: Reversible coercions using the reversible attribute": [[4, "example-reversible-coercion-attribute"]], "Example: Identity coercions.": [[4, "example-identity-coercion"]], "Example: Inheritance Graph": [[4, null]], "Micromega: solvers for arithmetic goals over ordered rings": [[5, "micromega-solvers-for-arithmetic-goals-over-ordered-rings"]], "Short description of the tactics": [[5, "short-description-of-the-tactics"]], "Positivstellensatz refutations": [[5, "positivstellensatz-refutations"]], "lra: a decision procedure for linear real and rational arithmetic": [[5, "lra-a-decision-procedure-for-linear-real-and-rational-arithmetic"]], "lia: a tactic for linear integer arithmetic": [[5, "lia-a-tactic-for-linear-integer-arithmetic"]], "High level view of lia": [[5, "high-level-view-of-lia"]], "Cutting plane proofs": [[5, "cutting-plane-proofs"]], "Example: Cutting plane": [[5, null]], "Case split": [[5, "case-split"]], "nra: a proof procedure for non-linear arithmetic": [[5, "nra-a-proof-procedure-for-non-linear-arithmetic"]], "nia: a proof procedure for non-linear integer arithmetic": [[5, "nia-a-proof-procedure-for-non-linear-integer-arithmetic"]], "psatz: a proof procedure for non-linear arithmetic": [[5, "psatz-a-proof-procedure-for-non-linear-arithmetic"]], "zify: pre-processing of arithmetic goals": [[5, "zify-pre-processing-of-arithmetic-goals"]], "Example: Lra": [[5, "lra-example"]], "Program derivation": [[6, "program-derivation"]], "Nsatz: a solver for equalities in integral domains": [[7, "nsatz-a-solver-for-equalities-in-integral-domains"]], "More about nsatz": [[7, "more-about-nsatz"]], "Asynchronous and Parallel Proof Processing": [[8, "asynchronous-and-parallel-proof-processing"]], "Proof annotations": [[8, "proof-annotations"]], "Automatic suggestion of proof annotations": [[8, "automatic-suggestion-of-proof-annotations"]], "Proof blocks and error resilience": [[8, "proof-blocks-and-error-resilience"]], "Caveats": [[8, "caveats"], [8, "id3"]], "Interactive mode": [[8, "interactive-mode"], [57, "interactive-mode"]], "Limiting the number of parallel workers": [[8, "limiting-the-number-of-parallel-workers"]], "Program": [[9, "program"]], "Elaborating programs": [[9, "elaborating-programs"]], "Syntactic control over equalities": [[9, "syntactic-control-over-equalities"]], "Program Definition": [[9, "program-definition"]], "Program Fixpoint": [[9, "program-fixpoint"]], "Program Lemma": [[9, "program-lemma"]], "Solving obligations": [[9, "solving-obligations"]], "Frequently Asked Questions": [[9, "frequently-asked-questions"]], "User-defined rewrite rules": [[10, "user-defined-rewrite-rules"]], "Symbols": [[10, "symbols"]], "Rewrite rules": [[10, "id1"]], "Pattern syntax": [[10, "pattern-syntax"]], "Higher-order pattern holes": [[10, "higher-order-pattern-holes"]], "Universe polymorphic rules": [[10, "universe-polymorphic-rules"]], "Rewrite rules, type preservation, confluence and termination": [[10, "rewrite-rules-type-preservation-confluence-and-termination"]], "Compatibility with the eta laws": [[10, "compatibility-with-the-eta-laws"]], "Level of support": [[10, "level-of-support"]], "ring and field: solvers for polynomial and rational equations": [[11, "ring-and-field-solvers-for-polynomial-and-rational-equations"]], "What does this tactic do?": [[11, "what-does-this-tactic-do"]], "The variables map": [[11, "the-variables-map"]], "Is it automatic?": [[11, "is-it-automatic"]], "Concrete usage": [[11, "concrete-usage"]], "Adding a ring structure": [[11, "adding-a-ring-structure"]], "How does it work?": [[11, "how-does-it-work"]], "Dealing with fields": [[11, "dealing-with-fields"]], "Example: field that generates side goals": [[11, null]], "Adding a new field structure": [[11, "adding-a-new-field-structure"]], "History of ring": [[11, "history-of-ring"]], "Discussion": [[11, "discussion"]], "SProp (proof irrelevant propositions)": [[12, "sprop-proof-irrelevant-propositions"]], "Basic constructs": [[12, "basic-constructs"]], "Encodings for strict propositions": [[12, "encodings-for-strict-propositions"]], "Definitional UIP": [[12, "definitional-uip"]], "Non Termination with UIP": [[12, "non-termination-with-uip"]], "Debugging \\SProp issues": [[12, "debugging-sprop-issues"]], "Typeclasses": [[13, "typeclasses"]], "Typeclass and instance declarations": [[13, "typeclass-and-instance-declarations"]], "Binding typeclasses": [[13, "binding-typeclasses"]], "Parameterized instances": [[13, "parameterized-instances"]], "Sections and contexts": [[13, "sections-and-contexts"]], "Building hierarchies": [[13, "building-hierarchies"]], "Superclasses": [[13, "superclasses"]], "Substructures": [[13, "substructures"]], "Command summary": [[13, "command-summary"]], "Typeclasses Transparent, Typeclasses Opaque": [[13, "typeclasses-transparent-typeclasses-opaque"]], "Settings": [[13, "settings"], [29, "settings"], [57, "settings"]], "Typeclasses eauto": [[13, "typeclasses-eauto"]], "Polymorphic Universes": [[14, "polymorphic-universes"]], "Polymorphic, Monomorphic": [[14, "polymorphic-monomorphic"]], "Cumulative, NonCumulative": [[14, "cumulative-noncumulative"]], "Specifying cumulativity": [[14, "specifying-cumulativity"]], "Example: Demonstration of universe variances": [[14, null]], "Example: A proof using cumulativity": [[14, null]], "Cumulativity Weak Constraints": [[14, "cumulativity-weak-constraints"]], "Global and local universes": [[14, 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"version-4"]], "Version 5": [[24, "version-5"]], "Versions 6": [[24, "versions-6"]], "Version 6.1": [[24, "version-6-1"]], "Version 6.2": [[24, "version-6-2"]], "Version 6.3": [[24, "version-6-3"]], "Versions 7": [[24, "versions-7"]], "Details of changes in 7.0 and 7.1": [[24, "details-of-changes-in-7-0-and-7-1"]], "Main novelties": [[24, "main-novelties"]], "Language: new \"let-in\" construction": [[24, "language-new-let-in-construction"]], "Language: long names": [[24, "language-long-names"]], "Language: miscellaneous": [[24, "language-miscellaneous"]], "Language: Cases": [[24, "language-cases"]], "Reduction": [[24, "reduction"], [37, "reduction"], [55, "reduction"]], "New tactics": [[24, "new-tactics"]], "Changes in existing tactics": [[24, "changes-in-existing-tactics"]], "Efficiency": [[24, "efficiency"]], "Concrete syntax of constructions": [[24, "concrete-syntax-of-constructions"]], "Parsing and grammar extension": [[24, "parsing-and-grammar-extension"]], "New commands": [[24, "new-commands"]], "Changes in existing commands": [[24, "changes-in-existing-commands"]], "New user contributions": [[24, "new-user-contributions"]], "Details of changes in 7.2": [[24, "details-of-changes-in-7-2"]], "Details of changes in 7.3": [[24, "details-of-changes-in-7-3"]], "Changes in 7.3.1": [[24, "changes-in-7-3-1"]], "Details of changes in 7.4": [[24, "details-of-changes-in-7-4"]], "Introduction and Contents": [[25, "introduction-and-contents"]], "Contents": [[25, "contents"]], "Specification language": [[25, null]], "Proofs": [[25, null]], "Using the Rocq Prover": [[25, null]], "Appendix": [[25, null]], "Typing rules": [[26, "typing-rules"], [26, "id4"]], "The terms": [[26, "the-terms"]], "Subtyping rules": [[26, "subtyping-rules"]], "The Calculus of Inductive Constructions with impredicative Set": [[26, "the-calculus-of-inductive-constructions-with-impredicative-set"]], "The Coq libraries": [[27, "the-coq-libraries"]], "The prelude": [[27, "the-prelude"]], "Logic": [[27, "logic"]], "Propositional Connectives": [[27, "propositional-connectives"]], "Quantifiers": [[27, "quantifiers"]], "Equality": [[27, "equality"]], "Lemmas": [[27, "lemmas"]], "Datatypes": [[27, "datatypes"]], "Programming": [[27, "programming"]], "Specification": [[27, "specification"]], "Basic Arithmetic": [[27, "basic-arithmetic"]], "Well-founded recursion": [[27, "well-founded-recursion"]], "Users\u2019 contributions": [[27, "users-contributions"]], "Functions and assumptions": [[28, "functions-and-assumptions"]], "Binders": [[28, "binders"]], "Functions (fun) and function types (forall)": [[28, "functions-fun-and-function-types-forall"]], "Function application": [[28, "function-application"]], "Assumptions": [[28, "assumptions"]], "Example: Simple assumptions": [[28, null]], "Basic notions and conventions": [[29, "basic-notions-and-conventions"]], "Syntax and lexical conventions": [[29, "syntax-and-lexical-conventions"]], "Syntax conventions": [[29, "syntax-conventions"]], "Lexical conventions": [[29, "lexical-conventions"]], "Example: Stack overflow with nat": [[29, null]], "Essential vocabulary": [[29, "essential-vocabulary"]], "Attributes": [[29, "attributes"]], "Generic attributes": [[29, "generic-attributes"]], "Document-level attributes": [[29, "document-level-attributes"]], "Flags, Options and Tables": [[29, "flags-options-and-tables"]], "Locality attributes supported by Set and Unset": [[29, "locality-attributes-supported-by-set-and-unset"]], "Coinductive types and corecursive functions": [[30, "coinductive-types-and-corecursive-functions"]], "Coinductive types": [[30, "coinductive-types"]], "Caveat": [[30, "caveat"]], "Co-recursive functions: cofix": [[30, "co-recursive-functions-cofix"]], "Top-level definitions of corecursive functions": [[30, "top-level-definitions-of-corecursive-functions"]], "Conversion rules": [[31, "conversion-rules"]], "\u03b1-conversion": [[31, "conversion"]], "\u03b2-reduction": [[31, "reduction"]], "\u03b4-reduction": [[31, "delta-reduction-sect"]], "\u03b9-reduction": [[31, "id4"]], "\u03b6-reduction": [[31, "id6"]], "\u03b7-expansion": [[31, "expansion"]], "Example: Simple delta, fix, beta and match reductions": [[31, null]], "Proof Irrelevance": [[31, "proof-irrelevance"]], "Convertibility": [[31, "convertibility"]], "Let-in definitions": [[32, "let-in-definitions"]], "Type cast": [[32, "type-cast"]], "Top-level definitions": [[32, "top-level-definitions"]], "Assertions and proofs": [[32, "assertions-and-proofs"]], "Core language": [[33, "core-language"]], "Inductive types and recursive functions": [[34, "inductive-types-and-recursive-functions"]], "Inductive types": [[34, "inductive-types"]], "Simple inductive types": [[34, "simple-inductive-types"]], "Automatic Prop lowering": [[34, "automatic-prop-lowering"]], "Simple indexed inductive types": [[34, "simple-indexed-inductive-types"]], "Parameterized inductive types": [[34, "parameterized-inductive-types"]], "Mutually defined inductive types": [[34, "mutually-defined-inductive-types"]], "Example: Mutually defined inductive types": [[34, null]], "Recursive functions: fix": [[34, "recursive-functions-fix"]], "Top-level recursive functions": [[34, "top-level-recursive-functions"]], "Example: Mutual fixpoints": [[34, null]], "Theory of inductive definitions": [[34, "theory-of-inductive-definitions"]], "Types of inductive objects": [[34, "types-of-inductive-objects"]], "Well-formed inductive definitions": [[34, "well-formed-inductive-definitions"]], "Arity of a given sort": [[34, "arity-of-a-given-sort"]], "Arity": [[34, "arity"]], "Type of constructor": [[34, "type-of-constructor"]], "Positivity Condition": [[34, "positivity-condition"]], "Strict positivity": [[34, "strict-positivity"]], "Nested Positivity": [[34, "nested-positivity"]], "Correctness rules": [[34, "correctness-rules"]], "Example: Negative occurrence (first example)": [[34, null]], "Example: Negative occurrence (second example)": [[34, null]], "Example: Non strictly positive occurrence": [[34, null]], "Template polymorphism": [[34, "template-polymorphism"]], "Destructors": [[34, "destructors"]], "The match ... with ... end construction": [[34, "the-match-with-end-construction"]], "Fixpoint definitions": [[34, "fixpoint-definitions"]], "Typing rule": [[34, "id10"]], "Reduction rule": [[34, "reduction-rule"]], "The Module System": [[35, "the-module-system"]], "Modules and module types": [[35, "modules-and-module-types"]], "Using modules": [[35, "using-modules"]], "Example: Defining a simple module interactively": [[35, null]], "Example: Defining a simple module type interactively": [[35, "example-def-simple-module-type"]], "Example: Creating a new module that omits some items from an existing module": [[35, "example-filter-module"]], "Example: Creating a functor (a module with parameters)": [[35, null]], "Example: A module type with two sub-modules, sharing some fields": [[35, null]], "Qualified names": [[35, "qualified-names"]], "Controlling the scope of commands with locality attributes": [[35, "controlling-the-scope-of-commands-with-locality-attributes"]], "Summary of locality attributes in a module": [[35, "summary-of-locality-attributes-in-a-module"]], "Typing Modules": [[35, "typing-modules"]], "Primitive objects": [[36, "primitive-objects"]], "Primitive Integers": [[36, "primitive-integers"]], "Primitive Floats": [[36, "primitive-floats"]], "Primitive Arrays": [[36, "primitive-arrays"]], "Primitive (Byte-Based) Strings": [[36, "primitive-byte-based-strings"]], "Record types": [[37, "record-types"]], "Defining record types": [[37, "defining-record-types"]], "Example: Defining a record": [[37, null]], "Example: Reusing a field name in multiple records": [[37, null]], "Example: Using the \"as\" clause in a record definition": [[37, null]], "Example: Argument name for a record type created using Class": [[37, null]], "Constructing records": [[37, "constructing-records"]], "Example: Constructing 1/2 as a record": [[37, null]], "Accessing fields (projections)": [[37, "accessing-fields-projections"]], "Example: Accessing record fields": [[37, null]], "Example: Matching on records": [[37, null]], "Example: Accessing anonymous record fields with match": [[37, null]], "Settings for printing records": [[37, "settings-for-printing-records"]], "Primitive Projections": [[37, "primitive-projections"]], "Compatibility Constants for Projections": [[37, "compatibility-constants-for-projections"]], "Sections": [[38, "sections"], [75, "sections"]], "Using sections": [[38, "using-sections"]], "Example: Section-local declarations": [[38, "section-local-declarations"]], "Summary of locality attributes in a section": [[38, "summary-of-locality-attributes-in-a-section"]], "Typing rules used at the end of a section": [[38, "typing-rules-used-at-the-end-of-a-section"]], "Sorts": [[39, "sorts"]], "Variants and the match construct": [[40, "variants-and-the-match-construct"]], "Variants": [[40, "id1"]], "Private (matching) inductive types": [[40, "private-matching-inductive-types"]], "Definition by cases: match": [[40, "definition-by-cases-match"]], "Setting properties of a function's arguments": [[41, "setting-properties-of-a-function-s-arguments"]], "Manual declaration of implicit arguments": [[41, "manual-declaration-of-implicit-arguments"]], "Example: Multiple alternatives with implicits_alt": [[41, "example-more-implicits"]], "Automatic declaration of implicit arguments": [[41, "automatic-declaration-of-implicit-arguments"]], "Example: Default implicits": [[41, null]], "Renaming implicit arguments": [[41, "renaming-implicit-arguments"]], "Example: (continued) Renaming implicit arguments": [[41, null]], "Binding arguments to scopes": [[41, "binding-arguments-to-scopes"]], "Effects of Arguments on unfolding": [[41, "effects-of-arguments-on-unfolding"]], "Bidirectionality hints": [[41, "bidirectionality-hints"]], "Example: Bidirectionality hints": [[41, null]], "Canonical Structures": [[42, "canonical-structures"]], "Declaration of canonical structures": [[42, "declaration-of-canonical-structures"]], "Notation overloading": [[42, "notation-overloading"]], "Derived Canonical Structures": [[42, "derived-canonical-structures"]], "Hierarchy of structures": [[42, "hierarchy-of-structures"]], "Compact declaration of Canonical Structures": [[42, "compact-declaration-of-canonical-structures"]], "Existential variables": [[43, "existential-variables"]], "Inferable subterms": [[43, "inferable-subterms"]], "e* tactics that can create existential variables": [[43, "e-tactics-that-can-create-existential-variables"]], "Example: apply vs eapply": [[43, null]], "Automatic resolution of existential variables": [[43, "automatic-resolution-of-existential-variables"]], "Example: Automatic resolution of existential variables": [[43, "automatic-evar-resolution"]], "Explicit display of existential instances for pretty-printing": [[43, "explicit-display-of-existential-instances-for-pretty-printing"]], "Solving existential variables using tactics": [[43, "solving-existential-variables-using-tactics"]], "Implicit arguments": [[44, "implicit-arguments"]], "The different kinds of implicit arguments": [[44, "the-different-kinds-of-implicit-arguments"]], "Implicit arguments inferable from the knowledge of other arguments of a function": [[44, "implicit-arguments-inferable-from-the-knowledge-of-other-arguments-of-a-function"]], "Implicit arguments inferable by resolution": [[44, "implicit-arguments-inferable-by-resolution"]], "Maximal and non-maximal insertion of implicit arguments": [[44, "maximal-and-non-maximal-insertion-of-implicit-arguments"]], "Trailing Implicit Arguments": [[44, "trailing-implicit-arguments"]], "Casual use of implicit arguments": [[44, "casual-use-of-implicit-arguments"]], "Declaration of implicit arguments": [[44, "declaration-of-implicit-arguments"]], "Implicit Argument Binders": [[44, "implicit-argument-binders"]], "Mode for automatic declaration of implicit arguments": [[44, "mode-for-automatic-declaration-of-implicit-arguments"]], "Controlling strict implicit arguments": [[44, "controlling-strict-implicit-arguments"]], "Controlling contextual implicit arguments": [[44, "controlling-contextual-implicit-arguments"]], "Controlling reversible-pattern implicit arguments": [[44, "controlling-reversible-pattern-implicit-arguments"]], "Controlling the insertion of implicit arguments not followed by explicit arguments": [[44, "controlling-the-insertion-of-implicit-arguments-not-followed-by-explicit-arguments"]], "Combining manual declaration and automatic declaration": [[44, "combining-manual-declaration-and-automatic-declaration"]], "Explicit applications": [[44, "explicit-applications"]], "Example: Syntax for explicitly giving implicit arguments (continued)": [[44, null]], "Displaying implicit arguments": [[44, "displaying-implicit-arguments"]], "Displaying implicit arguments when pretty-printing": [[44, "displaying-implicit-arguments-when-pretty-printing"]], "Interaction with subtyping": [[44, "interaction-with-subtyping"]], "Deactivation of implicit arguments for parsing": [[44, "deactivation-of-implicit-arguments-for-parsing"]], "Implicit types of variables": [[44, "implicit-types-of-variables"]], "Implicit generalization": [[44, "implicit-generalization"]], "Language extensions": [[45, "language-extensions"]], "Extended pattern matching": [[46, "extended-pattern-matching"]], "Variants and extensions of match": [[46, "variants-and-extensions-of-match"]], "Multiple and nested pattern matching": [[46, "multiple-and-nested-pattern-matching"]], "Pattern-matching on boolean values: the if expression": [[46, "pattern-matching-on-boolean-values-the-if-expression"]], "Irrefutable patterns: the destructuring let variants": [[46, "irrefutable-patterns-the-destructuring-let-variants"]], "First destructuring let syntax": [[46, "first-destructuring-let-syntax"]], "Second destructuring let syntax": [[46, "second-destructuring-let-syntax"]], "Controlling pretty-printing of match expressions": [[46, "controlling-pretty-printing-of-match-expressions"]], "Printing nested patterns": [[46, "printing-nested-patterns"]], "Factorization of clauses with same right-hand side": [[46, "factorization-of-clauses-with-same-right-hand-side"]], "Use of a default clause": [[46, "use-of-a-default-clause"]], "Printing of wildcard patterns": [[46, "printing-of-wildcard-patterns"]], "Printing of the elimination predicate": [[46, "printing-of-the-elimination-predicate"]], "Printing of hidden subterms": [[46, "printing-of-hidden-subterms"]], "Printing matching on irrefutable patterns": [[46, "printing-matching-on-irrefutable-patterns"]], "Printing matching on booleans": [[46, "printing-matching-on-booleans"]], "Conventions about unused pattern-matching variables": [[46, "conventions-about-unused-pattern-matching-variables"]], "Patterns": [[46, "patterns"]], "Multiple patterns": [[46, "multiple-patterns"]], "Aliasing subpatterns": [[46, "aliasing-subpatterns"]], "Nested patterns": [[46, "nested-patterns"]], "Disjunctive patterns": [[46, "disjunctive-patterns"]], "About patterns of parametric types": [[46, "about-patterns-of-parametric-types"]], "Parameters in patterns": [[46, "parameters-in-patterns"]], "Implicit arguments in patterns": [[46, "implicit-arguments-in-patterns"]], "Matching objects of dependent types": [[46, "matching-objects-of-dependent-types"]], "Understanding dependencies in patterns": [[46, "understanding-dependencies-in-patterns"]], "When the elimination predicate must be provided": [[46, "when-the-elimination-predicate-must-be-provided"]], "Dependent pattern matching": [[46, "dependent-pattern-matching"]], "Multiple dependent pattern matching": [[46, "multiple-dependent-pattern-matching"]], "Patterns in in": [[46, "patterns-in-in"]], "Using pattern matching to write proofs": [[46, "using-pattern-matching-to-write-proofs"]], "Pattern-matching on inductive objects involving local definitions": [[46, "pattern-matching-on-inductive-objects-involving-local-definitions"]], "Pattern-matching and coercions": [[46, "pattern-matching-and-coercions"]], "When does the expansion strategy fail?": [[46, "when-does-the-expansion-strategy-fail"]], "The Rocq Prover commands": [[51, "the-rocq-prover-commands"]], "Interactive use (rocq repl)": [[51, "interactive-use-rocq-repl"]], "Batch compilation (rocq compile)": [[51, "batch-compilation-rocq-compile"]], "Example: Compiling and loading a single file": [[51, null]], "Customization at launch time": [[51, "customization-at-launch-time"]], "Command parameters": [[51, "command-parameters"]], "coqrc start up script": [[51, "coqrc-start-up-script"]], "Environment variables": [[51, "environment-variables"]], "Command line options": [[51, "command-line-options"], [75, "command-line-options"]], "Profiling": [[51, "profiling"], [55, "profiling"]], "Compiled interfaces (produced using -vos)": [[51, "compiled-interfaces-produced-using-vos"]], "Compiled libraries checker (rocqchk)": [[51, "compiled-libraries-checker-rocqchk"]], "Managing files and buffers, basic editing": [[52, "managing-files-and-buffers-basic-editing"]], "Running Coq scripts": [[52, "running-coq-scripts"]], "Asynchronous mode": [[52, "asynchronous-mode"]], "Commands and templates": [[52, "commands-and-templates"]], "Queries": [[52, "queries"]], "Compilation": [[52, "compilation"]], "Customizations": [[52, "customizations"]], "Preferences": [[52, "preferences"]], "Key bindings": [[52, "key-bindings"]], "Using Unicode symbols": [[52, "using-unicode-symbols"]], "Displaying Unicode symbols": [[52, "displaying-unicode-symbols"]], "Bindings for input of Unicode symbols": [[52, "bindings-for-input-of-unicode-symbols"]], "Adding custom bindings": [[52, "adding-custom-bindings"]], "Character encoding for saved files": [[52, "character-encoding-for-saved-files"]], "Debugger": [[52, "debugger"]], "Breakpoints": [[52, "breakpoints"]], "Call Stack and Variables": [[52, "call-stack-and-variables"]], "Supported use cases": [[52, "supported-use-cases"]], "Building Rocq Projects": [[53, "building-rocq-projects"]], "Rocq configuration basics": [[53, "rocq-configuration-basics"]], "Installing the Rocq Prover and Rocq packages with opam": [[53, "installing-the-rocq-prover-and-rocq-packages-with-opam"]], "Setup for working on your own projects": [[53, "setup-for-working-on-your-own-projects"]], "Building a project with _CoqProject (overview)": [[53, "building-a-project-with-coqproject-overview"]], "Logical paths and the load path": [[53, "logical-paths-and-the-load-path"]], "Modifying multiple interdependent projects at the same time": [[53, "modifying-multiple-interdependent-projects-at-the-same-time"]], "Installed and uninstalled packages": [[53, "installed-and-uninstalled-packages"]], "Upgrading to a new version of Rocq": [[53, "upgrading-to-a-new-version-of-rocq"]], "Building a Rocq project with rocq makefile (details)": [[53, "building-a-rocq-project-with-rocq-makefile-details"]], "Comments": [[53, "comments"]], "Quoting arguments to rocq c": [[53, "quoting-arguments-to-rocq-c"]], "Forbidden filenames": [[53, "forbidden-filenames"]], "Warning: No common logical root": [[53, "warning-no-common-logical-root"]], "CoqMakefile.local": [[53, "coqmakefile-local"]], "CoqMakefile.local-late": [[53, "coqmakefile-local-late"]], "Timing targets and performance testing": [[53, "timing-targets-and-performance-testing"]], "Building a subset of the targets with -j": [[53, "building-a-subset-of-the-targets-with-j"]], "Precompiling for native_compute": [[53, "precompiling-for-native-compute"]], "The grammar of _CoqProject": [[53, "the-grammar-of-coqproject"]], "Building a Rocq project with Dune": [[53, "building-a-rocq-project-with-dune"]], "rocq dep: Computing Module dependencies": [[53, "rocq-dep-computing-module-dependencies"]], "Split compilation of native computation files": [[53, "split-compilation-of-native-computation-files"]], "Using Rocq as a library": [[53, "using-rocq-as-a-library"]], "Embedded Rocq phrases inside LaTeX documents": [[53, "embedded-rocq-phrases-inside-latex-documents"]], "Man pages": [[53, "man-pages"]], "Ltac": [[54, "ltac"]], "Example: Basic tactic macros": [[54, null]], "Defects": [[54, "defects"]], "Syntax": [[54, "syntax"], [55, "syntax"], [57, "syntax"], [71, "syntax"]], "Values": [[54, "values"]], "Syntactic values": [[54, "syntactic-values"]], "Substitution": [[54, "substitution"]], "Example: Substitution of global and local symbols": [[54, null]], "Local definitions: let": [[54, "local-definitions-let"]], "Function construction and application": [[54, "function-construction-and-application"]], "Tactics in terms": [[54, "tactics-in-terms"]], "Goal selectors": [[54, "goal-selectors"]], "Example: Selector reordering goals": [[54, "reordering-goals-ex"]], "Processing multiple goals": [[54, "processing-multiple-goals"]], "Example: Multiple focused goals": [[54, null]], "Branching and backtracking": [[54, "branching-and-backtracking"]], "Example: Backtracking": [[54, null]], "Control flow": [[54, "control-flow"], [57, "control-flow"]], "Sequence: ;": [[54, "sequence"]], "Do loop": [[54, "do-loop"]], "Repeat loop": [[54, "repeat-loop"]], "Catching errors: try": [[54, "catching-errors-try"]], "Conditional branching: tryif": [[54, "conditional-branching-tryif"]], "Alternatives": [[54, "alternatives"]], "Branching with backtracking: +": [[54, "branching-with-backtracking"]], "Example: Backtracking branching with +": [[54, null]], "Local application of tactics: [> ... ]": [[54, "local-application-of-tactics"]], "First tactic to succeed": [[54, "first-tactic-to-succeed"]], "Example: Backtracking inside a non-backtracking construct": [[54, null]], "Example: Referring to a list of tactics in Tactic Notation": [[54, null]], "Solving": [[54, "solving"]], "First tactic to make progress: ||": [[54, "first-tactic-to-make-progress"]], "Detecting progress": [[54, "detecting-progress"]], "Success and failure": [[54, "success-and-failure"]], "Checking for success: assert_succeeds": [[54, "checking-for-success-assert-succeeds"]], "Checking for failure: assert_fails": [[54, "checking-for-failure-assert-fails"]], "Failing": [[54, "failing"]], "Soft cut: once": [[54, "soft-cut-once"]], "Checking for a single success: exactly_once": [[54, "checking-for-a-single-success-exactly-once"]], "Manipulating values": [[54, "manipulating-values"]], "Pattern matching on terms: match": [[54, "pattern-matching-on-terms-match"]], "Example: Comparison of lazymatch and match": [[54, null]], "Example: Comparison of match and multimatch": [[54, null]], "Example: Matching a pattern with holes": [[54, null]], "Example: Multiple matches for a \"context\" pattern.": [[54, null]], "Pattern matching on goals and hypotheses: match goal": [[54, "pattern-matching-on-goals-and-hypotheses-match-goal"]], "Example: Matching hypotheses": [[54, null]], "Example: Matching hypotheses with reverse": [[54, null], [55, "ltac2-match-goal-hyps-rev-ex"]], "Example: Multiple ways to match hypotheses": [[54, null]], "Filling a term context": [[54, "filling-a-term-context"]], "Example: Substituting a matched context": [[54, null]], "Generating fresh hypothesis names": [[54, "generating-fresh-hypothesis-names"]], "Computing in a term: eval": [[54, "computing-in-a-term-eval"]], "Getting the type of a term": [[54, "getting-the-type-of-a-term"]], "Manipulating untyped terms: type_term": [[54, "manipulating-untyped-terms-type-term"]], "Counting goals: numgoals": [[54, "counting-goals-numgoals"]], "Testing boolean expressions: guard": [[54, "testing-boolean-expressions-guard"]], "Example: guard": [[54, null]], "Checking properties of terms": [[54, "checking-properties-of-terms"]], "Example: is_fix": [[54, null]], "Example: is_cofix": [[54, null]], "Example: is_proj": [[54, null]], "Timing": [[54, "timing"]], "Timeout": [[54, "timeout"]], "Timing a tactic": [[54, "timing-a-tactic"]], "Timing a tactic that evaluates to a term: time_constr": [[54, "timing-a-tactic-that-evaluates-to-a-term-time-constr"]], "Print/identity tactic: idtac": [[54, "print-identity-tactic-idtac"]], "Tactic toplevel definitions": [[54, "tactic-toplevel-definitions"]], "Defining Ltac symbols": [[54, "defining-ltac-symbols"]], "Printing Ltac tactics": [[54, "printing-ltac-tactics"]], "Examples of using Ltac": [[54, "examples-of-using-ltac"]], "Proof that the natural numbers have at least two elements": [[54, "proof-that-the-natural-numbers-have-at-least-two-elements"]], "Example: Proof that the natural numbers have at least two elements": [[54, null]], "Proving that a list is a permutation of a second list": [[54, "proving-that-a-list-is-a-permutation-of-a-second-list"]], "Example: Proving that a list is a permutation of a second list": [[54, null]], "Deciding intuitionistic propositional logic": [[54, "deciding-intuitionistic-propositional-logic"]], "Deciding type isomorphisms": [[54, "deciding-type-isomorphisms"]], "Debugging Ltac tactics": [[54, "debugging-ltac-tactics"]], "Backtraces": [[54, "backtraces"]], "Tracing execution": [[54, "tracing-execution"]], "Interactive debugger": [[54, "interactive-debugger"]], "Profiling Ltac tactics": [[54, "profiling-ltac-tactics"]], "Run-time optimization tactic": [[54, "run-time-optimization-tactic"]], "Ltac2": [[55, "ltac2"]], "General design": [[55, "general-design"]], "ML component": [[55, "ml-component"]], "Overview": [[55, "overview"], [55, "id3"]], "Type Syntax": [[55, "type-syntax"]], "Type declarations": [[55, "type-declarations"]], "APIs": [[55, "apis"]], "Term Syntax": [[55, "term-syntax"]], "Ltac2 Definitions": [[55, "ltac2-definitions"]], "Example: Dynamic nature of mutable cells": [[55, null]], "Example: Interaction with recursive calls": [[55, null]], "Printing Ltac2 tactics": [[55, "printing-ltac2-tactics"]], "Typing": [[55, "typing"]], "Effects": [[55, "effects"]], "Standard IO": [[55, "standard-io"]], "Fatal errors": [[55, "fatal-errors"]], "Backtracking": [[55, "backtracking"], [59, "backtracking"]], "Goals": [[55, "goals"]], "Meta-programming": [[55, "meta-programming"]], "Quotations": [[55, "quotations"]], "Built-in quotations": [[55, "built-in-quotations"]], "Strict vs. non-strict mode": [[55, "strict-vs-non-strict-mode"]], "Term Antiquotations": [[55, "term-antiquotations"]], "Semantics": [[55, "semantics"]], "Static semantics": [[55, "static-semantics"]], "Dynamic semantics": [[55, "dynamic-semantics"]], "Match over terms": [[55, "match-over-terms"]], "Example: Ltac2 Comparison of lazy_match! and match!": [[55, "ltac2-match-vs-lazymatch-ex"]], "Example: Ltac2 Comparison of match! and multi_match!": [[55, "ltac2-match-vs-multimatch-ex"]], "Example: Ltac2 Multiple matches for a \"context\" pattern.": [[55, "ltac2-match-term-context-ex"]], "Match over goals": [[55, "match-over-goals"]], "Example: Ltac2 Matching hypotheses": [[55, "ltac2-match-goal-hyps-ex"]], "Example: Multiple ways to match a hypotheses": [[55, "ltac2-match-goal-multiple-hyps-ex"]], "Match on values": [[55, "match-on-values"]], "Example: Printing a term": [[55, null]], "Example: Parsing a list of terms": [[55, null]], "Abbreviations": [[55, "abbreviations"], [57, "abbreviations"], [71, "abbreviations"]], "Defining tactics": [[55, "defining-tactics"]], "Syntactic classes": [[55, "syntactic-classes"]], "Evaluation": [[55, "evaluation"]], "Debug": [[55, "debug"]], "Compatibility layer with Ltac1": [[55, "compatibility-layer-with-ltac1"]], "Ltac1 from Ltac2": [[55, "ltac1-from-ltac2"]], "Simple API": [[55, "simple-api"]], "Low-level API": [[55, "low-level-api"]], "Ltac2 from Ltac1": [[55, "ltac2-from-ltac1"]], "Switching between Ltac languages": [[55, "switching-between-ltac-languages"]], "Transition from Ltac1": [[55, "transition-from-ltac1"]], "Syntax changes": [[55, "syntax-changes"]], "Tactic delay": [[55, "tactic-delay"]], "Variable binding": [[55, "variable-binding"]], "In Ltac expressions": [[55, "in-ltac-expressions"]], "In quotations": [[55, "in-quotations"]], "Exception catching": [[55, "exception-catching"]], "The SSReflect proof language": [[57, "the-ssr-proof-language"]], "Introduction": [[57, "introduction"]], "Acknowledgments": [[57, "acknowledgments"]], "Getting started": [[57, "getting-started"]], "Compatibility issues": [[57, "compatibility-issues"]], "Gallina extensions": [[57, "gallina-extensions"]], "Pattern assignment": [[57, "pattern-assignment"]], "Pattern conditional": [[57, "pattern-conditional"]], "Parametric polymorphism": [[57, "parametric-polymorphism"]], "Anonymous arguments": [[57, "anonymous-arguments"]], "Wildcards": [[57, "wildcards"]], "Matching": [[57, "matching"]], "Occurrence selection": [[57, "occurrence-selection"]], "Basic localization": [[57, "basic-localization"]], "Basic tactics": [[57, "basic-tactics"]], "Bookkeeping": [[57, "bookkeeping"]], "The defective tactics": [[57, "the-defective-tactics"]], "The move tactic.": [[57, "the-move-tactic"]], "The case tactic": [[57, "the-case-tactic"]], "The elim tactic": [[57, "the-elim-tactic"]], "The apply tactic": [[57, "the-apply-tactic"]], "Discharge": [[57, "discharge"]], "Clear rules": [[57, "clear-rules"]], "Matching for apply and exact": [[57, "matching-for-apply-and-exact"]], "The abstract tactic": [[57, "the-abstract-tactic"]], "Introduction in the context": [[57, "introduction-in-the-context"]], "Simplification items": [[57, "simplification-items"]], "Views": [[57, "views"]], "Intro patterns": [[57, "intro-patterns"], [58, "intro-patterns"]], "Clear switch": [[57, "clear-switch"]], "Branching and destructuring": [[57, "branching-and-destructuring"]], "Block introduction": [[57, "block-introduction"]], "Generation of equations": [[57, "generation-of-equations"]], "Type families": [[57, "type-families"]], "Indentation and bullets": [[57, "indentation-and-bullets"]], "Terminators": [[57, "terminators"]], "Selectors": [[57, "selectors"]], "Iteration": [[57, "iteration"]], "Localization": [[57, "localization"]], "Structure": [[57, "structure"]], "The have tactic.": [[57, "the-have-tactic"]], "Generating let in context entries with have": [[57, "generating-let-in-context-entries-with-have"]], "The have tactic and typeclass resolution": [[57, "the-have-tactic-and-typeclass-resolution"]], "Variants: the suff and wlog tactics": [[57, "variants-the-suff-and-wlog-tactics"]], "Advanced generalization": [[57, "advanced-generalization"]], "Rewriting": [[57, "rewriting"]], "An extended rewrite tactic": [[57, "an-extended-rewrite-tactic"]], "Remarks and examples": [[57, "remarks-and-examples"]], "Rewrite redex selection": [[57, "rewrite-redex-selection"]], "Chained rewrite steps": [[57, "chained-rewrite-steps"]], "Explicit redex switches are matched first": [[57, "explicit-redex-switches-are-matched-first"]], "Occurrence switches and redex switches": [[57, "occurrence-switches-and-redex-switches"]], "Occurrence selection and repetition": [[57, "occurrence-selection-and-repetition"]], "Multi-rule rewriting": [[57, "multi-rule-rewriting"]], "Wildcards vs abstractions": [[57, "wildcards-vs-abstractions"]], "When SSReflect rewrite fails on standard Rocq licit rewrite": [[57, "when-ssr-rewrite-fails-on-standard-rocq-licit-rewrite"]], "Existential metavariables and rewriting": [[57, "existential-metavariables-and-rewriting"]], "The under tactic": [[57, "the-under-tactic"]], "The over tactic": [[57, "the-over-tactic"]], "One-liner mode": [[57, "one-liner-mode"]], "Locking, unlocking": [[57, "locking-unlocking"]], "Congruence": [[57, "congruence"]], "Contextual patterns": [[57, "contextual-patterns"]], "Matching contextual patterns": [[57, "matching-contextual-patterns"]], "Contextual pattern in set and the : tactical": [[57, "contextual-pattern-in-set-and-the-tactical"]], "Contextual patterns in rewrite": [[57, "contextual-patterns-in-rewrite"]], "Patterns for recurrent contexts": [[57, "patterns-for-recurrent-contexts"]], "Views and reflection": [[57, "views-and-reflection"]], "Interpreting eliminations": [[57, "interpreting-eliminations"]], "Interpreting assumptions": [[57, "interpreting-assumptions"], [57, "id16"]], "Specializing assumptions": [[57, "specializing-assumptions"], [57, "id15"]], "Interpreting goals": [[57, "interpreting-goals"], [57, "id17"]], "Boolean reflection": [[57, "boolean-reflection"]], "The reflect predicate": [[57, "the-reflect-predicate"]], "General mechanism for interpreting goals and assumptions": [[57, "general-mechanism-for-interpreting-goals-and-assumptions"]], "Interpreting equivalences": [[57, "interpreting-equivalences"]], "Declaring new Hint Views": [[57, "declaring-new-hint-views"]], "Multiple views": [[57, "multiple-views"]], "Additional view shortcuts": [[57, "additional-view-shortcuts"]], "Synopsis and Index": [[57, "synopsis-and-index"]], "Parameters": [[57, "parameters"]], "Items and switches": [[57, "items-and-switches"]], "Tacticals": [[57, "tacticals"]], "Common elements of tactics": [[58, "common-elements-of-tactics"]], "Reserved keywords": [[58, "reserved-keywords"]], "Invocation of tactics": [[58, "invocation-of-tactics"]], "Bindings": [[58, "bindings"]], "Example: intro pattern for /\\": [[58, null]], "Example: intro pattern for \\/": [[58, null]], "Example: -> intro pattern": [[58, null]], "Example: [=] intro pattern": [[58, null]], "Example: (A & B & \u2026) intro pattern": [[58, null]], "Example: * intro pattern": [[58, null]], "Example: ** pattern (\"intros **\" is equivalent to \"intros\")": [[58, null]], "Example: compound intro pattern": [[58, null]], "Example: combined intro pattern using [=] -> and %": [[58, null]], "Occurrence clauses": [[58, "occurrence-clauses"]], "Applying theorems": [[58, "applying-theorems"]], "Example: Backward reasoning in the goal with apply": [[58, "apply-backward"]], "Example: Backward reasoning in the goal with apply including a premise": [[58, "apply-backward-w-premises"]], "Example: Forward reasoning in hypotheses with apply": [[58, "apply-forward"]], "Example: Apply a theorem with a binding in a goal": [[58, "apply-with-binding-goal"]], "Example: Apply a theorem with a binding in a hypothesis": [[58, "apply-with-binding-hyp"]], "Example: Applying theorems with <->": [[58, "apply-with-iff"]], "Example: Special case of second-order unification in apply": [[58, "example-apply-pattern"]], "Managing the local context": [[58, "managing-the-local-context"]], "Example: intro and intros": [[58, "intro-examples"]], "Example: intros until": [[58, null]], "Example: move": [[58, null]], "Example: set with a simple_binder": [[58, null]], "Controlling the proof flow": [[58, "controlling-the-proof-flow"]], "Example: partial application in specialize": [[58, null]], "Example: specialize with a non-dependent product": [[58, null]], "Example: contradiction tactic": [[58, null]], "Classical tactics": [[58, "classical-tactics"]], "Performance-oriented tactic variants": [[58, "performance-oriented-tactic-variants"]], "Displaying": [[59, "displaying"]], "Query commands": [[59, "query-commands"]], "Example: Searching for a pattern": [[59, "search-pattern"]], "Example: Searching for part of an identifier": [[59, "search-part-ident"]], "Example: Searching for a reference by notation": [[59, "search-by-notation"]], "Example: Disambiguating between part of identifier and notation": [[59, "search-disambiguate-notation"]], "Example: Search in hypotheses": [[59, "search-hyp"]], "Example: Search in conclusion": [[59, "search-concl"]], "Example: Search by keyword or status": [[59, "search-by-keyword"]], "Example: SearchPattern examples": [[59, null]], "Example: SearchRewrite examples": [[59, null]], "Requests to the environment": [[59, "requests-to-the-environment"]], "Example: Locate examples": [[59, null]], "Printing flags": [[59, "printing-flags"]], "Loading files": [[59, "loading-files"]], "Compiled files": [[59, "compiled-files"]], "Load paths": [[59, "load-paths"]], "Extra Dependencies": [[59, "extra-dependencies"]], "Quitting and debugging": [[59, "quitting-and-debugging"]], "Controlling display": [[59, "controlling-display"]], "Printing constructions in full": [[59, "printing-constructions-in-full"]], "Controlling Typing Flags": [[59, "controlling-typing-flags"]], "Internal registration commands": [[59, "internal-registration-commands"]], "Exposing constants to OCaml libraries": [[59, "exposing-constants-to-ocaml-libraries"]], "Inlining hints for the fast reduction machines": [[59, "inlining-hints-for-the-fast-reduction-machines"]], "Registering primitive operations": [[59, "registering-primitive-operations"]], "Programmable proof search": [[60, "programmable-proof-search"]], "Example: Ackermann function": [[60, null]], "Example: MacCarthy function": [[60, null]], "Hint databases": [[60, "hint-databases"]], "Creating hint databases": [[60, "creating-hint-databases"]], "Hint databases defined in the Rocq standard library": [[60, "hint-databases-defined-in-the-rocq-standard-library"]], "Creating Hints": [[60, "creating-hints"]], "Example: Logic programming with addition on natural numbers": [[60, null]], "Hint locality": [[60, "hint-locality"]], "Setting implicit automation tactics": [[60, "setting-implicit-automation-tactics"]], "Automatic solvers and programmable tactics": [[61, "automatic-solvers-and-programmable-tactics"]], "Solvers for logic and equality": [[62, "solvers-for-logic-and-equality"]], "Creating new tactics": [[63, "creating-new-tactics"]], "Reasoning with equalities": [[64, "reasoning-with-equalities"]], "Tactics for simple equalities": [[64, "tactics-for-simple-equalities"]], "Rewriting with Leibniz and setoid equality": [[64, "rewriting-with-leibniz-and-setoid-equality"]], "Rewriting with definitional equality": [[64, "rewriting-with-definitional-equality"]], "Applying conversion rules": [[64, "applying-conversion-rules"]], "Example: fold doesn't always undo unfold": [[64, null]], "Example: Use fold to reverse unfolding of fold_right": [[64, null]], "Fast reduction tactics: vm_compute and native_compute": [[64, "fast-reduction-tactics-vm-compute-and-native-compute"]], "Computing in a term: eval and Eval": [[64, "computing-in-a-term-eval-and-eval"]], "Controlling reduction strategies and the conversion algorithm": [[64, "controlling-reduction-strategies-and-the-conversion-algorithm"]], "Basic proof writing": [[65, "basic-proof-writing"]], "Proof mode": [[66, "proof-mode"]], "Proof State": [[66, "proof-state"]], "Entering and exiting proof mode": [[66, "entering-and-exiting-proof-mode"]], "Example: Declaring section variables": [[66, null]], "Proof using options": [[66, "proof-using-options"]], "Name a set of section hypotheses for Proof using": [[66, "name-a-set-of-section-hypotheses-for-proof-using"]], "Proof modes": [[66, "proof-modes"]], "Managing goals": [[66, "managing-goals"]], "Focusing goals": [[66, "focusing-goals"]], "Curly braces": [[66, "curly-braces"]], "Example: Working with named goals": [[66, null]], "Bullets": [[66, "bullets"]], "Example: Use of bullets": [[66, null]], "Other focusing commands": [[66, "other-focusing-commands"]], "Shelving goals": [[66, "shelving-goals"]], "Example: shelve_unifiable": [[66, null]], "Reordering goals": [[66, "reordering-goals"]], "Example: cycle": [[66, null]], "Example: swap": [[66, null]], "Example: revgoals": [[66, null]], "Proving a subgoal as a separate lemma: abstract": [[66, "proving-a-subgoal-as-a-separate-lemma-abstract"]], "Requesting information": [[66, "requesting-information"]], "Showing differences between proof steps": [[66, "showing-differences-between-proof-steps"]], "How to enable diffs": [[66, "how-to-enable-diffs"]], "How diffs are calculated": [[66, "how-diffs-are-calculated"]], "\"Show Proof\" differences": [[66, "show-proof-differences"]], "Delaying solving unification constraints": [[66, "delaying-solving-unification-constraints"]], "Proof maintenance": [[66, "proof-maintenance"]], "Controlling proof mode": [[66, "controlling-proof-mode"]], "Controlling memory usage": [[66, "controlling-memory-usage"]], "Reasoning with inductive types": [[67, "reasoning-with-inductive-types"]], "Applying constructors": [[67, "applying-constructors"]], "Example: constructor, left and right": [[67, null]], "Case analysis": [[67, "case-analysis"]], "Example: Using destruct on an argument with premises": [[67, "example-destruct-ind-concl"]], "Induction": [[67, "induction"]], "Example: induction with occurrences": [[67, null]], "Equality of inductive types": [[67, "equality-of-inductive-types"]], "Example: Proving 1 <> 2": [[67, null]], "Example: discriminate limitation: proving n <> S n": [[67, null]], "Example: inversion with as or_and_intropattern": [[67, null]], "Example: Non-dependent inversion": [[67, null]], "Example: Dependent inversion": [[67, null]], "Example: Using inversion_sigma": [[67, null]], "Helper tactics": [[67, "helper-tactics"]], "Example: Using decide to rewrite the goal": [[67, null]], "Generation of induction principles with Scheme": [[67, "generation-of-induction-principles-with-scheme"]], "Example: Induction scheme for tree and forest": [[67, null]], "Example: Predicates odd and even on naturals": [[67, null]], "Example: Scheme commands with various scheme_types": [[67, null]], "Automatic declaration of schemes": [[67, "automatic-declaration-of-schemes"]], "Combined Scheme": [[67, "combined-scheme"]], "Generation of inversion principles with Derive Inversion": [[67, "generation-of-inversion-principles-with-derive-inversion"]], "Examples of dependent destruction / dependent induction": [[67, "examples-of-dependent-destruction-dependent-induction"]], "A larger example": [[67, "a-larger-example"]], "Glossary index": [[69, "glossary-index"]], "Syntax extensions and notation scopes": [[71, "syntax-extensions-and-notation-scopes"]], "Basic notations": [[71, "basic-notations"]], "Precedences and associativity": [[71, "precedences-and-associativity"]], "Complex notations": [[71, "complex-notations"]], "Simple factorization rules": [[71, "simple-factorization-rules"]], "Use of notations for printing": [[71, "use-of-notations-for-printing"]], "The Infix command": [[71, "the-infix-command"]], "Reserving notations": [[71, "reserving-notations"]], "Simultaneous definition of terms and notations": [[71, "simultaneous-definition-of-terms-and-notations"]], "Enabling and disabling notations": [[71, "enabling-and-disabling-notations"]], "Example: Enabling and disabling notations": [[71, null]], "Displaying information about notations": [[71, "displaying-information-about-notations"]], "Example: Print Notation": [[71, null]], "Locating notations": [[71, "locating-notations"]], "Inheritance of the properties of arguments of constants bound to a notation": [[71, "inheritance-of-the-properties-of-arguments-of-constants-bound-to-a-notation"]], "Notations and binders": [[71, "notations-and-binders"]], "Binders bound in the notation and parsed as identifiers": [[71, "binders-bound-in-the-notation-and-parsed-as-identifiers"]], "Binders bound in the notation and parsed as patterns": [[71, "binders-bound-in-the-notation-and-parsed-as-patterns"]], "Binders bound in the notation and parsed as terms": [[71, "binders-bound-in-the-notation-and-parsed-as-terms"]], "Binders bound in the notation and parsed as general binders": [[71, "binders-bound-in-the-notation-and-parsed-as-general-binders"]], "Binders not bound in the notation": [[71, "binders-not-bound-in-the-notation"]], "Notations with expressions used both as binder and term": [[71, "notations-with-expressions-used-both-as-binder-and-term"]], "Notations with recursive patterns": [[71, "notations-with-recursive-patterns"]], "Notations with recursive patterns involving binders": [[71, "notations-with-recursive-patterns-involving-binders"]], "Predefined entries": [[71, "predefined-entries"]], "Custom entries": [[71, "custom-entries"]], "Notation scopes": [[71, "notation-scopes"]], "Global interpretation rules for notations": [[71, "global-interpretation-rules-for-notations"]], "Local interpretation rules for notations": [[71, "local-interpretation-rules-for-notations"]], "Opening a notation scope locally": [[71, "opening-a-notation-scope-locally"]], "Binding types or coercion classes to notation scopes": [[71, "binding-types-or-coercion-classes-to-notation-scopes"]], "Example: Binding scopes to a type": [[71, null]], "The type_scope notation scope": [[71, "the-type-scope-notation-scope"]], "The function_scope notation scope": [[71, "the-function-scope-notation-scope"]], "Notation scopes used in the standard library of Rocq": [[71, "notation-scopes-used-in-the-standard-library-of-rocq"]], "Displaying information about scopes": [[71, "displaying-information-about-scopes"]], "Numbers and strings": [[71, "numbers-and-strings"]], "Number notations": [[71, "number-notations"]], "String notations": [[71, "string-notations"]], "Example: Number Notation for radix 3": [[71, null]], "Example: Number Notation for primitive integers": [[71, "example-number-notation-primitive-int"]], "Example: Number Notation for a non-inductive type": [[71, "example-number-notation-non-inductive"]], "Example: Number Notation with implicit arguments": [[71, "example-number-notation-implicit-args"]], "Example: String Notation with a parameterized inductive type": [[71, "example-string-notation-parameterized-inductive"]], "Tactic Notations": [[71, "tactic-notations"]], "Functional induction": [[72, "functional-induction"]], "Advanced recursive functions": [[72, "advanced-recursive-functions"]], "Generation of induction principles with Functional Scheme": [[72, "generation-of-induction-principles-with-functional-scheme"]], "Libraries and plugins": [[73, "libraries-and-plugins"]], "Writing Rocq libraries and plugins": [[74, "writing-rocq-libraries-and-plugins"]], "Deprecating library objects, tactics or library files": [[74, "deprecating-library-objects-tactics-or-library-files"]], "Triggering warning for library objects or library files": [[74, "triggering-warning-for-library-objects-or-library-files"]], "Example: Deprecating a tactic.": [[74, null]], "Example: Introducing a compatibility alias": [[74, "compatibility-alias"]], "Documenting Rocq files with rocq doc": [[75, "documenting-rocq-files-with-rocq-doc"]], "Principles": [[75, "principles"]], "Rocq material inside documentation.": [[75, "rocq-material-inside-documentation"]], "Pretty-printing.": [[75, "pretty-printing"]], "Lists.": [[75, "lists"]], "Rules.": [[75, "rules"]], "Emphasis.": [[75, "emphasis"]], "Escaping to LaTeX and HTML.": [[75, "escaping-to-latex-and-html"]], "Verbatim": [[75, "verbatim"]], "Hyperlinks": [[75, "hyperlinks"]], "Hiding / Showing parts of the source": [[75, "hiding-showing-parts-of-the-source"]], "The rocq doc LaTeX style file": [[75, "the-rocq-doc-latex-style-file"]], "Command-line and graphical tools": [[76, "command-line-and-graphical-tools"]], "Bibliography": [[77, "bibliography"]]}, "indexentries": {"cd (command)": [[2, "coq:cmd.Cd"]], "extract callback (command)": [[2, "coq:cmd.Extract-Callback"]], "extract callback is supported only for ocaml extraction (error)": [[2, "coq:exn.Extract-Callback-is-supported-only-for-OCaml-extraction"]], "extract constant (command)": [[2, "coq:cmd.Extract-Constant"]], "extract foreign constant (command)": [[2, "coq:cmd.Extract-Foreign-Constant"]], "extract foreign constant is supported only for ocaml extraction (error)": [[2, "coq:exn.Extract-Foreign-Constant-is-supported-only-for-OCaml-extraction"]], "extract foreign constant is supported only for functions (error)": [[2, "coq:exn.Extract-Foreign-Constant-is-supported-only-for-functions"]], "extract inductive (command)": [[2, "coq:cmd.Extract-Inductive"]], "extract inlined constant (command)": [[2, "coq:cmd.Extract-Inlined-Constant"]], "extraction (command)": [[2, "coq:cmd.Extraction"]], "extraction autoinline (flag)": [[2, "coq:flag.Extraction-AutoInline"]], "extraction blacklist (command)": [[2, "coq:cmd.Extraction-Blacklist"]], "extraction conservative types (flag)": [[2, "coq:flag.Extraction-Conservative-Types"]], "extraction file comment (option)": [[2, "coq:opt.Extraction-File-Comment"]], "extraction flag (option)": [[2, "coq:opt.Extraction-Flag"]], "extraction implicit (command)": [[2, "coq:cmd.Extraction-Implicit"]], "extraction inline (command)": [[2, "coq:cmd.Extraction-Inline"]], "extraction keepsingleton (flag)": [[2, "coq:flag.Extraction-KeepSingleton"]], "extraction language (command)": [[2, "coq:cmd.Extraction-Language"]], "extraction library (command)": [[2, "coq:cmd.Extraction-Library"]], "extraction noinline (command)": [[2, "coq:cmd.Extraction-NoInline"]], "extraction optimize (flag)": [[2, "coq:flag.Extraction-Optimize"]], "extraction output directory (option)": [[2, "coq:opt.Extraction-Output-Directory"]], "extraction safeimplicits (flag)": [[2, "coq:flag.Extraction-SafeImplicits"]], "extraction testcompile (command)": [[2, "coq:cmd.Extraction-TestCompile"]], "extraction typeexpand (flag)": [[2, "coq:flag.Extraction-TypeExpand"]], "print extraction blacklist (command)": [[2, "coq:cmd.Print-Extraction-Blacklist"]], "print extraction callback (command)": [[2, "coq:cmd.Print-Extraction-Callback"]], "print extraction foreign (command)": [[2, "coq:cmd.Print-Extraction-Foreign"]], "print extraction inline (command)": [[2, "coq:cmd.Print-Extraction-Inline"]], "pwd (command)": [[2, "coq:cmd.Pwd"]], "recursive extraction (command)": [[2, "coq:cmd.Recursive-Extraction"]], "recursive extraction library (command)": [[2, "coq:cmd.Recursive-Extraction-Library"]], "reset extraction blacklist (command)": [[2, "coq:cmd.Reset-Extraction-Blacklist"]], "reset extraction callback (command)": [[2, "coq:cmd.Reset-Extraction-Callback"]], "reset extraction inline (command)": [[2, "coq:cmd.Reset-Extraction-Inline"]], "separate extraction (command)": [[2, "coq:cmd.Separate-Extraction"]], "show extraction (command)": [[2, "coq:cmd.Show-Extraction"]], "the term \u2018qualid\u2019 is already defined as foreign custom constant (error)": [[2, "coq:exn.The-term-\u2018qualid\u2019-is-already-defined-as-foreign-custom-constant"]], "the term \u2018qualid\u2019 is already defined as inline custom constant (error)": [[2, "coq:exn.The-term-\u2018qualid\u2019-is-already-defined-as-inline-custom-constant"]], "add morphism (command)": [[3, "coq:cmd.Add-Morphism"]], "add parametric morphism (command)": [[3, "coq:cmd.Add-Parametric-Morphism"]], "add parametric relation (command)": [[3, "coq:cmd.Add-Parametric-Relation"]], "add parametric setoid (command)": [[3, "coq:cmd.Add-Parametric-Setoid"]], "add relation (command)": [[3, "coq:cmd.Add-Relation"]], "add setoid (command)": [[3, "coq:cmd.Add-Setoid"]], "declare morphism (command)": [[3, "coq:cmd.Declare-Morphism"]], "no progress made (error)": [[3, "coq:exn.No-progress-made"]], "nothing to rewrite (error)": [[3, "coq:exn.Nothing-to-rewrite"]], "unable to satisfy the rewriting constraints (error)": [[3, "coq:exn.Unable-to-satisfy-the-rewriting-constraints"]], "head_of_constr (tactic)": [[3, "coq:tacn.head_of_constr"]], "rewrite_db (tactic)": [[3, "coq:tacn.rewrite_db"]], "rewrite_strat (tactic)": [[3, "coq:tacn.rewrite_strat"]], "setoid_etransitivity (tactic)": [[3, "coq:tacn.setoid_etransitivity"]], "setoid_reflexivity (tactic)": [[3, "coq:tacn.setoid_reflexivity"]], "setoid_replace (tactic)": [[3, "coq:tacn.setoid_replace"]], "setoid_rewrite (tactic)": [[3, "coq:tacn.setoid_rewrite"]], "setoid_symmetry (tactic)": [[3, "coq:tacn.setoid_symmetry"]], "setoid_transitivity (tactic)": [[3, "coq:tacn.setoid_transitivity"]], "... is not definitionally an identity function (warning)": [[4, "coq:warn....-is-not-definitionally-an-identity-function"]], ":> (coercion)": [[4, "index-0"]], "cannot find the source class of \u2018qualid\u2019 (error)": [[4, "coq:exn.Cannot-find-the-source-class-of-\u2018qualid\u2019"]], "cannot find the target class (error)": [[4, "coq:exn.Cannot-find-the-target-class"]], "cannot recognize \u2018coercion_class\u2019 as a source class of \u2018qualid\u2019 (error)": [[4, "coq:exn.Cannot-recognize-\u2018coercion_class\u2019-as-a-source-class-of-\u2018qualid\u2019"]], "coercion (command)": [[4, "coq:cmd.Coercion"]], "found target class \u2018coercion_class\u2019 instead of \u2018coercion_class\u2019 (error)": [[4, "coq:exn.Found-target-class-\u2018coercion_class\u2019-instead-of-\u2018coercion_class\u2019"]], "funclass cannot be a source class (error)": [[4, "coq:exn.Funclass-cannot-be-a-source-class"]], "identity coercion (command)": [[4, "coq:cmd.Identity-Coercion"]], "new coercion path ... is ambiguous with existing ... (warning)": [[4, "coq:warn.New-coercion-path-...-is-ambiguous-with-existing-..."]], "print classes (command)": [[4, "coq:cmd.Print-Classes"]], "print coercion paths (command)": [[4, "coq:cmd.Print-Coercion-Paths"]], "print coercions (command)": [[4, "coq:cmd.Print-Coercions"]], "print graph (command)": [[4, "coq:cmd.Print-Graph"]], "printing coercion (table)": [[4, "coq:table.Printing-Coercion"]], "printing coercions (flag)": [[4, "coq:flag.Printing-Coercions"]], "subclass (command)": [[4, "coq:cmd.SubClass"]], "nonuniform (attribute)": [[4, "coq:attr.nonuniform"]], "reversible (attribute)": [[4, "coq:attr.reversible"]], "\u2018coercion_class\u2019 must be a transparent constant (error)": [[4, "coq:exn.\u2018coercion_class\u2019-must-be-a-transparent-constant"]], "\u2018qualid\u2019 does not respect the uniform inheritance condition (warning)": [[4, "coq:warn.\u2018qualid\u2019-does-not-respect-the-uniform-inheritance-condition"]], "\u2018qualid\u2019 is already a coercion (error)": [[4, "coq:exn.\u2018qualid\u2019-is-already-a-coercion"]], "\u2018qualid\u2019 is not a function (error)": [[4, "coq:exn.\u2018qualid\u2019-is-not-a-function"]], "\u2018qualid\u2019 not declared (error)": [[4, "coq:exn.\u2018qualid\u2019-not-declared"]], "add zify (command)": [[5, "coq:cmd.Add-Zify"]], "bound on the ceiling function (theorem)": [[5, "coq:thm.Bound-on-the-ceiling-function"]], "case split (theorem)": [[5, "coq:thm.Case-split"]], "dump arith (option)": [[5, "coq:opt.Dump-Arith"]], "info micromega (flag)": [[5, "coq:flag.Info-Micromega"]], "lia cache (flag)": [[5, "coq:flag.Lia-Cache"]], "nia cache (flag)": [[5, "coq:flag.Nia-Cache"]], "nra cache (flag)": [[5, "coq:flag.Nra-Cache"]], "psatz (theorem)": [[5, "coq:thm.Psatz"]], "show lia profile (command)": [[5, "coq:cmd.Show-Lia-Profile"]], "show zify (command)": [[5, "coq:cmd.Show-Zify"]], "lia (tactic)": [[5, "coq:tacn.lia"]], "lra (tactic)": [[5, "coq:tacn.lra"]], "nia (tactic)": [[5, "coq:tacn.nia"]], "nra (tactic)": [[5, "coq:tacn.nra"]], "psatz (tactic)": [[5, "coq:tacn.psatz"]], "wlia (tactic)": [[5, "coq:tacn.wlia"]], "wlra_q (tactic)": [[5, "coq:tacn.wlra_Q"]], "wnia (tactic)": [[5, "coq:tacn.wnia"]], "wnra_q (tactic)": [[5, "coq:tacn.wnra_Q"]], "wpsatz_q (tactic)": [[5, "coq:tacn.wpsatz_Q"]], "wpsatz_z (tactic)": [[5, "coq:tacn.wpsatz_Z"]], "wsos_q (tactic)": [[5, "coq:tacn.wsos_Q"]], "wsos_z (tactic)": [[5, "coq:tacn.wsos_Z"]], "xlia (tactic)": [[5, "coq:tacn.xlia"]], "xlra_q (tactic)": [[5, "coq:tacn.xlra_Q"]], "xlra_r (tactic)": [[5, "coq:tacn.xlra_R"]], "xnia (tactic)": [[5, "coq:tacn.xnia"]], "xnra_q (tactic)": [[5, "coq:tacn.xnra_Q"]], "xnra_r (tactic)": [[5, "coq:tacn.xnra_R"]], "xpsatz_q (tactic)": [[5, "coq:tacn.xpsatz_Q"]], "xpsatz_r (tactic)": [[5, "coq:tacn.xpsatz_R"]], "xpsatz_z (tactic)": [[5, "coq:tacn.xpsatz_Z"]], "xsos_q (tactic)": [[5, "coq:tacn.xsos_Q"]], "xsos_r (tactic)": [[5, "coq:tacn.xsos_R"]], "xsos_z (tactic)": [[5, "coq:tacn.xsos_Z"]], "zify (tactic)": [[5, "coq:tacn.zify"]], "zify_elim_let (tactic)": [[5, "coq:tacn.zify_elim_let"]], "zify_iter_let (tactic)": [[5, "coq:tacn.zify_iter_let"]], "zify_iter_specs (tactic)": [[5, "coq:tacn.zify_iter_specs"]], "zify_op (tactic)": [[5, "coq:tacn.zify_op"]], "zify_saturate (tactic)": [[5, "coq:tacn.zify_saturate"]], "derive (command)": [[6, "coq:cmd.Derive"]], "nsatz (tactic)": [[7, "coq:tacn.nsatz"]], "nsatz_compute (tactic)": [[7, "coq:tacn.nsatz_compute"]], "admit obligations (command)": [[9, "coq:cmd.Admit-Obligations"]], "final obligation (command)": [[9, "coq:cmd.Final-Obligation"]], "ill-formed recursive definition (error)": [[9, "coq:exn.Ill-formed-recursive-definition"]], "next obligation (command)": [[9, "coq:cmd.Next-Obligation"]], "non extensible universe declaration not supported with monomorphic program definition (error)": [[9, "coq:exn.Non-extensible-universe-declaration-not-supported-with-monomorphic-Program-Definition"]], "obligation (command)": [[9, "coq:cmd.Obligation"]], "obligation tactic (command)": [[9, "coq:cmd.Obligation-Tactic"]], "obligations (command)": [[9, "coq:cmd.Obligations"]], "preterm (command)": [[9, "coq:cmd.Preterm"]], "program (attribute)": [[9, "coq:attr.Program"], [9, "coq:attr.program"]], "program cases (flag)": [[9, "coq:flag.Program-Cases"]], "program generalized coercion (flag)": [[9, "coq:flag.Program-Generalized-Coercion"]], "program mode (flag)": [[9, "coq:flag.Program-Mode"]], "show obligation tactic (command)": [[9, "coq:cmd.Show-Obligation-Tactic"]], "solve all obligations (command)": [[9, "coq:cmd.Solve-All-Obligations"]], "solve obligations (command)": [[9, "coq:cmd.Solve-Obligations"]], "transparent obligations (flag)": [[9, "coq:flag.Transparent-Obligations"]], "rewrite rule (command)": [[10, "coq:cmd.Rewrite-Rule"]], "rewrite rules (command)": [[10, "coq:cmd.Rewrite-Rules"]], "rewrite rule declaration requires passing the flag \"-allow-rewrite-rules\" (error)": [[10, "coq:exn.Rewrite-rule-declaration-requires-passing-the-flag-\"-allow-rewrite-rules\""]], "symbol (command)": [[10, "coq:cmd.Symbol"]], "symbols (command)": [[10, "coq:cmd.Symbols"]], "add field (command)": [[11, "coq:cmd.Add-Field"]], "add ring (command)": [[11, "coq:cmd.Add-Ring"]], "arguments of ring_simplify do not have all the same type (error)": [[11, "coq:exn.Arguments-of-ring_simplify-do-not-have-all-the-same-type"]], "bad lemma for decidability of equality (error)": [[11, "coq:exn.Bad-lemma-for-decidability-of-equality"]], "bad ring structure (error)": [[11, "coq:exn.Bad-ring-structure"]], "cannot find a declared ring structure for equality \u2018term\u2019 (error)": [[11, "coq:exn.Cannot-find-a-declared-ring-structure-for-equality-\u2018term\u2019"]], "cannot find a declared ring structure over \u2018term\u2019 (error)": [[11, "coq:exn.Cannot-find-a-declared-ring-structure-over-\u2018term\u2019"]], "not a valid ring equation (error)": [[11, "coq:exn.Not-a-valid-ring-equation"]], "print fields (command)": [[11, "coq:cmd.Print-Fields"]], "print rings (command)": [[11, "coq:cmd.Print-Rings"]], "ring operation should be declared as a morphism (error)": [[11, "coq:exn.Ring-operation-should-be-declared-as-a-morphism"]], "field (tactic)": [[11, "coq:tacn.field"]], "field_lookup (tactic)": [[11, "coq:tacn.field_lookup"]], "field_simplify (tactic)": [[11, "coq:tacn.field_simplify"]], "field_simplify_eq (tactic)": [[11, "coq:tacn.field_simplify_eq"]], "protect_fv (tactic)": [[11, "coq:tacn.protect_fv"]], "ring (tactic)": [[11, "coq:tacn.ring"]], "ring_lookup (tactic)": [[11, "coq:tacn.ring_lookup"]], "ring_simplify (tactic)": [[11, "coq:tacn.ring_simplify"]], "allow strictprop (flag)": [[12, "coq:flag.Allow-StrictProp"]], "bad relevance (warning)": [[12, "coq:warn.Bad-relevance"]], "definitional uip (flag)": [[12, "coq:flag.Definitional-UIP"]], "printing relevance marks (flag)": [[12, "coq:flag.Printing-Relevance-Marks"]], "sprop is disallowed because the \"allow strictprop\" flag is off (error)": [[12, "coq:exn.SProp-is-disallowed-because-the-\"Allow-StrictProp\"-flag-is-off"]], ":: (substructure)": [[13, "index-0"]], "class (command)": [[13, "coq:cmd.Class"]], "declare instance (command)": [[13, "coq:cmd.Declare-Instance"]], "existing class (command)": [[13, "coq:cmd.Existing-Class"]], "existing instance (command)": [[13, "coq:cmd.Existing-Instance"]], "existing instances (command)": [[13, "coq:cmd.Existing-Instances"]], "ignored instance declaration for \u201c\u2018ident\u2019\u201d: \u201c\u2018term\u2019\u201d is not a class (warning)": [[13, "coq:warn.Ignored-instance-declaration-for-\u201c\u2018ident\u2019\u201d:-\u201c\u2018term\u2019\u201d-is-not-a-class"]], "instance (command)": [[13, "coq:cmd.Instance"]], "print instances (command)": [[13, "coq:cmd.Print-Instances"]], "print typeclasses (command)": [[13, "coq:cmd.Print-Typeclasses"]], "typeclass resolution for conversion (flag)": [[13, "coq:flag.Typeclass-Resolution-For-Conversion"]], "typeclasses debug (flag)": [[13, "coq:flag.Typeclasses-Debug"]], "typeclasses debug verbosity (option)": [[13, "coq:opt.Typeclasses-Debug-Verbosity"]], "typeclasses default mode (option)": [[13, "coq:opt.Typeclasses-Default-Mode"]], "typeclasses dependency order (flag)": [[13, "coq:flag.Typeclasses-Dependency-Order"]], "typeclasses depth (option)": [[13, "coq:opt.Typeclasses-Depth"]], "typeclasses iterative deepening (flag)": [[13, "coq:flag.Typeclasses-Iterative-Deepening"]], "typeclasses limit intros (flag)": [[13, "coq:flag.Typeclasses-Limit-Intros"]], "typeclasses opaque (command)": [[13, "coq:cmd.Typeclasses-Opaque"]], "typeclasses strict resolution (flag)": [[13, "coq:flag.Typeclasses-Strict-Resolution"]], "typeclasses transparent (command)": [[13, "coq:cmd.Typeclasses-Transparent"]], "typeclasses unique instances (flag)": [[13, "coq:flag.Typeclasses-Unique-Instances"]], "typeclasses unique solutions (flag)": [[13, "coq:flag.Typeclasses-Unique-Solutions"]], "typeclasses eauto (command)": [[13, "coq:cmd.Typeclasses-eauto"]], "using inferred default mode: \u201cmode\u201d for \u201c\u2018ident\u2019\u201d (warning)": [[13, "coq:warn.Using-inferred-default-mode:-\u201cmode\u201d-for-\u201c\u2018ident\u2019\u201d"]], "autoapply (tactic)": [[13, "coq:tacn.autoapply"]], "mode (attribute)": [[13, "coq:attr.mode"]], "refine (attribute)": [[13, "coq:attr.refine"]], "typeclasses eauto (tactic)": [[13, "coq:tacn.typeclasses-eauto"]], "\u2018ident\u2019 is already declared as a typeclass (warning)": [[13, "coq:warn.\u2018ident\u2019-is-already-declared-as-a-typeclass"]], "constraint (command)": [[14, "coq:cmd.Constraint"]], "cumulative (attribute)": [[14, "coq:attr.Cumulative"]], "cumulativity weak constraints (flag)": [[14, "coq:flag.Cumulativity-Weak-Constraints"]], "monomorphic (attribute)": [[14, "coq:attr.Monomorphic"]], "noncumulative (attribute)": [[14, "coq:attr.NonCumulative"]], "polymorphic (attribute)": [[14, "coq:attr.Polymorphic"]], "polymorphic inductive cumulativity (flag)": [[14, "coq:flag.Polymorphic-Inductive-Cumulativity"]], "polymorphic universe constraints can only be declared inside sections, use monomorphic constraint instead (error)": [[14, "coq:exn.Polymorphic-universe-constraints-can-only-be-declared-inside-sections,-use-Monomorphic-Constraint-instead"]], "polymorphic universes can only be declared inside sections, use monomorphic universe instead (error)": [[14, "coq:exn.Polymorphic-universes-can-only-be-declared-inside-sections,-use-Monomorphic-Universe-instead"]], "print universes (command)": [[14, "coq:cmd.Print-Universes"]], "printing universes (flag)": [[14, "coq:flag.Printing-Universes"]], "private polymorphic universes (flag)": [[14, "coq:flag.Private-Polymorphic-Universes"]], "strict universe declaration (flag)": [[14, "coq:flag.Strict-Universe-Declaration"]], "the cumulative attribute can only be used in a polymorphic context (error)": [[14, "coq:exn.The-cumulative-attribute-can-only-be-used-in-a-polymorphic-context"]], "undeclared universe \u2018ident\u2019 (error)": [[14, "coq:exn.Undeclared-universe-\u2018ident\u2019"]], "universe (command)": [[14, "coq:cmd.Universe"]], "universe minimization toset (flag)": [[14, "coq:flag.Universe-Minimization-ToSet"]], "universe polymorphism (flag)": [[14, "coq:flag.Universe-Polymorphism"]], "universe inconsistency (error)": [[14, "coq:exn.Universe-inconsistency"]], "universes (command)": [[14, "coq:cmd.Universes"]], "universes(cumulative) (attribute)": [[14, "coq:attr.universes(cumulative)"]], "universes(polymorphic) (attribute)": [[14, "coq:attr.universes(polymorphic)"]], "* (term)": [[27, "index-9"]], "+ (term)": [[27, "index-9"]], "a*b (term)": [[27, "index-9"]], "a+b (term)": [[27, "index-9"]], "a+{b} (term)": [[27, "index-13"]], "acc (term)": [[27, "index-20"]], "acc_inv (term)": [[27, "index-20"]], "acc_rect (term)": [[27, "index-20"]], "choice (term)": [[27, "index-14"]], "choice2 (term)": [[27, "index-14"]], "connectives": [[27, "index-1"]], "datatypes": [[27, "index-7"]], "equality": [[27, "index-4"]], "exc (term)": [[27, "index-15"]], "false (term)": [[27, "index-1"], [27, "index-8"]], "false_rec (term)": [[27, "index-16"]], "false_rect (term)": [[27, "index-16"]], "fix_f (term)": [[27, "index-21"]], "fix_f_eq (term)": [[27, "index-21"]], "fix_f_inv (term)": [[27, "index-21"]], "fix_eq (term)": [[27, "index-21"]], "i (term)": [[27, "index-1"]], "issucc (term)": [[27, "index-17"]], "none (term)": [[27, "index-8"]], "o (term)": [[27, "index-8"]], "o_s (term)": [[27, "index-17"]], "programming": [[27, "index-8"]], "quantifiers": [[27, "index-3"]], "recursion": [[27, "index-20"]], "s (term)": [[27, "index-8"]], "some (term)": [[27, "index-8"]], "theories": [[27, "index-0"]], "true (term)": [[27, "index-1"], [27, "index-8"]], "well founded induction": [[27, "index-20"]], "well foundedness": [[27, "index-20"]], "absurd (term)": [[27, "index-5"]], "absurd_set (term)": [[27, "index-16"]], "all (term)": [[27, "index-3"]], "and (term)": [[27, "index-1"]], "and_rect (term)": [[27, "index-16"]], "bool (term)": [[27, "index-8"]], "bool_choice (term)": [[27, "index-14"]], "conj (term)": [[27, "index-1"]], "eq (term)": [[27, "index-4"]], "eq_s (term)": [[27, "index-17"]], "eq_add_s (term)": [[27, "index-17"]], "eq_ind_r (term)": [[27, "index-5"]], "eq_rec_r (term)": [[27, "index-5"]], "eq_rect (term)": [[27, "index-16"], [27, "index-5"]], "eq_rect_r (term)": [[27, "index-5"]], "eq_refl (term)": [[27, "index-4"]], "eq_sym (term)": [[27, "index-5"]], "eq_trans (term)": [[27, "index-5"]], "error (term)": [[27, "index-15"]], "ex (term)": [[27, "index-3"]], "ex2 (term)": [[27, "index-3"]], "ex_intro (term)": [[27, "index-3"]], "ex_intro2 (term)": [[27, "index-3"]], "exist (term)": [[27, "index-10"]], "exist2 (term)": [[27, "index-10"]], "existt (term)": [[27, "index-11"]], "existt2 (term)": [[27, "index-11"]], "exists (term)": [[27, "index-3"]], "exists2 (term)": [[27, "index-3"]], "f_equal (term)": [[27, "index-5"]], "f_equal2 ... f_equal5 (term)": [[27, "index-6"]], "fst (term)": [[27, "index-9"]], "ge (term)": [[27, "index-18"]], "gt (term)": [[27, "index-18"]], "identity (term)": [[27, "index-8"]], "iff (term)": [[27, "index-1"]], "inl (term)": [[27, "index-9"]], "inleft (term)": [[27, "index-13"]], "inr (term)": [[27, "index-9"]], "inright (term)": [[27, "index-13"]], "le (term)": [[27, "index-18"]], "le_s (term)": [[27, "index-18"]], "le_n (term)": [[27, "index-18"]], "left (term)": [[27, "index-12"]], "lt (term)": [[27, "index-18"]], "mult (term)": [[27, "index-17"]], "mult_n_o (term)": [[27, "index-17"]], "mult_n_sm (term)": [[27, "index-17"]], "n_sn (term)": [[27, "index-17"]], "nat (term)": [[27, "index-8"]], "nat_case (term)": [[27, "index-19"]], "nat_double_ind (term)": [[27, "index-19"]], "not (term)": [[27, "index-1"]], "nott (term)": [[27, "index-2"]], "not_eq_s (term)": [[27, "index-17"]], "option (term)": [[27, "index-8"]], "or (term)": [[27, "index-1"]], "or_introl (term)": [[27, "index-1"]], "or_intror (term)": [[27, "index-1"]], "pair (term)": [[27, "index-9"]], "plus (term)": [[27, "index-17"]], "plus_n_o (term)": [[27, "index-17"]], "plus_n_sm (term)": [[27, "index-17"]], "pred (term)": [[27, "index-17"]], "pred_sn (term)": [[27, "index-17"]], "prod (term)": [[27, "index-9"]], "proj1 (term)": [[27, "index-1"]], "proj2 (term)": [[27, "index-1"]], "projt1 (term)": [[27, "index-11"]], "projt2 (term)": [[27, "index-11"]], "refl_identity (term)": [[27, "index-8"]], "right (term)": [[27, "index-12"]], "sig (term)": [[27, "index-10"]], "sig2 (term)": [[27, "index-10"]], "sigt (term)": [[27, "index-11"]], "sigt2 (term)": [[27, "index-11"]], "snd (term)": [[27, "index-9"]], "sum (term)": [[27, "index-9"]], "sumbool (term)": [[27, "index-12"]], "sumor (term)": [[27, "index-13"]], "sym_not_eq (term)": [[27, "index-5"]], "tt (term)": [[27, "index-8"]], "unit (term)": [[27, "index-8"]], "value (term)": [[27, "index-15"]], "well_founded (term)": [[27, "index-20"]], "{a}+{b} (term)": [[27, "index-12"]], "{x:a & p x} (term)": [[27, "index-11"]], "{x:a | p x} (term)": [[27, "index-10"]], "axiom (command)": [[28, "coq:cmd.Axiom"]], "axioms (command)": [[28, "coq:cmd.Axioms"]], "conjecture (command)": [[28, "coq:cmd.Conjecture"]], "conjectures (command)": [[28, "coq:cmd.Conjectures"]], "hypotheses (command)": [[28, "coq:cmd.Hypotheses"]], "hypothesis (command)": [[28, "coq:cmd.Hypothesis"]], "parameter (command)": [[28, "coq:cmd.Parameter"]], "parameters (command)": [[28, "coq:cmd.Parameters"]], "use of \"variable\" or \"hypothesis\" outside sections behaves as \"#[local] parameter\" or \"#[local] axiom\" (warning)": [[28, "coq:warn.Use-of-\"Variable\"-or-\"Hypothesis\"-outside-sections-behaves-as-\"#[local]-Parameter\"-or-\"#[local]-Axiom\""]], "variable (command)": [[28, "coq:cmd.Variable"]], "variables (command)": [[28, "coq:cmd.Variables"]], "forall": [[28, "index-1"]], "fun": [[28, "index-0"]], "\u2018ident\u2019 already exists. (axiom) (error)": [[28, "coq:exn.\u2018ident\u2019-already-exists.-(Axiom)"]], "add (command)": [[29, "coq:cmd.Add"]], "attributes (command)": [[29, "coq:cmd.Attributes"]], "comments (command)": [[29, "coq:cmd.Comments"]], "print options (command)": [[29, "coq:cmd.Print-Options"]], "print table (command)": [[29, "coq:cmd.Print-Table"]], "print tables (command)": [[29, "coq:cmd.Print-Tables"]], "remove (command)": [[29, "coq:cmd.Remove"]], "set (command)": [[29, "coq:cmd.Set"]], "test (command)": [[29, "coq:cmd.Test"]], "there is no flag or option with this name: \"\u2018setting_name\u2019\" (warning)": [[29, "coq:warn.There-is-no-flag-or-option-with-this-name:-\"\u2018setting_name\u2019\""]], "there is no flag, option or table with this name: \"\u2018setting_name\u2019\" (error)": [[29, "coq:exn.There-is-no-flag,-option-or-table-with-this-name:-\"\u2018setting_name\u2019\""]], "there is no qualid-valued table with this name: \"\u2018setting_name\u2019\" (error)": [[29, "coq:exn.There-is-no-qualid-valued-table-with-this-name:-\"\u2018setting_name\u2019\""]], "there is no string-valued table with this name: \"\u2018setting_name\u2019\" (error)": [[29, "coq:exn.There-is-no-string-valued-table-with-this-name:-\"\u2018setting_name\u2019\""]], "this command does not support this attribute (warning)": [[29, "coq:warn.This-command-does-not-support-this-attribute"]], "unset (command)": [[29, "coq:cmd.Unset"]], "command": [[29, "term-command"]], "sentence": [[29, "term-sentence"]], "tactic": [[29, "term-tactic"]], "term": [[29, "term-term"]], "type": [[29, "term-type"], [39, "index-0"]], "warning (attribute)": [[29, "coq:attr.warning"]], "warnings (attribute)": [[29, "coq:attr.warnings"]], "cofixpoint (command)": [[30, "coq:cmd.CoFixpoint"]], "coinductive (command)": [[30, "coq:cmd.CoInductive"]], "cofix": [[30, "index-0"]], "... : ... (type cast)": [[32, "index-1"]], "... :> ... (volatile type cast)": [[32, "index-1"]], "... <: ... (vm type cast)": [[32, "index-1"]], "... <<: ... (native compute type cast)": [[32, "index-1"]], "corollary (command)": [[32, "coq:cmd.Corollary"]], "definition (command)": [[32, "coq:cmd.Definition"]], "example (command)": [[32, "coq:cmd.Example"]], "fact (command)": [[32, "coq:cmd.Fact"]], "lemma (command)": [[32, "coq:cmd.Lemma"]], "nested proofs are discouraged and not allowed by default. this error probably means that you forgot to close the last \"proof.\" with \"qed.\" or \"defined.\". if you really intended to use nested proofs, you can do so by turning the \"nested proofs allowed\" flag on (error)": [[32, "coq:exn.Nested-proofs-are-discouraged-and-not-allowed-by-default.-This-error-probably-means-that-you-forgot-to-close-the-last-\"Proof.\"-with-\"Qed.\"-or-\"Defined.\".-If-you-really-intended-to-use-nested-proofs,-you-can-do-so-by-turning-the-\"Nested-Proofs-Allowed\"-flag-on"]], "property (command)": [[32, "coq:cmd.Property"]], "proposition (command)": [[32, "coq:cmd.Proposition"]], "remark (command)": [[32, "coq:cmd.Remark"]], "the term \u2018term\u2019 has type \u2018type\u2019 which should be set, prop or type (error)": [[32, "coq:exn.The-term-\u2018term\u2019-has-type-\u2018type\u2019-which-should-be-Set,-Prop-or-Type"]], "the term \u2018term\u2019 has type \u2018type\u2019 while it is expected to have type \u2018type\u2019' (error)": [[32, "coq:exn.The-term-\u2018term\u2019-has-type-\u2018type\u2019-while-it-is-expected-to-have-type-\u2018type\u2019'"]], "theorem (command)": [[32, "coq:cmd.Theorem"]], "let ... := ... (term)": [[32, "index-0"]], "\u2018ident\u2019 already exists. (definition) (error)": [[32, "coq:exn.\u2018ident\u2019-already-exists.-(Definition)"]], "\u2018ident\u2019 already exists. (theorem) (error)": [[32, "coq:exn.\u2018ident\u2019-already-exists.-(Theorem)"]], "auto template polymorphism (flag)": [[34, "coq:flag.Auto-Template-Polymorphism"]], "automatically declaring \u2018ident\u2019 as template polymorphic (warning)": [[34, "coq:warn.Automatically-declaring-\u2018ident\u2019-as-template-polymorphic"]], "dependent proposition eliminators (flag)": [[34, "coq:flag.Dependent-Proposition-Eliminators"]], "fixpoint (command)": [[34, "coq:cmd.Fixpoint"]], "ill-formed template inductive declaration: not polymorphic on any universe (error)": [[34, "coq:exn.Ill-formed-template-inductive-declaration:-not-polymorphic-on-any-universe"]], "inductive (command)": [[34, "coq:cmd.Inductive"]], "non strictly positive occurrence of \u2018ident\u2019 in \u2018type\u2019 (error)": [[34, "coq:exn.Non-strictly-positive-occurrence-of-\u2018ident\u2019-in-\u2018type\u2019"]], "the conclusion of \u2018type\u2019 is not valid": [[34, "coq:exn.The-conclusion-of-\u2018type\u2019-is-not-valid;-it-must-be-built-from-\u2018ident\u2019"]], "uniform inductive parameters (flag)": [[34, "coq:flag.Uniform-Inductive-Parameters"]], "fix": [[34, "index-0"]], "it must be built from \u2018ident\u2019 (error)": [[34, "coq:exn.The-conclusion-of-\u2018type\u2019-is-not-valid;-it-must-be-built-from-\u2018ident\u2019"]], "template and polymorphism not compatible (error)": [[34, "coq:exn.template-and-polymorphism-not-compatible"]], "universes(template) (attribute)": [[34, "coq:attr.universes(template)"]], "cannot import local constant, it will be ignored (warning)": [[35, "coq:warn.Cannot-import-local-constant,-it-will-be-ignored"]], "declare module (command)": [[35, "coq:cmd.Declare-Module"]], "export (command)": [[35, "coq:cmd.Export"]], "import (command)": [[35, "coq:cmd.Import"]], "include (command)": [[35, "coq:cmd.Include"]], "include type (command)": [[35, "coq:cmd.Include-Type"]], "module (command)": [[35, "coq:cmd.Module"]], "module type (command)": [[35, "coq:cmd.Module-Type"]], "no field named \u2018ident\u2019 in \u2018qualid\u2019 (error)": [[35, "coq:exn.No-field-named-\u2018ident\u2019-in-\u2018qualid\u2019"]], "print module (command)": [[35, "coq:cmd.Print-Module"]], "print module type (command)": [[35, "coq:cmd.Print-Module-Type"]], "print namespace (command)": [[35, "coq:cmd.Print-Namespace"]], "short module printing (flag)": [[35, "coq:flag.Short-Module-Printing"]], "signature components for field \u2018ident\u2019 do not match (error)": [[35, "coq:exn.Signature-components-for-field-\u2018ident\u2019-do-not-match"]], "the field \u2018ident\u2019 is missing in \u2018qualid\u2019 (error)": [[35, "coq:exn.The-field-\u2018ident\u2019-is-missing-in-\u2018qualid\u2019"]], "trying to mask the absolute name \u2018qualid\u2019! (warning)": [[35, "coq:warn.Trying-to-mask-the-absolute-name-\u2018qualid\u2019!"]], "export (attribute)": [[35, "coq:attr.export"]], "global (attribute)": [[35, "coq:attr.global"]], "local (attribute)": [[35, "coq:attr.local"]], "\u2018qualid\u2019 is not a module (error)": [[35, "coq:exn.\u2018qualid\u2019-is-not-a-module"]], "primitive projections (flag)": [[37, "coq:flag.Primitive-Projections"]], "printing constructor (table)": [[37, "coq:table.Printing-Constructor"]], "printing primitive projection parameters (flag)": [[37, "coq:flag.Printing-Primitive-Projection-Parameters"]], "printing projections (flag)": [[37, "coq:flag.Printing-Projections"]], "printing record (table)": [[37, "coq:table.Printing-Record"]], "printing records (flag)": [[37, "coq:flag.Printing-Records"]], "printing unfolded projection as match (flag)": [[37, "coq:flag.Printing-Unfolded-Projection-As-Match"]], "record (command)": [[37, "coq:cmd.Record"]], "records declared with the keyword record or structure cannot be recursive (error)": [[37, "coq:exn.Records-declared-with-the-keyword-Record-or-Structure-cannot-be-recursive"]], "structure (command)": [[37, "coq:cmd.Structure"]], "projections(primitive) (attribute)": [[37, "coq:attr.projections(primitive)"]], "\u2018ident\u2019 already exists (error)": [[37, "coq:exn.\u2018ident\u2019-already-exists"]], "\u2018ident\u2019 cannot be defined (warning)": [[37, "coq:warn.\u2018ident\u2019-cannot-be-defined"]], "\u2018ident\u2019 cannot be defined because it is informative and \u2018ident\u2019 is not (warning)": [[37, "coq:warn.\u2018ident\u2019-cannot-be-defined-because-it-is-informative-and-\u2018ident\u2019-is-not"]], "\u2018ident\u2019 cannot be defined because the projection \u2018ident\u2019 was not defined (warning)": [[37, "coq:warn.\u2018ident\u2019-cannot-be-defined-because-the-projection-\u2018ident\u2019-was-not-defined"]], "context (command)": [[38, "coq:cmd.Context"]], "end (command)": [[38, "coq:cmd.End"]], "last block to end has name \u2018ident\u2019 (error)": [[38, "coq:exn.Last-block-to-end-has-name-\u2018ident\u2019"]], "let (command)": [[38, "coq:cmd.Let"]], "let cofixpoint (command)": [[38, "coq:cmd.Let-CoFixpoint"]], "let fixpoint (command)": [[38, "coq:cmd.Let-Fixpoint"]], "section (command)": [[38, "coq:cmd.Section"]], "there is nothing to end (error)": [[38, "coq:exn.There-is-nothing-to-end"]], "clearbody (attribute)": [[38, "coq:attr.clearbody"]], "prop": [[39, "index-0"]], "sprop": [[39, "index-0"]], "set (sort)": [[39, "index-0"]], "casts are not supported in this pattern (error)": [[40, "coq:exn.Casts-are-not-supported-in-this-pattern"]], "private (attribute)": [[40, "coq:attr.Private"]], "the \u2018natural\u2019 th argument of \u2018ident\u2019 must be \u2018ident\u2019 in \u2018type\u2019 (error)": [[40, "coq:exn.The-\u2018natural\u2019-th-argument-of-\u2018ident\u2019-must-be-\u2018ident\u2019-in-\u2018type\u2019"]], "variant (command)": [[40, "coq:cmd.Variant"]], "match ... with ...": [[40, "index-0"]], "private(matching) (attribute)": [[40, "coq:attr.private(matching)"]], "arguments (command)": [[41, "coq:cmd.Arguments"]], "arguments of section variables such as \u2018name\u2019 may not be renamed (error)": [[41, "coq:exn.Arguments-of-section-variables-such-as-\u2018name\u2019-may-not-be-renamed"]], "flag 'rename' expected to rename \u2018name\u2019 into \u2018name\u2019 (error)": [[41, "coq:exn.Flag-'rename'-expected-to-rename-\u2018name\u2019-into-\u2018name\u2019"]], "the & modifier may only occur once (error)": [[41, "coq:exn.The-&-modifier-may-only-occur-once"]], "the 'clear implicits' flag must be omitted if implicit annotations are given (error)": [[41, "coq:exn.The-'clear-implicits'-flag-must-be-omitted-if-implicit-annotations-are-given"]], "the 'default implicits' flag is incompatible with implicit annotations (error)": [[41, "coq:exn.The-'default-implicits'-flag-is-incompatible-with-implicit-annotations"]], "the / modifier may only occur once (error)": [[41, "coq:exn.The-/-modifier-may-only-occur-once"]], "this command is just asserting the names of arguments of \u2018qualid\u2019. if this is what you want, add ': assert' to silence the warning. if you want to clear implicit arguments, add ': clear implicits'. if you want to clear notation scopes, add ': clear scopes' (warning)": [[41, "coq:warn.This-command-is-just-asserting-the-names-of-arguments-of-\u2018qualid\u2019.-If-this-is-what-you-want,-add-':-assert'-to-silence-the-warning.-If-you-want-to-clear-implicit-arguments,-add-':-clear-implicits'.-If-you-want-to-clear-notation-scopes,-add-':-clear-scopes'"]], "to rename arguments the 'rename' flag must be specified (error)": [[41, "coq:exn.To-rename-arguments-the-'rename'-flag-must-be-specified"]], "canonical structure (command)": [[42, "coq:cmd.Canonical-Structure"]], "print canonical projections (command)": [[42, "coq:cmd.Print-Canonical-Projections"]], "canonical (attribute)": [[42, "coq:attr.canonical"]], "printing existential instances (flag)": [[43, "coq:flag.Printing-Existential-Instances"]], "_": [[43, "index-0"]], "argument at position \u2018natural\u2019 is mentioned more than once (error)": [[44, "coq:exn.Argument-at-position-\u2018natural\u2019-is-mentioned-more-than-once"]], "argument \u2018name\u2019 is a trailing implicit, so it can't be declared non maximal. please use { } instead of [ ] (error)": [[44, "coq:exn.Argument-\u2018name\u2019-is-a-trailing-implicit,-so-it-can't-be-declared-non-maximal.-Please-use-{-}-instead-of-[-]"]], "arguments given by name or position not supported in explicit mode (error)": [[44, "coq:exn.Arguments-given-by-name-or-position-not-supported-in-explicit-mode"]], "cannot infer a term for this placeholder. (casual use of implicit arguments) (error)": [[44, "coq:exn.Cannot-infer-a-term-for-this-placeholder.-(Casual-use-of-implicit-arguments)"]], "contextual implicit (flag)": [[44, "coq:flag.Contextual-Implicit"]], "generalizable (command)": [[44, "coq:cmd.Generalizable"]], "ignoring implicit binder declaration in unexpected position (warning)": [[44, "coq:warn.Ignoring-implicit-binder-declaration-in-unexpected-position"]], "implicit arguments (flag)": [[44, "coq:flag.Implicit-Arguments"]], "implicit type (command)": [[44, "coq:cmd.Implicit-Type"]], "implicit types (command)": [[44, "coq:cmd.Implicit-Types"]], "making shadowed name of implicit argument accessible by position (warning)": [[44, "coq:warn.Making-shadowed-name-of-implicit-argument-accessible-by-position"]], "maximal implicit insertion (flag)": [[44, "coq:flag.Maximal-Implicit-Insertion"]], "not enough non implicit arguments to accept the argument bound to \u2018ident\u2019 (error)": [[44, "coq:exn.Not-enough-non-implicit-arguments-to-accept-the-argument-bound-to-\u2018ident\u2019"]], "not enough non implicit arguments to accept the argument bound to \u2018natural\u2019 (error)": [[44, "coq:exn.Not-enough-non-implicit-arguments-to-accept-the-argument-bound-to-\u2018natural\u2019"]], "parsing explicit (flag)": [[44, "coq:flag.Parsing-Explicit"]], "print implicit (command)": [[44, "coq:cmd.Print-Implicit"]], "printing implicit (flag)": [[44, "coq:flag.Printing-Implicit"]], "printing implicit defensive (flag)": [[44, "coq:flag.Printing-Implicit-Defensive"]], "printing use implicit types (flag)": [[44, "coq:flag.Printing-Use-Implicit-Types"]], "reversible pattern implicit (flag)": [[44, "coq:flag.Reversible-Pattern-Implicit"]], "strict implicit (flag)": [[44, "coq:flag.Strict-Implicit"]], "strongly strict implicit (flag)": [[44, "coq:flag.Strongly-Strict-Implicit"]], "wrong argument name (error)": [[44, "coq:exn.Wrong-argument-name"]], "wrong argument position (error)": [[44, "coq:exn.Wrong-argument-position"]], "`( )": [[44, "index-2"]], "`(! )": [[44, "index-5"]], "`[ ]": [[44, "index-1"]], "`[! ]": [[44, "index-4"]], "`{ }": [[44, "index-0"]], "`{! }": [[44, "index-3"]], "asymmetric patterns (flag)": [[46, "coq:flag.Asymmetric-Patterns"]], "either there is a type incompatibility or the problem involves dependencies (error)": [[46, "coq:exn.Either-there-is-a-type-incompatibility-or-the-problem-involves-dependencies"]], "found a constructor of inductive type term while a constructor of term is expected (error)": [[46, "coq:exn.Found-a-constructor-of-inductive-type-term-while-a-constructor-of-term-is-expected"]], "non exhaustive pattern matching (error)": [[46, "coq:exn.Non-exhaustive-pattern-matching"]], "printing allow match default clause (flag)": [[46, "coq:flag.Printing-Allow-Match-Default-Clause"]], "printing factorizable match patterns (flag)": [[46, "coq:flag.Printing-Factorizable-Match-Patterns"]], "printing if (table)": [[46, "coq:table.Printing-If"]], "printing let (table)": [[46, "coq:table.Printing-Let"]], "printing match all subterms (flag)": [[46, "coq:flag.Printing-Match-All-Subterms"]], "printing matching (flag)": [[46, "coq:flag.Printing-Matching"]], "printing synth (flag)": [[46, "coq:flag.Printing-Synth"]], "printing wildcard (flag)": [[46, "coq:flag.Printing-Wildcard"]], "the constructor \u2018ident\u2019 expects \u2018natural\u2019 arguments (error)": [[46, "coq:exn.The-constructor-\u2018ident\u2019-expects-\u2018natural\u2019-arguments"]], "the elimination predicate term should be of arity \u2018natural\u2019 (for non dependent case) or \u2018natural\u2019 (for dependent case) (error)": [[46, "coq:exn.The-elimination-predicate-term-should-be-of-arity-\u2018natural\u2019-(for-non-dependent-case)-or-\u2018natural\u2019-(for-dependent-case)"]], "the variable ident is bound several times in pattern term (error)": [[46, "coq:exn.The-variable-ident-is-bound-several-times-in-pattern-term"]], "unable to infer a match predicate (error)": [[46, "coq:exn.Unable-to-infer-a-match-predicate"]], "unused variable \u2018ident\u2019 might be a misspelled constructor. use _ or _\u2018ident\u2019 to silence this warning (warning)": [[46, "coq:warn.Unused-variable-\u2018ident\u2019-might-be-a-misspelled-constructor.-Use-_-or-_\u2018ident\u2019-to-silence-this-warning."]], "coqtop exit on error (flag)": [[51, "coq:flag.Coqtop-Exit-On-Error"]], "+ (backtracking branching) (tactic)": [[54, "coq:tacn.+-(backtracking-branching)"]], "::=": [[54, "index-0"]], "argument of match does not evaluate to a term (error)": [[54, "coq:exn.Argument-of-match-does-not-evaluate-to-a-term"]], "condition not satisfied (error)": [[54, "coq:exn.Condition-not-satisfied"]], "debug (command)": [[54, "coq:cmd.Debug"]], "debug mode not available in the ide (error)": [[54, "coq:exn.Debug-mode-not-available-in-the-IDE"]], "expression does not evaluate to a tactic (error)": [[54, "coq:exn.Expression-does-not-evaluate-to-a-tactic"]], "failed to progress (error)": [[54, "coq:exn.Failed-to-progress"]], "info (command)": [[54, "coq:cmd.Info"]], "info level (option)": [[54, "coq:opt.Info-Level"]], "ltac (command)": [[54, "coq:cmd.Ltac"]], "ltac backtrace (flag)": [[54, "coq:flag.Ltac-Backtrace"]], "ltac batch debug (flag)": [[54, "coq:flag.Ltac-Batch-Debug"]], "ltac debug (flag)": [[54, "coq:flag.Ltac-Debug"]], "ltac profiler encountered an invalid stack (no self node). this can happen if you reset the profile during tactic execution (warning)": [[54, "coq:warn.Ltac-Profiler-encountered-an-invalid-stack-(no-self-node).-This-can-happen-if-you-reset-the-profile-during-tactic-execution"]], "ltac profiling (flag)": [[54, "coq:flag.Ltac-Profiling"]], "no applicable tactic (error)": [[54, "coq:exn.No-applicable-tactic"]], "no evars (error)": [[54, "coq:exn.No-evars"]], "no matching clauses for match (error)": [[54, "coq:exn.No-matching-clauses-for-match"]], "no matching clauses for match goal (error)": [[54, "coq:exn.No-matching-clauses-for-match-goal"]], "no such goal. (goal selector) (error)": [[54, "coq:exn.No-such-goal.-(Goal-selector)"]], "no such goal. (fail) (error)": [[54, "coq:exn.No-such-goal.-(fail)"]], "not a context variable (error)": [[54, "coq:exn.Not-a-context-variable"]], "not a variable or hypothesis (error)": [[54, "coq:exn.Not-a-variable-or-hypothesis"]], "not an evar (error)": [[54, "coq:exn.Not-an-evar"]], "not equal (due to universes) (error)": [[54, "coq:exn.Not-equal-(due-to-universes)"]], "not equal (error)": [[54, "coq:exn.Not-equal"]], "not ground (error)": [[54, "coq:exn.Not-ground"]], "print ltac (command)": [[54, "coq:cmd.Print-Ltac"]], "print ltac signatures (command)": [[54, "coq:cmd.Print-Ltac-Signatures"]], "reset ltac profile (command)": [[54, "coq:cmd.Reset-Ltac-Profile"]], "show ltac profile (command)": [[54, "coq:cmd.Show-Ltac-Profile"]], "tactic failure (error)": [[54, "coq:exn.Tactic-failure"]], "tactic failure (level \u2018natural\u2019) (error)": [[54, "coq:exn.Tactic-failure-(level-\u2018natural\u2019)"]], "tactic failure: succeeds (error)": [[54, "coq:exn.Tactic-failure:--succeeds"]], "there is already an ltac named \u2018qualid\u2019 (error)": [[54, "coq:exn.There-is-already-an-Ltac-named-\u2018qualid\u2019"]], "there is no ltac named \u2018qualid\u2019 (error)": [[54, "coq:exn.There-is-no-Ltac-named-\u2018qualid\u2019"]], "this tactic has more than one success (error)": [[54, "coq:exn.This-tactic-has-more-than-one-success"]], "unbound context identifier \u2018ident\u2019 (error)": [[54, "coq:exn.Unbound-context-identifier-\u2018ident\u2019"]], "[ \u2026 | \u2026 | \u2026 ] (dispatch) (tactic)": [[54, "coq:tacn.[-\u2026-|-\u2026-|-\u2026-]-(dispatch)"]], "[> \u2026 | \u2026 | \u2026 ] (dispatch) (tactic)": [[54, "coq:tacn.[>-\u2026-|-\u2026-|-\u2026-]-(dispatch)"]], "assert_fails (tactic)": [[54, "coq:tacn.assert_fails"]], "assert_succeeds (tactic)": [[54, "coq:tacn.assert_succeeds"]], "constr_eq (tactic)": [[54, "coq:tacn.constr_eq"]], "constr_eq_nounivs (tactic)": [[54, "coq:tacn.constr_eq_nounivs"]], "constr_eq_strict (tactic)": [[54, "coq:tacn.constr_eq_strict"]], "context (tactic)": [[54, "coq:tacn.context"]], "convert (tactic)": [[54, "coq:tacn.convert"]], "do (tactic)": [[54, "coq:tacn.do"]], "exactly_once (tactic)": [[54, "coq:tacn.exactly_once"]], "fail (tactic)": [[54, "coq:tacn.fail"]], "finish_timing (tactic)": [[54, "coq:tacn.finish_timing"]], "first (tactic)": [[54, "coq:tacn.first"]], "fresh (tactic)": [[54, "coq:tacn.fresh"]], "fun (tactic)": [[54, "coq:tacn.fun"]], "gfail (tactic)": [[54, "coq:tacn.gfail"]], "guard (tactic)": [[54, "coq:tacn.guard"]], "has_evar (tactic)": [[54, "coq:tacn.has_evar"]], "idtac (tactic)": [[54, "coq:tacn.idtac"]], "infoh (command)": [[54, "coq:cmd.infoH"]], "is_cofix (tactic)": [[54, "coq:tacn.is_cofix"]], "is_const (tactic)": [[54, "coq:tacn.is_const"]], "is_constructor (tactic)": [[54, "coq:tacn.is_constructor"]], "is_evar (tactic)": [[54, "coq:tacn.is_evar"]], "is_fix (tactic)": [[54, "coq:tacn.is_fix"]], "is_ground (tactic)": [[54, "coq:tacn.is_ground"]], "is_ind (tactic)": [[54, "coq:tacn.is_ind"]], "is_proj (tactic)": [[54, "coq:tacn.is_proj"]], "is_var (tactic)": [[54, "coq:tacn.is_var"]], "lazymatch (tactic)": [[54, "coq:tacn.lazymatch"]], "lazymatch goal (tactic)": [[54, "coq:tacn.lazymatch-goal"]], "let (tactic)": [[54, "coq:tacn.let"]], "ltac-seq (tactic)": [[54, "coq:tacn.ltac-seq"]], "match (tactic)": [[54, "coq:tacn.match"]], "match goal (tactic)": [[54, "coq:tacn.match-goal"]], "multimatch (tactic)": [[54, "coq:tacn.multimatch"]], "multimatch goal (tactic)": [[54, "coq:tacn.multimatch-goal"]], "not a cofix definition (error)": [[54, "coq:exn.not-a-cofix-definition"]], "not a constant (error)": [[54, "coq:exn.not-a-constant"]], "not a constructor (error)": [[54, "coq:exn.not-a-constructor"]], "not a fix definition (error)": [[54, "coq:exn.not-a-fix-definition"]], "not a primitive projection (error)": [[54, "coq:exn.not-a-primitive-projection"]], "not an (co)inductive datatype (error)": [[54, "coq:exn.not-an-(co)inductive-datatype"]], "not_evar (tactic)": [[54, "coq:tacn.not_evar"]], "numgoals (tactic)": [[54, "coq:tacn.numgoals"]], "once (tactic)": [[54, "coq:tacn.once"]], "only (tactic)": [[54, "coq:tacn.only"]], "optimize_heap (tactic)": [[54, "coq:tacn.optimize_heap"]], "progress (tactic)": [[54, "coq:tacn.progress"]], "repeat (tactic)": [[54, "coq:tacn.repeat"]], "reset ltac profile (tactic)": [[54, "coq:tacn.reset-ltac-profile"]], "restart_timer (tactic)": [[54, "coq:tacn.restart_timer"]], "show ltac profile (tactic)": [[54, "coq:tacn.show-ltac-profile"]], "solve (tactic)": [[54, "coq:tacn.solve"]], "start ltac profiling (tactic)": [[54, "coq:tacn.start-ltac-profiling"]], "stop ltac profiling (tactic)": [[54, "coq:tacn.stop-ltac-profiling"]], "time (tactic)": [[54, "coq:tacn.time"]], "time_constr (tactic)": [[54, "coq:tacn.time_constr"]], "timeout (tactic)": [[54, "coq:tacn.timeout"]], "try (tactic)": [[54, "coq:tacn.try"]], "tryif (tactic)": [[54, "coq:tacn.tryif"]], "type of (tactic)": [[54, "coq:tacn.type-of"]], "type_term (tactic)": [[54, "coq:tacn.type_term"]], "unify (tactic)": [[54, "coq:tacn.unify"]], "|| (first tactic making progress) (tactic)": [[54, "coq:tacn.||-(first-tactic-making-progress)"]], "\u2026 : \u2026 (goal selector) (tactic)": [[54, "coq:tacn.\u2026-:-\u2026-(goal-selector)"]], "ltac2 (command)": [[55, "coq:cmd.Ltac2"]], "ltac2 backtrace (flag)": [[55, "coq:flag.Ltac2-Backtrace"]], "ltac2 check (command)": [[55, "coq:cmd.Ltac2-Check"]], "ltac2 eval (command)": [[55, "coq:cmd.Ltac2-Eval"]], "ltac2 globalize (command)": [[55, "coq:cmd.Ltac2-Globalize"]], "ltac2 in ltac1 profiling (flag)": [[55, "coq:flag.Ltac2-In-Ltac1-Profiling"]], "ltac2 notation (abbreviation) (command)": [[55, "coq:cmd.Ltac2-Notation-(abbreviation)"]], "ltac2 notation (command)": [[55, "coq:cmd.Ltac2-Notation"]], "ltac2 set (command)": [[55, "coq:cmd.Ltac2-Set"]], "ltac2 type (command)": [[55, "coq:cmd.Ltac2-Type"]], "ltac2 typed notations (flag)": [[55, "coq:flag.Ltac2-Typed-Notations"]], "ltac2 external (command)": [[55, "coq:cmd.Ltac2-external"]], "notation levels must range between 0 and 6 (error)": [[55, "coq:exn.Notation-levels-must-range-between-0-and-6"]], "print ltac2 (command)": [[55, "coq:cmd.Print-Ltac2"]], "print ltac2 signatures (command)": [[55, "coq:cmd.Print-Ltac2-Signatures"]], "print ltac2 type (command)": [[55, "coq:cmd.Print-Ltac2-Type"]], "the reference x was not found in the current environment (error)": [[55, "coq:exn.The-reference-X-was-not-found-in-the-current-environment"]], "unbound [value|constructor] x (error)": [[55, "coq:exn.Unbound-[value|constructor]-X"]], "abstract (attribute)": [[55, "coq:attr.abstract"]], "if-then-else (ltac2) (tactic)": [[55, "coq:tacn.if-then-else-(Ltac2)"]], "lazy_match! (tactic)": [[55, "coq:tacn.lazy_match!"]], "lazy_match! goal (tactic)": [[55, "coq:tacn.lazy_match!-goal"]], "match (ltac2) (tactic)": [[55, "coq:tacn.match-(Ltac2)"]], "match! (tactic)": [[55, "coq:tacn.match!"]], "match! goal (tactic)": [[55, "coq:tacn.match!-goal"]], "multi_match! (tactic)": [[55, "coq:tacn.multi_match!"]], "multi_match! goal (tactic)": [[55, "coq:tacn.multi_match!-goal"]], "=> (tactic)": [[57, "coq:tacn.=>"]], "debug ssrmatching (flag)": [[57, "coq:flag.Debug-SsrMatching"]], "debug ssreflect (flag)": [[57, "coq:flag.Debug-Ssreflect"]], "duplicate clear of h. use { }h instead of { h }h (warning)": [[57, "coq:warn.Duplicate-clear-of-H.-Use-{-}H-instead-of-{-H-}H"]], "hint view for (command)": [[57, "coq:cmd.Hint-View-for"]], "hint view for apply (command)": [[57, "coq:cmd.Hint-View-for-apply"]], "hint view for move (command)": [[57, "coq:cmd.Hint-View-for-move"]], "incorrect number of tactics (expected n tactics, was given m) (error)": [[57, "coq:exn.Incorrect-number-of-tactics-(expected-N-tactics,-was-given-M)"]], "prenex implicits (command)": [[57, "coq:cmd.Prenex-Implicits"]], "ssreflect: cannot obtain new equations out of ... (warning)": [[57, "coq:warn.SSReflect:-cannot-obtain-new-equations-out-of-..."]], "ssrhave notcresolution (flag)": [[57, "coq:flag.SsrHave-NoTCResolution"]], "ssridents (flag)": [[57, "coq:flag.SsrIdents"]], "ssroldrewritegoalsorder (flag)": [[57, "coq:flag.SsrOldRewriteGoalsOrder"]], "ssrrewrite (flag)": [[57, "coq:flag.SsrRewrite"]], "abstract (ssreflect) (tactic)": [[57, "coq:tacn.abstract-(ssreflect)"]], "apply (ssreflect) (tactic)": [[57, "coq:tacn.apply-(ssreflect)"]], "by (tactic)": [[57, "coq:tacn.by"]], "case (ssreflect) (tactic)": [[57, "coq:tacn.case-(ssreflect)"]], "congr (tactic)": [[57, "coq:tacn.congr"]], "do (ssreflect) (tactic)": [[57, "coq:tacn.do-(ssreflect)"]], "done (tactic)": [[57, "coq:tacn.done"]], "elim (ssreflect) (tactic)": [[57, "coq:tacn.elim-(ssreflect)"]], "exact (ssreflect) (tactic)": [[57, "coq:tacn.exact-(ssreflect)"]], "first (ssreflect) (tactic)": [[57, "coq:tacn.first-(ssreflect)"]], "first last (tactic variant)": [[57, "coq:tacv.first-last"]], "generally have (tactic)": [[57, "coq:tacn.generally-have"]], "have (tactic)": [[57, "coq:tacn.have"]], "in (tactic)": [[57, "coq:tacn.in"]], "last (tactic)": [[57, "coq:tacn.last"]], "last first (tactic variant)": [[57, "coq:tacv.last-first"]], "move (ssreflect) (tactic)": [[57, "coq:tacn.move-(ssreflect)"]], "over (tactic)": [[57, "coq:tacn.over"]], "pose (ssreflect) (tactic)": [[57, "coq:tacn.pose-(ssreflect)"]], "rewrite (ssreflect) (tactic)": [[57, "coq:tacn.rewrite-(ssreflect)"]], "set (ssreflect) (tactic)": [[57, "coq:tacn.set-(ssreflect)"]], "suff (tactic)": [[57, "coq:tacn.suff"]], "suffices (tactic)": [[57, "coq:tacn.suffices"]], "under (tactic)": [[57, "coq:tacn.under"]], "unlock (tactic)": [[57, "coq:tacn.unlock"]], "without loss (tactic)": [[57, "coq:tacn.without-loss"]], "wlog (tactic)": [[57, "coq:tacn.wlog"]], "\u2026 : \u2026 (ssreflect) (tactic)": [[57, "coq:tacn.\u2026-:-\u2026-(ssreflect)"]], "cannot change \u2018ident\u2019, it is used in conclusion (error)": [[58, "coq:exn.Cannot-change-\u2018ident\u2019,-it-is-used-in-conclusion"]], "cannot change \u2018ident\u2019, it is used in hypothesis \u2018ident\u2019 (error)": [[58, "coq:exn.Cannot-change-\u2018ident\u2019,-it-is-used-in-hypothesis-\u2018ident\u2019"]], "cannot infer a term for this placeholder. (refine) (error)": [[58, "coq:exn.Cannot-infer-a-term-for-this-placeholder.-(refine)"]], "cannot move \u2018ident\u2019 after \u2018ident\u2019: it depends on \u2018ident\u2019 (error)": [[58, "coq:exn.Cannot-move-\u2018ident\u2019-after-\u2018ident\u2019:-it-depends-on-\u2018ident\u2019"]], "cannot move \u2018ident\u2019 after \u2018ident\u2019: it occurs in the type of \u2018ident\u2019 (error)": [[58, "coq:exn.Cannot-move-\u2018ident\u2019-after-\u2018ident\u2019:-it-occurs-in-the-type-of-\u2018ident\u2019"]], "default goal selector (option)": [[58, "coq:opt.Default-Goal-Selector"]], "no product even after head-reduction (error)": [[58, "coq:exn.No-product-even-after-head-reduction"]], "no quantified hypothesis named \u2018ident\u2019 in current goal even after head-reduction (error)": [[58, "coq:exn.No-quantified-hypothesis-named-\u2018ident\u2019-in-current-goal-even-after-head-reduction"]], "no such assumption (error)": [[58, "coq:exn.No-such-assumption"]], "no such binder (error)": [[58, "coq:exn.No-such-binder"]], "no such bound variable \u2018ident\u2019 (no bound variables at all in the expression) (error)": [[58, "coq:exn.No-such-bound-variable-\u2018ident\u2019-(no-bound-variables-at-all-in-the-expression)"]], "no such bound variable \u2018ident\u2019 (possible names are: \u2018ident\u2019 ...) (error)": [[58, "coq:exn.No-such-bound-variable-\u2018ident\u2019-(possible-names-are:-\u2018ident\u2019-...)"]], "no such hypothesis: \u2018ident\u2019 (error)": [[58, "coq:exn.No-such-hypothesis:-\u2018ident\u2019"]], "no \u2018natural\u2019-th non dependent hypothesis in current goal even after head-reduction (error)": [[58, "coq:exn.No-\u2018natural\u2019-th-non-dependent-hypothesis-in-current-goal-even-after-head-reduction"]], "not an exact proof (error)": [[58, "coq:exn.Not-an-exact-proof"]], "not the right number of missing arguments (expected \u2018natural\u2019) (error)": [[58, "coq:exn.Not-the-right-number-of-missing-arguments-(expected-\u2018natural\u2019)"]], "proof is not complete. (assert) (error)": [[58, "coq:exn.Proof-is-not-complete.-(assert)"]], "the term \"\u2018type\u2019\" has type \"\u2018type\u2019\" which should be set, prop or type (error)": [[58, "coq:exn.The-term-\"\u2018type\u2019\"-has-type-\"\u2018type\u2019\"-which-should-be-Set,-Prop-or-Type"]], "the variable \u2018ident\u2019 is already declared (error)": [[58, "coq:exn.The-variable-\u2018ident\u2019-is-already-declared"]], "unable to apply lemma of type \"...\" on hypothesis of type \"...\" (error)": [[58, "coq:exn.Unable-to-apply-lemma-of-type-\"...\"-on-hypothesis-of-type-\"...\""]], "unable to find an instance for the variables \u2018ident\u2019\u2026\u2018ident\u2019 (error)": [[58, "coq:exn.Unable-to-find-an-instance-for-the-variables-\u2018ident\u2019\u2026\u2018ident\u2019"]], "unable to unify \u2018one_term\u2019 with \u2018one_term\u2019 (error)": [[58, "coq:exn.Unable-to-unify-\u2018one_term\u2019-with-\u2018one_term\u2019"]], "absurd (tactic)": [[58, "coq:tacn.absurd"]], "apply (tactic)": [[58, "coq:tacn.apply"]], "assert (tactic)": [[58, "coq:tacn.assert"]], "assumption (tactic)": [[58, "coq:tacn.assumption"]], "classical_left (tactic)": [[58, "coq:tacn.classical_left"]], "classical_right (tactic)": [[58, "coq:tacn.classical_right"]], "clear (tactic)": [[58, "coq:tacn.clear"]], "clear dependent (tactic)": [[58, "coq:tacn.clear-dependent"]], "clearbody (tactic)": [[58, "coq:tacn.clearbody"]], "contradict (tactic)": [[58, "coq:tacn.contradict"]], "contradiction (tactic)": [[58, "coq:tacn.contradiction"]], "cut (tactic)": [[58, "coq:tacn.cut"]], "dependent generalize_eqs (tactic)": [[58, "coq:tacn.dependent-generalize_eqs"]], "dependent generalize_eqs_vars (tactic)": [[58, "coq:tacn.dependent-generalize_eqs_vars"]], "eapply (tactic)": [[58, "coq:tacn.eapply"]], "eassert (tactic)": [[58, "coq:tacn.eassert"]], "eassumption (tactic)": [[58, "coq:tacn.eassumption"]], "eenough (tactic)": [[58, "coq:tacn.eenough"]], "eexact (tactic)": [[58, "coq:tacn.eexact"]], "eintros (tactic)": [[58, "coq:tacn.eintros"]], "enough (tactic)": [[58, "coq:tacn.enough"]], "epose (tactic)": [[58, "coq:tacn.epose"]], "epose proof (tactic)": [[58, "coq:tacn.epose-proof"]], "eremember (tactic)": [[58, "coq:tacn.eremember"]], "eset (tactic)": [[58, "coq:tacn.eset"]], "evar (tactic)": [[58, "coq:tacn.evar"]], "exact (tactic)": [[58, "coq:tacn.exact"]], "exact_no_check (tactic)": [[58, "coq:tacn.exact_no_check"]], "exfalso (tactic)": [[58, "coq:tacn.exfalso"]], "generalize (tactic)": [[58, "coq:tacn.generalize"]], "generalize dependent (tactic)": [[58, "coq:tacn.generalize-dependent"]], "generalize_eqs (tactic)": [[58, "coq:tacn.generalize_eqs"]], "generalize_eqs_vars (tactic)": [[58, "coq:tacn.generalize_eqs_vars"]], "instantiate (tactic)": [[58, "coq:tacn.instantiate"]], "intro (tactic)": [[58, "coq:tacn.intro"]], "intros (tactic)": [[58, "coq:tacn.intros"]], "intros until (tactic)": [[58, "coq:tacn.intros-until"]], "lapply (tactic)": [[58, "coq:tacn.lapply"]], "lapply needs a non-dependent product (error)": [[58, "coq:exn.lapply-needs-a-non-dependent-product"]], "move (tactic)": [[58, "coq:tacn.move"]], "native_cast_no_check (tactic)": [[58, "coq:tacn.native_cast_no_check"]], "pose (tactic)": [[58, "coq:tacn.pose"]], "pose proof (tactic)": [[58, "coq:tacn.pose-proof"]], "rapply (tactic)": [[58, "coq:tacn.rapply"]], "refine (tactic)": [[58, "coq:tacn.refine"]], "remember (tactic)": [[58, "coq:tacn.remember"]], "rename (tactic)": [[58, "coq:tacn.rename"]], "revert (tactic)": [[58, "coq:tacn.revert"]], "revert dependent (tactic)": [[58, "coq:tacn.revert-dependent"]], "set (tactic)": [[58, "coq:tacn.set"]], "simple apply (tactic)": [[58, "coq:tacn.simple-apply"]], "simple eapply (tactic)": [[58, "coq:tacn.simple-eapply"]], "specialize (tactic)": [[58, "coq:tacn.specialize"]], "specialize_eqs (tactic)": [[58, "coq:tacn.specialize_eqs"]], "vm_cast_no_check (tactic)": [[58, "coq:tacn.vm_cast_no_check"]], "\u2018ident\u2019 is already used (error)": [[58, "coq:exn.\u2018ident\u2019-is-already-used"]], "\u2018ident\u2019 is not a local definition (error)": [[58, "coq:exn.\u2018ident\u2019-is-not-a-local-definition"]], "\u2018ident\u2019 is used in the conclusion (error)": [[58, "coq:exn.\u2018ident\u2019-is-used-in-the-conclusion"]], "\u2018ident\u2019 is used in the hypothesis \u2018ident\u2019 (error)": [[58, "coq:exn.\u2018ident\u2019-is-used-in-the-hypothesis-\u2018ident\u2019"]], "about (command)": [[59, "coq:cmd.About"]], "back (command)": [[59, "coq:cmd.Back"]], "backto (command)": [[59, "coq:cmd.BackTo"]], "bad magic number (error)": [[59, "coq:exn.Bad-magic-number"]], "cannot find library foo in loadpath (error)": [[59, "coq:exn.Cannot-find-library-foo-in-loadpath"]], "cannot load \u2018qualid\u2019: no physical path bound to \u2018dirpath\u2019 (error)": [[59, "coq:exn.Cannot-load-\u2018qualid\u2019:-no-physical-path-bound-to-\u2018dirpath\u2019"]], "can\u2019t find file \u2018ident\u2019 on loadpath (error)": [[59, "coq:exn.Can\u2019t-find-file-\u2018ident\u2019-on-loadpath"]], "check (command)": [[59, "coq:cmd.Check"]], "compiled library \u2018ident\u2019.vo makes inconsistent assumptions over library \u2018qualid\u2019 (error)": [[59, "coq:exn.Compiled-library-\u2018ident\u2019.vo-makes-inconsistent-assumptions-over-library-\u2018qualid\u2019"]], "debug (option)": [[59, "coq:opt.Debug"]], "declare ml module (command)": [[59, "coq:cmd.Declare-ML-Module"]], "default timeout (option)": [[59, "coq:opt.Default-Timeout"]], "drop (command)": [[59, "coq:cmd.Drop"]], "dynlink error: execution of module initializers in the (error)": [[59, "coq:exn.Dynlink-error:-execution-of-module-initializers-in-the"]], "fail (command)": [[59, "coq:cmd.Fail"]], "fast name printing (flag)": [[59, "coq:flag.Fast-Name-Printing"]], "file ... found twice in ... (warning)": [[59, "coq:warn.File-...-found-twice-in-..."]], "file not found on loadpath: \u2018string\u2019 (error)": [[59, "coq:exn.File-not-found-on-loadpath:-\u2018string\u2019"]], "files processed by load cannot leave open proofs (error)": [[59, "coq:exn.Files-processed-by-Load-cannot-leave-open-proofs"]], "from \u2026 dependency (command)": [[59, "coq:cmd.From-\u2026-Dependency"]], "from \u2026 require (command)": [[59, "coq:cmd.From-\u2026-Require"]], "guard checking (flag)": [[59, "coq:flag.Guard-Checking"]], "inspect (command)": [[59, "coq:cmd.Inspect"]], "instructions (command)": [[59, "coq:cmd.Instructions"]], "invalid backtrack (error)": [[59, "coq:exn.Invalid-backtrack"]], "load (command)": [[59, "coq:cmd.Load"]], "load is not supported inside proofs (error)": [[59, "coq:exn.Load-is-not-supported-inside-proofs"]], "locate (command)": [[59, "coq:cmd.Locate"]], "locate file (command)": [[59, "coq:cmd.Locate-File"]], "locate library (command)": [[59, "coq:cmd.Locate-Library"]], "locate ltac (command)": [[59, "coq:cmd.Locate-Ltac"]], "locate ltac2 (command)": [[59, "coq:cmd.Locate-Ltac2"]], "locate module (command)": [[59, "coq:cmd.Locate-Module"]], "locate term (command)": [[59, "coq:cmd.Locate-Term"]], "module/section \u2018qualid\u2019 not found (error)": [[59, "coq:exn.Module/section-\u2018qualid\u2019-not-found"]], "positivity checking (flag)": [[59, "coq:flag.Positivity-Checking"]], "primitive (command)": [[59, "coq:cmd.Primitive"]], "print (command)": [[59, "coq:cmd.Print"]], "print all (command)": [[59, "coq:cmd.Print-All"]], "print all dependencies (command)": [[59, "coq:cmd.Print-All-Dependencies"]], "print assumptions (command)": [[59, "coq:cmd.Print-Assumptions"]], "print libraries (command)": [[59, "coq:cmd.Print-Libraries"]], "print loadpath (command)": [[59, "coq:cmd.Print-LoadPath"]], "print ml modules (command)": [[59, "coq:cmd.Print-ML-Modules"]], "print ml path (command)": [[59, "coq:cmd.Print-ML-Path"]], "print opaque dependencies (command)": [[59, "coq:cmd.Print-Opaque-Dependencies"]], "print registered (command)": [[59, "coq:cmd.Print-Registered"]], "print registered schemes (command)": [[59, "coq:cmd.Print-Registered-Schemes"]], "print section (command)": [[59, "coq:cmd.Print-Section"]], "print transparent dependencies (command)": [[59, "coq:cmd.Print-Transparent-Dependencies"]], "print typing flags (command)": [[59, "coq:cmd.Print-Typing-Flags"]], "printing all (flag)": [[59, "coq:flag.Printing-All"]], "printing compact contexts (flag)": [[59, "coq:flag.Printing-Compact-Contexts"]], "printing dependent evars line (flag)": [[59, "coq:flag.Printing-Dependent-Evars-Line"]], "printing depth (option)": [[59, "coq:opt.Printing-Depth"]], "printing unfocused (flag)": [[59, "coq:flag.Printing-Unfocused"]], "printing width (option)": [[59, "coq:opt.Printing-Width"]], "profile (command)": [[59, "coq:cmd.Profile"]], "quit (command)": [[59, "coq:cmd.Quit"]], "redirect (command)": [[59, "coq:cmd.Redirect"]], "register (command)": [[59, "coq:cmd.Register"]], "register inline (command)": [[59, "coq:cmd.Register-Inline"]], "register scheme (command)": [[59, "coq:cmd.Register-Scheme"]], "require (command)": [[59, "coq:cmd.Require"]], "require export (command)": [[59, "coq:cmd.Require-Export"]], "require import (command)": [[59, "coq:cmd.Require-Import"]], "require inside a module is deprecated and strongly discouraged. you can require a module at toplevel and optionally import it inside another one (warning)": [[59, "coq:warn.Require-inside-a-module-is-deprecated-and-strongly-discouraged.-You-can-Require-a-module-at-toplevel-and-optionally-Import-it-inside-another-one"]], "required library \u2018qualid\u2019 matches several files in path (found file.vo, file.vo, ...) (error)": [[59, "coq:exn.Required-library-\u2018qualid\u2019-matches-several-files-in-path-(found-file.vo,-file.vo,-...)"]], "reset (command)": [[59, "coq:cmd.Reset"]], "reset initial (command)": [[59, "coq:cmd.Reset-Initial"]], "search (command)": [[59, "coq:cmd.Search"]], "search blacklist (table)": [[59, "coq:table.Search-Blacklist"]], "search output name only (flag)": [[59, "coq:flag.Search-Output-Name-Only"]], "searchpattern (command)": [[59, "coq:cmd.SearchPattern"]], "searchrewrite (command)": [[59, "coq:cmd.SearchRewrite"]], "silent (flag)": [[59, "coq:flag.Silent"]], "succeed (command)": [[59, "coq:cmd.Succeed"]], "the command has not failed! (error)": [[59, "coq:exn.The-command-has-not-failed!"]], "the file \u2018ident\u2019.vo contains library \u2018qualid\u2019 and not library \u2018qualid\u2019 (error)": [[59, "coq:exn.The-file-\u2018ident\u2019.vo-contains-library-\u2018qualid\u2019-and-not-library-\u2018qualid\u2019"]], "the type \u2018ident\u2019 must be registered before this construction can be typechecked (error)": [[59, "coq:exn.The-type-\u2018ident\u2019-must-be-registered-before-this-construction-can-be-typechecked"]], "this object does not support universe names (error)": [[59, "coq:exn.This-object-does-not-support-universe-names"]], "time (command)": [[59, "coq:cmd.Time"]], "timeout (command)": [[59, "coq:cmd.Timeout"]], "type (command)": [[59, "coq:cmd.Type"]], "universe checking (flag)": [[59, "coq:flag.Universe-Checking"]], "universe instance length is \u2018natural\u2019 but should be \u2018natural\u2019 (error)": [[59, "coq:exn.Universe-instance-length-is-\u2018natural\u2019-but-should-be-\u2018natural\u2019"]], "warnings (option)": [[59, "coq:opt.Warnings"]], "bypass_check(guard) (attribute)": [[59, "coq:attr.bypass_check(guard)"]], "bypass_check(positivity) (attribute)": [[59, "coq:attr.bypass_check(positivity)"]], "bypass_check(universes) (attribute)": [[59, "coq:attr.bypass_check(universes)"]], "package-name.foo and not foo_plugin (error)": [[59, "coq:exn.package-name.foo-and-not-foo_plugin"]], "plugin name anymore. plugins should be loaded using their (error)": [[59, "coq:exn.plugin-name-anymore.-Plugins-should-be-loaded-using-their"]], "public name according to findlib, for example (error)": [[59, "coq:exn.public-name-according-to-findlib,-for-example"]], "shared library failed: coq error: \u2018string\u2019 is not a valid (error)": [[59, "coq:exn.shared-library-failed:-Coq-Error:-\u2018string\u2019-is-not-a-valid"]], "\u2018qualid\u2019 not a defined object (error)": [[59, "coq:exn.\u2018qualid\u2019-not-a-defined-object"]], "cannot coerce \u2018qualid\u2019 to an evaluable reference (error)": [[60, "coq:exn.Cannot-coerce-\u2018qualid\u2019-to-an-evaluable-reference"]], "create hintdb (command)": [[60, "coq:cmd.Create-HintDb"]], "debug auto (flag)": [[60, "coq:flag.Debug-Auto"]], "debug eauto (flag)": [[60, "coq:flag.Debug-Eauto"]], "debug trivial (flag)": [[60, "coq:flag.Debug-Trivial"]], "declaring arbitrary terms as hints is fragile and deprecated": [[60, "coq:warn.Declaring-arbitrary-terms-as-hints-is-fragile-and-deprecated;-it-is-recommended-to-declare-a-toplevel-constant-instead"]], "hint constants (command)": [[60, "coq:cmd.Hint-Constants"]], "hint constructors (command)": [[60, "coq:cmd.Hint-Constructors"]], "hint cut (command)": [[60, "coq:cmd.Hint-Cut"]], "hint extern (command)": [[60, "coq:cmd.Hint-Extern"]], "hint immediate (command)": [[60, "coq:cmd.Hint-Immediate"]], "hint mode (command)": [[60, "coq:cmd.Hint-Mode"]], "hint opaque (command)": [[60, "coq:cmd.Hint-Opaque"]], "hint projections (command)": [[60, "coq:cmd.Hint-Projections"]], "hint resolve (command)": [[60, "coq:cmd.Hint-Resolve"]], "hint rewrite (command)": [[60, "coq:cmd.Hint-Rewrite"]], "hint transparent (command)": [[60, "coq:cmd.Hint-Transparent"]], "hint unfold (command)": [[60, "coq:cmd.Hint-Unfold"]], "hint variables (command)": [[60, "coq:cmd.Hint-Variables"]], "info auto (flag)": [[60, "coq:flag.Info-Auto"]], "info eauto (flag)": [[60, "coq:flag.Info-Eauto"]], "info trivial (flag)": [[60, "coq:flag.Info-Trivial"]], "loose hint behavior (option)": [[60, "coq:opt.Loose-Hint-Behavior"]], "print hint (command)": [[60, "coq:cmd.Print-Hint"]], "print hintdb (command)": [[60, "coq:cmd.Print-HintDb"]], "print rewrite hintdb (command)": [[60, "coq:cmd.Print-Rewrite-HintDb"]], "proof with (command)": [[60, "coq:cmd.Proof-with"]], "remove hints (command)": [[60, "coq:cmd.Remove-Hints"]], "the \"at\" syntax isn't available yet for the autorewrite tactic (error)": [[60, "coq:exn.The-\"at\"-syntax-isn't-available-yet-for-the-autorewrite-tactic"]], "this hint is not local but depends on a section variable. it will disappear when the section is closed (warning)": [[60, "coq:warn.This-hint-is-not-local-but-depends-on-a-section-variable.-It-will-disappear-when-the-section-is-closed"]], "auto (tactic)": [[60, "coq:tacn.auto"]], "autorewrite (tactic)": [[60, "coq:tacn.autorewrite"]], "autounfold (tactic)": [[60, "coq:tacn.autounfold"]], "autounfold_one (tactic)": [[60, "coq:tacn.autounfold_one"]], "debug auto (tactic)": [[60, "coq:tacn.debug-auto"]], "debug eauto (tactic)": [[60, "coq:tacn.debug-eauto"]], "debug trivial (tactic)": [[60, "coq:tacn.debug-trivial"]], "easy (tactic)": [[60, "coq:tacn.easy"]], "eauto (tactic)": [[60, "coq:tacn.eauto"]], "info_auto (tactic)": [[60, "coq:tacn.info_auto"]], "info_eauto (tactic)": [[60, "coq:tacn.info_eauto"]], "info_trivial (tactic)": [[60, "coq:tacn.info_trivial"]], "it is recommended to declare a toplevel constant instead (warning)": [[60, "coq:warn.Declaring-arbitrary-terms-as-hints-is-fragile-and-deprecated;-it-is-recommended-to-declare-a-toplevel-constant-instead"]], "mismatched-hint-db (warning)": [[60, "coq:warn.mismatched-hint-db"]], "now (tactic)": [[60, "coq:tacn.now"]], "trivial (tactic)": [[60, "coq:tacn.trivial"]], "\u2018qualid\u2019 cannot be used as a hint (error)": [[60, "coq:exn.\u2018qualid\u2019-cannot-be-used-as-a-hint"]], "\u2018qualid\u2019 is not an inductive type (error)": [[60, "coq:exn.\u2018qualid\u2019-is-not-an-inductive-type"]], "cannot recognize a boolean equality (error)": [[62, "coq:exn.Cannot-recognize-a-boolean-equality"]], "firstorder depth (option)": [[62, "coq:opt.Firstorder-Depth"]], "firstorder solver (option)": [[62, "coq:opt.Firstorder-Solver"]], "goal is solvable by congruence but some arguments are missing. try congruence with \u2018term\u2019\u2026\u2018term\u2019, replacing metavariables by arbitrary terms (error)": [[62, "coq:exn.Goal-is-solvable-by-congruence-but-some-arguments-are-missing.-Try-congruence-with-\u2018term\u2019\u2026\u2018term\u2019,-replacing-metavariables-by-arbitrary-terms"]], "i don\u2019t know how to handle dependent equality (error)": [[62, "coq:exn.I-don\u2019t-know-how-to-handle-dependent-equality"]], "intuition negation unfolding (flag)": [[62, "coq:flag.Intuition-Negation-Unfolding"]], "print firstorder solver (command)": [[62, "coq:cmd.Print-Firstorder-Solver"]], "btauto (tactic)": [[62, "coq:tacn.btauto"]], "congruence (tactic)": [[62, "coq:tacn.congruence"]], "dintuition (tactic)": [[62, "coq:tacn.dintuition"]], "dtauto (tactic)": [[62, "coq:tacn.dtauto"]], "firstorder (tactic)": [[62, "coq:tacn.firstorder"]], "intuition (tactic)": [[62, "coq:tacn.intuition"]], "rtauto (tactic)": [[62, "coq:tacn.rtauto"]], "simple congruence (tactic)": [[62, "coq:tacn.simple-congruence"]], "tauto (tactic)": [[62, "coq:tacn.tauto"]], "bad occurrence number of \u2018qualid\u2019 (error)": [[64, "coq:exn.Bad-occurrence-number-of-\u2018qualid\u2019"]], "cannot find a relation to rewrite (error)": [[64, "coq:exn.Cannot-find-a-relation-to-rewrite"]], "cannot find any non-recursive equality over \u2018ident\u2019 (error)": [[64, "coq:exn.Cannot-find-any-non-recursive-equality-over-\u2018ident\u2019"]], "cannot turn [inductive|constructor] into an evaluable reference (error)": [[64, "coq:exn.Cannot-turn-[inductive|constructor]-into-an-evaluable-reference"]], "compute (command)": [[64, "coq:cmd.Compute"]], "declare equivalent keys (command)": [[64, "coq:cmd.Declare-Equivalent-Keys"]], "declare left step (command)": [[64, "coq:cmd.Declare-Left-Step"]], "declare reduction (command)": [[64, "coq:cmd.Declare-Reduction"]], "declare right step (command)": [[64, "coq:cmd.Declare-Right-Step"]], "eval (command)": [[64, "coq:cmd.Eval"]], "found an \"at\" clause without \"with\" clause (error)": [[64, "coq:exn.Found-an-\"at\"-clause-without-\"with\"-clause"]], "found no subterm matching \u2018term\u2019 in the current goal (error)": [[64, "coq:exn.Found-no-subterm-matching-\u2018term\u2019-in-the-current-goal"]], "found no subterm matching \u2018term\u2019 in \u2018ident\u2019 (error)": [[64, "coq:exn.Found-no-subterm-matching-\u2018term\u2019-in-\u2018ident\u2019"]], "kernel term sharing (flag)": [[64, "coq:flag.Kernel-Term-Sharing"]], "keyed unification (flag)": [[64, "coq:flag.Keyed-Unification"]], "nativecompute profile filename (option)": [[64, "coq:opt.NativeCompute-Profile-Filename"]], "nativecompute profiling (flag)": [[64, "coq:flag.NativeCompute-Profiling"]], "nativecompute timing (flag)": [[64, "coq:flag.NativeCompute-Timing"]], "no head constant to reduce (error)": [[64, "coq:exn.No-head-constant-to-reduce"]], "not convertible (error)": [[64, "coq:exn.Not-convertible"]], "opaque (command)": [[64, "coq:cmd.Opaque"]], "print equivalent keys (command)": [[64, "coq:cmd.Print-Equivalent-Keys"]], "print strategies (command)": [[64, "coq:cmd.Print-Strategies"]], "print strategy (command)": [[64, "coq:cmd.Print-Strategy"]], "regular subst tactic (flag)": [[64, "coq:flag.Regular-Subst-Tactic"]], "section variable \u2018ident\u2019 occurs implicitly in global declaration \u2018qualid\u2019 present in hypothesis \u2018ident\u2019 (error)": [[64, "coq:exn.Section-variable-\u2018ident\u2019-occurs-implicitly-in-global-declaration-\u2018qualid\u2019-present-in-hypothesis-\u2018ident\u2019"]], "section variable \u2018ident\u2019 occurs implicitly in global declaration \u2018qualid\u2019 present in the conclusion (error)": [[64, "coq:exn.Section-variable-\u2018ident\u2019-occurs-implicitly-in-global-declaration-\u2018qualid\u2019-present-in-the-conclusion"]], "strategy (command)": [[64, "coq:cmd.Strategy"]], "tactic failure: setoid library not loaded (error)": [[64, "coq:exn.Tactic-failure:-Setoid-library-not-loaded"]], "tactic generated a subgoal identical to the original goal (error)": [[64, "coq:exn.Tactic-generated-a-subgoal-identical-to-the-original-goal"]], "terms do not have convertible types (error)": [[64, "coq:exn.Terms-do-not-have-convertible-types"]], "the reference is not unfoldable (error)": [[64, "coq:exn.The-reference-is-not-unfoldable"]], "the reference \u2018qualid\u2019 was not found in the current environment (error)": [[64, "coq:exn.The-reference-\u2018qualid\u2019-was-not-found-in-the-current-environment"]], "the relation \u2018ident\u2019 is not a declared reflexive relation. maybe you need to require the stdlib.classes.relationclasses library (error)": [[64, "coq:exn.The-relation-\u2018ident\u2019-is-not-a-declared-reflexive-relation.-Maybe-you-need-to-require-the-Stdlib.Classes.RelationClasses-library"]], "the relation \u2018ident\u2019 is not a declared symmetric relation. maybe you need to require the stdlib.classes.relationclasses library (error)": [[64, "coq:exn.The-relation-\u2018ident\u2019-is-not-a-declared-symmetric-relation.-Maybe-you-need-to-require-the-Stdlib.Classes.RelationClasses-library"]], "the relation \u2018ident\u2019 is not a declared transitive relation. maybe you need to require the stdlib.classes.relationclasses library (error)": [[64, "coq:exn.The-relation-\u2018ident\u2019-is-not-a-declared-transitive-relation.-Maybe-you-need-to-require-the-Stdlib.Classes.RelationClasses-library"]], "transparent (command)": [[64, "coq:cmd.Transparent"]], "cbn (tactic)": [[64, "coq:tacn.cbn"]], "cbv (tactic)": [[64, "coq:tacn.cbv"]], "change (tactic)": [[64, "coq:tacn.change"]], "change_no_check (tactic)": [[64, "coq:tacn.change_no_check"]], "compute (tactic)": [[64, "coq:tacn.compute"]], "erewrite (tactic)": [[64, "coq:tacn.erewrite"]], "etransitivity (tactic)": [[64, "coq:tacn.etransitivity"]], "eval (tactic)": [[64, "coq:tacn.eval"]], "f_equal (tactic)": [[64, "coq:tacn.f_equal"]], "fold (tactic)": [[64, "coq:tacn.fold"]], "hnf (tactic)": [[64, "coq:tacn.hnf"]], "lazy (tactic)": [[64, "coq:tacn.lazy"]], "native_compute (tactic)": [[64, "coq:tacn.native_compute"]], "now_show (tactic)": [[64, "coq:tacn.now_show"]], "pattern (tactic)": [[64, "coq:tacn.pattern"]], "red (tactic)": [[64, "coq:tacn.red"]], "reflexivity (tactic)": [[64, "coq:tacn.reflexivity"]], "replace (tactic)": [[64, "coq:tacn.replace"]], "rewrite (tactic)": [[64, "coq:tacn.rewrite"]], "rewrite * (tactic)": [[64, "coq:tacn.rewrite-*"]], "simpl (tactic)": [[64, "coq:tacn.simpl"]], "simple subst (tactic)": [[64, "coq:tacn.simple-subst"]], "stepl (tactic)": [[64, "coq:tacn.stepl"]], "stepr (tactic)": [[64, "coq:tacn.stepr"]], "subst (tactic)": [[64, "coq:tacn.subst"]], "substitute (tactic)": [[64, "coq:tacn.substitute"]], "symmetry (tactic)": [[64, "coq:tacn.symmetry"]], "transitivity (tactic)": [[64, "coq:tacn.transitivity"]], "unfold (tactic)": [[64, "coq:tacn.unfold"]], "vm_compute (tactic)": [[64, "coq:tacn.vm_compute"]], "with_strategy (tactic)": [[64, "coq:tacn.with_strategy"]], "\u2018ident\u2019 is opaque (error)": [[64, "coq:exn.\u2018ident\u2019-is-opaque"]], "\u2018qualid\u2019 does not occur (error)": [[64, "coq:exn.\u2018qualid\u2019-does-not-occur"]], "\"all\" is a predefined collection containing all variables. it can't be redefined (error)": [[66, "coq:exn.\"All\"-is-a-predefined-collection-containing-all-variables.-It-can't-be-redefined"]], "abort (command)": [[66, "coq:cmd.Abort"]], "admitted (command)": [[66, "coq:cmd.Admitted"]], "attempt to save an incomplete proof (error)": [[66, "coq:exn.Attempt-to-save-an-incomplete-proof"]], "brackets do not support multi-goal selectors (error)": [[66, "coq:exn.Brackets-do-not-support-multi-goal-selectors"]], "bullet behavior (option)": [[66, "coq:opt.Bullet-Behavior"]], "collection (command)": [[66, "coq:cmd.Collection"]], "default proof mode (option)": [[66, "coq:opt.Default-Proof-Mode"]], "default proof using (option)": [[66, "coq:opt.Default-Proof-Using"]], "defined (command)": [[66, "coq:cmd.Defined"]], "diffs (option)": [[66, "coq:opt.Diffs"]], "focus (command)": [[66, "coq:cmd.Focus"]], "goal (command)": [[66, "coq:cmd.Goal"]], "guarded (command)": [[66, "coq:cmd.Guarded"]], "hyps limit (option)": [[66, "coq:opt.Hyps-Limit"]], "mangle names (flag)": [[66, "coq:flag.Mangle-Names"]], "mangle names light (flag)": [[66, "coq:flag.Mangle-Names-Light"]], "mangle names prefix (option)": [[66, "coq:opt.Mangle-Names-Prefix"]], "nested proofs allowed (flag)": [[66, "coq:flag.Nested-Proofs-Allowed"]], "new collection definition of \u2018ident\u2019 shadows the previous one (warning)": [[66, "coq:warn.New-Collection-definition-of-\u2018ident\u2019-shadows-the-previous-one"]], "no focused proof (no proof-editing in progress) (error)": [[66, "coq:exn.No-focused-proof-(No-proof-editing-in-progress)"]], "no focused proof (error)": [[66, "coq:exn.No-focused-proof"]], "no focused proof to restart (error)": [[66, "coq:exn.No-focused-proof-to-restart"]], "no such goal (error)": [[66, "coq:exn.No-such-goal"]], "no such goal (\u2018ident\u2019) (error)": [[66, "coq:exn.No-such-goal-(\u2018ident\u2019)"]], "no such goal (\u2018natural\u2019) (error)": [[66, "coq:exn.No-such-goal-(\u2018natural\u2019)"]], "no such goal. focus next goal with bullet \u2018bullet\u2019 (error)": [[66, "coq:exn.No-such-goal.-Focus-next-goal-with-bullet-\u2018bullet\u2019"]], "no such goal. try unfocusing with } (error)": [[66, "coq:exn.No-such-goal.-Try-unfocusing-with-}"]], "optimize heap (command)": [[66, "coq:cmd.Optimize-Heap"]], "optimize proof (command)": [[66, "coq:cmd.Optimize-Proof"]], "print debug gc (command)": [[66, "coq:cmd.Print-Debug-GC"]], "printing goal names (flag)": [[66, "coq:flag.Printing-Goal-Names"]], "printing goal tags (flag)": [[66, "coq:flag.Printing-Goal-Tags"]], "proof (command)": [[66, "coq:cmd.Proof"]], "proof mode (command)": [[66, "coq:cmd.Proof-Mode"]], "proof `term` (command)": [[66, "coq:cmd.Proof-`term`"]], "proof is not complete. (abstract) (error)": [[66, "coq:exn.Proof-is-not-complete.-(abstract)"]], "proof using (command)": [[66, "coq:cmd.Proof-using"]], "qed (command)": [[66, "coq:cmd.Qed"]], "restart (command)": [[66, "coq:cmd.Restart"]], "save (command)": [[66, "coq:cmd.Save"]], "show (command)": [[66, "coq:cmd.Show"]], "show conjectures (command)": [[66, "coq:cmd.Show-Conjectures"]], "show existentials (command)": [[66, "coq:cmd.Show-Existentials"]], "show goal (command)": [[66, "coq:cmd.Show-Goal"]], "show intro (command)": [[66, "coq:cmd.Show-Intro"]], "show intros (command)": [[66, "coq:cmd.Show-Intros"]], "show match (command)": [[66, "coq:cmd.Show-Match"]], "show proof (command)": [[66, "coq:cmd.Show-Proof"]], "show universes (command)": [[66, "coq:cmd.Show-Universes"]], "solve unification constraints (flag)": [[66, "coq:flag.Solve-Unification-Constraints"]], "suggest proof using (flag)": [[66, "coq:flag.Suggest-Proof-Using"]], "this proof is focused, but cannot be unfocused this way (error)": [[66, "coq:exn.This-proof-is-focused,-but-cannot-be-unfocused-this-way"]], "undo (command)": [[66, "coq:cmd.Undo"]], "unfocus (command)": [[66, "coq:cmd.Unfocus"]], "unfocused (command)": [[66, "coq:cmd.Unfocused"]], "unknown inductive type (error)": [[66, "coq:exn.Unknown-inductive-type"]], "unshelve (command)": [[66, "coq:cmd.Unshelve"]], "validate proof (command)": [[66, "coq:cmd.Validate-Proof"]], "variable all is shadowed by collection named all containing all variables (warning)": [[66, "coq:warn.Variable-All-is-shadowed-by-Collection-named-All-containing-all-variables"]], "wrong bullet \u2018bullet\u2019: bullet \u2018bullet\u2019 is mandatory here (error)": [[66, "coq:exn.Wrong-bullet-\u2018bullet\u2019:-Bullet-\u2018bullet\u2019-is-mandatory-here"]], "wrong bullet \u2018bullet\u2019: current bullet \u2018bullet\u2019 is not finished (error)": [[66, "coq:exn.Wrong-bullet-\u2018bullet\u2019:-Current-bullet-\u2018bullet\u2019-is-not-finished"]], "abstract (tactic)": [[66, "coq:tacn.abstract"]], "admit (tactic)": [[66, "coq:tacn.admit"]], "bullet (- + *) (tactic)": [[66, "coq:tacn.bullet-(--+-*)"]], "cycle (tactic)": [[66, "coq:tacn.cycle"]], "give_up (tactic)": [[66, "coq:tacn.give_up"]], "revgoals (tactic)": [[66, "coq:tacn.revgoals"]], "shelve (tactic)": [[66, "coq:tacn.shelve"]], "shelve_unifiable (tactic)": [[66, "coq:tacn.shelve_unifiable"]], "solve_constraints (tactic)": [[66, "coq:tacn.solve_constraints"]], "swap (tactic)": [[66, "coq:tacn.swap"]], "transparent_abstract (tactic)": [[66, "coq:tacn.transparent_abstract"]], "unshelve (tactic)": [[66, "coq:tacn.unshelve"]], "using (attribute)": [[66, "coq:attr.using"]], "{ (tactic)": [[66, "coq:tacn.{"]], "} (tactic)": [[66, "coq:tacn.}"]], "\u2018ident\u2019 is both name of a collection and variable, collection \u2018ident\u2019 takes precedence over variable (warning)": [[66, "coq:warn.\u2018ident\u2019-is-both-name-of-a-Collection-and-Variable,-Collection-\u2018ident\u2019-takes-precedence-over-Variable"]], "\u2018ident\u2019 was already a defined variable, the name \u2018ident\u2019 will refer to collection when executing \"proof using\" command (warning)": [[66, "coq:warn.\u2018ident\u2019-was-already-a-defined-Variable,-the-name-\u2018ident\u2019-will-refer-to-Collection-when-executing-\"Proof-using\"-command"]], "boolean equality schemes (flag)": [[67, "coq:flag.Boolean-Equality-Schemes"]], "cannot recognize a statement based on \u2018reference\u2019 (error)": [[67, "coq:exn.Cannot-recognize-a-statement-based-on-\u2018reference\u2019"]], "case analysis schemes (flag)": [[67, "coq:flag.Case-Analysis-Schemes"]], "combined scheme (command)": [[67, "coq:cmd.Combined-Scheme"]], "decidable equality schemes (flag)": [[67, "coq:flag.Decidable-Equality-Schemes"]], "derive dependent inversion (command)": [[67, "coq:cmd.Derive-Dependent-Inversion"]], "derive dependent inversion_clear (command)": [[67, "coq:cmd.Derive-Dependent-Inversion_clear"]], "derive inversion (command)": [[67, "coq:cmd.Derive-Inversion"]], "derive inversion_clear (command)": [[67, "coq:cmd.Derive-Inversion_clear"]], "elimination schemes (flag)": [[67, "coq:flag.Elimination-Schemes"]], "keep equalities (table)": [[67, "coq:table.Keep-Equalities"]], "keep proof equalities (flag)": [[67, "coq:flag.Keep-Proof-Equalities"]], "no information can be deduced from this equality and the injectivity of constructors. this may be because the terms are convertible, or due to pattern matching restrictions in the sort prop. you can try to use option set keep proof equalities (error)": [[67, "coq:exn.No-information-can-be-deduced-from-this-equality-and-the-injectivity-of-constructors.-This-may-be-because-the-terms-are-convertible,-or-due-to-pattern-matching-restrictions-in-the-sort-Prop.-You-can-try-to-use-option-Set-Keep-Proof-Equalities"]], "no primitive equality found (error)": [[67, "coq:exn.No-primitive-equality-found"]], "nonrecursive elimination schemes (flag)": [[67, "coq:flag.Nonrecursive-Elimination-Schemes"]], "not a discriminable equality (error)": [[67, "coq:exn.Not-a-discriminable-equality"]], "not a negated primitive equality (error)": [[67, "coq:exn.Not-a-negated-primitive-equality"]], "not an inductive goal with 1 constructor (error)": [[67, "coq:exn.Not-an-inductive-goal-with-1-constructor"]], "not an inductive goal with 2 constructors (error)": [[67, "coq:exn.Not-an-inductive-goal-with-2-constructors"]], "not an inductive product (error)": [[67, "coq:exn.Not-an-inductive-product"]], "not enough constructors (error)": [[67, "coq:exn.Not-enough-constructors"]], "nothing to inject (error)": [[67, "coq:exn.Nothing-to-inject"]], "rewriting schemes (flag)": [[67, "coq:flag.Rewriting-Schemes"]], "scheme (command)": [[67, "coq:cmd.Scheme"]], "scheme boolean equality (command)": [[67, "coq:cmd.Scheme-Boolean-Equality"]], "scheme equality (command)": [[67, "coq:cmd.Scheme-Equality"]], "structural injection (flag)": [[67, "coq:flag.Structural-Injection"]], "the type has no constructors (error)": [[67, "coq:exn.The-type-has-no-constructors"]], "type of \u2018ident\u2019 is not an equality of recognized \u03c3 types: expected one of sig sig2 sigt sigt2 sigt2 ex or ex2 but got \u2018term\u2019 (error)": [[67, "coq:exn.Type-of-\u2018ident\u2019-is-not-an-equality-of-recognized-\u03a3-types:-expected-one-of-sig-sig2-sigT-sigT2-sigT2-ex-or-ex2-but-got-\u2018term\u2019"]], "unable to find an instance for the variables \u2018ident\u2019 \u2026 \u2018ident\u2019 (error)": [[67, "coq:exn.Unable-to-find-an-instance-for-the-variables-\u2018ident\u2019-\u2026-\u2018ident\u2019"]], "case (tactic)": [[67, "coq:tacn.case"]], "case_eq (tactic)": [[67, "coq:tacn.case_eq"]], "cofix (tactic)": [[67, "coq:tacn.cofix"]], "compare (tactic)": [[67, "coq:tacn.compare"]], "constructor (tactic)": [[67, "coq:tacn.constructor"]], "decide (tactic)": [[67, "coq:tacn.decide"]], "decide equality (tactic)": [[67, "coq:tacn.decide-equality"]], "decompose (tactic)": [[67, "coq:tacn.decompose"]], "decompose record (tactic)": [[67, "coq:tacn.decompose-record"]], "decompose sum (tactic)": [[67, "coq:tacn.decompose-sum"]], "dependent destruction (tactic)": [[67, "coq:tacn.dependent-destruction"]], "dependent induction (tactic)": [[67, "coq:tacn.dependent-induction"]], "dependent inversion (tactic)": [[67, "coq:tacn.dependent-inversion"]], "dependent inversion_clear (tactic)": [[67, "coq:tacn.dependent-inversion_clear"]], "dependent rewrite (tactic)": [[67, "coq:tacn.dependent-rewrite"]], "dependent simple inversion (tactic)": [[67, "coq:tacn.dependent-simple-inversion"]], "destauto (tactic)": [[67, "coq:tacn.destauto"]], "destruct (tactic)": [[67, "coq:tacn.destruct"]], "discriminate (tactic)": [[67, "coq:tacn.discriminate"]], "ecase (tactic)": [[67, "coq:tacn.ecase"]], "econstructor (tactic)": [[67, "coq:tacn.econstructor"]], "edestruct (tactic)": [[67, "coq:tacn.edestruct"]], "ediscriminate (tactic)": [[67, "coq:tacn.ediscriminate"]], "eelim (tactic)": [[67, "coq:tacn.eelim"]], "eexists (tactic)": [[67, "coq:tacn.eexists"]], "einduction (tactic)": [[67, "coq:tacn.einduction"]], "einjection (tactic)": [[67, "coq:tacn.einjection"]], "eleft (tactic)": [[67, "coq:tacn.eleft"]], "elim (tactic)": [[67, "coq:tacn.elim"]], "eright (tactic)": [[67, "coq:tacn.eright"]], "esimplify_eq (tactic)": [[67, "coq:tacn.esimplify_eq"]], "esplit (tactic)": [[67, "coq:tacn.esplit"]], "exists (tactic)": [[67, "coq:tacn.exists"]], "fix (tactic)": [[67, "coq:tacn.fix"]], "induction (tactic)": [[67, "coq:tacn.induction"]], "injection (tactic)": [[67, "coq:tacn.injection"]], "inversion (tactic)": [[67, "coq:tacn.inversion"]], "inversion_clear (tactic)": [[67, "coq:tacn.inversion_clear"]], "inversion_sigma (tactic)": [[67, "coq:tacn.inversion_sigma"]], "left (tactic)": [[67, "coq:tacn.left"]], "right (tactic)": [[67, "coq:tacn.right"]], "simple destruct (tactic)": [[67, "coq:tacn.simple-destruct"]], "simple induction (tactic)": [[67, "coq:tacn.simple-induction"]], "simple injection (tactic)": [[67, "coq:tacn.simple-injection"]], "simple inversion (tactic)": [[67, "coq:tacn.simple-inversion"]], "simplify_eq (tactic)": [[67, "coq:tacn.simplify_eq"]], "split (tactic)": [[67, "coq:tacn.split"]], "\u2018ident\u2019 is not an equality of \u03c3 types (error)": [[67, "coq:exn.\u2018ident\u2019-is-not-an-equality-of-\u03a3-types"]], "'via' and 'abstract' cannot be used together (error)": [[71, "coq:exn.'via'-and-'abstract'-cannot-be-used-together"]], "activation of abbreviations does not expect mentioning a grammar entry (warning)": [[71, "coq:warn.Activation-of-abbreviations-does-not-expect-mentioning-a-grammar-entry"]], "activation of abbreviations does not expect mentioning a scope (warning)": [[71, "coq:warn.Activation-of-abbreviations-does-not-expect-mentioning-a-scope"]], "bind scope (command)": [[71, "coq:cmd.Bind-Scope"]], "cannot interpret in \u2018scope_name\u2019 because \u2018qualid\u2019 could not be found in the current environment (error)": [[71, "coq:exn.Cannot-interpret-in-\u2018scope_name\u2019-because-\u2018qualid\u2019-could-not-be-found-in-the-current-environment"]], "cannot interpret this number as a value of type \u2018type\u2019 (error)": [[71, "coq:exn.Cannot-interpret-this-number-as-a-value-of-type-\u2018type\u2019"]], "cannot interpret this string as a value of type \u2018type\u2019 (error)": [[71, "coq:exn.Cannot-interpret-this-string-as-a-value-of-type-\u2018type\u2019"]], "close scope (command)": [[71, "coq:cmd.Close-Scope"]], "declare custom entry (command)": [[71, "coq:cmd.Declare-Custom-Entry"]], "declare scope (command)": [[71, "coq:cmd.Declare-Scope"]], "delimit scope (command)": [[71, "coq:cmd.Delimit-Scope"]], "disable notation (command)": [[71, "coq:cmd.Disable-Notation"]], "enable notation (command)": [[71, "coq:cmd.Enable-Notation"]], "end of quoted string not followed by a space in notation (error)": [[71, "coq:exn.End-of-quoted-string-not-followed-by-a-space-in-notation"]], "found no matching notation to enable or disable (warning)": [[71, "coq:warn.Found-no-matching-notation-to-enable-or-disable"]], "infix (command)": [[71, "coq:cmd.Infix"]], "missing mapping for constructor \u2018qualid\u2019 (error)": [[71, "coq:exn.Missing-mapping-for-constructor-\u2018qualid\u2019"]], "more than one interpretation bound to this notation, confirm with the \"all\" modifier (error)": [[71, "coq:exn.More-than-one-interpretation-bound-to-this-notation,-confirm-with-the-\"all\"-modifier"]], "multiple 'via' options (error)": [[71, "coq:exn.Multiple-'via'-options"]], "multiple 'warning after' or 'abstract after' options (error)": [[71, "coq:exn.Multiple-'warning-after'-or-'abstract-after'-options"]], "no notation provided (error)": [[71, "coq:exn.No-notation-provided"]], "notation (abbreviation) (command)": [[71, "coq:cmd.Notation-(abbreviation)"]], "notation (command)": [[71, "coq:cmd.Notation"]], "number notation (command)": [[71, "coq:cmd.Number-Notation"]], "open scope (command)": [[71, "coq:cmd.Open-Scope"]], "print custom grammar (command)": [[71, "coq:cmd.Print-Custom-Grammar"]], "print grammar (command)": [[71, "coq:cmd.Print-Grammar"]], "print keywords (command)": [[71, "coq:cmd.Print-Keywords"]], "print notation (command)": [[71, "coq:cmd.Print-Notation"]], "print scope (command)": [[71, "coq:cmd.Print-Scope"]], "print scopes (command)": [[71, "coq:cmd.Print-Scopes"]], "print visibility (command)": [[71, "coq:cmd.Print-Visibility"]], "printing notations (flag)": [[71, "coq:flag.Printing-Notations"]], "printing parentheses (flag)": [[71, "coq:flag.Printing-Parentheses"]], "printing raw literals (flag)": [[71, "coq:flag.Printing-Raw-Literals"]], "reserved infix (command)": [[71, "coq:cmd.Reserved-Infix"]], "reserved notation (command)": [[71, "coq:cmd.Reserved-Notation"]], "scope delimiters should not start with an underscore (error)": [[71, "coq:exn.Scope-delimiters-should-not-start-with-an-underscore"]], "scope names should not start with an underscore (error)": [[71, "coq:exn.Scope-names-should-not-start-with-an-underscore"]], "stack overflow or segmentation fault happens when working with large numbers in \u2018type\u2019 (threshold may vary depending on your system limits and on the command executed) (warning)": [[71, "coq:warn.Stack-overflow-or-segmentation-fault-happens-when-working-with-large-numbers-in-\u2018type\u2019-(threshold-may-vary-depending-on-your-system-limits-and-on-the-command-executed)"]], "string notation (command)": [[71, "coq:cmd.String-Notation"]], "syntax error: [prim:reference] expected after 'notation' (in [vernac:command]) (error)": [[71, "coq:exn.Syntax-error:-[prim:reference]-expected-after-'Notation'-(in-[vernac:command])"]], "syntax error: [prim:reference] expected after [prim:reference] (in [vernac:command]) (error)": [[71, "coq:exn.Syntax-error:-[prim:reference]-expected-after-[prim:reference]-(in-[vernac:command])"]], "tactic notation (command)": [[71, "coq:cmd.Tactic-Notation"]], "the 'abstract after' directive has no effect when the parsing function (\u2018qualid\u2019) targets an option type (warning)": [[71, "coq:warn.The-'abstract-after'-directive-has-no-effect-when-the-parsing-function-(\u2018qualid\u2019)-targets-an-option-type"]], "to avoid stack overflow, large numbers in \u2018type\u2019 are interpreted as applications of \u2018qualid\u2019 (warning)": [[71, "coq:warn.To-avoid-stack-overflow,-large-numbers-in-\u2018type\u2019-are-interpreted-as-applications-of-\u2018qualid\u2019"]], "type of \u2018qualid\u2019 seems incompatible with the type of \u2018qualid\u2019. expected type is: \u2018type\u2019 instead of \u2018type\u2019. this might yield ill typed terms when using the notation (warning)": [[71, "coq:warn.Type-of-\u2018qualid\u2019-seems-incompatible-with-the-type-of-\u2018qualid\u2019.-Expected-type-is:-\u2018type\u2019-instead-of-\u2018type\u2019.-This-might-yield-ill-typed-terms-when-using-the-notation"]], "undelimit scope (command)": [[71, "coq:cmd.Undelimit-Scope"]], "unexpected non-option term \u2018term\u2019 while parsing a number notation (error)": [[71, "coq:exn.Unexpected-non-option-term-\u2018term\u2019-while-parsing-a-number-notation"]], "unexpected non-option term \u2018term\u2019 while parsing a string notation (error)": [[71, "coq:exn.Unexpected-non-option-term-\u2018term\u2019-while-parsing-a-string-notation"]], "unexpected only parsing for an only printing notation (error)": [[71, "coq:exn.Unexpected-only-parsing-for-an-only-printing-notation"]], "unexpected only printing for an only parsing notation (error)": [[71, "coq:exn.Unexpected-only-printing-for-an-only-parsing-notation"]], "unexpected term \u2018term\u2019 while parsing a number notation (error)": [[71, "coq:exn.Unexpected-term-\u2018term\u2019-while-parsing-a-number-notation"]], "unexpected term \u2018term\u2019 while parsing a string notation (error)": [[71, "coq:exn.Unexpected-term-\u2018term\u2019-while-parsing-a-string-notation"]], "unknown custom entry (error)": [[71, "coq:exn.Unknown-custom-entry"]], "unknown custom entry: \u2018ident\u2019 (error)": [[71, "coq:exn.Unknown-custom-entry:-\u2018ident\u2019"]], "unterminated string in notation (error)": [[71, "coq:exn.Unterminated-string-in-notation"]], "use of \u2018string\u2019 notation is deprecated as it is inconsistent with pattern syntax (warning)": [[71, "coq:warn.Use-of-\u2018string\u2019-Notation-is-deprecated-as-it-is-inconsistent-with-pattern-syntax"]], "add_bottom (attribute)": [[71, "coq:attr.add_bottom"]], "add_top (attribute)": [[71, "coq:attr.add_top"]], "closed-notation-not-level-0 (warning)": [[71, "coq:warn.closed-notation-not-level-0"]], "function_scope": [[71, "index-1"]], "notation-incompatible-prefix (warning)": [[71, "coq:warn.notation-incompatible-prefix"]], "overflow in int63 literal \u2018bigint\u2019 (error)": [[71, "coq:exn.overflow-in-int63-literal-\u2018bigint\u2019"]], "postfix-notation-not-level-1 (warning)": [[71, "coq:warn.postfix-notation-not-level-1"]], "type_scope": [[71, "index-0"]], "\u2018qualid\u2019 is bound to a notation that does not denote a reference (error)": [[71, "coq:exn.\u2018qualid\u2019-is-bound-to-a-notation-that-does-not-denote-a-reference"]], "\u2018qualid\u2019 should go from byte.byte, (list byte.byte), or primstring.string to \u2018type\u2019 or (option \u2018type\u2019) (error)": [[71, "coq:exn.\u2018qualid\u2019-should-go-from-Byte.byte,-(list-Byte.byte),-or-PrimString.string-to-\u2018type\u2019-or-(option-\u2018type\u2019)"]], "\u2018qualid\u2019 should go from number.int to \u2018type\u2019 or (option \u2018type\u2019). instead of number.int, the types number.uint or z or primint63.pos_neg_int63 or primfloat.float or number.number could be used (you may need to require binnums or number or primint63 or primfloat first) (error)": [[71, "coq:exn.\u2018qualid\u2019-should-go-from-Number.int-to-\u2018type\u2019-or-(option-\u2018type\u2019).-Instead-of-Number.int,-the-types-Number.uint-or-Z-or-PrimInt63.pos_neg_int63-or-PrimFloat.float-or-Number.number-could-be-used-(you-may-need-to-require-BinNums-or-Number-or-PrimInt63-or-PrimFloat-first)"]], "\u2018qualid\u2019 should go from \u2018type\u2019 to number.int or (option number.int). instead of number.int, the types number.uint or z or primint63.pos_neg_int63 or number.number could be used (you may need to require binnums or number or primint63 first) (error)": [[71, "coq:exn.\u2018qualid\u2019-should-go-from-\u2018type\u2019-to-Number.int-or-(option-Number.int).-Instead-of-Number.int,-the-types-Number.uint-or-Z-or-PrimInt63.pos_neg_int63-or-Number.number-could-be-used-(you-may-need-to-require-BinNums-or-Number-or-PrimInt63-first)"]], "\u2018qualid\u2019 should go from \u2018type\u2019 to t or (option t), where t is either byte.byte, (list byte.byte), or primstring.string (error)": [[71, "coq:exn.\u2018qualid\u2019-should-go-from-\u2018type\u2019-to-T-or-(option-T),-where-T-is-either-Byte.byte,-(list-Byte.byte),-or-PrimString.string"]], "\u2018qualid\u2019 was already mapped to \u2018qualid\u2019 and cannot be remapped to \u2018qualid\u2019 (error)": [[71, "coq:exn.\u2018qualid\u2019-was-already-mapped-to-\u2018qualid\u2019-and-cannot-be-remapped-to-\u2018qualid\u2019"]], "\u2018string\u2019 cannot be interpreted as a known notation in \u2018ident\u2019 entry. make sure that symbols are surrounded by spaces and that holes are explicitly denoted by \"_\" (error)": [[71, "coq:exn.\u2018string\u2019-cannot-be-interpreted-as-a-known-notation-in-\u2018ident\u2019-entry.-Make-sure-that-symbols-are-surrounded-by-spaces-and-that-holes-are-explicitly-denoted-by-\"_\""]], "\u2018string\u2019 cannot be interpreted as a known notation. make sure that symbols are surrounded by spaces and that holes are explicitly denoted by \"_\" (error)": [[71, "coq:exn.\u2018string\u2019-cannot-be-interpreted-as-a-known-notation.-Make-sure-that-symbols-are-surrounded-by-spaces-and-that-holes-are-explicitly-denoted-by-\"_\""]], "\u2018type\u2019 is not an inductive type (error)": [[71, "coq:exn.\u2018type\u2019-is-not-an-inductive-type"]], "\u2018type\u2019 was already mapped to \u2018type\u2019, mapping it also to \u2018type\u2019 might yield ill typed terms when using the notation (warning)": [[71, "coq:warn.\u2018type\u2019-was-already-mapped-to-\u2018type\u2019,-mapping-it-also-to-\u2018type\u2019-might-yield-ill-typed-terms-when-using-the-notation"]], "cannot build functional inversion principle (warning)": [[72, "coq:warn.Cannot-build-functional-inversion-principle"]], "cannot define graph for \u2018ident\u2019 (warning)": [[72, "coq:warn.Cannot-define-graph-for-\u2018ident\u2019"]], "cannot define principle(s) for \u2018ident\u2019 (warning)": [[72, "coq:warn.Cannot-define-principle(s)-for-\u2018ident\u2019"]], "cannot find induction information on \u2018qualid\u2019 (error)": [[72, "coq:exn.Cannot-find-induction-information-on-\u2018qualid\u2019"]], "cannot find inversion information for hypothesis \u2018ident\u2019 (error)": [[72, "coq:exn.Cannot-find-inversion-information-for-hypothesis-\u2018ident\u2019"]], "cannot use mutual definition with well-founded recursion or measure (error)": [[72, "coq:exn.Cannot-use-mutual-definition-with-well-founded-recursion-or-measure"]], "function (command)": [[72, "coq:cmd.Function"]], "functional case (command)": [[72, "coq:cmd.Functional-Case"]], "functional scheme (command)": [[72, "coq:cmd.Functional-Scheme"]], "generate graph for (command)": [[72, "coq:cmd.Generate-graph-for"]], "hypothesis \u2018ident\u2019 must contain at least one function (error)": [[72, "coq:exn.Hypothesis-\u2018ident\u2019-must-contain-at-least-one-Function"]], "no argument name \u2018ident\u2019 (error)": [[72, "coq:exn.No-argument-name-\u2018ident\u2019"]], "not the right number of induction arguments (error)": [[72, "coq:exn.Not-the-right-number-of-induction-arguments"]], "the recursive argument must be specified (error)": [[72, "coq:exn.The-recursive-argument-must-be-specified"]], "functional induction (tactic)": [[72, "coq:tacn.functional-induction"]], "functional inversion (tactic)": [[72, "coq:tacn.functional-inversion"]], "soft functional induction (tactic)": [[72, "coq:tacn.soft-functional-induction"]], "library file (transitively required) \u2018qualid\u2019 is deprecated since \u2018string\u2019. \u2018string\u2019. use \u2018qualid\u2019 instead (warning)": [[74, "coq:warn.Library-File-(transitively-required)-\u2018qualid\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019.-Use-\u2018qualid\u2019-instead"]], "library file \u2018qualid\u2019 is deprecated since \u2018string\u2019. \u2018string\u2019. use \u2018qualid\u2019 instead (warning)": [[74, "coq:warn.Library-File-\u2018qualid\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019.-Use-\u2018qualid\u2019-instead"]], "ltac2 alias \u2018qualid\u2019 is deprecated since \u2018string\u2019. \u2018string\u2019 (warning)": [[74, "coq:warn.Ltac2-alias-\u2018qualid\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019"]], "ltac2 constructor \u2018qualid\u2019 is deprecated since \u2018string\u2019. \u2018string\u2019 (warning)": [[74, "coq:warn.Ltac2-constructor-\u2018qualid\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019"]], "ltac2 definition \u2018qualid\u2019 is deprecated since \u2018string\u2019. \u2018string\u2019 (warning)": [[74, "coq:warn.Ltac2-definition-\u2018qualid\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019"]], "ltac2 notation \u2018ltac2_scope\u2019\u2026\u2018ltac2_scope\u2019 is deprecated since \u2018string\u2019. \u2018string\u2019 (warning)": [[74, "coq:warn.Ltac2-notation-\u2018ltac2_scope\u2019\u2026\u2018ltac2_scope\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019"]], "notation \u2018string\u2019 is deprecated since \u2018string\u2019. \u2018string\u2019. use \u2018qualid\u2019 instead (warning)": [[74, "coq:warn.Notation-\u2018string\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019.-Use-\u2018qualid\u2019-instead"]], "tactic notation \u2018qualid\u2019 is deprecated since \u2018string\u2019. \u2018string\u2019 (warning)": [[74, "coq:warn.Tactic-Notation-\u2018qualid\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019"]], "tactic \u2018qualid\u2019 is deprecated since \u2018string\u2019. \u2018string\u2019 (warning)": [[74, "coq:warn.Tactic-\u2018qualid\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019"]], "deprecated (attribute)": [[74, "coq:attr.deprecated"]], "warn (attribute)": [[74, "coq:attr.warn"]], "\u2018string\u2019 (warning)": [[74, "coq:warn.\u2018string\u2019"]], "coqdoc": [[75, "index-0"]]}}) \ No newline at end of file +Search.setIndex({"docnames": ["addendum/canonical-structures", "addendum/extended-pattern-matching", "addendum/extraction", "addendum/generalized-rewriting", "addendum/implicit-coercions", "addendum/micromega", "addendum/miscellaneous-extensions", "addendum/nsatz", "addendum/parallel-proof-processing", "addendum/program", "addendum/rewrite-rules", "addendum/ring", "addendum/sprop", "addendum/type-classes", "addendum/universe-polymorphism", "appendix/history-and-changes/index", "appendix/indexes/index", "changes", "coq-attrindex", "coq-cmdindex", "coq-exnindex", "coq-optindex", "coq-tacindex", "genindex", "history", "index", "language/cic", "language/coq-library", "language/core/assumptions", "language/core/basic", "language/core/coinductive", "language/core/conversion", "language/core/definitions", "language/core/index", "language/core/inductive", "language/core/modules", "language/core/primitive", "language/core/records", "language/core/sections", "language/core/sorts", "language/core/variants", "language/extensions/arguments-command", "language/extensions/canonical", "language/extensions/evars", "language/extensions/implicit-arguments", "language/extensions/index", "language/extensions/match", "language/gallina-extensions", "language/gallina-specification-language", "language/module-system", "license", "practical-tools/coq-commands", "practical-tools/coqide", "practical-tools/utilities", "proof-engine/ltac", "proof-engine/ltac2", "proof-engine/proof-handling", "proof-engine/ssreflect-proof-language", "proof-engine/tactics", "proof-engine/vernacular-commands", "proofs/automatic-tactics/auto", "proofs/automatic-tactics/index", "proofs/automatic-tactics/logic", "proofs/creating-tactics/index", "proofs/writing-proofs/equality", "proofs/writing-proofs/index", "proofs/writing-proofs/proof-mode", "proofs/writing-proofs/reasoning-inductives", 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75, 76, 77], "wfe": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "e": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "wft": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "wftwolin": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "begin": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "arrai": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "l": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "wse": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "wt": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "wte": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "wteg": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "gamma": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "wtm": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "c": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "i": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "cic": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "\u03b2\u03b4\u03b9\u03b6": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "latex": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77], "tac": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "p": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "program": [0, 1, 3, 4, 5, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "ssreflect": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "t": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "m": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "x": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], "author": [2, 3, 4, 5, 7, 8, 9, 11, 14, 17, 27, 29, 42, 46, 57, 73, 74], "jean": [2, 17, 24, 77], "christoph": [2, 17, 24, 77], "filli\u00e2tr": [2, 17, 24, 77], "pierr": [2, 17, 24, 77], "letouzei": [2, 17, 24, 77], "we": [2, 3, 4, 5, 9, 11, 12, 13, 14, 16, 17, 24, 26, 27, 28, 29, 30, 31, 33, 34, 35, 38, 39, 40, 42, 44, 45, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 72, 75], "present": [2, 3, 6, 9, 11, 13, 15, 17, 24, 25, 26, 29, 30, 32, 33, 34, 37, 41, 42, 44, 45, 46, 50, 53, 54, 55, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 71, 73, 74, 75, 76], "here": [2, 3, 4, 5, 9, 11, 13, 14, 16, 17, 24, 29, 31, 33, 34, 35, 37, 38, 41, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 75], "command": [2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 25, 26, 27, 28, 29, 30, 32, 34, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 53, 54, 55, 58, 60, 62, 63, 64, 72, 73, 74], "us": [2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 39, 40, 41, 42, 45, 55, 57, 59, 60, 61, 62, 63, 65, 72, 73, 74, 75, 77], "build": [2, 5, 9, 11, 14, 17, 24, 25, 26, 27, 32, 33, 34, 37, 42, 46, 51, 54, 55, 57, 59, 60, 63, 65, 66, 67, 72, 75, 76, 77], "certifi": [2, 9, 17, 24, 77], "rel": [2, 14, 17, 26, 35, 51, 53, 55, 59, 71], "effici": [2, 11, 12, 13, 17, 25, 29, 36, 57, 60, 64, 77], "function": [2, 3, 5, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 27, 31, 33, 35, 36, 37, 39, 42, 45, 46, 51, 52, 55, 57, 58, 59, 62, 64, 67, 71, 73, 77], "them": [2, 3, 8, 9, 10, 11, 13, 14, 17, 24, 26, 27, 28, 31, 34, 35, 37, 38, 40, 41, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 73, 75], "from": [2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 34, 36, 37, 38, 39, 40, 41, 42, 43, 46, 51, 52, 53, 54, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 72, 73, 75, 77], "either": [2, 5, 8, 11, 14, 17, 26, 28, 29, 31, 34, 35, 36, 37, 39, 40, 41, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 74, 75], "proof": [2, 3, 6, 7, 9, 11, 13, 17, 24, 26, 29, 30, 33, 34, 36, 37, 38, 39, 40, 42, 43, 44, 51, 52, 53, 55, 59, 61, 62, 64, 67, 72, 73, 74, 75, 76, 77], "specif": [2, 3, 5, 9, 11, 24, 28, 31, 32, 34, 35, 36, 39, 40, 42, 51, 52, 53, 55, 57, 58, 59, 60, 61, 64, 66, 67, 71, 77], "The": [2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 17, 24, 25, 28, 29, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 46, 52, 54, 55, 58, 59, 60, 62, 63, 64, 65, 66, 67, 72, 73, 74, 76, 77], "avail": [2, 9, 11, 12, 13, 17, 24, 25, 27, 30, 35, 36, 37, 38, 40, 42, 46, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 71, 72, 74, 75, 76, 77], "output": [2, 3, 4, 11, 14, 17, 24, 33, 42, 51, 52, 53, 54, 59, 60, 64, 66, 71, 75], "ar": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 50, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 63, 64, 65, 67, 71, 72, 73, 74, 75], "current": [2, 3, 4, 5, 8, 9, 10, 12, 14, 17, 24, 28, 29, 32, 34, 35, 36, 37, 38, 41, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 75], "ocaml": [2, 11, 17, 24, 25, 29, 32, 36, 51, 53, 54, 55, 63, 64, 66, 71, 73, 75], "haskel": [2, 13, 17, 24, 25, 57, 64, 77], "scheme": [2, 11, 17, 24, 25, 26, 27, 34, 37, 40, 46, 51, 57, 59, 62, 77], "follow": [2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74, 75], "abus": [2, 55], "refer": [2, 3, 4, 5, 8, 10, 13, 14, 16, 24, 25, 28, 29, 31, 32, 34, 35, 36, 37, 38, 39, 41, 42, 44, 46, 50, 51, 52, 53, 55, 57, 58, 60, 62, 64, 66, 67, 71, 72, 74, 75], "ani": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 26, 28, 29, 30, 31, 32, 34, 35, 37, 38, 39, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 75], "three": [2, 4, 9, 11, 17, 24, 25, 34, 40, 52, 53, 54, 57, 59, 60, 67, 71], "chang": [2, 4, 5, 8, 9, 11, 13, 14, 25, 26, 28, 29, 31, 34, 36, 37, 38, 41, 43, 51, 52, 53, 54, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 73, 74, 75], "version": [2, 3, 4, 7, 9, 13, 14, 15, 25, 29, 32, 35, 36, 37, 41, 46, 50, 51, 52, 57, 58, 59, 60, 62, 66, 73, 74, 75, 77], "8": [2, 3, 4, 13, 24, 25, 30, 35, 41, 51, 52, 53, 54, 57, 58, 59, 60, 64, 66, 71, 75], "11": [2, 24, 25, 34, 53, 57, 60], "befor": [2, 4, 5, 13, 14, 17, 28, 29, 32, 34, 37, 41, 42, 44, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 73, 74, 75], "describ": [2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 17, 24, 29, 31, 32, 34, 35, 37, 39, 40, 42, 43, 46, 51, 52, 53, 54, 55, 57, 58, 59, 64, 65, 66, 67, 71, 72, 75], "thi": [2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 71, 72, 73, 74, 75, 76], "chapter": [2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 24, 26, 27, 29, 31, 32, 33, 34, 38, 40, 42, 45, 52, 54, 55, 57, 58, 59, 61, 63, 65, 71, 72, 73, 75, 76], "framework": [2, 17, 24], "should": [2, 3, 9, 10, 11, 12, 13, 14, 17, 24, 26, 28, 29, 30, 32, 34, 35, 40, 41, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 74], "first": [2, 4, 5, 6, 8, 9, 11, 13, 14, 15, 17, 24, 25, 26, 27, 35, 37, 38, 40, 41, 42, 43, 44, 51, 52, 53, 55, 58, 59, 60, 62, 64, 65, 66, 67, 71, 72, 74, 75, 77], "load": [2, 3, 5, 6, 7, 11, 17, 24, 25, 27, 29, 34, 35, 54, 55, 57, 58, 60, 64, 66, 67, 71, 72, 73], "explicitli": [2, 4, 12, 13, 14, 17, 24, 27, 28, 29, 34, 38, 39, 43, 46, 51, 52, 53, 55, 57, 58, 59, 60, 64, 66, 67, 71, 74], "via": [2, 5, 8, 11, 17, 35, 51, 53, 54, 55, 57, 59, 71, 72], "corelib": [2, 6, 9, 35, 36, 51, 54, 57, 59, 64, 66], "requir": [2, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 17, 24, 27, 28, 29, 30, 31, 32, 34, 35, 36, 38, 42, 44, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 72, 73, 74, 75], "file": [2, 3, 5, 6, 7, 8, 9, 11, 17, 24, 25, 27, 29, 34, 35, 41, 54, 55, 57, 60, 64, 71, 72, 73, 76], "runtim": [2, 3, 5, 6, 11, 17, 29, 34, 51, 53, 54, 55, 57, 59, 60, 72, 73], "plugin": [2, 3, 5, 6, 11, 12, 17, 24, 25, 29, 33, 34, 35, 53, 54, 55, 57, 59, 60, 63, 66, 71, 72], "done": [2, 3, 5, 6, 7, 9, 10, 11, 13, 17, 24, 29, 30, 32, 34, 35, 38, 40, 43, 46, 52, 53, 54, 55, 57, 58, 59, 60, 64, 67, 71, 72, 75], "qualifi": [2, 17, 24, 25, 28, 32, 38, 51, 53, 54, 55, 57, 58, 59, 64, 66, 71], "identifi": [2, 3, 9, 14, 17, 24, 25, 28, 29, 30, 31, 35, 38, 40, 41, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 60, 66, 67, 72, 75], "qualid": [2, 3, 4, 5, 10, 11, 13, 14, 17, 29, 35, 37, 39, 40, 41, 42, 46, 51, 54, 55, 57, 59, 60, 62, 64, 66, 67, 71, 72, 74], "can": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 71, 72, 73, 74, 75], "kind": [2, 8, 10, 11, 17, 25, 27, 29, 34, 42, 46, 53, 55, 57, 59, 67, 72], "global": [2, 3, 4, 5, 8, 9, 13, 17, 24, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 39, 41, 42, 44, 51, 53, 55, 57, 58, 59, 60, 62, 64, 66, 67, 75], "object": [2, 3, 4, 8, 9, 11, 13, 14, 17, 24, 25, 26, 28, 29, 30, 31, 33, 35, 37, 38, 39, 40, 41, 42, 44, 51, 53, 55, 57, 59, 64, 67, 71, 72], "constant": [2, 4, 5, 6, 9, 10, 11, 13, 14, 17, 24, 25, 26, 30, 31, 32, 34, 35, 36, 38, 41, 42, 44, 46, 51, 54, 55, 57, 58, 60, 64, 66, 67, 74], "constructor": [2, 4, 9, 10, 12, 13, 14, 17, 24, 25, 26, 27, 30, 31, 32, 35, 36, 37, 40, 41, 42, 43, 44, 46, 54, 55, 57, 58, 59, 60, 62, 64, 66, 71, 74], "modul": [2, 3, 5, 6, 7, 9, 10, 11, 13, 17, 24, 25, 27, 28, 29, 32, 33, 36, 37, 38, 40, 41, 42, 44, 51, 52, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 72, 75], "name": [2, 3, 4, 5, 6, 8, 9, 10, 11, 13, 14, 17, 25, 26, 27, 28, 29, 31, 32, 34, 36, 38, 39, 40, 41, 42, 43, 44, 46, 51, 52, 53, 55, 57, 58, 59, 60, 64, 67, 71, 72, 74, 75], "recurs": [2, 5, 9, 17, 24, 25, 31, 32, 33, 37, 40, 41, 44, 46, 51, 53, 54, 57, 58, 59, 60, 64, 66, 67, 75, 77], "string": [2, 11, 13, 14, 17, 25, 29, 40, 51, 53, 54, 55, 57, 59, 64, 66, 74, 75], "two": [2, 3, 4, 5, 8, 9, 10, 11, 13, 14, 15, 17, 24, 25, 26, 27, 29, 30, 31, 34, 36, 37, 38, 40, 41, 42, 44, 46, 51, 52, 53, 55, 57, 58, 59, 60, 63, 64, 66, 67, 71, 74, 75], "form": [2, 3, 4, 5, 6, 7, 9, 11, 13, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 35, 37, 38, 39, 40, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 75], "displai": [2, 9, 12, 14, 16, 17, 25, 35, 37, 41, 42, 46, 51, 53, 54, 55, 57, 58, 60, 64, 66], "term": [2, 3, 4, 9, 10, 11, 12, 13, 14, 17, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 50, 53, 57, 58, 59, 60, 62, 63, 66, 67, 72, 75], "conveni": [2, 4, 6, 12, 17, 24, 28, 29, 33, 34, 35, 44, 46, 52, 53, 54, 57, 66, 67, 71], "preview": [2, 52], "result": [2, 3, 4, 5, 8, 10, 11, 12, 13, 14, 17, 24, 26, 27, 31, 32, 34, 39, 40, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 75], "second": [2, 3, 4, 8, 9, 10, 11, 13, 15, 17, 24, 25, 26, 28, 35, 37, 38, 40, 42, 44, 51, 52, 53, 55, 57, 59, 60, 64, 66, 67, 71, 75], "all": [2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 26, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 73], "depend": [2, 3, 7, 8, 9, 12, 13, 14, 24, 25, 26, 27, 28, 29, 30, 32, 34, 35, 36, 37, 38, 40, 42, 43, 44, 51, 52, 54, 55, 57, 60, 62, 64, 66, 71, 72, 77], "third": [2, 3, 17, 25, 40, 41, 44, 51, 52, 53, 54, 57, 58, 75], "produc": [2, 5, 7, 8, 9, 11, 13, 14, 17, 24, 25, 29, 32, 34, 36, 38, 40, 41, 44, 52, 53, 54, 55, 57, 64, 66, 71, 72, 73, 74, 75], "singl": [2, 3, 4, 13, 14, 17, 24, 25, 28, 29, 30, 34, 35, 37, 40, 44, 46, 52, 53, 55, 57, 58, 59, 60, 64, 66, 67, 71, 75], "specifi": [2, 3, 4, 5, 6, 8, 9, 11, 13, 17, 24, 25, 28, 29, 32, 34, 35, 36, 37, 40, 41, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 75], "local": [2, 3, 4, 5, 9, 13, 17, 24, 25, 26, 28, 30, 31, 32, 34, 41, 42, 52, 55, 59, 62, 64, 66, 67, 75], "renam": [2, 17, 24, 25, 34, 37, 55, 57, 58, 59, 71, 74], "need": [2, 3, 5, 8, 9, 10, 11, 13, 14, 17, 24, 25, 28, 29, 31, 32, 34, 35, 38, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 73, 75, 76], "fulfil": [2, 17, 67], "syntact": [2, 3, 11, 17, 24, 25, 26, 27, 28, 29, 30, 31, 34, 35, 37, 39, 41, 57, 58, 59, 64, 66, 71, 74], "keep": [2, 3, 12, 14, 17, 24, 33, 34, 36, 42, 46, 52, 53, 55, 57, 64, 67], "origin": [2, 3, 4, 9, 11, 17, 24, 29, 31, 34, 38, 43, 44, 46, 53, 57, 58, 62, 64, 66, 67, 71], "much": [2, 11, 13, 17, 25, 33, 51, 53, 57, 59, 63, 64, 71], "possibl": [2, 3, 4, 5, 8, 9, 11, 13, 14, 17, 24, 27, 28, 31, 34, 35, 37, 41, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 74, 75], "also": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 72, 73, 74, 75, 77], "work": [2, 3, 4, 5, 9, 10, 12, 13, 17, 24, 25, 26, 27, 32, 35, 41, 42, 43, 46, 51, 52, 54, 55, 57, 58, 59, 64, 67, 71, 74, 77], "directori": [2, 14, 17, 24, 27, 35, 51, 52, 53, 59, 60, 71, 75], "It": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 27, 28, 29, 30, 31, 32, 34, 35, 37, 38, 40, 41, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74, 75], "inspect": [2, 17, 57, 59], "what": [2, 3, 5, 10, 13, 16, 17, 24, 25, 27, 29, 33, 34, 35, 41, 42, 46, 51, 53, 54, 55, 57, 59, 60, 64, 66, 67, 71], "pwd": [2, 14, 59], "cd": [2, 17, 53], "librari": [2, 5, 7, 8, 11, 25, 29, 35, 40, 41, 52, 54, 55, 57, 58, 64, 66, 67, 72, 75], "ident": [2, 3, 5, 6, 9, 10, 11, 12, 13, 14, 17, 24, 25, 27, 28, 29, 30, 31, 32, 34, 35, 37, 38, 40, 43, 44, 46, 51, 53, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 73, 74], "whole": [2, 3, 9, 11, 17, 29, 40, 46, 51, 52, 53, 55, 57, 59, 71, 75], "v": [2, 3, 7, 8, 11, 12, 13, 14, 17, 24, 25, 26, 27, 34, 35, 37, 42, 44, 46, 51, 52, 53, 54, 58, 59, 67, 71, 75], "an": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 58, 60, 62, 63, 64, 66, 71, 72, 74, 75, 77], "clash": [2, 17, 53, 54, 57], "prefix": [2, 3, 9, 11, 14, 17, 24, 27, 28, 34, 35, 38, 40, 41, 42, 44, 51, 52, 54, 57, 58, 59, 64, 66, 67, 71, 75], "coq_": 2, "ensur": [2, 10, 13, 14, 17, 24, 30, 34, 39, 52, 55, 59, 64, 71, 72], "session": [2, 14, 17, 51, 52, 59], "independ": [2, 13, 14, 17, 24, 34, 51, 52, 53, 54, 55, 57, 67], "other": [2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 41, 42, 43, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 67, 71, 72, 76], "separ": [2, 3, 10, 14, 17, 24, 25, 26, 29, 33, 34, 35, 40, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 67, 71, 74], "mention": [2, 3, 14, 17, 24, 26, 34, 39, 44, 46, 51, 54, 57, 58, 60, 64, 66, 71], "just": [2, 3, 4, 8, 9, 11, 13, 17, 24, 28, 31, 34, 35, 37, 41, 42, 46, 51, 52, 53, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 75], "instead": [2, 3, 4, 7, 8, 11, 12, 13, 14, 17, 24, 26, 28, 33, 34, 35, 36, 37, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74, 75], "one": [2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 15, 17, 24, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 40, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 72, 74, 75, 77], "monolith": [2, 17], "split": [2, 17, 25, 29, 34, 42, 51, 54, 57, 58, 60, 66, 67, 75], "per": [2, 3, 11, 17, 24, 52, 53, 57, 59, 71], "correspond": [2, 3, 8, 9, 11, 13, 14, 15, 17, 24, 26, 28, 33, 34, 35, 37, 38, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 72, 75], "henc": [2, 3, 4, 5, 8, 9, 13, 14, 17, 26, 34, 37, 42, 51, 53, 54, 57, 58, 64, 67, 71], "quit": [2, 3, 11, 13, 17, 25, 34, 42, 54, 55, 57, 60], "similar": [2, 3, 5, 9, 13, 17, 24, 26, 34, 35, 37, 38, 51, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 72, 74, 75], "except": [2, 3, 4, 11, 12, 13, 14, 17, 24, 25, 26, 27, 29, 31, 34, 35, 36, 38, 40, 43, 51, 52, 53, 54, 57, 58, 59, 60, 64, 66, 67, 71, 75], "onli": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 46, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 73, 74, 75], "part": [2, 3, 10, 11, 13, 15, 17, 24, 25, 27, 29, 34, 35, 37, 46, 51, 52, 53, 54, 55, 57, 58, 66, 67, 71, 72, 73, 74], "convent": [2, 17, 25, 33, 42, 51, 57, 59, 71], "same": [2, 3, 4, 6, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 28, 29, 30, 31, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 51, 52, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 75], "meant": [2, 3, 14, 17, 55, 59, 64], "help": [2, 3, 8, 13, 14, 15, 16, 17, 24, 25, 27, 29, 41, 46, 51, 52, 53, 54, 55, 57, 58, 60, 62, 67, 75], "automat": [2, 3, 5, 7, 9, 10, 13, 14, 17, 24, 25, 27, 28, 35, 37, 40, 42, 46, 52, 53, 54, 55, 57, 58, 60, 64, 65, 66, 71, 72, 75, 77], "test": [2, 3, 4, 9, 10, 11, 13, 17, 24, 25, 29, 30, 34, 42, 46, 55, 57, 59, 66], "see": [2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 14, 17, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74, 75], "instanc": [2, 4, 5, 10, 11, 12, 14, 17, 25, 26, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 46, 51, 52, 53, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 75], "suit": [2, 17, 53, 57, 58, 63], "sourc": [2, 4, 5, 14, 24, 25, 51, 52, 53, 55, 57, 71, 73], "testcompil": [2, 17], "temporari": [2, 14, 17, 24, 57], "Then": [2, 4, 5, 11, 14, 24, 26, 27, 29, 32, 34, 41, 42, 46, 51, 53, 54, 55, 57, 58, 59, 60, 64, 65, 66, 67, 71, 74, 75], "its": [2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 14, 17, 24, 25, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 72, 73, 74, 75, 77], "signatur": [2, 3, 11, 17, 24, 34, 35, 54, 55, 59], "compil": [2, 3, 8, 9, 10, 11, 12, 24, 25, 26, 27, 29, 32, 35, 36, 38, 46, 54, 55, 57, 64, 66, 73, 74, 75, 77], "built": [2, 4, 11, 17, 24, 25, 26, 31, 32, 34, 37, 41, 42, 52, 53, 54, 58, 60, 61, 62, 67, 71, 72], "succe": [2, 3, 13, 17, 25, 44, 46, 51, 55, 57, 58, 59, 60, 62, 64, 66], "fail": [2, 3, 4, 5, 8, 9, 10, 12, 13, 14, 17, 24, 25, 26, 29, 30, 34, 35, 40, 41, 42, 43, 44, 52, 53, 55, 58, 59, 60, 62, 64, 66, 67, 71, 72, 75], "show": [2, 3, 5, 7, 8, 9, 11, 13, 14, 17, 24, 25, 27, 34, 35, 37, 38, 42, 51, 52, 53, 54, 57, 58, 59, 60, 64, 67, 71], "where": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 26, 27, 29, 30, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 75], "deprec": [2, 4, 13, 17, 25, 28, 29, 32, 35, 41, 51, 55, 58, 59, 60, 64, 66, 71, 72], "sinc": [2, 3, 4, 5, 8, 10, 11, 12, 13, 14, 17, 24, 26, 28, 30, 34, 35, 37, 41, 42, 44, 46, 51, 52, 53, 54, 57, 58, 59, 60, 66, 67, 71, 74, 75], "20": [2, 3, 25, 46, 57, 67, 77], "line": [2, 8, 10, 12, 14, 24, 25, 26, 29, 42, 52, 53, 54, 55, 57, 58, 59, 64, 66, 71], "If": [2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 17, 26, 28, 29, 30, 32, 34, 35, 37, 38, 39, 41, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 73, 74, 75], "accord": [2, 11, 17, 26, 34, 35, 41, 51, 53, 55, 57, 59, 60, 64, 71], "which": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 71, 72, 73, 75], "valid": [2, 3, 4, 5, 8, 10, 11, 14, 17, 25, 26, 29, 32, 34, 35, 40, 42, 51, 54, 55, 57, 58, 59, 66, 71, 72], "path": [2, 4, 5, 17, 24, 25, 35, 51, 52, 54, 60], "otherwis": [2, 3, 9, 13, 14, 17, 28, 29, 34, 41, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 73], "doe": [2, 3, 4, 5, 8, 9, 12, 13, 14, 17, 24, 25, 26, 27, 29, 30, 34, 35, 36, 38, 39, 41, 42, 44, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 75], "json": [2, 17, 51, 53, 59], "abil": [2, 3, 11, 12, 13, 17, 30, 52], "most": [2, 3, 4, 10, 12, 17, 24, 27, 29, 34, 38, 41, 45, 46, 51, 52, 53, 54, 55, 57, 58, 60, 63, 64, 66, 67, 71, 72, 73], "import": [2, 3, 4, 5, 7, 9, 11, 13, 17, 24, 25, 26, 28, 29, 31, 32, 34, 35, 36, 38, 40, 42, 44, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72], "default": [2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 27, 28, 29, 32, 34, 35, 37, 38, 43, 44, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 74, 75], "mostli": [2, 3, 17, 24, 52, 57, 60], "develop": [2, 3, 12, 13, 14, 17, 24, 25, 27, 32, 35, 42, 44, 51, 52, 53, 54, 57, 58, 59, 60, 64, 66, 67, 71, 74, 77], "debug": [2, 5, 9, 13, 14, 17, 24, 25, 28, 52, 53, 57, 58, 60, 62, 64, 66, 72], "contain": [2, 5, 7, 8, 10, 13, 14, 15, 17, 24, 27, 29, 30, 31, 34, 35, 38, 39, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 73, 74, 75], "raw": [2, 14, 17, 54, 55, 71], "intermediari": [2, 64], "strict": [2, 5, 13, 14, 17, 24, 25, 31, 39, 41, 42, 54, 57, 58, 59, 60, 66, 71], "ha": [2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 72, 73, 74], "order": [2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 15, 17, 24, 25, 26, 27, 29, 30, 32, 34, 35, 37, 40, 42, 43, 46, 51, 52, 53, 54, 55, 57, 60, 61, 62, 64, 66, 67, 71, 72, 75, 77], "when": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 24, 25, 27, 28, 29, 30, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 51, 52, 53, 54, 55, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74, 75], "principl": [2, 5, 17, 24, 25, 27, 30, 34, 37, 51, 57, 58, 63, 64, 71, 77], "do": [2, 3, 4, 7, 8, 10, 13, 14, 17, 24, 25, 29, 31, 32, 34, 35, 37, 38, 42, 46, 51, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 74, 75], "want": [2, 11, 13, 17, 34, 35, 36, 41, 42, 43, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 73, 74], "comput": [2, 3, 7, 8, 9, 11, 17, 24, 25, 29, 30, 32, 34, 35, 36, 37, 41, 42, 46, 52, 55, 57, 59, 67, 71, 72, 77], "call": [2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 39, 40, 42, 44, 45, 46, 51, 53, 54, 57, 58, 59, 60, 64, 66, 67, 71, 72], "ones": [2, 3, 4, 6, 8, 13, 14, 17, 25, 28, 34, 35, 37, 44, 46, 52, 53, 54, 57, 58, 59, 63, 66, 67, 71, 75], "so": [2, 3, 4, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 26, 29, 31, 32, 34, 35, 36, 37, 38, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 73, 74, 75], "mechan": [2, 3, 4, 9, 10, 13, 17, 24, 25, 29, 34, 38, 41, 46, 51, 52, 53, 55, 59, 64, 65, 66, 71, 72, 77], "provid": [2, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 24, 25, 26, 27, 29, 30, 32, 33, 34, 35, 36, 37, 41, 42, 43, 44, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 71, 72, 73, 74, 75], "routin": 2, "each": [2, 3, 5, 6, 8, 9, 10, 11, 13, 14, 17, 24, 26, 29, 30, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 72, 74, 75], "time": [2, 3, 5, 8, 9, 11, 12, 13, 14, 17, 24, 25, 27, 28, 29, 32, 34, 36, 37, 41, 42, 44, 46, 52, 55, 57, 58, 59, 64, 66, 67, 71], "group": [2, 4, 17, 24, 37, 42, 52, 53, 54, 57, 58, 60], "preserv": [2, 5, 14, 17, 24, 25, 29, 30, 34, 42, 55, 57, 64, 67, 71], "essenti": [2, 17, 25, 34, 55, 57, 67, 71], "reduct": [2, 3, 9, 10, 11, 12, 17, 25, 26, 30, 32, 36, 41, 44, 46, 51, 53, 57, 58, 67, 77], "non": [2, 3, 4, 6, 8, 9, 10, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 35, 37, 40, 41, 46, 51, 52, 53, 57, 59, 60, 62, 64, 66, 72, 75], "abstract": [2, 4, 5, 11, 13, 14, 17, 24, 25, 26, 27, 28, 29, 34, 35, 38, 42, 44, 54, 55, 58, 59, 64, 67, 71], "dummi": [2, 14, 17, 24, 55, 77], "remov": [2, 3, 4, 5, 11, 14, 17, 24, 29, 31, 37, 41, 46, 51, 52, 53, 55, 57, 58, 59, 60, 66, 67, 71, 72, 74, 75], "deem": [2, 51], "safe": [2, 11, 17, 34], "have": [2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 44, 46, 51, 52, 53, 55, 58, 59, 60, 62, 64, 66, 67, 71, 73, 75], "more": [2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 38, 40, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 72, 73, 74, 75], "eleg": [2, 55, 59], "therefor": [2, 17, 29, 31, 37, 52, 53, 57, 58, 62, 72, 73], "mai": [2, 3, 4, 5, 8, 9, 10, 12, 13, 14, 15, 17, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 40, 41, 42, 43, 44, 46, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 73, 74, 75, 77], "appear": [2, 6, 9, 10, 11, 13, 14, 17, 24, 28, 29, 31, 34, 35, 37, 38, 39, 41, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 74, 75], "modular": [2, 17, 24], "nevertheless": [2, 17], "print": [2, 5, 6, 8, 11, 12, 13, 17, 24, 25, 27, 29, 31, 34, 35, 36, 38, 39, 41, 42, 51, 52, 53, 57, 58, 60, 62, 64, 66, 67, 74], "concern": [2, 12, 17, 24, 26], "less": [2, 4, 8, 11, 14, 17, 24, 34, 46, 51, 53, 54, 55, 57, 59, 60, 64, 71, 77], "becaus": [2, 3, 4, 8, 11, 12, 14, 17, 24, 26, 28, 29, 31, 33, 34, 35, 37, 39, 40, 41, 43, 44, 45, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72], "lazi": [2, 8, 9, 12, 17, 24, 55, 64], "still": [2, 3, 7, 9, 10, 13, 17, 24, 29, 32, 34, 36, 37, 38, 42, 44, 46, 51, 53, 54, 57, 58, 59, 60, 64, 66, 67, 74], "make": [2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 28, 29, 30, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 51, 52, 53, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 75, 77], "readabl": [2, 17, 24, 29, 53, 57, 64, 71, 75], "control": [2, 3, 13, 14, 16, 17, 24, 25, 34, 37, 41, 51, 52, 53, 55, 60, 62, 67, 71, 75], "flag": [2, 4, 5, 8, 9, 10, 12, 13, 14, 16, 24, 25, 26, 32, 34, 35, 37, 38, 40, 41, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 60, 62, 64, 66, 67, 71], "made": [2, 3, 14, 17, 24, 29, 34, 35, 38, 41, 46, 51, 53, 54, 55, 57, 58, 64, 66, 71, 72, 75], "beta": [2, 11, 17, 24, 55, 57, 58, 64, 71, 77], "redex": [2, 17, 25, 31, 34, 64, 71], "simplif": [2, 11, 17, 24, 25, 41, 54, 67], "etc": [2, 4, 9, 14, 17, 24, 25, 26, 27, 33, 35, 42, 44, 45, 51, 52, 53, 54, 55, 57, 59, 71, 75], "turn": [2, 8, 10, 12, 13, 14, 17, 24, 27, 29, 32, 37, 41, 42, 44, 46, 51, 52, 54, 55, 57, 58, 59, 64, 66, 67, 71], "off": [2, 8, 10, 12, 13, 14, 17, 24, 29, 34, 35, 37, 43, 44, 46, 51, 52, 53, 54, 57, 59, 64, 66, 67, 71], "you": [2, 3, 4, 7, 8, 10, 11, 13, 14, 15, 16, 17, 24, 25, 27, 29, 32, 34, 35, 37, 41, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 73, 74, 75], "close": [2, 3, 4, 5, 7, 9, 11, 14, 17, 24, 28, 29, 32, 34, 35, 38, 44, 51, 52, 55, 57, 59, 60, 64, 66, 67, 71, 75], "conserv": [2, 17], "try": [2, 3, 11, 14, 17, 24, 25, 34, 35, 40, 41, 43, 46, 53, 55, 57, 60, 62, 64, 66, 67, 71], "sure": [2, 4, 17, 35, 52, 53, 58, 71], "impli": [2, 3, 10, 14, 17, 24, 30, 34, 57, 67, 71], "respect": [2, 3, 4, 5, 11, 13, 14, 17, 24, 26, 30, 34, 38, 40, 42, 44, 52, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 72, 74, 75], "keepsingleton": [2, 17], "normal": [2, 3, 4, 5, 11, 17, 24, 26, 29, 30, 31, 34, 35, 41, 44, 51, 52, 53, 54, 55, 57, 59, 64, 66, 67, 71, 72, 77], "singleton": [2, 13, 17, 24, 34, 54, 58], "structur": [2, 3, 4, 8, 9, 13, 17, 24, 25, 32, 34, 35, 36, 37, 38, 40, 44, 45, 53, 54, 58, 59, 66, 67, 71, 72, 77], "seen": [2, 4, 13, 14, 17, 24, 32, 34, 55, 57, 67, 71], "alia": [2, 17, 24, 29, 35, 46, 55, 58], "inner": [2, 14, 17, 35, 42, 43, 54, 55, 57, 59, 62, 64, 66, 67, 71, 75], "typic": [2, 4, 6, 12, 14, 17, 24, 28, 29, 30, 34, 35, 44, 46, 51, 53, 55, 57, 58, 59, 60, 64, 67, 71], "sig": [2, 17, 27, 28, 35, 67, 71], "allow": [2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 37, 38, 40, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 72], "disabl": [2, 8, 9, 12, 13, 14, 17, 25, 28, 32, 34, 35, 37, 44, 51, 52, 54, 57, 59, 64, 66], "wish": [2, 5, 17, 53], "autoinlin": [2, 17], "enabl": [2, 4, 7, 8, 9, 10, 11, 12, 13, 14, 17, 25, 29, 34, 37, 42, 51, 52, 53, 54, 57, 58, 59, 60, 67, 75], "bodi": [2, 4, 6, 13, 14, 17, 24, 32, 35, 37, 38, 41, 42, 44, 51, 55, 57, 58, 59, 64, 72, 75], "defin": [2, 3, 4, 5, 6, 7, 9, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 36, 38, 39, 40, 41, 42, 43, 44, 46, 51, 52, 53, 57, 58, 59, 62, 64, 66, 67, 71, 72, 74, 77], "heurist": [2, 5, 14, 17, 55, 57, 58, 66], "like": [2, 4, 8, 9, 10, 11, 13, 14, 17, 24, 26, 27, 29, 32, 34, 35, 38, 39, 41, 42, 43, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 73, 75], "size": [2, 3, 9, 13, 17, 24, 34, 37, 51, 52, 55, 57, 59, 64, 71, 72], "recursor": [2, 17], "_rect": [2, 17, 34, 35, 40, 71, 72], "_rec": [2, 34, 35, 40, 71, 72], "nat_rect": [2, 27, 34, 59], "project": [2, 3, 9, 10, 12, 13, 14, 15, 17, 24, 25, 27, 29, 30, 34, 40, 41, 42, 51, 52, 54, 55, 57, 59, 60, 64, 72, 73, 74, 76], "few": [2, 3, 17, 24, 27, 29, 34, 35, 36, 37, 51, 52, 53, 55, 57, 58, 71, 73, 75], "andb": [2, 13, 17, 27, 62], "orb": [2, 27, 57, 62], "behaviour": [2, 17, 38, 53], "well": [2, 3, 4, 8, 9, 10, 11, 13, 14, 17, 24, 25, 26, 29, 30, 31, 32, 33, 35, 37, 39, 43, 45, 46, 51, 52, 53, 54, 55, 57, 58, 59, 63, 64, 66, 67, 71, 72, 74, 75], "found": [2, 4, 5, 9, 11, 13, 17, 25, 29, 30, 34, 35, 36, 38, 39, 42, 46, 51, 54, 55, 57, 58, 59, 62, 64, 67, 71, 72, 75], "combin": [2, 3, 5, 9, 12, 14, 17, 24, 25, 26, 27, 29, 34, 37, 40, 42, 46, 52, 53, 54, 55, 57, 59, 63, 64, 75], "featur": [2, 3, 8, 11, 17, 24, 25, 29, 32, 33, 35, 36, 44, 46, 51, 52, 53, 54, 55, 57, 59, 66, 71, 72, 73, 74, 76], "alwai": [2, 3, 4, 6, 9, 10, 11, 12, 13, 14, 17, 24, 26, 34, 35, 37, 41, 42, 44, 51, 52, 53, 54, 55, 57, 58, 60, 66, 67, 71, 74, 75], "dure": [2, 9, 11, 13, 14, 17, 24, 25, 37, 42, 46, 51, 53, 54, 55, 57, 58, 60, 64, 66, 67, 71, 72], "noinlin": 2, "convers": [2, 3, 7, 8, 9, 11, 12, 13, 17, 24, 25, 26, 30, 32, 33, 34, 35, 37, 54, 55, 57, 58, 60, 66, 71, 75], "never": [2, 13, 14, 17, 24, 35, 41, 42, 44, 51, 54, 55, 57, 58, 60, 64], "state": [2, 3, 5, 7, 8, 11, 13, 17, 24, 25, 27, 29, 31, 32, 37, 51, 52, 54, 55, 57, 58, 59, 62, 64, 67, 71], "tabl": [2, 3, 4, 16, 17, 24, 25, 27, 35, 37, 38, 46, 51, 53, 54, 55, 57, 59, 67, 71, 75], "record": [2, 3, 8, 10, 11, 12, 13, 14, 17, 24, 25, 30, 33, 34, 42, 54, 55, 57, 59, 60, 62, 67, 71], "custom": [2, 3, 11, 13, 17, 24, 25, 29, 36, 53, 54, 57], "declar": [2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 43, 46, 51, 53, 54, 58, 59, 60, 64, 71, 72, 75], "previou": [2, 3, 4, 8, 9, 11, 13, 15, 17, 24, 27, 29, 31, 34, 37, 40, 41, 42, 45, 46, 51, 52, 54, 55, 57, 59, 60, 62, 64, 66, 67, 71, 74], "reset": [2, 17, 24, 29, 30, 34, 40, 41, 46, 51, 52, 54, 59, 72], "empti": [2, 3, 5, 7, 12, 13, 17, 24, 26, 34, 40, 43, 51, 53, 55, 57, 58, 59, 60, 67, 71, 72], "ask": [2, 3, 17, 25, 42, 43, 53], "mean": [2, 3, 5, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 31, 32, 34, 35, 38, 40, 42, 43, 44, 46, 51, 52, 53, 54, 57, 58, 59, 64, 65, 66, 71], "both": [2, 3, 4, 11, 14, 17, 24, 25, 26, 27, 28, 29, 31, 34, 37, 38, 40, 42, 43, 44, 46, 51, 52, 53, 54, 57, 58, 60, 61, 64, 66, 67, 73, 74], "But": [2, 11, 17, 34, 39, 41, 46, 51, 53, 54, 64, 75], "For": [2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 14, 16, 17, 24, 26, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 75], "reason": [2, 3, 5, 9, 10, 11, 17, 24, 25, 34, 44, 51, 53, 54, 55, 57, 59, 62, 65, 71, 72, 75, 77], "decis": [2, 17, 24, 25, 58, 62, 64, 77], "taken": [2, 9, 13, 17, 24, 34, 36, 42, 44, 53, 57, 64, 67, 71], "whether": [2, 3, 9, 10, 12, 13, 14, 17, 29, 34, 35, 41, 44, 51, 52, 53, 54, 55, 57, 59, 60, 62, 64, 66, 71, 75], "occurr": [2, 3, 11, 14, 17, 24, 25, 26, 43, 44, 46, 52, 54, 55, 59, 60, 64, 71], "replac": [2, 3, 4, 7, 9, 10, 11, 17, 24, 25, 28, 31, 32, 34, 37, 41, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 62, 64, 66, 67, 71, 74, 75], "manual": [2, 11, 24, 25, 29, 50, 52, 53, 57, 60, 66, 67, 71], "perform": [2, 3, 5, 7, 8, 11, 13, 17, 24, 25, 26, 34, 41, 42, 46, 51, 54, 55, 57, 60, 62, 64, 66, 67, 71, 72], "wai": [2, 3, 5, 11, 12, 13, 14, 17, 24, 25, 26, 27, 29, 30, 31, 32, 34, 35, 37, 42, 43, 44, 46, 51, 52, 53, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 72, 73, 75], "complementari": [2, 17, 24, 42, 57], "main": [2, 8, 9, 11, 13, 17, 25, 27, 29, 34, 40, 41, 51, 52, 53, 54, 55, 57, 60, 64, 71], "logic": [2, 3, 9, 12, 13, 14, 17, 24, 25, 26, 28, 29, 30, 34, 35, 39, 51, 57, 58, 59, 61, 66, 67, 75, 77], "implicit": [2, 3, 5, 9, 13, 17, 24, 25, 28, 33, 34, 37, 38, 42, 43, 45, 51, 53, 55, 57, 58, 59, 66, 67, 75], "integ": [2, 3, 7, 11, 14, 17, 24, 25, 29, 34, 39, 52, 53, 54, 55, 57, 59, 60, 64, 66], "thei": [2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 72, 73, 74, 75], "omit": [2, 3, 8, 14, 17, 27, 28, 29, 30, 32, 34, 37, 38, 40, 41, 42, 44, 45, 46, 53, 54, 55, 57, 58, 59, 60, 66, 67, 71, 75], "position": [2, 58], "start": [2, 3, 6, 8, 9, 13, 17, 24, 25, 26, 27, 29, 32, 34, 35, 37, 40, 41, 42, 44, 46, 52, 53, 54, 55, 58, 59, 60, 64, 66, 67, 71, 74, 75], "actual": [2, 3, 5, 8, 11, 14, 17, 24, 34, 37, 42, 43, 44, 46, 54, 55, 57, 60, 64, 67, 71, 72], "take": [2, 3, 5, 8, 11, 12, 13, 17, 24, 26, 28, 29, 31, 32, 37, 40, 41, 42, 46, 51, 52, 53, 54, 55, 57, 58, 60, 62, 64, 66, 67, 71, 75], "place": [2, 3, 17, 32, 40, 43, 51, 53, 57, 58, 59, 64, 66, 67, 71, 75], "error": [2, 3, 4, 9, 10, 11, 12, 13, 14, 16, 17, 24, 25, 27, 28, 29, 32, 34, 35, 37, 38, 39, 40, 41, 42, 44, 46, 51, 52, 53, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 75], "rais": [2, 3, 10, 13, 17, 29, 35, 54, 55, 64, 72], "cannot": [2, 3, 4, 8, 9, 10, 11, 12, 13, 14, 17, 26, 28, 29, 32, 34, 35, 36, 37, 40, 41, 44, 46, 51, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 75], "honor": [2, 8, 17, 51, 57, 71], "occur": [2, 3, 4, 8, 17, 24, 26, 28, 30, 34, 37, 38, 41, 42, 44, 46, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71], "final": [2, 3, 4, 5, 6, 8, 9, 10, 11, 13, 14, 17, 24, 25, 27, 29, 35, 40, 51, 52, 53, 54, 57, 59, 64, 66, 67, 71, 75], "behavior": [2, 3, 4, 11, 13, 14, 17, 24, 29, 30, 32, 34, 41, 43, 44, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 73, 75], "relax": [2, 17, 30, 44, 53, 57, 60], "safeimplicit": 2, "warn": [2, 3, 4, 10, 12, 13, 16, 17, 24, 25, 27, 28, 29, 32, 34, 35, 37, 41, 42, 44, 46, 51, 52, 54, 55, 57, 59, 60, 62, 66, 71, 72], "emit": [2, 10, 12, 13, 17, 34, 53, 71, 74], "obtain": [2, 3, 4, 5, 17, 34, 36, 54, 55, 57, 58, 64, 67, 72, 75], "nonetheless": [2, 17, 30, 32, 36, 51, 66], "review": [2, 17, 27], "locat": [2, 17, 24, 25, 35, 51, 52, 53, 54, 55], "issu": [2, 3, 24, 25, 46, 52, 54, 55, 58, 64, 66, 71, 73], "comment": [2, 5, 17, 24, 25, 29, 52, 54, 57, 60, 66, 75], "mark": [2, 12, 17, 24, 31, 35, 37, 38, 41, 44, 51, 52, 53, 54, 55, 57, 59, 60, 64, 66, 71], "remain": [2, 3, 9, 11, 13, 14, 17, 24, 34, 36, 39, 41, 42, 44, 46, 52, 57, 58, 64, 66], "note": [2, 3, 4, 5, 7, 8, 10, 11, 12, 13, 14, 15, 17, 24, 26, 27, 28, 29, 34, 35, 37, 40, 41, 42, 43, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74, 77], "might": [2, 3, 5, 13, 17, 46, 51, 53, 55, 57, 62, 64, 67, 71, 72, 75], "run": [2, 5, 8, 9, 13, 14, 17, 24, 25, 29, 51, 53, 57, 59, 60, 64, 66, 71, 73], "properli": [2, 8, 9, 10, 17, 29, 52, 53, 57, 59, 66], "encount": [2, 11, 17, 52, 53, 54, 64], "inform": [2, 3, 4, 10, 12, 13, 14, 17, 24, 25, 26, 27, 29, 30, 34, 37, 39, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 67, 72, 75, 77], "remind": [2, 3, 57], "inconsist": [2, 8, 10, 12, 14, 17, 24, 26, 34, 39, 44, 51, 59, 66, 67, 71], "lead": [2, 10, 14, 17, 24, 26, 29, 34, 39, 57, 58, 60, 64, 71, 74, 75], "incorrect": [2, 8, 12, 14, 17, 25, 34, 37, 46, 52, 57, 66], "termin": [2, 8, 9, 17, 24, 25, 27, 29, 30, 32, 34, 35, 38, 52, 55, 59, 60, 66, 71, 72], "assum": [2, 3, 5, 11, 13, 17, 26, 27, 28, 32, 34, 35, 36, 38, 39, 42, 44, 46, 51, 53, 54, 55, 57, 58, 59, 64, 66, 71, 75], "while": [2, 3, 4, 9, 10, 12, 13, 14, 17, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 36, 37, 40, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 73], "proposit": [2, 3, 5, 10, 17, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 39, 40, 51, 57, 58, 62, 64, 66, 67, 77], "perfectli": 2, "content": [2, 17, 24, 27, 32, 35, 42, 51, 52, 53, 54, 57, 59, 66, 71, 75], "must": [2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 27, 29, 30, 34, 35, 36, 37, 39, 40, 41, 44, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74, 75], "cours": [2, 14, 17, 24, 42, 51, 52, 57, 64, 71], "guess": [2, 4, 11, 17, 32, 43, 53, 57, 67], "tell": [2, 3, 11, 17, 24, 34, 41, 42, 44, 46, 51, 55, 57, 60, 64, 67, 71, 75], "given": [2, 3, 4, 5, 9, 10, 11, 13, 14, 17, 24, 25, 27, 28, 29, 32, 35, 36, 37, 40, 41, 42, 43, 44, 46, 51, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74, 75], "tv": 2, "give": [2, 3, 4, 5, 7, 8, 9, 11, 13, 14, 17, 24, 25, 26, 27, 28, 29, 31, 32, 34, 35, 37, 40, 41, 42, 45, 46, 51, 52, 53, 54, 55, 57, 58, 59, 64, 66, 67, 71, 75], "ariti": [2, 17, 24, 25, 46, 55], "sequenc": [2, 3, 5, 17, 24, 25, 28, 29, 30, 46, 51, 57, 58, 59, 60, 64, 66, 71, 75], "product": [2, 3, 5, 10, 11, 13, 14, 17, 24, 26, 27, 28, 34, 36, 39, 40, 46, 54, 55, 57, 59, 60, 64, 66, 67, 71], "variabl": [2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 31, 32, 34, 35, 37, 38, 39, 40, 41, 42, 45, 53, 54, 57, 58, 59, 60, 62, 64, 67, 71, 72, 75], "quot": [2, 5, 13, 17, 24, 25, 28, 29, 44, 51, 55, 59, 66, 71, 75], "number": [2, 3, 4, 5, 7, 11, 13, 14, 17, 24, 25, 26, 27, 29, 30, 34, 36, 37, 39, 40, 41, 42, 43, 44, 46, 52, 53, 55, 57, 58, 59, 62, 64, 66, 67, 72, 74, 77], "check": [2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 30, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 46, 51, 52, 53, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74, 75], "y": [2, 3, 4, 5, 9, 11, 12, 13, 14, 17, 24, 26, 27, 28, 31, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 46, 52, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 77], "b": [2, 3, 4, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 27, 28, 31, 34, 35, 37, 38, 40, 41, 42, 44, 46, 50, 51, 52, 53, 54, 55, 57, 59, 60, 62, 64, 66, 67, 71, 72, 77], "recogn": [2, 4, 5, 8, 11, 17, 24, 29, 34, 46, 51, 52, 55, 62, 67, 71, 75], "becom": [2, 8, 11, 17, 24, 26, 28, 34, 35, 40, 44, 46, 52, 53, 55, 57, 58, 59, 64, 66, 67, 71], "int": [2, 3, 17, 36, 55, 71, 75], "0": [2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 25, 26, 27, 28, 29, 30, 31, 34, 35, 36, 37, 41, 43, 44, 46, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74, 75, 77], "respons": [2, 10, 17, 52, 55, 75], "expect": [2, 3, 4, 11, 12, 14, 17, 24, 26, 29, 31, 32, 33, 34, 40, 41, 42, 43, 44, 46, 51, 52, 54, 55, 57, 58, 60, 64, 67, 71], "fact": [2, 5, 11, 14, 17, 24, 28, 32, 34, 39, 41, 42, 46, 54, 55, 57, 58, 62, 64, 66, 67, 71, 75], "copi": [2, 17, 36, 46, 52, 53, 54, 57, 75], "everywher": [2, 17, 55, 58, 64], "being": [2, 3, 9, 11, 12, 13, 14, 17, 24, 32, 33, 34, 35, 37, 38, 40, 42, 46, 51, 52, 53, 54, 55, 57, 60, 64, 66, 67, 71, 72, 75], "sugar": [2, 7, 17, 28, 54, 55, 59, 77], "effect": [2, 3, 9, 11, 13, 14, 17, 24, 25, 29, 30, 34, 35, 38, 43, 51, 52, 53, 54, 57, 59, 64, 66, 71, 75], "alreadi": [2, 4, 13, 17, 24, 27, 28, 32, 37, 41, 42, 44, 51, 52, 53, 54, 55, 57, 58, 59, 60, 66, 67, 71, 73], "foreign": [2, 17], "wa": [2, 3, 10, 11, 12, 17, 24, 27, 28, 29, 32, 34, 35, 37, 38, 41, 42, 43, 44, 51, 52, 53, 54, 55, 57, 58, 59, 60, 63, 64, 66, 67, 71, 72], "previous": [2, 13, 17, 28, 34, 38, 52, 54, 57, 59, 71], "would": [2, 3, 4, 11, 14, 17, 28, 29, 30, 31, 32, 34, 37, 41, 42, 43, 44, 46, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 75], "overrid": [2, 14, 17, 37, 51, 53, 57, 66, 67, 71], "been": [2, 3, 8, 9, 10, 11, 13, 14, 17, 24, 25, 27, 28, 29, 32, 34, 35, 41, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 63, 64, 66, 67, 71, 72, 73, 74], "definit": [2, 4, 8, 10, 11, 13, 17, 24, 25, 26, 27, 28, 29, 31, 33, 35, 36, 38, 41, 42, 43, 44, 51, 53, 58, 59, 60, 62, 66, 67, 72, 73, 74, 75, 77], "fill": [2, 9, 13, 17, 25, 52, 55, 57, 62, 71], "label": [2, 8, 14, 17, 29, 54, 59], "TO": 2, "BE": 2, "search": [2, 4, 5, 7, 13, 17, 24, 25, 42, 44, 51, 52, 53, 61, 62, 64], "insid": [2, 3, 4, 8, 9, 13, 14, 17, 24, 25, 28, 29, 34, 35, 38, 46, 52, 55, 57, 58, 59, 60, 64, 66, 67, 71, 74], "real": [2, 3, 7, 11, 24, 25, 34, 46, 53, 55, 66, 67, 71], "nativ": [2, 5, 10, 12, 24, 25, 36, 51, 55, 58, 59, 64], "boolean": [2, 5, 9, 11, 13, 14, 17, 24, 25, 27, 29, 34, 37, 39, 40, 42, 55, 59, 60, 62, 64, 67, 71], "syntax": [2, 4, 5, 6, 8, 9, 11, 13, 14, 25, 26, 27, 30, 32, 34, 35, 37, 39, 40, 41, 42, 43, 45, 51, 52, 53, 58, 59, 60, 63, 64, 66, 75, 77], "itself": [2, 3, 8, 9, 11, 12, 13, 14, 17, 30, 34, 39, 40, 41, 42, 43, 44, 51, 53, 54, 55, 57, 58, 60, 63, 64, 67, 71], "initi": [2, 6, 7, 11, 13, 17, 24, 27, 29, 38, 46, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 71, 74, 75], "datatyp": [2, 17, 24, 25, 26, 35, 44, 46, 54, 55, 57, 59, 60, 67, 71], "pattern": [2, 9, 13, 17, 24, 25, 27, 28, 30, 32, 34, 40, 41, 42, 45, 60, 64, 67, 72, 77], "charact": [2, 8, 10, 13, 14, 17, 24, 25, 27, 29, 35, 36, 40, 44, 46, 53, 54, 55, 57, 58, 59, 64, 66, 71, 72, 74, 75], "char": [2, 17, 53], "prelud": [2, 17, 25, 29, 51, 59, 66], "liter": [2, 5, 17, 29, 36, 42, 54, 55, 57, 71], "handl": [2, 3, 8, 9, 11, 17, 24, 26, 37, 43, 46, 53, 55, 57, 58, 59, 61, 62, 66, 67, 71], "special": [2, 3, 4, 9, 12, 13, 16, 17, 24, 25, 27, 28, 29, 34, 51, 52, 53, 54, 55, 59, 60, 64, 66, 67, 71, 75], "design": [2, 8, 11, 17, 24, 25, 37, 44, 57, 64, 71, 77], "regist": [2, 3, 4, 5, 7, 9, 11, 13, 17, 25, 32, 42, 57, 64, 67, 71, 72], "standard": [2, 3, 5, 9, 14, 25, 27, 29, 35, 36, 40, 51, 52, 53, 54, 58, 59, 62, 64, 65, 66, 67, 72, 73, 74, 75], "indic": [2, 8, 11, 12, 13, 14, 17, 24, 26, 31, 34, 35, 39, 40, 41, 42, 43, 46, 51, 52, 53, 54, 57, 58, 59, 62, 64, 66, 67, 71], "how": [2, 7, 8, 13, 17, 24, 25, 27, 29, 30, 34, 35, 37, 42, 43, 45, 51, 53, 54, 57, 58, 59, 60, 62, 64, 67, 71, 72, 74, 77], "over": [2, 3, 11, 14, 17, 24, 25, 26, 27, 28, 30, 32, 34, 37, 38, 39, 40, 41, 42, 44, 46, 52, 53, 54, 58, 59, 60, 61, 62, 64, 66, 67], "could": [2, 3, 4, 5, 6, 11, 12, 17, 24, 29, 31, 34, 37, 42, 46, 51, 52, 55, 57, 58, 60, 62, 66, 71, 72, 73], "arbitrari": [2, 3, 5, 10, 11, 14, 17, 24, 31, 44, 46, 53, 57, 60, 62, 71], "k": [2, 3, 6, 14, 17, 24, 26, 34, 42, 54, 57, 67, 72, 77], "emul": [2, 12, 17, 40, 57], "branch": [2, 5, 9, 17, 25, 34, 40, 45, 46, 55, 59, 60, 66, 67, 72], "element": [2, 3, 11, 12, 17, 25, 26, 27, 34, 35, 36, 46, 57, 59, 60, 71], "destruct": [2, 13, 17, 24, 25, 34, 54, 55, 57, 58, 64, 71], "foo": [2, 11, 14, 17, 29, 35, 38, 40, 43, 51, 52, 53, 55, 57, 58, 59, 64, 66, 71, 74, 75], "fun": [2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 14, 17, 25, 26, 27, 29, 30, 31, 32, 34, 35, 37, 38, 40, 41, 42, 43, 44, 46, 54, 55, 57, 58, 59, 64, 66, 67, 71, 72, 75], "consid": [2, 3, 4, 5, 9, 11, 12, 13, 14, 17, 24, 26, 28, 29, 30, 31, 34, 37, 41, 42, 44, 46, 52, 53, 54, 55, 57, 58, 59, 60, 64, 67, 71, 73, 75], "unit": [2, 12, 13, 14, 17, 27, 34, 40, 46, 53, 54, 55, 57, 62, 64, 71], "block": [2, 9, 10, 14, 17, 25, 29, 30, 34, 37, 38, 44, 46, 54, 64, 65, 67], "earli": [2, 15, 17, 25, 26, 54, 64], "evalu": [2, 3, 9, 11, 17, 24, 25, 28, 30, 34, 35, 41, 53, 57, 60, 64, 71], "bar": [2, 8, 14, 17, 29, 35, 51, 52, 53, 55, 57, 64, 66, 71, 74], "As": [2, 3, 5, 6, 9, 10, 11, 13, 14, 17, 26, 28, 30, 34, 36, 37, 38, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 66, 67, 71, 72], "care": [2, 13, 14, 17, 46, 53, 54, 64, 67, 71, 75], "pre": [2, 17, 25, 53, 60], "sound": [2, 17, 34], "ad": [2, 4, 9, 13, 14, 17, 24, 25, 29, 34, 37, 42, 44, 51, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 73, 75, 77], "hoc": [2, 3, 17, 71, 77], "often": [2, 3, 10, 13, 14, 17, 25, 28, 43, 46, 52, 53, 54, 55, 57, 58, 66], "fulli": [2, 3, 8, 17, 24, 26, 28, 31, 32, 35, 38, 44, 51, 52, 53, 54, 55, 58, 59, 64, 66, 71, 72], "rigor": [2, 24], "correct": [2, 8, 9, 11, 17, 24, 25, 28, 32, 35, 46, 51, 53, 57, 59, 64, 66, 67, 71], "theoret": [2, 17, 24, 31, 39, 77], "valu": [2, 4, 5, 6, 9, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 31, 32, 34, 36, 37, 38, 40, 42, 43, 51, 52, 53, 57, 58, 59, 60, 62, 64, 66, 67, 71, 74], "larger": [2, 13, 14, 17, 25, 51, 52, 57, 60, 71, 75], "than": [2, 3, 5, 8, 11, 12, 13, 14, 17, 24, 29, 30, 31, 34, 35, 37, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 73, 75], "max_int": 2, "overflow": [2, 17, 59, 66, 71], "bad": [2, 11, 12, 14, 17, 34, 59, 64], "event": [2, 17, 51], "practic": [2, 3, 5, 17, 24, 25, 32, 34, 39, 42, 53, 55, 57, 58, 64, 66, 71, 74, 77], "translat": [2, 3, 17, 24, 25, 33, 41, 45, 57, 71, 75], "magic": [2, 17, 24, 55, 59], "improv": [2, 3, 8, 11, 17, 24, 29, 52, 54, 57, 67], "asymptot": [2, 59], "complex": [2, 11, 17, 24, 25, 29, 33, 35, 52, 54, 55, 57, 59, 61, 63, 66, 67], "represent": [2, 3, 5, 11, 12, 17, 24, 29, 34, 37, 51, 53, 57, 64, 71], "mul": [2, 5, 17, 36, 52, 57, 59, 71], "stai": [2, 27], "quadrat": [2, 17], "interest": [2, 4, 5, 11, 17, 24, 31, 42, 54, 57, 67], "associ": [2, 3, 11, 13, 14, 17, 24, 25, 26, 27, 28, 29, 31, 32, 34, 35, 36, 37, 38, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67], "primit": [2, 10, 12, 13, 14, 17, 24, 25, 27, 30, 33, 34, 41, 46, 54, 55, 57, 64, 67], "counterpart": [2, 3, 9, 11, 17, 30, 34, 57], "bool": [2, 3, 4, 5, 12, 13, 17, 24, 27, 30, 35, 36, 37, 40, 41, 42, 44, 46, 55, 57, 58, 59, 60, 71], "true": [2, 3, 4, 5, 7, 9, 11, 12, 13, 14, 17, 24, 26, 27, 34, 35, 36, 37, 40, 41, 44, 46, 51, 53, 54, 55, 57, 58, 59, 62, 64, 67, 71, 74], "fals": [2, 4, 5, 9, 10, 12, 13, 17, 24, 27, 34, 37, 40, 41, 46, 51, 54, 55, 57, 58, 59, 62, 64, 66, 67, 71], "sumbool": [2, 27, 46, 71], "enclos": [2, 29, 41, 53, 54, 55, 66, 71, 75], "parenthes": [2, 3, 8, 17, 24, 28, 29, 35, 37, 46, 54, 55, 57, 58, 67, 71], "meet": [2, 9, 71], "lexic": [2, 17, 25, 51, 59, 71, 75], "criteria": [2, 17, 72], "infix": [2, 14, 17, 24, 25, 27, 42, 57, 58, 64, 74], "symbol": [2, 3, 11, 14, 17, 24, 25, 27, 28, 29, 31, 41, 42, 43, 46, 57, 59, 60, 62, 64, 67, 71, 75, 77], "rest": [2, 3, 13, 17, 26, 29, 36, 42, 52, 57, 66], "prod": [2, 17, 26, 27, 34, 46, 62, 67], "caveat": [2, 17, 25, 55, 57, 60], "abov": [2, 3, 5, 11, 13, 14, 17, 24, 28, 30, 34, 37, 38, 42, 44, 51, 52, 53, 54, 55, 57, 58, 59, 64, 66, 71, 72, 75], "succ": [2, 24, 54, 59, 64], "fo": 2, "els": [2, 4, 9, 11, 12, 13, 17, 29, 30, 35, 40, 41, 46, 52, 54, 55, 57, 59, 62, 67, 71, 75], "interfac": [2, 17, 24, 25, 35, 52, 53, 66, 74, 75, 76], "link": [2, 16, 17, 24, 27, 46, 53, 57, 72, 75], "linker": [2, 24], "know": [2, 8, 17, 24, 27, 32, 34, 42, 46, 52, 53, 54, 55, 57, 59, 60, 62, 64, 67, 71], "extern": [2, 5, 11, 13, 17, 29, 33, 52, 54, 55, 59, 60, 63, 66, 73, 74, 75], "shall": [2, 17, 24, 26, 31, 34, 39, 42, 57, 71], "access": [2, 5, 14, 17, 24, 25, 28, 32, 33, 34, 35, 36, 38, 44, 51, 52, 53, 55, 57, 59, 71], "callback": [2, 17], "referenc": [2, 17, 53, 71], "stdlib": [2, 3, 5, 7, 9, 11, 12, 14, 17, 27, 28, 29, 35, 51, 53, 54, 55, 57, 59, 60, 64, 67, 72, 75], "f_impl": 2, "compat": [2, 3, 4, 13, 14, 24, 25, 29, 34, 42, 51, 52, 53, 58, 62, 63, 64, 71], "support": [2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 17, 24, 25, 30, 32, 34, 35, 36, 37, 40, 41, 42, 44, 51, 53, 54, 55, 57, 59, 60, 62, 63, 64, 66, 71, 72, 74, 75, 76], "thrown": 2, "after": [2, 4, 5, 7, 8, 9, 11, 13, 17, 24, 29, 32, 34, 35, 38, 41, 42, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72], "callabl": 2, "express": [2, 3, 4, 5, 9, 10, 11, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 39, 40, 41, 43, 44, 57, 58, 59, 60, 64, 66, 67, 75], "signal": [2, 8, 17, 57], "alias": [2, 17, 24, 25, 29, 35, 55], "uniqu": [2, 3, 12, 13, 17, 24, 31, 35, 38, 57, 59, 67, 71], "multipl": [2, 3, 4, 9, 14, 17, 24, 25, 27, 29, 34, 35, 40, 44, 52, 58, 59, 60, 64, 66, 67, 71], "expos": [2, 17, 25, 40, 41, 57, 71], "share": [2, 11, 13, 14, 17, 24, 28, 29, 34, 46, 51, 52, 53, 57, 59, 60, 64, 67, 71], "impact": [2, 17, 53, 66, 71], "synthesis": 2, "thu": [2, 3, 4, 5, 10, 12, 17, 24, 32, 34, 42, 43, 46, 51, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71, 72, 75], "safeti": 2, "registr": [2, 17, 25], "usabl": [2, 17, 24, 38, 52, 66, 67, 71], "togeth": [2, 3, 9, 17, 24, 25, 27, 31, 34, 35, 43, 53, 54, 55, 57, 66, 71, 75], "map": [2, 3, 5, 13, 17, 24, 25, 26, 34, 35, 36, 39, 41, 44, 51, 53, 57, 58, 59, 60, 71, 72, 75], "directli": [2, 3, 4, 9, 13, 14, 17, 24, 27, 28, 34, 43, 51, 52, 53, 55, 57, 58, 60, 64, 67, 72, 75], "happen": [2, 4, 9, 10, 13, 17, 34, 38, 46, 52, 54, 55, 57, 58, 64, 71, 72], "instruct": [2, 5, 17, 53, 58, 59], "particular": [2, 3, 6, 9, 10, 12, 13, 17, 29, 30, 31, 32, 33, 34, 37, 38, 40, 42, 52, 53, 54, 55, 57, 59, 60, 64, 66, 71, 75], "blacklist": [2, 17, 59], "includ": [2, 3, 5, 8, 9, 12, 13, 14, 17, 24, 25, 27, 28, 29, 34, 35, 36, 38, 39, 40, 41, 43, 44, 51, 52, 53, 54, 55, 57, 59, 60, 62, 64, 66, 67, 71, 73, 75], "natur": [2, 5, 7, 9, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 34, 35, 37, 39, 40, 42, 44, 46, 52, 53, 57, 58, 59, 62, 64, 66, 71, 72], "finer": [2, 17, 34, 57], "grain": [2, 17, 41], "bit": [2, 5, 17, 29, 30, 34, 36, 51, 53, 66, 71, 75, 77], "mask": [2, 35], "unless": [2, 3, 13, 14, 17, 29, 40, 41, 42, 44, 51, 52, 57, 58, 64, 71, 72, 75], "treatment": [2, 9, 17, 40], "fixpoint": [2, 3, 10, 13, 17, 24, 25, 27, 29, 30, 31, 32, 37, 38, 41, 44, 46, 52, 57, 59, 64, 66, 67, 71, 72], "simplifi": [2, 11, 17, 24, 41, 54, 57, 64, 67], "redux": 2, "factor": [2, 5, 11, 17, 25, 34, 45], "16": [2, 25, 53, 54, 57, 71], "32": [2, 17, 36, 51, 53, 66], "6": [2, 9, 25, 29, 35, 53, 54, 55, 57, 58, 71, 74, 77], "64": [2, 36, 51, 66], "swap": [2, 17, 54, 57, 58], "lambda": [2, 3, 10, 11, 17, 31, 52, 55, 64, 67, 71, 77], "7": [2, 11, 25, 54, 57, 64, 71, 74, 75, 77], "128": 2, "256": 2, "push": [2, 17, 57, 71], "9": [2, 24, 25, 29, 30, 35, 53, 54, 57, 64, 71, 74, 77], "512": 2, "linear": [2, 3, 11, 14, 17, 24, 25, 46, 51, 54, 55, 57, 64], "10": [2, 5, 24, 25, 29, 31, 52, 54, 57, 59, 60, 64, 71, 74, 77], "1024": 2, "typeexpand": 2, "expand": [2, 13, 14, 17, 28, 29, 30, 31, 35, 37, 41, 46, 52, 54, 55, 57, 58, 64, 67, 71], "learn": [2, 17, 25, 54, 72], "written": [2, 3, 5, 11, 13, 17, 24, 26, 28, 29, 34, 35, 36, 37, 42, 43, 44, 46, 52, 53, 54, 55, 57, 59, 64, 71, 73, 74], "due": [2, 3, 13, 14, 17, 24, 27, 30, 34, 46, 52, 54, 55, 59, 64, 66, 67, 71, 72, 73], "typabl": [2, 4, 34], "now": [2, 3, 4, 11, 13, 14, 17, 24, 26, 27, 30, 34, 35, 41, 42, 46, 51, 52, 53, 54, 55, 57, 59, 60, 64, 67, 71, 72, 74], "solv": [2, 3, 5, 7, 11, 13, 17, 24, 25, 39, 42, 44, 57, 60, 61, 62, 64, 67], "problem": [2, 4, 7, 9, 13, 17, 24, 29, 34, 42, 44, 46, 51, 52, 53, 54, 58, 62, 66, 67], "least": [2, 3, 12, 13, 17, 25, 28, 29, 30, 34, 41, 46, 52, 53, 57, 58, 64, 66, 67, 71, 72, 74, 75], "unsaf": [2, 17, 55, 66], "cast": [2, 12, 17, 25, 40, 46, 54, 55, 57, 58, 60, 64, 71], "obj": [2, 24, 42], "veri": [2, 8, 9, 11, 13, 17, 24, 25, 27, 29, 34, 42, 46, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67], "polymorph": [2, 3, 13, 17, 24, 25, 26, 29, 30, 31, 32, 33, 37, 39, 40, 41, 44, 46, 51, 59, 66, 67, 71], "alright": 2, "refus": [2, 3, 64], "checker": [2, 9, 11, 17, 24, 25, 26, 29, 33, 73], "known": [2, 8, 10, 12, 13, 17, 24, 27, 30, 33, 34, 39, 41, 44, 51, 55, 57, 66, 71], "distr": 2, "dp": [2, 17], "foral": [2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 25, 26, 27, 29, 30, 31, 32, 34, 36, 37, 41, 42, 43, 44, 46, 52, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 75], "direct": [2, 9, 12, 16, 17, 24, 31, 34, 42, 46, 52, 53, 57, 58, 71], "restrict": [2, 3, 12, 14, 17, 24, 26, 34, 35, 40, 51, 54, 57, 58, 59, 60, 62, 67, 71], "secondli": [2, 17], "quantif": [2, 3, 4, 13, 14, 17, 24, 26, 27, 28, 60, 67], "anyth": [2, 13, 17, 35, 44, 46, 51, 55, 57, 58, 64, 75], "anything_rect": 2, "anything_ind": 2, "anything_rec": 2, "anything_sind": 2, "dynam": [2, 11, 13, 17, 25, 36, 59, 71], "gadt": 2, "yet": [2, 17, 42, 43, 46, 51, 52, 54, 55, 57, 58, 60, 66, 71, 72], "those": [2, 3, 5, 10, 11, 12, 17, 24, 26, 33, 34, 35, 37, 43, 46, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72], "get": [2, 5, 9, 11, 13, 14, 17, 24, 25, 28, 29, 34, 36, 42, 51, 52, 53, 55, 58, 59, 60, 64, 66, 67], "segment": [2, 17, 24, 52, 59, 71], "fault": [2, 24, 71], "your": [2, 3, 8, 11, 14, 15, 17, 25, 29, 51, 52, 54, 55, 57, 58, 59, 60, 62, 66, 71, 73, 74, 75], "seem": [2, 5, 17, 71], "ill": [2, 4, 9, 10, 17, 24, 26, 30, 34, 51, 55, 64, 71, 72], "go": [2, 5, 9, 17, 24, 30, 42, 51, 52, 54, 55, 57, 59, 60, 64, 67, 71, 75], "wrong": [2, 3, 17, 24, 44, 51, 54, 66, 72], "come": [2, 6, 8, 13, 17, 24, 27, 34, 43, 51, 52, 54, 55, 57, 59, 60, 64, 71], "Of": [2, 14, 42, 51, 57], "launch": [2, 13, 17, 25, 52, 53], "appli": [2, 3, 4, 5, 9, 10, 11, 13, 14, 17, 24, 25, 26, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 40, 41, 42, 44, 46, 51, 53, 54, 55, 59, 60, 62, 66, 71, 72, 75], "shape": [2, 3, 57], "point": [2, 3, 11, 13, 17, 24, 25, 26, 32, 34, 35, 36, 39, 51, 52, 53, 54, 55, 57, 66, 71], "view": [2, 11, 17, 25, 26, 29, 32, 34, 39, 41, 52, 55, 60, 66], "about": [2, 3, 5, 11, 13, 14, 15, 17, 24, 25, 29, 30, 34, 37, 39, 41, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 72], "let02": [2, 77], "sai": [2, 3, 4, 17, 24, 26, 27, 28, 29, 31, 34, 42, 52, 53, 54, 55, 57, 58, 64, 71, 74], "though": [2, 8, 9, 17, 24, 29, 35, 37, 46, 51, 53, 54, 55, 64, 67, 71], "realist": [2, 42], "accept": [2, 3, 8, 13, 17, 24, 28, 29, 30, 32, 34, 40, 44, 45, 46, 51, 52, 53, 54, 55, 57, 58, 60, 64, 66, 71, 72], "without": [2, 3, 5, 8, 9, 11, 13, 14, 17, 24, 26, 29, 32, 33, 34, 35, 37, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 63, 64, 66, 67, 71, 74, 75, 77], "below": [2, 4, 5, 8, 9, 10, 11, 13, 14, 17, 25, 26, 27, 31, 34, 35, 38, 40, 41, 43, 51, 52, 53, 54, 55, 57, 64, 66, 71, 72, 74, 75], "choos": [2, 3, 17, 32, 34, 42, 43, 52, 53, 54, 57, 58, 67, 71, 72, 75], "everyth": [2, 17, 52, 53], "slight": [2, 17, 24, 58], "modif": [2, 4, 11, 17, 36, 41, 58, 71], "find": [2, 3, 4, 5, 7, 11, 13, 14, 16, 17, 25, 27, 29, 34, 42, 43, 51, 52, 53, 54, 55, 57, 58, 59, 62, 64, 66, 67, 71, 72, 77], "Its": [2, 3, 11, 17, 24, 52, 55, 57, 60, 67, 74], "euclid": [2, 17, 24], "unari": [2, 3, 26, 29, 34, 64], "repres": [2, 3, 5, 11, 13, 14, 17, 24, 26, 27, 28, 29, 31, 32, 34, 36, 37, 39, 40, 42, 43, 51, 52, 53, 54, 55, 57, 58, 59, 64, 65, 66, 67, 71], "theorem": [2, 5, 7, 8, 11, 12, 17, 24, 25, 27, 29, 32, 33, 35, 37, 38, 42, 43, 51, 52, 57, 59, 60, 62, 65, 66, 71, 73, 74, 75, 77], "eucl_dev": 2, "whose": [2, 3, 4, 5, 11, 13, 14, 17, 24, 26, 30, 31, 33, 34, 35, 37, 39, 41, 42, 44, 46, 53, 54, 55, 57, 58, 59, 60, 64, 67, 71, 75], "diveucl": 2, "quotient": [2, 5, 17, 40, 57, 64], "modulo": [2, 4, 5, 11, 17, 24, 34, 54, 57, 58, 59, 71], "assert": [2, 17, 24, 25, 26, 28, 34, 41, 54, 55, 57, 58, 62, 64, 66, 67, 71], "disappear": [2, 17, 24, 34, 55, 60, 67, 71], "wf_nat": [2, 17, 24], "gt_wf_rec": 2, "lt_wf_rec": [2, 24], "induction_ltof2": 2, "val": [2, 34, 55, 57], "sub": [2, 4, 8, 17, 36, 41, 46, 51, 53, 54, 57, 59, 60, 67, 71], "rec": [2, 17, 24, 35, 54, 55, 75], "le_lt_dec": [2, 17, 24], "n0": [2, 9, 31, 46, 57, 58, 67, 72], "n1": [2, 9, 34, 53, 57, 72], "le_gt_dec": 2, "divex": 2, "d": [2, 4, 5, 11, 14, 17, 24, 26, 34, 46, 51, 52, 53, 54, 57, 58, 62, 67, 75, 77], "q": [2, 3, 5, 7, 10, 11, 12, 17, 24, 27, 34, 35, 46, 51, 53, 54, 55, 57, 58, 59, 67, 71, 75], "r": [2, 3, 5, 7, 9, 11, 13, 14, 17, 24, 27, 28, 34, 35, 37, 41, 44, 51, 53, 54, 57, 58, 59, 60, 64, 67, 71, 72, 75, 77], "mandatori": [2, 8, 17, 32, 57, 66, 71], "enhanc": [2, 17, 52, 57], "past": [2, 17, 52, 64], "u": [2, 3, 4, 9, 10, 11, 14, 17, 24, 26, 27, 31, 34, 35, 38, 39, 41, 42, 46, 51, 53, 54, 55, 57, 58, 62, 64, 67, 71], "plai": [2, 17, 26, 42, 64, 66], "toplevel": [2, 10, 13, 14, 17, 24, 25, 27, 29, 35, 44, 46, 51, 52, 53, 55, 57, 58, 59, 60, 64, 71, 72, 74], "easier": [2, 10, 17, 24, 45, 52, 57, 58, 67, 71], "nat_of_int": 2, "int_of_nat": 2, "div": [2, 3, 5, 11, 17, 59], "173": [2, 14], "15": [2, 13, 25, 52, 53, 57, 66], "mere": [2, 17, 55, 57, 64, 71], "extrocamlintconv": 2, "concret": [2, 13, 14, 17, 25, 26, 29, 34, 42, 46, 51, 57, 64, 71], "patholog": 2, "success": [2, 3, 4, 5, 13, 17, 24, 25, 34, 51, 52, 55, 57, 59, 60, 62, 64, 66, 67, 74], "sever": [2, 3, 4, 5, 11, 17, 24, 25, 26, 28, 29, 30, 31, 32, 34, 40, 42, 44, 46, 51, 52, 54, 55, 57, 59, 60, 64, 65, 67, 71, 72, 75, 76], "chain": [2, 17, 25, 51, 64, 71, 74], "http": [2, 5, 17, 24, 25, 27, 50, 51, 52, 53, 59, 64, 75, 77], "github": [2, 5, 17, 51, 52], "com": [2, 5, 17, 51, 52, 54], "coq": [2, 8, 9, 11, 13, 15, 17, 25, 26, 29, 30, 46, 51, 53, 54, 55, 57, 58, 59, 63, 66, 71, 72, 73, 75, 76, 77], "commun": [2, 17, 24, 27, 29, 51], "hydra": 2, "battl": 2, "bdd": 2, "contrib": [2, 17, 24, 53, 55], "canon": [2, 4, 5, 11, 13, 17, 24, 25, 30, 32, 34, 35, 37, 38, 44, 45, 53, 57, 59, 71, 77], "chines": [2, 24], "continu": [2, 17, 24, 52, 53, 54, 55, 57, 71, 73], "fire": [2, 14, 17], "squad": 2, "founifi": 2, "graph": [2, 14, 17, 24, 25, 39, 54, 72], "higman": 2, "cf": [2, 9, 17, 24, 29, 34, 40, 42, 46, 59, 67], "nw": 2, "hardwar": [2, 8, 24], "multipli": [2, 57], "stalmarck": [2, 24], "probabl": [2, 17, 32, 44, 51, 54, 57, 58, 59, 75], "heavi": 2, "impred": [2, 12, 14, 17, 24, 25, 34, 51, 53, 77], "thank": [2, 5, 12, 17, 24, 34, 42, 55, 57, 64, 71], "matthieu": [3, 9, 14, 17, 77], "sozeau": [3, 9, 14, 17, 77], "equal": [3, 5, 8, 10, 11, 12, 13, 14, 17, 24, 25, 26, 30, 31, 32, 34, 35, 36, 39, 40, 42, 44, 46, 52, 54, 55, 57, 58, 60, 61, 65, 71, 72, 77], "equip": [3, 4, 17, 24, 27, 36, 42, 64], "equival": [3, 9, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 32, 34, 35, 36, 37, 38, 41, 42, 46, 51, 52, 53, 54, 55, 59, 60, 62, 64, 66, 67, 71, 75], "behav": [3, 11, 17, 24, 28, 29, 31, 34, 35, 43, 53, 54, 55, 57, 58, 60, 62, 64, 67, 71], "weaker": [3, 17, 24, 60], "g": [3, 4, 5, 8, 9, 10, 13, 14, 17, 24, 27, 28, 29, 30, 31, 34, 35, 36, 41, 43, 44, 46, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 75, 77], "system": [3, 8, 9, 11, 17, 24, 25, 26, 27, 28, 29, 32, 33, 34, 38, 39, 46, 51, 52, 53, 54, 55, 57, 59, 60, 62, 71, 73, 77], "toolbox": [3, 17], "extend": [3, 4, 5, 9, 10, 11, 14, 17, 24, 25, 26, 27, 28, 29, 32, 34, 35, 37, 40, 41, 42, 45, 51, 52, 53, 55, 59, 60, 71, 77], "capabl": [3, 17, 51, 53, 54, 55, 64], "document": [3, 8, 9, 11, 12, 16, 17, 24, 25, 42, 51, 52, 54, 55, 57, 59, 64, 65, 66, 67, 71, 72, 74, 76], "adapt": [3, 7, 17, 24, 51, 57, 63], "claudio": [3, 17, 24], "sacerdoti": [3, 17, 24], "coen": [3, 17, 24], "base": [3, 5, 10, 11, 12, 13, 14, 17, 24, 25, 29, 33, 35, 39, 42, 43, 44, 51, 52, 53, 54, 55, 57, 58, 60, 62, 63, 64, 66, 67, 71, 73, 74, 75, 77], "cl\u00e9ment": [3, 17], "renard": [3, 24], "implement": [3, 8, 11, 12, 13, 17, 24, 25, 29, 34, 35, 36, 37, 39, 43, 46, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 77], "drop": [3, 17, 51, 54, 59, 71], "old": [3, 11, 24, 25, 51, 53, 55, 58, 60, 66, 67], "complet": [3, 4, 5, 6, 7, 8, 9, 10, 11, 17, 24, 29, 30, 32, 34, 36, 40, 42, 51, 52, 53, 54, 57, 58, 59, 60, 62, 66, 67, 71], "typeclass": [3, 4, 5, 7, 17, 25, 35, 37, 38, 44, 45, 58, 60, 64, 66, 71], "infrastructur": [3, 25, 42, 53], "algorithm": [3, 7, 9, 11, 13, 17, 24, 25, 41, 51, 54, 57, 59, 62, 66, 77], "constraint": [3, 5, 8, 9, 10, 13, 17, 24, 25, 34, 35, 39, 43, 44, 51, 53, 54, 55, 58, 67, 71], "ml": [3, 5, 6, 8, 11, 17, 24, 25, 26, 29, 34, 36, 46, 51, 52, 53, 54, 57, 59, 60, 63, 64, 72, 77], "resolut": [3, 13, 17, 24, 25, 58, 60, 66, 71, 75], "anoth": [3, 4, 9, 11, 13, 14, 17, 24, 27, 31, 32, 34, 35, 40, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 62, 63, 64, 66, 67, 71], "pure": [3, 7, 11, 17, 55, 57, 64, 71, 72, 75], "again": [3, 13, 17, 24, 34, 42, 52, 53, 55, 57, 60, 64, 66, 71], "ordinari": [3, 17, 26, 37, 39, 71], "rocq": [3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 17, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 41, 42, 43, 44, 45, 46, 50, 52, 54, 55, 58, 59, 62, 63, 64, 65, 66, 67, 72, 73, 76], "manipul": [3, 9, 10, 17, 24, 25, 34, 37, 39, 55, 57, 63, 77], "put": [3, 5, 13, 14, 17, 34, 35, 43, 51, 53, 54, 57, 58, 59, 60, 66, 67, 71, 72, 75], "lemma": [3, 5, 11, 13, 14, 17, 24, 25, 32, 34, 35, 36, 38, 42, 44, 46, 54, 57, 58, 59, 60, 62, 64, 67, 72], "prove": [3, 5, 7, 8, 9, 11, 17, 24, 25, 27, 30, 32, 34, 35, 42, 43, 57, 58, 60, 62, 64, 72, 77], "higher": [3, 14, 17, 24, 25, 27, 40, 51, 54, 57, 58, 59, 60, 64, 67, 71, 73, 77], "depth": [3, 5, 13, 17, 29, 54, 57, 58, 59, 60, 62, 64, 71, 75], "solut": [3, 5, 13, 17, 42, 44, 58, 59, 63, 67], "fast": [3, 17, 24, 25, 53], "besid": [3, 17, 24, 34, 57], "necessari": [3, 4, 9, 13, 17, 24, 29, 31, 33, 37, 53, 55, 57, 59, 62, 64, 67, 71], "nicola": [3, 17, 77], "tabareau": [3, 17, 77], "glu": 3, "A": [3, 4, 5, 7, 9, 10, 11, 12, 13, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 50, 51, 52, 53, 54, 55, 57, 59, 60, 62, 63, 64, 66, 71, 72, 74, 75, 76, 77], "x1": [3, 9, 13, 17, 27, 42, 54, 57, 59, 60, 72], "t1": [3, 13, 17, 34, 42, 46, 57], "xn": [3, 9, 17, 57], "tn": [3, 13, 17, 57], "carrier": [3, 11, 14, 42, 57], "said": [3, 4, 17, 26, 34, 36, 42, 44, 55, 59, 71], "possibli": [3, 4, 17, 24, 34, 35, 42, 43, 51, 53, 54, 57, 59, 64, 67, 71, 73], "paramet": [3, 4, 5, 7, 8, 13, 14, 17, 24, 25, 28, 29, 34, 37, 40, 41, 42, 43, 44, 53, 54, 55, 58, 59, 60, 64, 66, 67, 71, 72], "finit": [3, 5, 17, 24, 30, 34], "unord": [3, 17, 57], "set_eq": 3, "satisfi": [3, 4, 5, 11, 13, 14, 17, 30, 34, 35, 54, 55, 59, 64, 67, 71], "convert": [3, 4, 12, 13, 14, 17, 25, 26, 34, 37, 41, 44, 54, 55, 57, 58, 64, 67], "reflex": [3, 5, 6, 11, 13, 17, 24, 27, 34, 36, 51, 54, 57, 59, 60, 62, 64, 66, 67, 71], "symmetri": [3, 17, 24, 34, 44, 57, 60, 64], "transit": [3, 7, 8, 13, 14, 17, 24, 25, 26, 35, 41, 44, 51, 54, 57, 58, 59, 60, 64, 66, 74], "symmetr": [3, 17, 24, 31, 59, 64, 71], "a1": [3, 27, 34, 46, 57, 58, 71], "a2": [3, 27, 34, 58], "covariantli": 3, "r1": [3, 5, 17, 27, 41, 44, 57, 59], "r2": [3, 17, 27, 41, 44, 57, 59], "whenev": [3, 7, 14, 17, 27, 29, 42, 55, 57, 62, 64, 67, 71], "imag": [3, 11, 17, 24, 51, 52, 66], "input": [3, 4, 9, 10, 13, 14, 17, 25, 27, 29, 35, 44, 46, 51, 54, 57, 58, 60, 64, 71, 72, 74, 75], "monoton": [3, 4, 17], "i_": [3, 34, 57], "r_1": 3, "r_2": 3, "notic": [3, 4, 5, 17, 26, 34, 35, 38, 46, 51, 52, 54, 57, 58, 64, 66, 71, 72, 74], "arrow": [3, 4, 14, 17, 52, 57, 60, 64, 67], "reader": [3, 11, 24, 29, 31, 42, 57], "between": [3, 4, 10, 11, 13, 14, 17, 24, 25, 26, 27, 29, 33, 34, 38, 39, 43, 44, 46, 51, 52, 53, 54, 57, 58, 60, 64, 65, 67, 71, 72, 75], "introduc": [3, 5, 8, 10, 11, 13, 14, 17, 24, 25, 28, 30, 31, 34, 35, 37, 38, 43, 44, 46, 51, 52, 55, 57, 58, 59, 60, 62, 66, 67, 71, 72, 75], "straightforwardli": 3, "ari": [3, 17, 34], "simultan": [3, 17, 24, 25, 26, 30, 32, 34, 42, 53, 57, 58], "everi": [3, 9, 11, 12, 13, 14, 17, 28, 29, 34, 40, 51, 52, 54, 55, 57, 58, 64, 71], "argument": [3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 17, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 38, 40, 42, 43, 45, 51, 52, 54, 55, 58, 59, 60, 62, 64, 66, 72, 75], "invers": [3, 11, 17, 24, 25, 31, 58, 60, 64, 72, 77], "t_1": [3, 26, 31, 34, 35], "ldot": [3, 7, 34], "t_n": [3, 26, 34, 66], "union": [3, 13, 17, 54, 59, 66, 77], "append": [3, 17, 29, 35, 43, 53, 54, 66, 75], "binari": [3, 5, 7, 11, 14, 17, 24, 29, 37, 42, 51, 53, 57, 58, 60, 64, 71], "latter": [3, 11, 17, 28, 34, 35, 42, 51, 54, 55, 57, 58, 64, 66, 67, 75], "condit": [3, 4, 9, 11, 17, 24, 25, 30, 50, 53, 59, 60, 63, 64, 66, 67], "s1": [3, 30, 38, 57], "s2": [3, 30], "divis": [3, 11, 17, 24, 25, 57], "rdiv": [3, 5], "le": [3, 5, 13, 14, 17, 24, 27, 42, 46, 52, 55, 57, 64, 67, 77], "usual": [3, 8, 9, 12, 17, 25, 26, 27, 28, 30, 34, 35, 37, 40, 43, 44, 46, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 74, 75], "leibniz": [3, 5, 7, 11, 13, 17, 24, 25, 27, 35, 40, 57, 58, 67], "unfortun": [3, 5, 17, 42, 46, 57], "intend": [3, 17, 24, 28, 32, 39, 51, 57, 64, 66, 71], "next": [3, 9, 13, 17, 24, 27, 29, 33, 34, 42, 44, 46, 51, 52, 54, 55, 57, 60, 64, 65, 66, 67, 71], "section": [3, 5, 6, 7, 8, 9, 10, 11, 12, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 40, 41, 42, 43, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 65, 67, 71, 74], "deal": [3, 5, 8, 13, 17, 24, 25, 42, 46, 57, 60, 64, 71, 72], "exact": [3, 12, 14, 17, 24, 25, 35, 40, 43, 53, 54, 55, 58, 59, 60, 64, 66, 67, 71], "goal": [3, 6, 7, 8, 9, 12, 13, 14, 17, 24, 25, 27, 29, 31, 34, 35, 36, 37, 38, 42, 43, 44, 52, 53, 59, 60, 61, 62, 64, 71, 72, 74], "howev": [3, 4, 5, 9, 12, 13, 14, 17, 24, 27, 29, 34, 36, 37, 41, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 64, 66, 67, 71, 72], "verifi": [3, 7, 9, 11, 14, 17, 24, 25, 29, 31, 32, 33, 35, 51, 60, 66], "verif": [3, 24, 25, 32, 66, 67, 77], "consist": [3, 4, 5, 11, 13, 14, 17, 24, 27, 30, 31, 34, 35, 52, 55, 57, 58, 59, 64, 65, 66, 71], "composit": [3, 71], "some": [3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 37, 38, 40, 41, 42, 44, 45, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 71, 72, 73, 75], "obviou": [3, 34, 57, 71], "suppos": [3, 9, 17, 55, 57, 64], "hypothesi": [3, 9, 11, 17, 24, 25, 27, 28, 29, 34, 38, 55, 57, 59, 60, 62, 64, 66, 67, 71, 72, 75], "h": [3, 4, 6, 9, 11, 12, 13, 14, 17, 24, 27, 34, 40, 44, 46, 51, 54, 55, 57, 58, 62, 64, 66, 67, 72, 75, 77], "These": [3, 11, 13, 14, 17, 24, 25, 27, 28, 29, 31, 32, 34, 36, 37, 38, 40, 52, 53, 54, 55, 57, 58, 60, 64, 66, 67, 71, 72, 73], "attribut": [3, 5, 9, 13, 14, 16, 25, 28, 30, 32, 34, 37, 40, 41, 42, 44, 51, 54, 55, 59, 60, 62, 64, 66, 71, 74], "univers": [3, 4, 8, 9, 12, 13, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 37, 39, 40, 44, 46, 51, 54, 57, 59, 62, 66, 67, 71, 77], "add": [3, 4, 5, 8, 9, 10, 11, 13, 14, 17, 24, 25, 29, 31, 32, 34, 37, 41, 42, 44, 46, 51, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 73, 75], "one_term": [3, 5, 7, 11, 13, 29, 34, 54, 58, 60, 62, 64, 67, 71, 72], "aeq": 3, "\u03b1": [3, 14, 25, 54, 55, 57], "typeabl": 3, "fresh": [3, 14, 17, 24, 25, 31, 34, 53, 57, 58, 64, 66, 67, 71], "intern": [3, 5, 11, 14, 17, 24, 25, 31, 34, 37, 44, 51, 53, 54, 55, 58, 60, 62, 66, 67, 71, 72, 73, 74, 77], "although": [3, 5, 9, 17, 35, 37, 53, 55, 57, 58, 60, 64, 66], "depart": 3, "To": [3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 17, 24, 25, 27, 29, 30, 32, 34, 37, 39, 41, 42, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 64, 66, 67, 71, 72, 74, 75], "eq": [3, 5, 11, 14, 17, 27, 35, 40, 42, 54, 57, 58, 59, 64, 67, 71], "refl_equ": [3, 17, 57], "properti": [3, 4, 6, 9, 11, 12, 13, 17, 24, 25, 26, 27, 30, 31, 32, 34, 38, 39, 42, 45, 46, 57, 58, 67, 72, 77], "deriv": [3, 5, 9, 13, 17, 24, 25, 26, 30, 34, 38, 40, 54, 64, 66, 73], "autorewrit": [3, 17, 24, 60], "abl": [3, 8, 11, 13, 14, 17, 24, 25, 34, 42, 44, 46, 51, 53, 55, 57, 58, 59, 61, 62, 67], "defined": 3, "interact": [3, 6, 10, 13, 17, 24, 25, 32, 33, 37, 38, 40, 42, 43, 52, 59, 65, 66, 67, 71, 75, 76, 77], "denot": [3, 4, 11, 17, 24, 26, 28, 29, 30, 34, 35, 39, 40, 42, 43, 52, 54, 57, 58, 67, 71], "small": [3, 5, 8, 11, 14, 17, 25, 26, 33, 34, 39, 42, 44, 52, 53, 57, 64], "theori": [3, 4, 5, 11, 17, 24, 25, 26, 27, 28, 29, 39, 42, 46, 51, 53, 57, 58, 60, 62, 67, 71, 77], "homogen": [3, 17], "export": [3, 5, 8, 9, 11, 13, 17, 24, 29, 35, 38, 51, 52, 54, 55, 59, 60, 71], "relation_definit": [3, 13, 17, 42, 59], "eq_set": 3, "axiom": [3, 6, 7, 9, 10, 11, 12, 14, 17, 24, 25, 27, 28, 29, 30, 31, 32, 34, 35, 36, 38, 42, 44, 51, 52, 54, 57, 58, 59, 60, 64, 66, 67, 71, 72, 74], "eq_set_refl": 3, "eq_set_sym": 3, "eq_set_tran": 3, "empty_neutr": 3, "union_compat": 3, "eq_set_rel": 3, "eq_set_rel_rel": 3, "eq_set_rel_reflex": 3, "eq_set_rel_symmetr": 3, "eq_set_rel_transit": 3, "union_mor": 3, "x0": [3, 13, 17, 37, 43, 44, 54, 66, 71], "y0": [3, 13, 43], "No": [3, 5, 6, 9, 11, 12, 13, 14, 17, 24, 25, 26, 30, 34, 35, 36, 40, 42, 44, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74], "qed": [3, 5, 6, 8, 9, 12, 13, 14, 17, 24, 29, 32, 34, 36, 38, 40, 42, 51, 52, 54, 57, 58, 59, 60, 62, 64, 66, 67, 72], "reduc": [3, 7, 8, 10, 11, 12, 13, 17, 24, 26, 31, 32, 34, 36, 37, 40, 41, 44, 51, 53, 57, 58, 59, 60, 64, 66, 67, 71], "burden": [3, 63], "maxim": [3, 13, 17, 25, 41, 51, 57, 71, 77], "insert": [3, 4, 9, 12, 13, 17, 24, 25, 29, 41, 46, 52, 53, 55, 57, 66, 71, 75], "write": [3, 4, 8, 11, 13, 14, 17, 24, 25, 26, 27, 29, 31, 32, 33, 34, 38, 39, 43, 51, 53, 54, 55, 57, 58, 59, 63, 66, 67, 71, 73, 75], "proce": [3, 11, 13, 52, 57, 71], "simpl": [3, 4, 10, 11, 17, 24, 25, 29, 37, 41, 42, 43, 46, 52, 53, 54, 57, 58, 59, 60, 62, 67, 72], "step": [3, 5, 7, 11, 13, 17, 24, 25, 26, 29, 41, 51, 52, 53, 54, 58, 60, 64, 65, 67], "applic": [3, 5, 10, 11, 13, 14, 17, 24, 25, 26, 29, 30, 35, 36, 37, 41, 46, 52, 55, 57, 59, 60, 64, 66, 67, 71, 72, 77], "establish": [3, 17, 57], "intro": [3, 5, 11, 12, 13, 17, 24, 25, 34, 42, 43, 44, 52, 54, 55, 60, 62, 64, 66, 67, 71, 72], "manag": [3, 13, 17, 24, 25, 32, 38, 51, 53, 57, 59, 60, 62, 73], "hypothes": [3, 5, 9, 13, 17, 24, 25, 28, 32, 34, 51, 57, 60, 62, 64, 67, 71], "One": [3, 8, 9, 13, 14, 17, 25, 31, 32, 34, 37, 38, 39, 44, 51, 53, 54, 55, 59, 60, 64, 66, 67, 71, 75], "cmd": [3, 17, 38, 51, 52, 54], "exist": [3, 4, 5, 9, 11, 13, 14, 17, 25, 26, 27, 28, 29, 31, 32, 34, 36, 37, 39, 41, 42, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 63, 64, 66, 67, 71, 74], "outsid": [3, 5, 9, 11, 12, 13, 14, 17, 28, 29, 35, 38, 40, 41, 42, 43, 53, 54, 59, 60, 66, 71], "suffix": [3, 17, 35, 51, 52, 53, 54, 57, 59, 71, 75], "_morphism": 3, "modifi": [3, 4, 8, 11, 13, 14, 17, 24, 25, 29, 36, 38, 41, 51, 52, 54, 55, 57, 58, 64, 66, 67, 71], "themselv": [3, 13, 14, 17, 26, 35, 37, 39, 41, 42, 53, 57, 59, 64, 71], "exploit": [3, 17, 24, 57, 67], "monotoni": 3, "hand": [3, 10, 12, 13, 17, 25, 27, 29, 33, 35, 52, 53, 54, 55, 57, 58, 64, 67, 71, 72], "partial": [3, 13, 17, 24, 34, 35, 37, 44, 51, 53, 54, 57, 59, 62, 66, 71, 72], "domain": [3, 5, 11, 14, 17, 24, 25, 26, 34, 42, 61, 64, 71], "compris": [3, 24], "eqo": 3, "smallest": [3, 5, 27, 34, 67], "nonzero": [3, 11, 37, 54], "eq0": 3, "open": [3, 5, 6, 11, 13, 17, 25, 27, 35, 36, 38, 50, 52, 54, 55, 57, 59, 60, 64, 66], "addit": [3, 4, 5, 8, 9, 13, 17, 24, 25, 27, 29, 31, 34, 35, 39, 51, 52, 53, 54, 55, 58, 59, 62, 64, 65, 66, 67, 71, 72, 73], "up": [3, 8, 13, 17, 24, 25, 26, 31, 34, 35, 38, 42, 43, 52, 53, 54, 55, 57, 58, 64, 66, 67, 71, 75], "longer": [3, 9, 17, 24, 31, 34, 38, 44, 52, 53, 58, 66, 67, 71], "posit": [3, 4, 5, 7, 9, 10, 11, 14, 17, 24, 25, 30, 36, 37, 39, 41, 44, 46, 51, 52, 54, 55, 57, 58, 59, 64, 66, 67, 71], "z": [3, 5, 7, 11, 13, 14, 17, 24, 26, 27, 28, 29, 34, 35, 37, 40, 41, 42, 43, 44, 54, 55, 57, 58, 59, 60, 64, 66, 67, 71], "lt": [3, 9, 13, 17, 27, 42, 71, 72], "increas": [3, 5, 8, 17, 24, 53, 57, 62], "decreas": [3, 7, 9, 17, 30, 34, 55, 59, 72], "dualli": [3, 44, 57], "hold": [3, 4, 17, 30, 34, 35, 40, 42, 55, 58, 75], "On": [3, 10, 12, 17, 24, 27, 30, 32, 37, 40, 44, 46, 51, 52, 53, 54, 57, 58, 64, 71], "contrari": [3, 4, 9, 13, 17, 30, 40, 44, 57, 67], "messag": [3, 4, 8, 11, 12, 13, 14, 16, 17, 24, 26, 28, 29, 30, 34, 35, 37, 40, 41, 42, 43, 44, 46, 51, 52, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 74], "rewritten": [3, 9, 11, 24, 30, 46, 57, 58, 64], "compos": [3, 4, 34, 44, 57, 67, 71], "propag": [3, 11, 17, 41], "varianc": [3, 17], "annot": [3, 9, 14, 17, 24, 25, 27, 34, 41, 42, 45, 51, 53, 55, 57, 66], "switch": [3, 8, 13, 14, 17, 24, 25, 51, 53, 66], "travers": [3, 17, 57, 58, 67], "detail": [3, 5, 7, 14, 25, 31, 36, 37, 41, 42, 51, 52, 55, 57, 58, 59, 64, 66, 71, 72, 74, 75], "contravariantli": 3, "differ": [3, 4, 9, 11, 13, 14, 15, 17, 24, 25, 26, 29, 31, 34, 35, 37, 38, 41, 43, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 67, 71, 72, 73, 75, 77], "duplic": [3, 11, 17, 43, 57, 67, 71], "multiset_eq": 3, "repeat": [3, 17, 25, 43, 44, 52, 55, 57, 58, 59, 66, 67], "request": [3, 14, 17, 25, 43, 51, 64], "unclear": [3, 10, 54], "analog": [3, 17, 34, 54, 57, 58, 66], "crelat": 3, "cmorphism": [3, 17], "cequival": 3, "rewriterel": [3, 17, 57], "index": [3, 13, 17, 24, 25, 26, 27, 29, 39, 40, 44, 52, 58, 60, 64, 66, 67, 73, 75], "iff": [3, 17, 26, 27, 31, 57, 59, 71], "impl": [3, 5, 59], "flip": [3, 17], "pointwis": 3, "simpli": [3, 4, 11, 13, 14, 17, 24, 31, 39, 54, 55, 57, 59, 62, 67, 71, 75], "machineri": [3, 17, 57], "infer": [3, 4, 9, 10, 13, 14, 24, 25, 26, 34, 37, 40, 41, 42, 45, 46, 51, 57, 58, 60, 62, 67, 71], "face": [3, 17, 75], "situat": [3, 4, 11, 17, 46, 54, 57, 71], "instanti": [3, 10, 13, 14, 17, 24, 34, 35, 43, 44, 54, 55, 57, 58, 60, 62, 67, 71], "discharg": [3, 14, 17, 24, 25, 28, 38, 72], "That": [3, 27, 29, 30, 34, 36, 52, 54, 55, 58, 64, 66], "variou": [3, 16, 17, 24, 25, 28, 29, 34, 44, 51, 52, 53, 55, 57, 58, 59, 60, 64, 66, 71], "hint": [3, 13, 14, 17, 24, 25, 27, 35, 38, 54, 62, 64, 75], "databas": [3, 13, 17, 25, 54, 57, 62, 64], "refl": [3, 17], "sym": [3, 17, 44], "tran": [3, 17], "id": [3, 4, 9, 10, 14, 17, 24, 26, 34, 35, 42, 44, 51, 52, 53, 54, 55, 57, 58, 64, 66, 71, 75], "equivalence_reflex": [3, 59], "equivalence_symmetr": [3, 59], "equivalence_transit": 3, "amount": [3, 5, 8, 14, 17, 51, 54, 58], "relationclass": [3, 17, 64], "further": [3, 17, 30, 35, 41, 51, 52, 54, 55, 57, 64, 66, 67, 71], "explan": [3, 13, 37, 45, 51, 58, 59, 67], "encod": [3, 13, 17, 24, 25, 27, 34, 53, 71, 75], "car": 3, "eq_rel": 3, "eq_rel_rel": 3, "eq_rel_reflex": 3, "eq_rel_symmetr": 3, "eq_rel_transit": 3, "x2": [3, 27, 42, 59, 60, 72], "apply_mor": 3, "setoid_": [3, 17], "moreov": [3, 5, 17, 28, 44, 46, 51, 52, 57, 62, 71], "unprefix": 3, "fall": [3, 9, 10, 13, 24, 53], "back": [3, 9, 14, 17, 24, 51, 52, 54, 57, 59, 66, 67], "involv": [3, 4, 9, 12, 17, 24, 25, 26, 34, 41, 42, 51, 52, 53, 54, 57, 59, 60, 62, 64, 67], "pass": [3, 5, 8, 10, 12, 17, 24, 37, 38, 42, 51, 52, 53, 54, 55, 57, 60, 64, 66, 67, 71, 75], "etransit": [3, 17, 43, 64], "one_term_with_bind": [3, 58, 64, 67, 72], "rewrite_occ": [3, 64], "int_or_var": [3, 54, 66, 71], "ltac_expr3": [3, 29, 54, 58, 64, 66], "defaultrel": 3, "By": [3, 4, 5, 11, 12, 13, 14, 17, 29, 37, 44, 46, 51, 53, 54, 55, 57, 60, 64, 66, 67, 71], "recent": [3, 24, 25, 53, 71], "environ": [3, 8, 9, 11, 12, 13, 14, 17, 24, 25, 26, 28, 30, 31, 32, 34, 35, 38, 42, 43, 52, 53, 55, 57, 60, 62, 64, 66, 67, 71, 72, 75], "simul": [3, 17, 24, 57, 66], "understand": [3, 5, 10, 12, 15, 17, 24, 25, 29, 33, 51, 53, 54, 55, 59, 60], "congruenc": [3, 12, 17, 24, 25, 34, 54, 62, 64, 67], "pack": [3, 42, 53], "slightli": [3, 17, 24, 35, 51, 52, 54, 55, 57, 58, 67], "permut": [3, 17, 25, 55, 57], "bi": 3, "implic": [3, 17, 26, 27, 28, 42, 54, 57, 60, 66, 67, 71], "port": [3, 17, 24, 55, 72], "semant": [3, 11, 13, 14, 17, 24, 25, 26, 29, 35, 36, 39, 41, 44, 53, 54, 57, 58, 71, 77], "limit": [3, 5, 9, 10, 13, 14, 17, 24, 25, 29, 35, 41, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 63, 64, 66, 71, 72], "lift": [3, 12, 14, 17], "were": [3, 11, 13, 17, 24, 34, 35, 36, 38, 42, 44, 51, 53, 54, 55, 59, 60, 66, 71, 72, 75], "discuss": [3, 17, 24, 25, 54], "setoid_rewrit": [3, 17, 24, 60, 64], "head": [3, 10, 13, 14, 17, 24, 26, 30, 35, 41, 42, 44, 53, 54, 55, 57, 58, 59, 60, 64, 67, 71], "constr": [3, 5, 14, 17, 24, 34, 42, 54, 55, 57, 71], "bind": [3, 9, 10, 14, 17, 24, 25, 28, 32, 34, 35, 37, 40, 43, 44, 46, 51, 54, 57, 64, 66, 67, 72], "construct": [3, 4, 5, 8, 9, 10, 11, 13, 14, 17, 25, 27, 28, 29, 30, 31, 33, 35, 41, 42, 43, 46, 52, 53, 55, 57, 58, 62, 63, 64, 65, 66, 67, 71, 77], "ex": [3, 17, 24, 27, 44, 58, 67, 71], "existenti": [3, 6, 9, 10, 13, 17, 24, 25, 26, 34, 41, 45, 54, 58, 59, 60, 64, 66, 67], "morphisms_prop": [3, 17], "all_iff_morph": 3, "pointwise_rel": 3, "simpl_rel": [3, 17], "predic": [3, 9, 17, 24, 25, 26, 27, 30, 34, 40, 42, 54, 60, 64, 77], "onc": [3, 8, 9, 10, 11, 13, 14, 17, 24, 25, 27, 32, 34, 41, 42, 44, 46, 51, 53, 55, 57, 58, 59, 60, 64, 66, 67, 71, 72], "implicitli": [3, 13, 14, 17, 24, 34, 51, 55, 59, 60, 64], "inde": [3, 4, 11, 12, 13, 14, 17, 25, 26, 29, 30, 34, 35, 40, 41, 42, 43, 44, 46, 53, 54, 55, 57, 58, 60, 64, 66, 67, 71, 72], "surround": [3, 17, 44, 57, 59, 71], "whatev": [3, 44, 64, 75], "map_morph": 3, "eqa": [3, 13], "eqb": [3, 5, 13, 17, 36, 59], "list_equiv": 3, "parameter": [3, 5, 11, 14, 17, 24, 25, 28, 37, 40, 54], "captur": [3, 17, 34, 44, 57, 64, 71], "bound": [3, 5, 6, 7, 10, 14, 17, 24, 25, 26, 28, 31, 32, 34, 39, 41, 42, 44, 46, 52, 54, 55, 57, 58, 59, 60, 62, 64, 72], "With": [3, 4, 13, 14, 17, 46, 53, 57, 58, 67, 71], "subterm": [3, 9, 10, 11, 17, 24, 25, 31, 34, 41, 54, 55, 57, 58, 59, 64, 66, 67, 71, 72], "almost": [3, 17, 57, 67, 75], "recov": [3, 8, 14, 17, 30, 46, 51, 54, 67], "smaller": [3, 11, 14, 17, 32, 33, 34, 53, 58, 62, 67, 72], "dual": [3, 9, 24, 55], "why": [3, 11, 17, 34, 37, 43, 55], "conjunct": [3, 5, 11, 17, 24, 34, 57, 59, 60, 67, 71], "suffici": [3, 5, 11, 13, 53], "aris": [3, 9, 13, 17, 30, 67, 71], "through": [3, 4, 12, 17, 24, 28, 29, 30, 32, 34, 35, 36, 37, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 65, 66, 67, 71, 72, 73, 74], "prime": [3, 17, 29, 34, 57], "space": [3, 17, 29, 52, 53, 57, 59, 66, 71, 74, 75], "rewrite_strat": [3, 17], "rule": [3, 4, 5, 11, 12, 13, 14, 17, 24, 25, 29, 32, 33, 35, 36, 37, 39, 41, 42, 44, 46, 51, 53, 54, 55, 58, 59, 60, 62, 66, 67, 77], "slow": [3, 11, 17, 53, 54, 55], "down": [3, 14, 24, 25, 45, 51, 52, 54, 55, 57, 59], "wherea": [3, 17, 29, 54, 55, 57, 58, 62, 74], "opaqu": [3, 6, 8, 9, 14, 17, 24, 25, 31, 32, 35, 38, 51, 57, 59, 60, 64, 66, 67, 71, 75], "caus": [3, 8, 12, 14, 17, 32, 51, 52, 53, 54, 55, 57, 58, 59, 63, 64, 66, 71, 75], "miss": [3, 5, 10, 13, 17, 24, 35, 43, 51, 52, 55, 57, 58, 62, 64, 71, 75], "configur": [3, 8, 17, 24, 25, 29, 40, 51, 52, 59, 64, 66, 73], "transpar": [3, 4, 6, 9, 14, 17, 24, 25, 31, 32, 35, 37, 41, 51, 54, 55, 57, 59, 60, 64, 66, 67, 75], "unif": [3, 10, 13, 17, 24, 25, 37, 40, 42, 43, 54, 60, 64, 71], "eauto": [3, 17, 25, 43, 54, 57, 60], "individu": [3, 17, 53, 55, 64, 67, 71], "double_f": 3, "unifi": [3, 12, 13, 14, 17, 34, 41, 42, 43, 54, 57, 58, 64, 66], "assert_succe": [3, 17, 25], "bottomup": 3, "hide": [3, 17, 25, 34, 41, 44, 57, 58, 66, 71], "side": [3, 10, 13, 14, 17, 24, 25, 27, 32, 34, 35, 38, 43, 52, 54, 55, 57, 58, 60, 62, 64, 67, 71], "behind": [3, 4, 17, 28, 34, 57], "assert_fail": [3, 17, 25], "disallow": [3, 12, 14, 17, 37, 51], "substitut": [3, 10, 11, 17, 24, 25, 26, 34, 38, 46, 51, 55, 57, 58, 64, 67, 71], "distinct": [3, 9, 13, 17, 26, 34, 42, 44, 46, 53, 54, 55, 57, 60, 64, 67, 71], "eq_refl": [3, 5, 9, 11, 12, 13, 14, 17, 27, 40, 64, 66, 67, 71], "resolv": [3, 9, 13, 14, 17, 35, 43, 52, 55, 57, 58, 59, 60, 64, 66, 67, 71], "treat": [3, 9, 12, 13, 17, 29, 46, 53, 54, 57, 59, 60, 62, 64, 67, 71, 72], "lot": [3, 11, 17, 24, 52, 55], "tri": [3, 4, 5, 9, 13, 14, 17, 34, 35, 41, 46, 52, 53, 54, 55, 57, 58, 59, 60, 62, 66, 67], "speed": [3, 13, 17, 24, 34, 64], "abbrevi": [3, 4, 5, 13, 14, 17, 24, 25, 27, 32, 35, 38, 59, 74], "typeclass_inst": [3, 13, 17, 60], "strat": 3, "rewstrategi": [3, 17], "conclus": [3, 11, 13, 17, 24, 28, 34, 54, 55, 57, 58, 60, 64, 66, 67, 71], "noth": [3, 17, 38, 41, 51, 54, 55, 57, 58, 60, 62, 64, 66, 67], "didn": [3, 17, 51, 53], "progress": [3, 17, 24, 25, 51, 52, 55, 60, 66, 77], "succeed": [3, 17, 54, 59, 72], "unabl": [3, 14, 34, 43, 46, 53, 57, 58, 59, 66, 67], "basic": [3, 9, 11, 17, 24, 25, 32, 33, 34, 35, 37, 40, 42, 44, 46, 51, 58, 59, 60, 63, 66, 67, 73], "db": [3, 17], "topdown": 3, "creat": [3, 8, 9, 13, 17, 24, 25, 29, 34, 38, 40, 42, 51, 52, 53, 54, 57, 58, 59, 64, 66, 67, 72, 75], "procedur": [3, 4, 11, 17, 24, 25, 54, 57, 60, 62, 64, 77], "programm": [3, 24, 25, 65], "visser": [3, 77], "et": [3, 24, 77], "al": [3, 57], "lv97": [3, 77], "vbt98": [3, 77], "core": [3, 13, 17, 24, 25, 27, 29, 41, 45, 51, 57, 59, 60, 62, 65, 71], "stratego": [3, 77], "transform": [3, 4, 11, 17, 29, 57, 58, 66, 67, 77], "languag": [3, 9, 11, 14, 26, 29, 36, 37, 39, 40, 41, 46, 53, 54, 63, 64, 65, 66, 74, 75, 77], "vis01": [3, 77], "rewstrategy1": [3, 17], "choic": [3, 17, 27, 34, 51, 52, 55, 62, 71, 75], "rewstrategy0": 3, "eval": [3, 5, 12, 14, 17, 24, 25, 29, 30, 31, 32, 35, 37, 42, 51, 52, 53, 55, 59], "red_expr": [3, 17, 32, 54, 64], "fold": [3, 17, 37, 57], "failur": [3, 8, 13, 14, 17, 24, 25, 46, 53, 55, 57, 59, 60, 62, 64, 71, 77], "catch": [3, 17, 25, 42, 46, 57], "zero": [3, 7, 11, 17, 26, 27, 37, 42, 46, 53, 54, 55, 58, 59, 60, 64], "nest": [3, 9, 17, 24, 25, 29, 32, 35, 38, 40, 54, 57, 58, 59, 64, 66, 71, 75], "andbc": [3, 57], "bottom": [3, 17, 37, 46, 52, 54, 55, 58, 64, 71], "top": [3, 8, 10, 12, 13, 14, 17, 24, 25, 29, 35, 37, 46, 51, 52, 53, 54, 55, 57, 58, 59, 64, 67, 71, 73, 75], "oper": [3, 5, 9, 10, 11, 14, 17, 24, 25, 27, 32, 34, 36, 51, 52, 54, 55, 57, 60, 64, 66, 67, 71], "texttt": 3, "conceptu": [3, 34], "straightforward": [3, 55], "root": [3, 17, 25, 27, 46, 51], "iter": [3, 5, 13, 17, 25, 26, 28, 30, 71], "consider": [3, 9, 17, 37, 39, 46, 64, 67, 71], "stop": [3, 5, 12, 17, 24, 32, 38, 52, 54, 57, 71], "Their": [3, 17, 32, 34, 39, 55, 57, 59, 71], "mani": [3, 8, 11, 13, 14, 17, 24, 25, 27, 29, 33, 34, 35, 39, 42, 51, 52, 53, 54, 55, 57, 58, 60, 64, 66, 71, 73], "stronger": [3, 12, 17, 34], "interpret": [3, 5, 9, 11, 13, 17, 24, 25, 27, 29, 32, 34, 35, 41, 44, 51, 52, 53, 54, 55, 59, 75], "ssrbool": [3, 17, 57], "ssrmatch": [3, 17, 57], "scope": [3, 5, 11, 17, 24, 25, 27, 29, 32, 36, 38, 43, 45, 52, 54, 55, 57, 59, 60, 64, 66], "bool_scop": [3, 17, 41, 71], "abort": [3, 11, 17, 34, 42, 44, 54, 55, 57, 64, 66, 67], "amokran": [4, 24], "sa\u00efbi": [4, 24], "prover": [4, 5, 15, 17, 24, 26, 29, 31, 33, 52, 55, 59, 65, 73, 75, 76], "power": [4, 5, 11, 17, 24, 54, 57, 67, 71, 72], "our": [4, 5, 7, 11, 17, 24, 34, 35, 54], "determin": [4, 13, 17, 31, 34, 36, 40, 41, 43, 53, 54, 57, 58, 64, 66, 67, 71, 72, 75], "appropri": [4, 13, 14, 17, 29, 53, 55, 57, 59, 62, 64, 66, 67, 75], "sens": [4, 24, 26, 30, 54, 55, 57, 71], "subtyp": [4, 9, 14, 17, 25, 31, 35, 39, 77], "certain": [4, 11, 17, 24, 29, 44, 46, 51, 54, 57, 58, 59, 64, 67, 71], "categori": [4, 8, 13, 17, 35, 51, 59, 61, 74, 75], "biject": [4, 17], "morphism": [4, 11, 17, 25, 59, 71], "famili": [4, 14, 17, 24, 25, 34, 40, 54, 55, 63, 67, 71], "coercion_class": [4, 71], "user": [4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 17, 25, 29, 32, 33, 34, 35, 36, 37, 39, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 57, 58, 59, 61, 62, 64, 65, 66, 67, 71, 72, 73, 74, 75, 76, 77], "sortclass": [4, 17, 57, 71], "funclass": [4, 17, 41, 71], "formal": [4, 6, 10, 17, 24, 25, 26, 29, 31, 32, 34, 37, 39, 41, 51, 55, 57, 67, 77], "don": [4, 10, 13, 14, 17, 28, 34, 35, 37, 46, 52, 53, 54, 57, 58, 60, 62, 64, 66], "confus": [4, 10, 13, 17, 24, 26, 29, 34, 44, 46, 52, 55, 57, 71], "target": [4, 11, 17, 25, 51, 58, 71], "x\u2081": 4, "a\u2081": 4, "x\u2096": 4, "a\u2096": 4, "v\u2081": 4, "v\u2099": [4, 55], "u\u2081": 4, "u\u2098": 4, "new": [4, 5, 6, 8, 10, 13, 14, 15, 25, 27, 29, 31, 32, 34, 36, 37, 39, 42, 43, 46, 51, 52, 54, 55, 58, 59, 60, 61, 64, 66, 67, 71, 72, 73, 75, 77], "ignor": [4, 13, 14, 17, 24, 29, 31, 34, 35, 44, 51, 52, 53, 54, 57, 58, 60, 64, 66, 71], "exactli": [4, 10, 11, 13, 17, 26, 27, 34, 40, 42, 44, 46, 51, 52, 54, 55, 57, 59, 66, 67, 71], "uniform": [4, 17, 24, 34, 40, 44, 54, 55], "recommend": [4, 8, 13, 14, 15, 17, 32, 35, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 72, 74, 75], "guarante": [4, 14, 17, 51, 52, 53, 55], "spuriou": [4, 17, 57, 71], "coerc": [4, 41, 57, 60, 64], "t\u2081": 4, "t\u2099": 4, "toward": [4, 17, 53], "intuit": [4, 11, 17, 24, 29, 55, 58, 62], "synthes": [4, 17, 24, 27, 28, 42, 46, 77], "precis": [4, 8, 13, 17, 24, 26, 29, 31, 33, 34, 35, 37, 39, 46, 51, 57, 64, 71], "doesn": [4, 14, 17, 29, 31, 35, 46, 51, 52, 53, 54, 55, 57, 58, 59, 62, 66, 67, 71, 73], "look": [4, 8, 9, 11, 13, 14, 16, 17, 25, 51, 53, 54, 55, 57, 58, 59, 60, 66, 67, 71, 72, 75], "incom": [4, 17], "necessarili": [4, 46, 67, 72], "semi": [4, 11, 17], "lattic": 4, "forget": [4, 11, 37, 55, 59, 60, 67], "harder": [4, 17, 58], "There": [4, 9, 10, 11, 14, 17, 24, 25, 26, 27, 28, 29, 34, 37, 38, 39, 40, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 63, 64, 66, 67, 71, 72, 75], "subclass": [4, 10, 13, 27, 39, 42, 59], "oldest": [4, 17], "notat": [4, 5, 9, 10, 11, 14, 24, 25, 26, 28, 29, 31, 33, 34, 35, 36, 37, 38, 40, 41, 45, 46, 51, 52, 53, 57, 58, 60, 64, 67, 73, 74, 75, 77], "f\u2081": 4, "f\u2096": 4, "ident_decl": [4, 9, 13, 28, 30, 32, 34, 37, 38, 40, 42, 59], "def_bodi": [4, 32, 38, 42], "unspecifi": [4, 14, 17, 43, 55, 62, 67], "ye": [4, 9, 11, 14, 17, 29, 34, 37, 42, 51, 53, 59, 67], "field": [4, 5, 7, 12, 13, 14, 17, 24, 25, 42, 51, 53, 55, 59, 61, 74], "nonuniform": [4, 17], "silenc": [4, 17, 24, 41, 46, 57, 62, 74], "18": [4, 13, 25, 57, 58, 59, 60, 64], "futur": [4, 9, 10, 13, 14, 17, 32, 41, 51, 52, 53, 57, 62, 66, 71, 77], "ambigu": [4, 17, 25, 46, 53, 57, 59, 60, 66, 71], "yield": [4, 11, 17, 24, 31, 46, 54, 55, 58, 67, 71], "f\u2099": 4, "report": [4, 8, 12, 17, 24, 29, 52, 54, 55, 59, 64, 72, 77], "definition": [4, 12, 17, 31, 32, 35, 37, 64], "circular": [4, 17, 57], "assumpt": [4, 10, 17, 24, 25, 26, 32, 33, 34, 35, 36, 44, 51, 52, 53, 54, 58, 59, 60, 66, 67, 77], "induct": [4, 5, 9, 10, 11, 12, 13, 14, 17, 24, 25, 27, 29, 30, 31, 32, 33, 35, 37, 41, 42, 44, 52, 54, 55, 57, 58, 59, 60, 62, 64, 65, 66, 73, 75, 77], "of_typ": [4, 17, 28], "src": [4, 53], "dest": [4, 17], "x\u2099": [4, 55], "t\u2098": 4, "word": [4, 14, 17, 30, 42, 51, 52, 53, 55, 58, 66], "context": [4, 5, 9, 10, 11, 14, 17, 24, 25, 26, 29, 30, 31, 32, 34, 35, 38, 41, 43, 44, 51, 52, 59, 60, 62, 64, 66, 67, 71], "forc": [4, 8, 11, 17, 24, 34, 42, 44, 52, 53, 54, 57, 60, 64, 66, 67, 71], "updat": [4, 8, 15, 17, 24, 36, 37, 46, 52, 53, 58, 59, 67, 71], "last": [4, 5, 9, 17, 24, 32, 34, 35, 37, 38, 42, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 65, 66, 67, 71, 72], "record_definit": [4, 13, 30, 34, 37], "redefin": [4, 17, 54, 55, 57, 66, 71, 75], "forgotten": 4, "atom": [4, 5, 8, 14, 17, 26, 60, 62, 67, 71], "bool_in_nat": 4, "unset": [4, 5, 12, 14, 17, 24, 25, 34, 35, 37, 38, 42, 44, 46, 51, 54, 55, 57, 59, 66, 67, 71], "none": [4, 5, 13, 17, 24, 27, 34, 40, 42, 46, 51, 54, 55, 57, 66, 71], "remark": [4, 17, 24, 25, 32, 34], "co": [4, 10, 11, 17, 24, 25, 42, 44, 54, 57, 59, 64, 67, 71, 77], "fg": 4, "bij": 4, "ap": [4, 11], "ssort": 4, "sstuff": 4, "s_nat": 4, "compar": [4, 5, 11, 14, 17, 24, 25, 37, 42, 53, 54, 55, 57, 58, 64, 66, 67, 73], "fct": 4, "incr_fct": 4, "fct_of_incr_fct": 4, "illeg": 4, "id_fct_funclass": 4, "reverse_coercion": [4, 17], "reversecoercionsourc": 4, "reversecoerciontarget": 4, "fr\u00e9d\u00e9ric": [5, 17, 57], "besson": [5, 17], "evgeni": [5, 17], "makarov": [5, 17], "mathbb": [5, 7, 17], "lqa": 5, "incomplet": [5, 8, 10, 17, 24, 46, 58, 66, 67, 71], "option": [5, 8, 9, 10, 11, 13, 14, 16, 24, 25, 26, 27, 34, 35, 38, 40, 42, 44, 46, 50, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 67, 71, 74], "john": [5, 77], "harrison": 5, "hol": 5, "light": [5, 17, 24, 52, 66, 75], "driver": 5, "csdp": 5, "gener": [5, 7, 8, 9, 12, 13, 17, 24, 25, 27, 28, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 43, 46, 51, 52, 53, 58, 59, 60, 61, 62, 64, 66, 75, 77], "cach": [5, 12, 17], "rerun": 5, "script": [5, 8, 17, 24, 25, 35, 42, 43, 53, 54, 55, 57, 58, 59, 60, 63, 64, 66, 73], "info": [5, 17, 54, 60], "dump": [5, 17, 24, 51, 75], "arith": [5, 11, 17, 24, 53, 59, 60, 72], "profil": [5, 17, 25, 53, 59, 64], "statist": [5, 17, 66], "pivot": 5, "detect": [5, 8, 17, 25, 41, 44, 52, 53, 57, 66], "ineffici": [5, 17, 24, 57], "formula": [5, 7, 26, 57, 58, 62, 77], "numer": [5, 11, 17, 24, 27, 29, 59, 71], "subtract": [5, 57], "exponenti": [5, 17, 29], "implb": [5, 17, 27], "negb": [5, 13, 27, 62, 71], "comparison": [5, 14, 17, 24, 42], "gtb": 5, "ltb": [5, 17, 59], "geb": 5, "leb": [5, 9, 17, 57, 59], "rather": [5, 11, 13, 17, 24, 29, 30, 34, 35, 53, 54, 55, 57, 58, 59, 64, 67, 71], "resp": [5, 17, 34, 36, 46, 57], "rang": [5, 17, 26, 29, 52, 55, 58, 71], "r0": [5, 17], "rmult": [5, 11], "rplu": 5, "rminu": 5, "izr": [5, 17, 71], "q2r": [5, 57], "rinv": 5, "decim": [5, 17, 27, 29, 59, 71], "hilbert": [5, 7, 17], "nullstellensatz": [5, 7, 17], "reli": [5, 17, 24, 30, 32, 33, 34, 38, 46, 51, 52, 53, 54, 55, 57, 58, 59, 64, 66, 67, 71], "notion": [5, 11, 17, 24, 25, 26, 27, 33, 34, 46, 51, 54, 55, 58, 64, 71, 77], "cone": [5, 17], "polynomi": [5, 7, 17, 24, 25, 61], "mathit": [5, 26, 34], "under": [5, 9, 11, 17, 25, 32, 40, 44, 46, 52, 53, 54, 55, 59, 64, 66, 67], "dfrac": 5, "quad": 5, "p_1": [5, 7, 34, 35], "p_2": [5, 35], "join": [5, 24], "inequ": [5, 17, 24, 60], "belong": [5, 8, 11, 26, 29, 34, 37, 39, 53, 54, 57, 59, 60, 63, 67, 71, 75], "bigwedge_": 5, "ge": [5, 17, 27], "unsatisfi": [5, 60], "neg": [5, 17, 29, 30, 37, 64, 66, 71], "absurd": [5, 27, 34, 51, 58], "squar": [5, 17, 24, 44, 54, 59, 71, 75], "bigwedge_i": 5, "c_i": [5, 34, 35], "j": [5, 6, 8, 14, 17, 24, 25, 26, 34, 36, 39, 43, 51, 54, 57, 64, 72, 77], "s_i": [5, 7, 34], "p_j": [5, 34], "oracl": 5, "within": [5, 17, 24, 28, 29, 31, 33, 35, 37, 38, 41, 42, 44, 51, 52, 54, 55, 58, 59, 60, 64, 66, 71], "upon": [5, 11, 36, 43, 51], "equat": [5, 6, 14, 17, 24, 25, 27, 34, 40, 42, 46, 53, 55, 58, 60, 61, 64, 67, 72], "explor": [5, 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"div_theori": 11, "7x": 11, "good": [11, 17, 53, 54, 55, 57, 66], "philosoph": 11, "calculu": [11, 14, 17, 24, 25, 27, 29, 31, 33, 34, 35, 37, 46, 54, 57, 58, 62, 64, 66, 67, 71, 77], "strongli": [11, 15, 17, 34, 35, 44, 53, 54, 57, 59], "advis": [11, 17, 24, 25, 28, 29, 30, 54, 60], "ring_polynom": 11, "pexpr": 11, "pesub": 11, "peopp": 11, "pepow": 11, "pol": 11, "pc": 11, "pinj": 11, "px": [11, 24, 57], "v_i": [11, 31], "big": [11, 14, 17, 57, 59, 71], "pphi_dev_ok": 11, "pe": 11, "npe": 11, "piec": [11, 42, 43, 53, 55, 57], "summar": [11, 51, 57, 66], "diagram": 11, "chosen": [11, 34, 54, 55, 57, 58, 66, 71], "denomin": [11, 17, 37, 71], "neq": 11, "broken": [11, 17, 71], "proven": [11, 17, 52, 58, 64, 66, 67], "rbase": [11, 17, 24], "qcanon": 11, "r_scope": [11, 71], "auto": [11, 13, 14, 17, 24, 29, 34, 41, 44, 51, 52, 54, 57, 58, 59, 60, 62, 66, 67, 72], "h1": [11, 17, 34, 43, 54, 55, 57, 58, 62, 66, 67], "f_1": [11, 34], "f_2": [11, 34], "n_1": [11, 26], "d_1": 11, "n_2": 11, "d_2": 11, "cancel": [11, 38, 41, 57, 66], "field_theori": 11, "semi_field_theori": 11, "semifield": 11, "mk_field": 11, "f_r": 11, "ro": 11, "ri": [11, 17, 51], "radd": 11, "rmul": 11, "rsub": 11, "ropp": 11, "req": 11, "f_1_neq_0": 11, "fdiv_def": 11, "finv_l": 11, "mk_sfield": 11, "sf_sr": 11, "sf_1_neq_0": 11, "sfdiv_def": 11, "sfinv_l": 11, "mk_linear": 11, "num": [11, 17], "denum": 11, "field_mod": 11, "samuel": [11, 17, 24], "boutin": [11, 24, 77], "acdsimpl": 11, "zmult_comm": 11, "eq_ind_r": [11, 27], "z0": [11, 17, 71], "mul_comm": [11, 59], "hundr": [11, 64], "rewrot": [11, 17], "bou97": [11, 77], "later": [11, 17, 25, 31, 32, 43, 44, 50, 53, 55, 57, 58, 66, 67, 71], "patrick": [11, 24], "loiseleur": [11, 24], "interleav": [11, 17, 58], "he": [11, 17, 24, 57], "wrote": [11, 17, 24], "larg": [11, 14, 17, 25, 26, 29, 34, 35, 39, 52, 53, 54, 57, 61, 64, 66, 67, 71, 75], "motiv": [11, 17, 55, 57, 77], "34": [11, 53, 71, 77], "12": [11, 25, 29, 53, 54, 57, 58, 60, 71], "46": [11, 77], "ominu": 11, "v_3": 11, "far": [11, 24, 46, 52, 57, 66, 71], "faster": [11, 17, 24, 51, 58, 59, 62, 64], "free": [11, 17, 24, 26, 34, 44, 52, 54, 55, 57, 58, 62, 64, 71, 75, 77], "difficult": [11, 17, 29, 55, 72], "ultim": 11, "answer": [11, 46, 53], "intens": [11, 17, 24, 64], "classic": [11, 17, 24, 25, 34, 51, 55, 57, 66], "tautologi": [11, 17, 24, 54, 62], "backtrack": [11, 13, 17, 24, 25, 52, 58, 60, 67], "clearli": [11, 24, 71, 74], "significantli": [11, 17, 24, 57, 66], "idea": [11, 17, 34, 42, 54], "suggest": [11, 17, 24, 25, 34, 51, 52, 53, 57, 66], "werner": [11, 17, 24, 77], "coupl": [11, 17, 46, 53, 57, 75], "tool": [11, 14, 25, 29, 51, 52, 53, 54, 57, 59, 66, 71, 72, 75, 77], "model": [11, 17, 24, 57, 77], "trace": [11, 13, 17, 25, 32, 51, 53, 57, 58, 59], "replai": [11, 57], "footnot": [11, 38, 57, 71], "bytecod": [12, 17, 59, 64], "gcst19": [12, 39, 77], "strictprop": [12, 17], "startup": [12, 51, 53, 60], "purpos": [12, 14, 17, 24, 27, 34, 35, 42, 51, 52, 54, 55, 57, 64, 66, 67, 71], "hx": [12, 57, 58], "\u03b7": [12, 17, 25, 30], "tractabl": 12, "cumul": [12, 13, 17, 24, 25, 26, 29, 30, 31, 34, 37, 40, 71], "forbidden": [12, 17, 24, 25], "relev": [12, 17, 24, 28, 30, 32, 34, 40, 46, 51, 53, 54, 57, 58, 64, 66, 71], "world": [12, 17, 24, 55, 57, 77], "escap": [12, 17, 25, 51, 53, 71], "box": [12, 17, 29, 54, 71], "box_rect": 12, "box_ind": 12, "box_rec": 12, "box_sind": 12, "box_irrelev": 12, "squash": [12, 14, 17], "isquash": 12, "isquash_sind": 12, "Or": [12, 17, 41, 53, 58, 71], "sempti": 12, "sempty_rect": 12, "sempty_ind": 12, "sempty_rec": 12, "sempty_sind": 12, "foo_sind": 12, "foo_ind": [12, 17, 57], "sprod": 12, "sfst": 12, "ssnd": 12, "extension": [12, 17, 27, 30, 57], "rbox": 12, "runbox": 12, "ssig": 12, "spr1": 12, "spr2": 12, "trivial": [12, 13, 14, 17, 34, 46, 53, 54, 55, 57, 58, 60, 66, 67], "sunit": 12, "stt": 12, "sunit_rect": 12, "is_tru": [12, 57], "is_true_eq_tru": 12, "eq_true_is_tru": 12, "seq": [12, 13, 30, 46, 55, 57, 67], "srefl": [12, 46], "seq_rect": [12, 46], "seq_ind": [12, 46], "seq_rec": [12, 46], "seq_sind": [12, 46], "hidden_arrow": 12, "stuck": [12, 13, 17], "Such": [12, 30, 35, 42, 44, 53, 55, 59, 71, 75], "around": [12, 17, 24, 29, 46, 52, 53, 55, 57, 58, 59, 64, 67, 71, 75], "ac19": [12, 77], "all_eq": 12, "transport": [12, 17], "timeout": [12, 17, 25, 59, 64], "infinit": [12, 30, 34, 39], "binder": [12, 13, 17, 24, 25, 30, 32, 34, 37, 38, 40, 52, 54, 55, 58, 59, 63, 64, 67, 75], "bug": [12, 17, 24, 52, 54, 66], "incorrectli": [12, 17, 55], "leav": [12, 13, 17, 32, 35, 52, 54, 57, 58, 59, 60, 64, 66, 67], "silent": [12, 14, 17, 24, 29, 51, 53, 59, 66, 72], "repair": [12, 17], "affect": [12, 17, 24, 29, 34, 41, 44, 46, 53, 54, 55, 57, 59, 60, 64, 66, 71], "programmat": 13, "quick": [13, 17, 24, 27, 54, 57, 66, 74], "paper": [13, 24, 42, 54, 57, 72, 77], "so08": [13, 77], "literatur": [13, 34], "class": [13, 17, 24, 25, 27, 28, 35, 39, 42, 44, 57, 59, 60, 62, 64], "classnam": 13, "p1": [13, 17, 37, 57, 67], "pn": [13, 17, 57], "f1": [13, 17, 41, 51, 57, 71], "fm": 13, "um": [13, 57], "instancenam": 13, "qm": 13, "tm": 13, "pi": [13, 17, 52], "ti": [13, 57], "fi": 13, "rise": [13, 24], "ll": [13, 17, 34, 52, 53], "eqdec": [13, 38, 60], "eqb_leibniz": 13, "unit_eqdec": 13, "member": [13, 42, 55], "oblig": [13, 17, 25, 37, 57, 62, 72], "eq_bool": 13, "discrimin": [13, 17, 24, 54, 57, 58, 59, 60, 62, 64, 66], "richer": [13, 25], "facil": [13, 17, 24, 52, 54, 55, 57, 59], "neqb": 13, "generaliz": [13, 17, 44], "neqb_implicit": 13, "prod_eqb": 13, "ea": 13, "eb": 13, "la": [13, 17, 24, 52, 55, 77], "ra": 13, "lb": 13, "rb": 13, "prod_eqb_obligation_1": 13, "eas": [13, 17, 37, 53, 55, 57, 58, 66], "eqdec_def": 13, "option_eqb": 13, "program_branch_2": 13, "y1": [13, 27, 42, 46, 59], "option_eqb_obligation_1": 13, "option_eqb_obligation_2": 13, "option_eqb_obligation_3": 13, "type_scop": [13, 14, 17, 25, 34, 44, 46, 52, 54, 58, 66, 67], "1182": 13, "1383": 13, "redeclar": 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52, 58], "breadth": 13, "deepen": 13, "best_effort": [13, 17], "couldn": 13, "unbound": [13, 14, 17, 54, 55, 58], "count": [13, 17, 25, 51, 57, 58, 59, 64, 66, 67], "faithfulli": 13, "mimic": [13, 37, 57], "move": [13, 17, 24, 25, 43, 52, 53, 55, 66, 67, 71], "autoappli": [13, 17], "shortcut": [13, 17, 25, 52, 55, 64, 71], "prevent": [13, 17, 29, 34, 41, 42, 51, 53, 54, 57, 64, 71], "releas": [13, 15, 17, 24, 25, 52, 53, 57, 63, 74], "filter": [13, 17, 30, 51, 53, 59, 60], "eta": [13, 17, 25, 31, 37], "expens": [13, 17, 54, 66], "rebuild": [13, 17], "benefit": [13, 17, 51, 57], "invert": [13, 17, 57, 67, 72], "elabor": [13, 14, 17, 25, 33, 37, 41, 44, 45, 51, 55, 58], "stricter": [13, 14, 17], "freez": 13, "verbos": [13, 17, 42, 51, 59], "successfulli": [13, 51, 52, 54, 57, 62, 63], "reus": [14, 17, 41, 57, 58, 59, 63, 64, 66], "sometim": [14, 17, 24, 25, 31, 34, 46, 53, 54, 55, 57, 59, 60, 66, 67, 71], "incompat": [14, 24, 25, 34, 41, 46, 57, 59, 66, 71], "self": [14, 17, 54, 55, 67, 71], "selfid": 14, "pident": 14, "167": 14, "176": 14, "selfpid": 14, "monoid": [14, 55], "ourselv": [14, 34], "mon_car": 14, "mon_unit": 14, "mon_op": 14, "build_monoid": 14, "function_scop": [14, 17, 25, 34, 46, 57, 67], "unit_monoid": 14, "greater": [14, 17, 24, 34, 52, 71], "pprod": 14, "max": [14, 17, 24, 39, 46, 54, 59], "ppair": 14, "pfst": 14, "psnd": 14, "40": [14, 17, 27, 41, 71], "core_scop": [14, 71], "cartesian": [14, 54], "monoid_op": 14, "prod_monoid": 14, "monoids_monoid": 14, "live": [14, 17, 51, 55], "coinduct": [14, 17, 25, 26, 32, 33, 34, 37, 40, 46, 54, 59, 67, 71], "attribtu": 14, "list_rect": [14, 34, 41, 44, 46, 57, 67], "list_ind": [14, 34, 41, 44, 46, 57, 67], "list_rec": [14, 34, 41, 44, 46, 57, 67], "list_sind": [14, 34, 41, 44, 46, 57, 67], "invari": [14, 17, 55], "covari": 14, "irrelev": [14, 17, 25, 32, 33, 34, 39, 54, 55, 57, 64, 77], "contravari": 14, "\u03b3": [14, 26, 31, 34, 35, 38, 55], "\u03b2\u03b4\u03b9\u03b6\u03b7": [14, 26, 31, 34, 35], 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"coq:exn.\"All\"-is-a-predefined-collection-containing-all-variables.-It-can't-be-redefined", " It can't be redefined"]], "": [[71, 0, 1, "coq:exn.'via'-and-'abstract'-cannot-be-used-together", "'via' and 'abstract' cannot be used together"], [54, 1, 1, "coq:tacn.+-(backtracking-branching)", "+ (backtracking branching)"], [57, 1, 1, "coq:tacn.=>", "=>"], [66, 3, 1, "coq:cmd.Abort", "Abort"], [59, 3, 1, "coq:cmd.About", "About"], [71, 2, 1, "coq:warn.Activation-of-abbreviations-does-not-expect-mentioning-a-grammar-entry", "Activation of abbreviations does not expect mentioning a grammar entry"], [71, 2, 1, "coq:warn.Activation-of-abbreviations-does-not-expect-mentioning-a-scope", "Activation of abbreviations does not expect mentioning a scope"], [29, 3, 1, "coq:cmd.Add", "Add"], [11, 3, 1, "coq:cmd.Add-Field", "Add Field"], [3, 3, 1, "coq:cmd.Add-Morphism", "Add Morphism"], [3, 3, 1, "coq:cmd.Add-Parametric-Morphism", "Add Parametric Morphism"], [3, 3, 1, "coq:cmd.Add-Parametric-Relation", "Add Parametric Relation"], [3, 3, 1, "coq:cmd.Add-Parametric-Setoid", "Add Parametric Setoid"], [3, 3, 1, "coq:cmd.Add-Relation", "Add Relation"], [11, 3, 1, "coq:cmd.Add-Ring", "Add Ring"], [3, 3, 1, "coq:cmd.Add-Setoid", "Add Setoid"], [5, 3, 1, "coq:cmd.Add-Zify", "Add Zify"], [9, 3, 1, "coq:cmd.Admit-Obligations", "Admit Obligations"], [66, 3, 1, "coq:cmd.Admitted", "Admitted"], [12, 4, 1, "coq:flag.Allow-StrictProp", "Allow StrictProp"], [44, 0, 1, "coq:exn.Argument-at-position-\u2018natural\u2019-is-mentioned-more-than-once", "Argument at position \u2018natural\u2019 is mentioned more than once"], [54, 0, 1, "coq:exn.Argument-of-match-does-not-evaluate-to-a-term", "Argument of match does not evaluate to a term"], [41, 3, 1, "coq:cmd.Arguments", "Arguments"], [44, 0, 1, "coq:exn.Arguments-given-by-name-or-position-not-supported-in-explicit-mode", "Arguments given by name or position not supported in explicit mode"], [11, 0, 1, "coq:exn.Arguments-of-ring_simplify-do-not-have-all-the-same-type", "Arguments of ring_simplify do not have all the same type"], [41, 0, 1, "coq:exn.Arguments-of-section-variables-such-as-\u2018name\u2019-may-not-be-renamed", "Arguments of section variables such as \u2018name\u2019 may not be renamed"], [46, 4, 1, "coq:flag.Asymmetric-Patterns", "Asymmetric Patterns"], [66, 0, 1, "coq:exn.Attempt-to-save-an-incomplete-proof", "Attempt to save an incomplete proof"], [29, 3, 1, "coq:cmd.Attributes", "Attributes"], [34, 4, 1, "coq:flag.Auto-Template-Polymorphism", "Auto Template Polymorphism"], [34, 2, 1, "coq:warn.Automatically-declaring-\u2018ident\u2019-as-template-polymorphic", "Automatically declaring \u2018ident\u2019 as template polymorphic"], [28, 3, 1, "coq:cmd.Axiom", "Axiom"], [28, 3, 1, "coq:cmd.Axioms", "Axioms"], [59, 3, 1, "coq:cmd.Back", "Back"], [59, 3, 1, "coq:cmd.BackTo", "BackTo"], [11, 0, 1, "coq:exn.Bad-lemma-for-decidability-of-equality", "Bad lemma for decidability of equality"], [59, 0, 1, "coq:exn.Bad-magic-number", "Bad magic number"], [64, 0, 1, "coq:exn.Bad-occurrence-number-of-\u2018qualid\u2019", "Bad occurrence number of \u2018qualid\u2019"], [12, 2, 1, "coq:warn.Bad-relevance", "Bad relevance"], [11, 0, 1, "coq:exn.Bad-ring-structure", "Bad ring structure"], [71, 3, 1, "coq:cmd.Bind-Scope", "Bind Scope"], [67, 4, 1, "coq:flag.Boolean-Equality-Schemes", "Boolean Equality Schemes"], [5, 5, 1, "coq:thm.Bound-on-the-ceiling-function", "Bound on the ceiling function"], [66, 0, 1, "coq:exn.Brackets-do-not-support-multi-goal-selectors", "Brackets do not support multi-goal selectors"], [66, 6, 1, "coq:opt.Bullet-Behavior", "Bullet Behavior"], [72, 2, 1, "coq:warn.Cannot-build-functional-inversion-principle", "Cannot build functional inversion principle"], [58, 0, 1, "coq:exn.Cannot-change-\u2018ident\u2019,-it-is-used-in-conclusion", "Cannot change \u2018ident\u2019, it is used in conclusion"], [58, 0, 1, "coq:exn.Cannot-change-\u2018ident\u2019,-it-is-used-in-hypothesis-\u2018ident\u2019", "Cannot change \u2018ident\u2019, it is used in hypothesis \u2018ident\u2019"], [60, 0, 1, "coq:exn.Cannot-coerce-\u2018qualid\u2019-to-an-evaluable-reference", "Cannot coerce \u2018qualid\u2019 to an evaluable reference"], [72, 2, 1, "coq:warn.Cannot-define-graph-for-\u2018ident\u2019", "Cannot define graph for \u2018ident\u2019"], [72, 2, 1, "coq:warn.Cannot-define-principle(s)-for-\u2018ident\u2019", "Cannot define principle(s) for \u2018ident\u2019"], [11, 0, 1, "coq:exn.Cannot-find-a-declared-ring-structure-for-equality-\u2018term\u2019", "Cannot find a declared ring structure for equality \u2018term\u2019"], [11, 0, 1, "coq:exn.Cannot-find-a-declared-ring-structure-over-\u2018term\u2019", "Cannot find a declared ring structure over \u2018term\u2019"], [64, 0, 1, "coq:exn.Cannot-find-a-relation-to-rewrite", "Cannot find a relation to rewrite"], [64, 0, 1, "coq:exn.Cannot-find-any-non-recursive-equality-over-\u2018ident\u2019", "Cannot find any non-recursive equality over \u2018ident\u2019"], [72, 0, 1, "coq:exn.Cannot-find-induction-information-on-\u2018qualid\u2019", "Cannot find induction information on \u2018qualid\u2019"], [72, 0, 1, "coq:exn.Cannot-find-inversion-information-for-hypothesis-\u2018ident\u2019", "Cannot find inversion information for hypothesis \u2018ident\u2019"], [59, 0, 1, "coq:exn.Cannot-find-library-foo-in-loadpath", "Cannot find library foo in loadpath"], [4, 0, 1, "coq:exn.Cannot-find-the-source-class-of-\u2018qualid\u2019", "Cannot find the source class of \u2018qualid\u2019"], [4, 0, 1, "coq:exn.Cannot-find-the-target-class", "Cannot find the target class"], [35, 2, 1, "coq:warn.Cannot-import-local-constant,-it-will-be-ignored", "Cannot import local constant, it will be ignored"], [71, 0, 1, "coq:exn.Cannot-interpret-in-\u2018scope_name\u2019-because-\u2018qualid\u2019-could-not-be-found-in-the-current-environment", "Cannot interpret in \u2018scope_name\u2019 because \u2018qualid\u2019 could not be found in the current environment"], [71, 0, 1, "coq:exn.Cannot-interpret-this-number-as-a-value-of-type-\u2018type\u2019", "Cannot interpret this number as a value of type \u2018type\u2019"], [71, 0, 1, "coq:exn.Cannot-interpret-this-string-as-a-value-of-type-\u2018type\u2019", "Cannot interpret this string as a value of type \u2018type\u2019"], [59, 0, 1, "coq:exn.Cannot-load-\u2018qualid\u2019:-no-physical-path-bound-to-\u2018dirpath\u2019", "Cannot load \u2018qualid\u2019: no physical path bound to \u2018dirpath\u2019"], [58, 0, 1, "coq:exn.Cannot-move-\u2018ident\u2019-after-\u2018ident\u2019:-it-depends-on-\u2018ident\u2019", "Cannot move \u2018ident\u2019 after \u2018ident\u2019: it depends on \u2018ident\u2019"], [58, 0, 1, "coq:exn.Cannot-move-\u2018ident\u2019-after-\u2018ident\u2019:-it-occurs-in-the-type-of-\u2018ident\u2019", "Cannot move \u2018ident\u2019 after \u2018ident\u2019: it occurs in the type of \u2018ident\u2019"], [62, 0, 1, "coq:exn.Cannot-recognize-a-boolean-equality", "Cannot recognize a boolean equality"], [67, 0, 1, "coq:exn.Cannot-recognize-a-statement-based-on-\u2018reference\u2019", "Cannot recognize a statement based on \u2018reference\u2019"], [4, 0, 1, "coq:exn.Cannot-recognize-\u2018coercion_class\u2019-as-a-source-class-of-\u2018qualid\u2019", "Cannot recognize \u2018coercion_class\u2019 as a source class of \u2018qualid\u2019"], [64, 0, 1, "coq:exn.Cannot-turn-[inductive|constructor]-into-an-evaluable-reference", "Cannot turn [inductive|constructor] into an evaluable reference"], [72, 0, 1, "coq:exn.Cannot-use-mutual-definition-with-well-founded-recursion-or-measure", "Cannot use mutual definition with well-founded recursion or measure"], [42, 3, 1, "coq:cmd.Canonical-Structure", "Canonical Structure"], [59, 0, 1, "coq:exn.Can\u2019t-find-file-\u2018ident\u2019-on-loadpath", "Can\u2019t find file \u2018ident\u2019 on loadpath"], [67, 4, 1, "coq:flag.Case-Analysis-Schemes", "Case Analysis Schemes"], [5, 5, 1, "coq:thm.Case-split", "Case split"], [40, 0, 1, "coq:exn.Casts-are-not-supported-in-this-pattern", "Casts are not supported in this pattern"], [2, 3, 1, "coq:cmd.Cd", "Cd"], [59, 3, 1, "coq:cmd.Check", "Check"], [13, 3, 1, "coq:cmd.Class", "Class"], [71, 3, 1, "coq:cmd.Close-Scope", "Close Scope"], [30, 3, 1, "coq:cmd.CoFixpoint", "CoFixpoint"], [30, 3, 1, "coq:cmd.CoInductive", "CoInductive"], [4, 3, 1, "coq:cmd.Coercion", "Coercion"], [66, 3, 1, "coq:cmd.Collection", "Collection"], [67, 3, 1, "coq:cmd.Combined-Scheme", "Combined Scheme"], [29, 3, 1, "coq:cmd.Comments", "Comments"], [64, 3, 1, "coq:cmd.Compute", "Compute"], [54, 0, 1, "coq:exn.Condition-not-satisfied", "Condition not satisfied"], [28, 3, 1, "coq:cmd.Conjecture", "Conjecture"], [28, 3, 1, "coq:cmd.Conjectures", "Conjectures"], [14, 3, 1, "coq:cmd.Constraint", "Constraint"], [38, 3, 1, "coq:cmd.Context", "Context"], [44, 4, 1, "coq:flag.Contextual-Implicit", "Contextual Implicit"], [51, 4, 1, "coq:flag.Coqtop-Exit-On-Error", "Coqtop Exit On Error"], [32, 3, 1, "coq:cmd.Corollary", "Corollary"], [60, 3, 1, "coq:cmd.Create-HintDb", "Create HintDb"], [14, 7, 1, "coq:attr.Cumulative", "Cumulative"], [14, 4, 1, "coq:flag.Cumulativity-Weak-Constraints", "Cumulativity Weak Constraints"], [54, 3, 1, "coq:cmd.Debug", "Debug"], [59, 6, 1, "coq:opt.Debug", "Debug"], [60, 4, 1, "coq:flag.Debug-Auto", "Debug Auto"], [60, 4, 1, "coq:flag.Debug-Eauto", "Debug Eauto"], [57, 4, 1, "coq:flag.Debug-SsrMatching", "Debug SsrMatching"], [57, 4, 1, "coq:flag.Debug-Ssreflect", "Debug Ssreflect"], [60, 4, 1, "coq:flag.Debug-Trivial", "Debug Trivial"], [54, 0, 1, "coq:exn.Debug-mode-not-available-in-the-IDE", "Debug mode not available in the IDE"], [67, 4, 1, "coq:flag.Decidable-Equality-Schemes", "Decidable Equality Schemes"], [71, 3, 1, "coq:cmd.Declare-Custom-Entry", "Declare Custom Entry"], [64, 3, 1, "coq:cmd.Declare-Equivalent-Keys", "Declare Equivalent Keys"], [13, 3, 1, "coq:cmd.Declare-Instance", "Declare Instance"], [64, 3, 1, "coq:cmd.Declare-Left-Step", "Declare Left Step"], [59, 3, 1, "coq:cmd.Declare-ML-Module", "Declare ML Module"], [35, 3, 1, "coq:cmd.Declare-Module", "Declare Module"], [3, 3, 1, "coq:cmd.Declare-Morphism", "Declare Morphism"], [64, 3, 1, "coq:cmd.Declare-Reduction", "Declare Reduction"], [64, 3, 1, "coq:cmd.Declare-Right-Step", "Declare Right Step"], [71, 3, 1, "coq:cmd.Declare-Scope", "Declare Scope"], [60, 2, 1, "coq:warn.Declaring-arbitrary-terms-as-hints-is-fragile-and-deprecated;-it-is-recommended-to-declare-a-toplevel-constant-instead", "Declaring arbitrary terms as hints is fragile and deprecated; it is recommended to declare a toplevel constant instead"], [58, 6, 1, "coq:opt.Default-Goal-Selector", "Default Goal Selector"], [66, 6, 1, "coq:opt.Default-Proof-Mode", "Default Proof Mode"], [66, 6, 1, "coq:opt.Default-Proof-Using", "Default Proof Using"], [59, 6, 1, "coq:opt.Default-Timeout", "Default Timeout"], [66, 3, 1, "coq:cmd.Defined", "Defined"], [32, 3, 1, "coq:cmd.Definition", "Definition"], [12, 4, 1, "coq:flag.Definitional-UIP", "Definitional UIP"], [71, 3, 1, "coq:cmd.Delimit-Scope", "Delimit Scope"], [34, 4, 1, "coq:flag.Dependent-Proposition-Eliminators", "Dependent Proposition Eliminators"], [6, 3, 1, "coq:cmd.Derive", "Derive"], [67, 3, 1, "coq:cmd.Derive-Dependent-Inversion", "Derive Dependent Inversion"], [67, 3, 1, "coq:cmd.Derive-Dependent-Inversion_clear", "Derive Dependent Inversion_clear"], [67, 3, 1, "coq:cmd.Derive-Inversion", "Derive Inversion"], [67, 3, 1, "coq:cmd.Derive-Inversion_clear", "Derive Inversion_clear"], [66, 6, 1, "coq:opt.Diffs", "Diffs"], [71, 3, 1, "coq:cmd.Disable-Notation", "Disable Notation"], [59, 3, 1, "coq:cmd.Drop", "Drop"], [5, 6, 1, "coq:opt.Dump-Arith", "Dump Arith"], [59, 0, 1, "coq:exn.Dynlink-error:-execution-of-module-initializers-in-the", "Dynlink error: execution of module initializers in the"], [46, 0, 1, "coq:exn.Either-there-is-a-type-incompatibility-or-the-problem-involves-dependencies", "Either there is a type incompatibility or the problem involves dependencies"], [67, 4, 1, "coq:flag.Elimination-Schemes", "Elimination Schemes"], [71, 3, 1, "coq:cmd.Enable-Notation", "Enable Notation"], [38, 3, 1, "coq:cmd.End", "End"], [71, 0, 1, "coq:exn.End-of-quoted-string-not-followed-by-a-space-in-notation", "End of quoted string not followed by a space in notation"], [64, 3, 1, "coq:cmd.Eval", "Eval"], [32, 3, 1, "coq:cmd.Example", "Example"], [13, 3, 1, "coq:cmd.Existing-Class", "Existing Class"], [13, 3, 1, "coq:cmd.Existing-Instance", "Existing Instance"], [13, 3, 1, "coq:cmd.Existing-Instances", "Existing Instances"], [35, 3, 1, "coq:cmd.Export", "Export"], [54, 0, 1, "coq:exn.Expression-does-not-evaluate-to-a-tactic", "Expression does not evaluate to a tactic"], [2, 3, 1, "coq:cmd.Extract-Callback", "Extract Callback"], [2, 0, 1, "coq:exn.Extract-Callback-is-supported-only-for-OCaml-extraction", "Extract Callback is supported only for OCaml extraction"], [2, 3, 1, "coq:cmd.Extract-Constant", "Extract Constant"], [2, 3, 1, "coq:cmd.Extract-Foreign-Constant", "Extract Foreign Constant"], [2, 0, 1, "coq:exn.Extract-Foreign-Constant-is-supported-only-for-OCaml-extraction", "Extract Foreign Constant is supported only for OCaml extraction"], [2, 0, 1, "coq:exn.Extract-Foreign-Constant-is-supported-only-for-functions", "Extract Foreign Constant is supported only for functions"], [2, 3, 1, "coq:cmd.Extract-Inductive", "Extract Inductive"], [2, 3, 1, "coq:cmd.Extract-Inlined-Constant", "Extract Inlined Constant"], [2, 3, 1, "coq:cmd.Extraction", "Extraction"], [2, 4, 1, "coq:flag.Extraction-AutoInline", "Extraction AutoInline"], [2, 3, 1, "coq:cmd.Extraction-Blacklist", "Extraction Blacklist"], [2, 4, 1, "coq:flag.Extraction-Conservative-Types", "Extraction Conservative Types"], [2, 6, 1, "coq:opt.Extraction-File-Comment", "Extraction File Comment"], [2, 6, 1, "coq:opt.Extraction-Flag", "Extraction Flag"], [2, 3, 1, "coq:cmd.Extraction-Implicit", "Extraction Implicit"], [2, 3, 1, "coq:cmd.Extraction-Inline", "Extraction Inline"], [2, 4, 1, "coq:flag.Extraction-KeepSingleton", "Extraction KeepSingleton"], [2, 3, 1, "coq:cmd.Extraction-Language", "Extraction Language"], [2, 3, 1, "coq:cmd.Extraction-Library", "Extraction Library"], [2, 3, 1, "coq:cmd.Extraction-NoInline", "Extraction NoInline"], [2, 4, 1, "coq:flag.Extraction-Optimize", "Extraction Optimize"], [2, 6, 1, "coq:opt.Extraction-Output-Directory", "Extraction Output Directory"], [2, 4, 1, "coq:flag.Extraction-SafeImplicits", "Extraction SafeImplicits"], [2, 3, 1, "coq:cmd.Extraction-TestCompile", "Extraction TestCompile"], [2, 4, 1, "coq:flag.Extraction-TypeExpand", "Extraction TypeExpand"], [32, 3, 1, "coq:cmd.Fact", "Fact"], [59, 3, 1, "coq:cmd.Fail", "Fail"], [54, 0, 1, "coq:exn.Failed-to-progress", "Failed to progress"], [59, 4, 1, "coq:flag.Fast-Name-Printing", "Fast Name Printing"], [59, 0, 1, "coq:exn.File-not-found-on-loadpath:-\u2018string\u2019", "File not found on loadpath: \u2018string\u2019"], [59, 0, 1, "coq:exn.Files-processed-by-Load-cannot-leave-open-proofs", "Files processed by Load cannot leave open proofs"], [9, 3, 1, "coq:cmd.Final-Obligation", "Final Obligation"], [62, 6, 1, "coq:opt.Firstorder-Depth", "Firstorder Depth"], [62, 6, 1, "coq:opt.Firstorder-Solver", "Firstorder Solver"], [34, 3, 1, "coq:cmd.Fixpoint", "Fixpoint"], [41, 0, 1, "coq:exn.Flag-'rename'-expected-to-rename-\u2018name\u2019-into-\u2018name\u2019", "Flag 'rename' expected to rename \u2018name\u2019 into \u2018name\u2019"], [66, 3, 1, "coq:cmd.Focus", "Focus"], [46, 0, 1, "coq:exn.Found-a-constructor-of-inductive-type-term-while-a-constructor-of-term-is-expected", "Found a constructor of inductive type term while a constructor of term is expected"], [64, 0, 1, "coq:exn.Found-an-\"at\"-clause-without-\"with\"-clause", "Found an "at" clause without "with" clause"], [71, 2, 1, "coq:warn.Found-no-matching-notation-to-enable-or-disable", "Found no matching notation to enable or disable"], [64, 0, 1, "coq:exn.Found-no-subterm-matching-\u2018term\u2019-in-the-current-goal", "Found no subterm matching \u2018term\u2019 in the current goal"], [64, 0, 1, "coq:exn.Found-no-subterm-matching-\u2018term\u2019-in-\u2018ident\u2019", "Found no subterm matching \u2018term\u2019 in \u2018ident\u2019"], [4, 0, 1, "coq:exn.Found-target-class-\u2018coercion_class\u2019-instead-of-\u2018coercion_class\u2019", "Found target class \u2018coercion_class\u2019 instead of \u2018coercion_class\u2019"], [59, 3, 1, "coq:cmd.From-\u2026-Dependency", "From \u2026 Dependency"], [59, 3, 1, "coq:cmd.From-\u2026-Require", "From \u2026 Require"], [4, 0, 1, "coq:exn.Funclass-cannot-be-a-source-class", "Funclass cannot be a source class"], [72, 3, 1, "coq:cmd.Function", "Function"], [72, 3, 1, "coq:cmd.Functional-Case", "Functional Case"], [72, 3, 1, "coq:cmd.Functional-Scheme", "Functional Scheme"], [44, 3, 1, "coq:cmd.Generalizable", "Generalizable"], [72, 3, 1, "coq:cmd.Generate-graph-for", "Generate graph for"], [66, 3, 1, "coq:cmd.Goal", "Goal"], [59, 4, 1, "coq:flag.Guard-Checking", "Guard Checking"], [66, 3, 1, "coq:cmd.Guarded", "Guarded"], [60, 3, 1, "coq:cmd.Hint-Constants", "Hint Constants"], [60, 3, 1, "coq:cmd.Hint-Constructors", "Hint Constructors"], [60, 3, 1, "coq:cmd.Hint-Cut", "Hint Cut"], [60, 3, 1, "coq:cmd.Hint-Extern", "Hint Extern"], [60, 3, 1, "coq:cmd.Hint-Immediate", "Hint Immediate"], [60, 3, 1, "coq:cmd.Hint-Mode", "Hint Mode"], [60, 3, 1, "coq:cmd.Hint-Opaque", "Hint Opaque"], [60, 3, 1, "coq:cmd.Hint-Projections", "Hint Projections"], [60, 3, 1, "coq:cmd.Hint-Resolve", "Hint Resolve"], [60, 3, 1, "coq:cmd.Hint-Rewrite", "Hint Rewrite"], [60, 3, 1, "coq:cmd.Hint-Transparent", "Hint Transparent"], [60, 3, 1, "coq:cmd.Hint-Unfold", "Hint Unfold"], [60, 3, 1, "coq:cmd.Hint-Variables", "Hint Variables"], [57, 3, 1, "coq:cmd.Hint-View-for", "Hint View for"], [57, 3, 1, "coq:cmd.Hint-View-for-apply", "Hint View for apply"], [57, 3, 1, "coq:cmd.Hint-View-for-move", "Hint View for move"], [28, 3, 1, "coq:cmd.Hypotheses", "Hypotheses"], [28, 3, 1, "coq:cmd.Hypothesis", "Hypothesis"], [72, 0, 1, "coq:exn.Hypothesis-\u2018ident\u2019-must-contain-at-least-one-Function", "Hypothesis \u2018ident\u2019 must contain at least one Function"], [66, 6, 1, "coq:opt.Hyps-Limit", "Hyps Limit"], [62, 0, 1, "coq:exn.I-don\u2019t-know-how-to-handle-dependent-equality", "I don\u2019t know how to handle dependent equality"], [4, 3, 1, "coq:cmd.Identity-Coercion", "Identity Coercion"], [13, 2, 1, "coq:warn.Ignored-instance-declaration-for-\u201c\u2018ident\u2019\u201d:-\u201c\u2018term\u2019\u201d-is-not-a-class", "Ignored instance declaration for \u201c\u2018ident\u2019\u201d: \u201c\u2018term\u2019\u201d is not a class"], [44, 2, 1, "coq:warn.Ignoring-implicit-binder-declaration-in-unexpected-position", "Ignoring implicit binder declaration in unexpected position"], [9, 0, 1, "coq:exn.Ill-formed-recursive-definition", "Ill-formed recursive definition"], [34, 0, 1, "coq:exn.Ill-formed-template-inductive-declaration:-not-polymorphic-on-any-universe", "Ill-formed template inductive declaration: not polymorphic on any universe"], [44, 4, 1, "coq:flag.Implicit-Arguments", "Implicit Arguments"], [44, 3, 1, "coq:cmd.Implicit-Type", "Implicit Type"], [44, 3, 1, "coq:cmd.Implicit-Types", "Implicit Types"], [35, 3, 1, "coq:cmd.Import", "Import"], [35, 3, 1, "coq:cmd.Include", "Include"], [35, 3, 1, "coq:cmd.Include-Type", "Include Type"], [57, 0, 1, "coq:exn.Incorrect-number-of-tactics-(expected-N-tactics,-was-given-M)", "Incorrect number of tactics (expected N tactics, was given M)"], [34, 3, 1, "coq:cmd.Inductive", "Inductive"], [71, 3, 1, "coq:cmd.Infix", "Infix"], [54, 3, 1, "coq:cmd.Info", "Info"], [60, 4, 1, "coq:flag.Info-Auto", "Info Auto"], [60, 4, 1, "coq:flag.Info-Eauto", "Info Eauto"], [54, 6, 1, "coq:opt.Info-Level", "Info Level"], [5, 4, 1, "coq:flag.Info-Micromega", "Info Micromega"], [60, 4, 1, "coq:flag.Info-Trivial", "Info Trivial"], [59, 3, 1, "coq:cmd.Inspect", "Inspect"], [13, 3, 1, "coq:cmd.Instance", "Instance"], [59, 3, 1, "coq:cmd.Instructions", "Instructions"], [62, 4, 1, "coq:flag.Intuition-Negation-Unfolding", "Intuition Negation Unfolding"], [59, 0, 1, "coq:exn.Invalid-backtrack", "Invalid backtrack"], [67, 8, 1, "coq:table.Keep-Equalities", "Keep Equalities"], [67, 4, 1, "coq:flag.Keep-Proof-Equalities", "Keep Proof Equalities"], [64, 4, 1, "coq:flag.Kernel-Term-Sharing", "Kernel Term Sharing"], [64, 4, 1, "coq:flag.Keyed-Unification", "Keyed Unification"], [38, 0, 1, "coq:exn.Last-block-to-end-has-name-\u2018ident\u2019", "Last block to end has name \u2018ident\u2019"], [32, 3, 1, "coq:cmd.Lemma", "Lemma"], [38, 3, 1, "coq:cmd.Let", "Let"], [38, 3, 1, "coq:cmd.Let-CoFixpoint", "Let CoFixpoint"], [38, 3, 1, "coq:cmd.Let-Fixpoint", "Let Fixpoint"], [5, 4, 1, "coq:flag.Lia-Cache", "Lia Cache"], [59, 3, 1, "coq:cmd.Load", "Load"], [59, 0, 1, "coq:exn.Load-is-not-supported-inside-proofs", "Load is not supported inside proofs"], [59, 3, 1, "coq:cmd.Locate", "Locate"], [59, 3, 1, "coq:cmd.Locate-File", "Locate File"], [59, 3, 1, "coq:cmd.Locate-Library", "Locate Library"], [59, 3, 1, "coq:cmd.Locate-Ltac", "Locate Ltac"], [59, 3, 1, "coq:cmd.Locate-Ltac2", "Locate Ltac2"], [59, 3, 1, "coq:cmd.Locate-Module", "Locate Module"], [59, 3, 1, "coq:cmd.Locate-Term", "Locate Term"], [60, 6, 1, "coq:opt.Loose-Hint-Behavior", "Loose Hint Behavior"], [54, 3, 1, "coq:cmd.Ltac", "Ltac"], [54, 4, 1, "coq:flag.Ltac-Backtrace", "Ltac Backtrace"], [54, 4, 1, "coq:flag.Ltac-Batch-Debug", "Ltac Batch Debug"], [54, 4, 1, "coq:flag.Ltac-Debug", "Ltac Debug"], [54, 4, 1, "coq:flag.Ltac-Profiling", "Ltac Profiling"], [55, 3, 1, "coq:cmd.Ltac2", "Ltac2"], [55, 4, 1, "coq:flag.Ltac2-Backtrace", "Ltac2 Backtrace"], [55, 3, 1, "coq:cmd.Ltac2-Check", "Ltac2 Check"], [55, 3, 1, "coq:cmd.Ltac2-Eval", "Ltac2 Eval"], [55, 3, 1, "coq:cmd.Ltac2-Globalize", "Ltac2 Globalize"], [55, 4, 1, "coq:flag.Ltac2-In-Ltac1-Profiling", "Ltac2 In Ltac1 Profiling"], [55, 3, 1, "coq:cmd.Ltac2-Notation", "Ltac2 Notation"], [55, 3, 1, "coq:cmd.Ltac2-Notation-(abbreviation)", "Ltac2 Notation (abbreviation)"], [55, 3, 1, "coq:cmd.Ltac2-Set", "Ltac2 Set"], [55, 3, 1, "coq:cmd.Ltac2-Type", "Ltac2 Type"], [55, 4, 1, "coq:flag.Ltac2-Typed-Notations", "Ltac2 Typed Notations"], [55, 3, 1, "coq:cmd.Ltac2-external", "Ltac2 external"], [44, 2, 1, "coq:warn.Making-shadowed-name-of-implicit-argument-accessible-by-position", "Making shadowed name of implicit argument accessible by position"], [66, 4, 1, "coq:flag.Mangle-Names", "Mangle Names"], [66, 4, 1, "coq:flag.Mangle-Names-Light", "Mangle Names Light"], [66, 6, 1, "coq:opt.Mangle-Names-Prefix", "Mangle Names Prefix"], [44, 4, 1, "coq:flag.Maximal-Implicit-Insertion", "Maximal Implicit Insertion"], [71, 0, 1, "coq:exn.Missing-mapping-for-constructor-\u2018qualid\u2019", "Missing mapping for constructor \u2018qualid\u2019"], [35, 3, 1, "coq:cmd.Module", "Module"], [35, 3, 1, "coq:cmd.Module-Type", "Module Type"], [59, 0, 1, "coq:exn.Module/section-\u2018qualid\u2019-not-found", "Module/section \u2018qualid\u2019 not found"], [14, 7, 1, "coq:attr.Monomorphic", "Monomorphic"], [71, 0, 1, "coq:exn.More-than-one-interpretation-bound-to-this-notation,-confirm-with-the-\"all\"-modifier", "More than one interpretation bound to this notation, confirm with the "all" modifier"], [71, 0, 1, "coq:exn.Multiple-'via'-options", "Multiple 'via' options"], [71, 0, 1, "coq:exn.Multiple-'warning-after'-or-'abstract-after'-options", "Multiple 'warning after' or 'abstract after' options"], [64, 6, 1, "coq:opt.NativeCompute-Profile-Filename", "NativeCompute Profile Filename"], [64, 4, 1, "coq:flag.NativeCompute-Profiling", "NativeCompute Profiling"], [64, 4, 1, "coq:flag.NativeCompute-Timing", "NativeCompute Timing"], [66, 4, 1, "coq:flag.Nested-Proofs-Allowed", "Nested Proofs Allowed"], [66, 2, 1, "coq:warn.New-Collection-definition-of-\u2018ident\u2019-shadows-the-previous-one", "New Collection definition of \u2018ident\u2019 shadows the previous one"], [9, 3, 1, "coq:cmd.Next-Obligation", "Next Obligation"], [5, 4, 1, "coq:flag.Nia-Cache", "Nia Cache"], [54, 0, 1, "coq:exn.No-applicable-tactic", "No applicable tactic"], [72, 0, 1, "coq:exn.No-argument-name-\u2018ident\u2019", "No argument name \u2018ident\u2019"], [54, 0, 1, "coq:exn.No-evars", "No evars"], [35, 0, 1, "coq:exn.No-field-named-\u2018ident\u2019-in-\u2018qualid\u2019", "No field named \u2018ident\u2019 in \u2018qualid\u2019"], [66, 0, 1, "coq:exn.No-focused-proof", "No focused proof"], [66, 0, 1, "coq:exn.No-focused-proof-(No-proof-editing-in-progress)", "No focused proof (No proof-editing in progress)"], [66, 0, 1, "coq:exn.No-focused-proof-to-restart", "No focused proof to restart"], [64, 0, 1, "coq:exn.No-head-constant-to-reduce", "No head constant to reduce"], [54, 0, 1, "coq:exn.No-matching-clauses-for-match", "No matching clauses for match"], [54, 0, 1, "coq:exn.No-matching-clauses-for-match-goal", "No matching clauses for match goal"], [71, 0, 1, "coq:exn.No-notation-provided", "No notation provided"], [67, 0, 1, "coq:exn.No-primitive-equality-found", "No primitive equality found"], [58, 0, 1, "coq:exn.No-product-even-after-head-reduction", "No product even after head-reduction"], [3, 0, 1, "coq:exn.No-progress-made", "No progress made"], [58, 0, 1, "coq:exn.No-quantified-hypothesis-named-\u2018ident\u2019-in-current-goal-even-after-head-reduction", "No quantified hypothesis named \u2018ident\u2019 in current goal even after head-reduction"], [58, 0, 1, "coq:exn.No-such-assumption", "No such assumption"], [58, 0, 1, "coq:exn.No-such-binder", "No such binder"], [58, 0, 1, "coq:exn.No-such-bound-variable-\u2018ident\u2019-(no-bound-variables-at-all-in-the-expression)", "No such bound variable \u2018ident\u2019 (no bound variables at all in the expression)"], [66, 0, 1, "coq:exn.No-such-goal", "No such goal"], [66, 0, 1, "coq:exn.No-such-goal-(\u2018ident\u2019)", "No such goal (\u2018ident\u2019)"], [66, 0, 1, "coq:exn.No-such-goal-(\u2018natural\u2019)", "No such goal (\u2018natural\u2019)"], [58, 0, 1, "coq:exn.No-such-hypothesis:-\u2018ident\u2019", "No such hypothesis: \u2018ident\u2019"], [58, 0, 1, "coq:exn.No-\u2018natural\u2019-th-non-dependent-hypothesis-in-current-goal-even-after-head-reduction", "No \u2018natural\u2019-th non dependent hypothesis in current goal even after head-reduction"], [46, 0, 1, "coq:exn.Non-exhaustive-pattern-matching", "Non exhaustive pattern matching"], [9, 0, 1, "coq:exn.Non-extensible-universe-declaration-not-supported-with-monomorphic-Program-Definition", "Non extensible universe declaration not supported with monomorphic Program Definition"], [34, 0, 1, "coq:exn.Non-strictly-positive-occurrence-of-\u2018ident\u2019-in-\u2018type\u2019", "Non strictly positive occurrence of \u2018ident\u2019 in \u2018type\u2019"], [14, 7, 1, "coq:attr.NonCumulative", "NonCumulative"], [67, 4, 1, "coq:flag.Nonrecursive-Elimination-Schemes", "Nonrecursive Elimination Schemes"], [54, 0, 1, "coq:exn.Not-a-context-variable", "Not a context variable"], [67, 0, 1, "coq:exn.Not-a-discriminable-equality", "Not a discriminable equality"], [67, 0, 1, "coq:exn.Not-a-negated-primitive-equality", "Not a negated primitive equality"], [11, 0, 1, "coq:exn.Not-a-valid-ring-equation", "Not a valid ring equation"], [54, 0, 1, "coq:exn.Not-a-variable-or-hypothesis", "Not a variable or hypothesis"], [54, 0, 1, "coq:exn.Not-an-evar", "Not an evar"], [58, 0, 1, "coq:exn.Not-an-exact-proof", "Not an exact proof"], [67, 0, 1, "coq:exn.Not-an-inductive-goal-with-1-constructor", "Not an inductive goal with 1 constructor"], [67, 0, 1, "coq:exn.Not-an-inductive-goal-with-2-constructors", "Not an inductive goal with 2 constructors"], [67, 0, 1, "coq:exn.Not-an-inductive-product", "Not an inductive product"], [64, 0, 1, "coq:exn.Not-convertible", "Not convertible"], [67, 0, 1, "coq:exn.Not-enough-constructors", "Not enough constructors"], [44, 0, 1, "coq:exn.Not-enough-non-implicit-arguments-to-accept-the-argument-bound-to-\u2018ident\u2019", "Not enough non implicit arguments to accept the argument bound to \u2018ident\u2019"], [44, 0, 1, "coq:exn.Not-enough-non-implicit-arguments-to-accept-the-argument-bound-to-\u2018natural\u2019", "Not enough non implicit arguments to accept the argument bound to \u2018natural\u2019"], [54, 0, 1, "coq:exn.Not-equal", "Not equal"], [54, 0, 1, "coq:exn.Not-equal-(due-to-universes)", "Not equal (due to universes)"], [54, 0, 1, "coq:exn.Not-ground", "Not ground"], [72, 0, 1, "coq:exn.Not-the-right-number-of-induction-arguments", "Not the right number of induction arguments"], [58, 0, 1, "coq:exn.Not-the-right-number-of-missing-arguments-(expected-\u2018natural\u2019)", "Not the right number of missing arguments (expected \u2018natural\u2019)"], [71, 3, 1, "coq:cmd.Notation", "Notation"], [71, 3, 1, "coq:cmd.Notation-(abbreviation)", "Notation (abbreviation)"], [55, 0, 1, "coq:exn.Notation-levels-must-range-between-0-and-6", "Notation levels must range between 0 and 6"], [67, 0, 1, "coq:exn.Nothing-to-inject", "Nothing to inject"], [3, 0, 1, "coq:exn.Nothing-to-rewrite", "Nothing to rewrite"], [5, 4, 1, "coq:flag.Nra-Cache", "Nra Cache"], [71, 3, 1, "coq:cmd.Number-Notation", "Number Notation"], [9, 3, 1, "coq:cmd.Obligation", "Obligation"], [9, 3, 1, "coq:cmd.Obligation-Tactic", "Obligation Tactic"], [9, 3, 1, "coq:cmd.Obligations", "Obligations"], [64, 3, 1, "coq:cmd.Opaque", "Opaque"], [71, 3, 1, "coq:cmd.Open-Scope", "Open Scope"], [66, 3, 1, "coq:cmd.Optimize-Heap", "Optimize Heap"], [66, 3, 1, "coq:cmd.Optimize-Proof", "Optimize Proof"], [28, 3, 1, "coq:cmd.Parameter", "Parameter"], [28, 3, 1, "coq:cmd.Parameters", "Parameters"], [44, 4, 1, "coq:flag.Parsing-Explicit", "Parsing Explicit"], [14, 7, 1, "coq:attr.Polymorphic", "Polymorphic"], [14, 4, 1, "coq:flag.Polymorphic-Inductive-Cumulativity", "Polymorphic Inductive Cumulativity"], [14, 0, 1, "coq:exn.Polymorphic-universe-constraints-can-only-be-declared-inside-sections,-use-Monomorphic-Constraint-instead", "Polymorphic universe constraints can only be declared inside sections, use Monomorphic Constraint instead"], [14, 0, 1, "coq:exn.Polymorphic-universes-can-only-be-declared-inside-sections,-use-Monomorphic-Universe-instead", "Polymorphic universes can only be declared inside sections, use Monomorphic Universe instead"], [59, 4, 1, "coq:flag.Positivity-Checking", "Positivity Checking"], [57, 3, 1, "coq:cmd.Prenex-Implicits", "Prenex Implicits"], [9, 3, 1, "coq:cmd.Preterm", "Preterm"], [59, 3, 1, "coq:cmd.Primitive", "Primitive"], [37, 4, 1, "coq:flag.Primitive-Projections", "Primitive Projections"], [59, 3, 1, "coq:cmd.Print", "Print"], [59, 3, 1, "coq:cmd.Print-All", "Print All"], [59, 3, 1, "coq:cmd.Print-All-Dependencies", "Print All Dependencies"], [59, 3, 1, "coq:cmd.Print-Assumptions", "Print Assumptions"], [42, 3, 1, "coq:cmd.Print-Canonical-Projections", "Print Canonical Projections"], [4, 3, 1, "coq:cmd.Print-Classes", "Print Classes"], [4, 3, 1, "coq:cmd.Print-Coercion-Paths", "Print Coercion Paths"], [4, 3, 1, "coq:cmd.Print-Coercions", "Print Coercions"], [71, 3, 1, "coq:cmd.Print-Custom-Grammar", "Print Custom Grammar"], [66, 3, 1, "coq:cmd.Print-Debug-GC", "Print Debug GC"], [64, 3, 1, "coq:cmd.Print-Equivalent-Keys", "Print Equivalent Keys"], [2, 3, 1, "coq:cmd.Print-Extraction-Blacklist", "Print Extraction Blacklist"], [2, 3, 1, "coq:cmd.Print-Extraction-Callback", "Print Extraction Callback"], [2, 3, 1, "coq:cmd.Print-Extraction-Foreign", "Print Extraction Foreign"], [2, 3, 1, "coq:cmd.Print-Extraction-Inline", "Print Extraction Inline"], [11, 3, 1, "coq:cmd.Print-Fields", "Print Fields"], [62, 3, 1, "coq:cmd.Print-Firstorder-Solver", "Print Firstorder Solver"], [71, 3, 1, "coq:cmd.Print-Grammar", "Print Grammar"], [4, 3, 1, "coq:cmd.Print-Graph", "Print Graph"], [60, 3, 1, "coq:cmd.Print-Hint", "Print Hint"], [60, 3, 1, "coq:cmd.Print-HintDb", "Print HintDb"], [44, 3, 1, "coq:cmd.Print-Implicit", "Print Implicit"], [13, 3, 1, "coq:cmd.Print-Instances", "Print Instances"], [71, 3, 1, "coq:cmd.Print-Keywords", "Print Keywords"], [59, 3, 1, "coq:cmd.Print-Libraries", "Print Libraries"], [59, 3, 1, "coq:cmd.Print-LoadPath", "Print LoadPath"], [54, 3, 1, "coq:cmd.Print-Ltac", "Print Ltac"], [54, 3, 1, "coq:cmd.Print-Ltac-Signatures", "Print Ltac Signatures"], [55, 3, 1, "coq:cmd.Print-Ltac2", "Print Ltac2"], [55, 3, 1, "coq:cmd.Print-Ltac2-Signatures", "Print Ltac2 Signatures"], [55, 3, 1, "coq:cmd.Print-Ltac2-Type", "Print Ltac2 Type"], [59, 3, 1, "coq:cmd.Print-ML-Modules", "Print ML Modules"], [59, 3, 1, "coq:cmd.Print-ML-Path", "Print ML Path"], [35, 3, 1, "coq:cmd.Print-Module", "Print Module"], [35, 3, 1, "coq:cmd.Print-Module-Type", "Print Module Type"], [35, 3, 1, "coq:cmd.Print-Namespace", "Print Namespace"], [71, 3, 1, "coq:cmd.Print-Notation", "Print Notation"], [59, 3, 1, "coq:cmd.Print-Opaque-Dependencies", "Print Opaque Dependencies"], [29, 3, 1, "coq:cmd.Print-Options", "Print Options"], [59, 3, 1, "coq:cmd.Print-Registered", "Print Registered"], [59, 3, 1, "coq:cmd.Print-Registered-Schemes", "Print Registered Schemes"], [60, 3, 1, "coq:cmd.Print-Rewrite-HintDb", "Print Rewrite HintDb"], [11, 3, 1, "coq:cmd.Print-Rings", "Print Rings"], [71, 3, 1, "coq:cmd.Print-Scope", "Print Scope"], [71, 3, 1, "coq:cmd.Print-Scopes", "Print Scopes"], [59, 3, 1, "coq:cmd.Print-Section", "Print Section"], [64, 3, 1, "coq:cmd.Print-Strategies", "Print Strategies"], [64, 3, 1, "coq:cmd.Print-Strategy", "Print Strategy"], [29, 3, 1, "coq:cmd.Print-Table", "Print Table"], [29, 3, 1, "coq:cmd.Print-Tables", "Print Tables"], [59, 3, 1, "coq:cmd.Print-Transparent-Dependencies", "Print Transparent Dependencies"], [13, 3, 1, "coq:cmd.Print-Typeclasses", "Print Typeclasses"], [59, 3, 1, "coq:cmd.Print-Typing-Flags", "Print Typing Flags"], [14, 3, 1, "coq:cmd.Print-Universes", "Print Universes"], [71, 3, 1, "coq:cmd.Print-Visibility", "Print Visibility"], [59, 4, 1, "coq:flag.Printing-All", "Printing All"], [46, 4, 1, "coq:flag.Printing-Allow-Match-Default-Clause", "Printing Allow Match Default Clause"], [4, 8, 1, "coq:table.Printing-Coercion", "Printing Coercion"], [4, 4, 1, "coq:flag.Printing-Coercions", "Printing Coercions"], [59, 4, 1, "coq:flag.Printing-Compact-Contexts", "Printing Compact Contexts"], [37, 8, 1, "coq:table.Printing-Constructor", "Printing Constructor"], [59, 4, 1, "coq:flag.Printing-Dependent-Evars-Line", "Printing Dependent Evars Line"], [59, 6, 1, "coq:opt.Printing-Depth", "Printing Depth"], [43, 4, 1, "coq:flag.Printing-Existential-Instances", "Printing Existential Instances"], [46, 4, 1, "coq:flag.Printing-Factorizable-Match-Patterns", "Printing Factorizable Match Patterns"], [66, 4, 1, "coq:flag.Printing-Goal-Names", "Printing Goal Names"], [66, 4, 1, "coq:flag.Printing-Goal-Tags", "Printing Goal Tags"], [46, 8, 1, "coq:table.Printing-If", "Printing If"], [44, 4, 1, "coq:flag.Printing-Implicit", "Printing Implicit"], [44, 4, 1, "coq:flag.Printing-Implicit-Defensive", "Printing Implicit Defensive"], [46, 8, 1, "coq:table.Printing-Let", "Printing Let"], [46, 4, 1, "coq:flag.Printing-Match-All-Subterms", "Printing Match All Subterms"], [46, 4, 1, "coq:flag.Printing-Matching", "Printing Matching"], [71, 4, 1, "coq:flag.Printing-Notations", "Printing Notations"], [71, 4, 1, "coq:flag.Printing-Parentheses", "Printing Parentheses"], [37, 4, 1, "coq:flag.Printing-Primitive-Projection-Parameters", "Printing Primitive Projection Parameters"], [37, 4, 1, "coq:flag.Printing-Projections", "Printing Projections"], [71, 4, 1, "coq:flag.Printing-Raw-Literals", "Printing Raw Literals"], [37, 8, 1, "coq:table.Printing-Record", "Printing Record"], [37, 4, 1, "coq:flag.Printing-Records", "Printing Records"], [12, 4, 1, "coq:flag.Printing-Relevance-Marks", "Printing Relevance Marks"], [46, 4, 1, "coq:flag.Printing-Synth", "Printing Synth"], [59, 4, 1, "coq:flag.Printing-Unfocused", "Printing Unfocused"], [37, 4, 1, "coq:flag.Printing-Unfolded-Projection-As-Match", "Printing Unfolded Projection As Match"], [14, 4, 1, "coq:flag.Printing-Universes", "Printing Universes"], [44, 4, 1, "coq:flag.Printing-Use-Implicit-Types", "Printing Use Implicit Types"], [59, 6, 1, "coq:opt.Printing-Width", "Printing Width"], [46, 4, 1, "coq:flag.Printing-Wildcard", "Printing Wildcard"], [40, 7, 1, "coq:attr.Private", "Private"], [14, 4, 1, "coq:flag.Private-Polymorphic-Universes", "Private Polymorphic Universes"], [59, 3, 1, "coq:cmd.Profile", "Profile"], [9, 7, 1, "coq:attr.Program", "Program"], [9, 4, 1, "coq:flag.Program-Cases", "Program Cases"], [9, 4, 1, "coq:flag.Program-Generalized-Coercion", "Program Generalized Coercion"], [9, 4, 1, "coq:flag.Program-Mode", "Program Mode"], [66, 3, 1, "coq:cmd.Proof", "Proof"], [66, 3, 1, "coq:cmd.Proof-Mode", "Proof Mode"], [66, 3, 1, "coq:cmd.Proof-`term`", "Proof `term`"], [66, 3, 1, "coq:cmd.Proof-using", "Proof using"], [60, 3, 1, "coq:cmd.Proof-with", "Proof with"], [32, 3, 1, "coq:cmd.Property", "Property"], [32, 3, 1, "coq:cmd.Proposition", "Proposition"], [5, 5, 1, "coq:thm.Psatz", "Psatz"], [2, 3, 1, "coq:cmd.Pwd", "Pwd"], [66, 3, 1, "coq:cmd.Qed", "Qed"], [59, 3, 1, "coq:cmd.Quit", "Quit"], [37, 3, 1, "coq:cmd.Record", "Record"], [37, 0, 1, "coq:exn.Records-declared-with-the-keyword-Record-or-Structure-cannot-be-recursive", "Records declared with the keyword Record or Structure cannot be recursive"], [2, 3, 1, "coq:cmd.Recursive-Extraction", "Recursive Extraction"], [2, 3, 1, "coq:cmd.Recursive-Extraction-Library", "Recursive Extraction Library"], [59, 3, 1, "coq:cmd.Redirect", "Redirect"], [59, 3, 1, "coq:cmd.Register", "Register"], [59, 3, 1, "coq:cmd.Register-Inline", "Register Inline"], [59, 3, 1, "coq:cmd.Register-Scheme", "Register Scheme"], [64, 4, 1, "coq:flag.Regular-Subst-Tactic", "Regular Subst Tactic"], [32, 3, 1, "coq:cmd.Remark", "Remark"], [29, 3, 1, "coq:cmd.Remove", "Remove"], [60, 3, 1, "coq:cmd.Remove-Hints", "Remove Hints"], [59, 3, 1, "coq:cmd.Require", "Require"], [59, 3, 1, "coq:cmd.Require-Export", "Require Export"], [59, 3, 1, "coq:cmd.Require-Import", "Require Import"], [71, 3, 1, "coq:cmd.Reserved-Infix", "Reserved Infix"], [71, 3, 1, "coq:cmd.Reserved-Notation", "Reserved Notation"], [59, 3, 1, "coq:cmd.Reset", "Reset"], [2, 3, 1, "coq:cmd.Reset-Extraction-Blacklist", "Reset Extraction Blacklist"], [2, 3, 1, "coq:cmd.Reset-Extraction-Callback", "Reset Extraction Callback"], [2, 3, 1, "coq:cmd.Reset-Extraction-Inline", "Reset Extraction Inline"], [59, 3, 1, "coq:cmd.Reset-Initial", "Reset Initial"], [54, 3, 1, "coq:cmd.Reset-Ltac-Profile", "Reset Ltac Profile"], [66, 3, 1, "coq:cmd.Restart", "Restart"], [44, 4, 1, "coq:flag.Reversible-Pattern-Implicit", "Reversible Pattern Implicit"], [10, 3, 1, "coq:cmd.Rewrite-Rule", "Rewrite Rule"], [10, 3, 1, "coq:cmd.Rewrite-Rules", "Rewrite Rules"], [10, 0, 1, "coq:exn.Rewrite-rule-declaration-requires-passing-the-flag-\"-allow-rewrite-rules\"", "Rewrite rule declaration requires passing the flag "-allow-rewrite-rules""], [67, 4, 1, "coq:flag.Rewriting-Schemes", "Rewriting Schemes"], [11, 0, 1, "coq:exn.Ring-operation-should-be-declared-as-a-morphism", "Ring operation should be declared as a morphism"], [12, 0, 1, "coq:exn.SProp-is-disallowed-because-the-\"Allow-StrictProp\"-flag-is-off", "SProp is disallowed because the "Allow StrictProp" flag is off"], [66, 3, 1, "coq:cmd.Save", "Save"], [67, 3, 1, "coq:cmd.Scheme", "Scheme"], [67, 3, 1, "coq:cmd.Scheme-Boolean-Equality", "Scheme Boolean Equality"], [67, 3, 1, "coq:cmd.Scheme-Equality", "Scheme Equality"], [71, 0, 1, "coq:exn.Scope-delimiters-should-not-start-with-an-underscore", "Scope delimiters should not start with an underscore"], [71, 0, 1, "coq:exn.Scope-names-should-not-start-with-an-underscore", "Scope names should not start with an underscore"], [59, 3, 1, "coq:cmd.Search", "Search"], [59, 8, 1, "coq:table.Search-Blacklist", "Search Blacklist"], [59, 4, 1, "coq:flag.Search-Output-Name-Only", "Search Output Name Only"], [59, 3, 1, "coq:cmd.SearchPattern", "SearchPattern"], [59, 3, 1, "coq:cmd.SearchRewrite", "SearchRewrite"], [38, 3, 1, "coq:cmd.Section", "Section"], [64, 0, 1, "coq:exn.Section-variable-\u2018ident\u2019-occurs-implicitly-in-global-declaration-\u2018qualid\u2019-present-in-hypothesis-\u2018ident\u2019", "Section variable \u2018ident\u2019 occurs implicitly in global declaration \u2018qualid\u2019 present in hypothesis \u2018ident\u2019"], [64, 0, 1, "coq:exn.Section-variable-\u2018ident\u2019-occurs-implicitly-in-global-declaration-\u2018qualid\u2019-present-in-the-conclusion", "Section variable \u2018ident\u2019 occurs implicitly in global declaration \u2018qualid\u2019 present in the conclusion"], [2, 3, 1, "coq:cmd.Separate-Extraction", "Separate Extraction"], [29, 3, 1, "coq:cmd.Set", "Set"], [35, 4, 1, "coq:flag.Short-Module-Printing", "Short Module Printing"], [66, 3, 1, "coq:cmd.Show", "Show"], [66, 3, 1, "coq:cmd.Show-Conjectures", "Show Conjectures"], [66, 3, 1, "coq:cmd.Show-Existentials", "Show Existentials"], [2, 3, 1, "coq:cmd.Show-Extraction", "Show Extraction"], [66, 3, 1, "coq:cmd.Show-Goal", "Show Goal"], [66, 3, 1, "coq:cmd.Show-Intro", "Show Intro"], [66, 3, 1, "coq:cmd.Show-Intros", "Show Intros"], [5, 3, 1, "coq:cmd.Show-Lia-Profile", "Show Lia Profile"], [54, 3, 1, "coq:cmd.Show-Ltac-Profile", "Show Ltac Profile"], [66, 3, 1, "coq:cmd.Show-Match", "Show Match"], [9, 3, 1, "coq:cmd.Show-Obligation-Tactic", "Show Obligation Tactic"], [66, 3, 1, "coq:cmd.Show-Proof", "Show Proof"], [66, 3, 1, "coq:cmd.Show-Universes", "Show Universes"], [5, 3, 1, "coq:cmd.Show-Zify", "Show Zify"], [35, 0, 1, "coq:exn.Signature-components-for-field-\u2018ident\u2019-do-not-match", "Signature components for field \u2018ident\u2019 do not match"], [59, 4, 1, "coq:flag.Silent", "Silent"], [9, 3, 1, "coq:cmd.Solve-All-Obligations", "Solve All Obligations"], [9, 3, 1, "coq:cmd.Solve-Obligations", "Solve Obligations"], [66, 4, 1, "coq:flag.Solve-Unification-Constraints", "Solve Unification Constraints"], [57, 4, 1, "coq:flag.SsrHave-NoTCResolution", "SsrHave NoTCResolution"], [57, 4, 1, "coq:flag.SsrIdents", "SsrIdents"], [57, 4, 1, "coq:flag.SsrOldRewriteGoalsOrder", "SsrOldRewriteGoalsOrder"], [57, 4, 1, "coq:flag.SsrRewrite", "SsrRewrite"], [71, 2, 1, "coq:warn.Stack-overflow-or-segmentation-fault-happens-when-working-with-large-numbers-in-\u2018type\u2019-(threshold-may-vary-depending-on-your-system-limits-and-on-the-command-executed)", "Stack overflow or segmentation fault happens when working with large numbers in \u2018type\u2019 (threshold may vary depending on your system limits and on the command executed)"], [64, 3, 1, "coq:cmd.Strategy", "Strategy"], [44, 4, 1, "coq:flag.Strict-Implicit", "Strict Implicit"], [14, 4, 1, "coq:flag.Strict-Universe-Declaration", "Strict Universe Declaration"], [71, 3, 1, "coq:cmd.String-Notation", "String Notation"], [44, 4, 1, "coq:flag.Strongly-Strict-Implicit", "Strongly Strict Implicit"], [67, 4, 1, "coq:flag.Structural-Injection", "Structural Injection"], [37, 3, 1, "coq:cmd.Structure", "Structure"], [4, 3, 1, "coq:cmd.SubClass", "SubClass"], [59, 3, 1, "coq:cmd.Succeed", "Succeed"], [66, 4, 1, "coq:flag.Suggest-Proof-Using", "Suggest Proof Using"], [10, 3, 1, "coq:cmd.Symbol", "Symbol"], [10, 3, 1, "coq:cmd.Symbols", "Symbols"], [71, 0, 1, "coq:exn.Syntax-error:-[prim:reference]-expected-after-'Notation'-(in-[vernac:command])", "Syntax error: [prim:reference] expected after 'Notation' (in [vernac:command])"], [71, 0, 1, "coq:exn.Syntax-error:-[prim:reference]-expected-after-[prim:reference]-(in-[vernac:command])", "Syntax error: [prim:reference] expected after [prim:reference] (in [vernac:command])"], [71, 3, 1, "coq:cmd.Tactic-Notation", "Tactic Notation"], [54, 0, 1, "coq:exn.Tactic-failure", "Tactic failure"], [54, 0, 1, "coq:exn.Tactic-failure-(level-\u2018natural\u2019)", "Tactic failure (level \u2018natural\u2019)"], [54, 0, 1, "coq:exn.Tactic-failure:--succeeds", "Tactic failure: <tactic closure> succeeds"], [64, 0, 1, "coq:exn.Tactic-failure:-Setoid-library-not-loaded", "Tactic failure: Setoid library not loaded"], [64, 0, 1, "coq:exn.Tactic-generated-a-subgoal-identical-to-the-original-goal", "Tactic generated a subgoal identical to the original goal"], [64, 0, 1, "coq:exn.Terms-do-not-have-convertible-types", "Terms do not have convertible types"], [29, 3, 1, "coq:cmd.Test", "Test"], [60, 0, 1, "coq:exn.The-\"at\"-syntax-isn't-available-yet-for-the-autorewrite-tactic", "The "at" syntax isn't available yet for the autorewrite tactic"], [41, 0, 1, "coq:exn.The-&-modifier-may-only-occur-once", "The & modifier may only occur once"], [71, 2, 1, "coq:warn.The-'abstract-after'-directive-has-no-effect-when-the-parsing-function-(\u2018qualid\u2019)-targets-an-option-type", "The 'abstract after' directive has no effect when the parsing function (\u2018qualid\u2019) targets an option type"], [41, 0, 1, "coq:exn.The-'clear-implicits'-flag-must-be-omitted-if-implicit-annotations-are-given", "The 'clear implicits' flag must be omitted if implicit annotations are given"], [41, 0, 1, "coq:exn.The-'default-implicits'-flag-is-incompatible-with-implicit-annotations", "The 'default implicits' flag is incompatible with implicit annotations"], [41, 0, 1, "coq:exn.The-/-modifier-may-only-occur-once", "The / modifier may only occur once"], [59, 0, 1, "coq:exn.The-command-has-not-failed!", "The command has not failed!"], [34, 0, 1, "coq:exn.The-conclusion-of-\u2018type\u2019-is-not-valid;-it-must-be-built-from-\u2018ident\u2019", "The conclusion of \u2018type\u2019 is not valid; it must be built from \u2018ident\u2019"], [46, 0, 1, "coq:exn.The-constructor-\u2018ident\u2019-expects-\u2018natural\u2019-arguments", "The constructor \u2018ident\u2019 expects \u2018natural\u2019 arguments"], [14, 0, 1, "coq:exn.The-cumulative-attribute-can-only-be-used-in-a-polymorphic-context", "The cumulative attribute can only be used in a polymorphic context"], [46, 0, 1, "coq:exn.The-elimination-predicate-term-should-be-of-arity-\u2018natural\u2019-(for-non-dependent-case)-or-\u2018natural\u2019-(for-dependent-case)", "The elimination predicate term should be of arity \u2018natural\u2019 (for non dependent case) or \u2018natural\u2019 (for dependent case)"], [35, 0, 1, "coq:exn.The-field-\u2018ident\u2019-is-missing-in-\u2018qualid\u2019", "The field \u2018ident\u2019 is missing in \u2018qualid\u2019"], [72, 0, 1, "coq:exn.The-recursive-argument-must-be-specified", "The recursive argument must be specified"], [55, 0, 1, "coq:exn.The-reference-X-was-not-found-in-the-current-environment", "The reference X was not found in the current environment"], [64, 0, 1, "coq:exn.The-reference-is-not-unfoldable", "The reference is not unfoldable"], [64, 0, 1, "coq:exn.The-reference-\u2018qualid\u2019-was-not-found-in-the-current-environment", "The reference \u2018qualid\u2019 was not found in the current environment"], [58, 0, 1, "coq:exn.The-term-\"\u2018type\u2019\"-has-type-\"\u2018type\u2019\"-which-should-be-Set,-Prop-or-Type", "The term "\u2018type\u2019" has type "\u2018type\u2019" which should be Set, Prop or Type"], [2, 0, 1, "coq:exn.The-term-\u2018qualid\u2019-is-already-defined-as-foreign-custom-constant", "The term \u2018qualid\u2019 is already defined as foreign custom constant"], [2, 0, 1, "coq:exn.The-term-\u2018qualid\u2019-is-already-defined-as-inline-custom-constant", "The term \u2018qualid\u2019 is already defined as inline custom constant"], [32, 0, 1, "coq:exn.The-term-\u2018term\u2019-has-type-\u2018type\u2019-which-should-be-Set,-Prop-or-Type", "The term \u2018term\u2019 has type \u2018type\u2019 which should be Set, Prop or Type"], [32, 0, 1, "coq:exn.The-term-\u2018term\u2019-has-type-\u2018type\u2019-while-it-is-expected-to-have-type-\u2018type\u2019'", "The term \u2018term\u2019 has type \u2018type\u2019 while it is expected to have type \u2018type\u2019'"], [67, 0, 1, "coq:exn.The-type-has-no-constructors", "The type has no constructors"], [59, 0, 1, "coq:exn.The-type-\u2018ident\u2019-must-be-registered-before-this-construction-can-be-typechecked", "The type \u2018ident\u2019 must be registered before this construction can be typechecked"], [46, 0, 1, "coq:exn.The-variable-ident-is-bound-several-times-in-pattern-term", "The variable ident is bound several times in pattern term"], [58, 0, 1, "coq:exn.The-variable-\u2018ident\u2019-is-already-declared", "The variable \u2018ident\u2019 is already declared"], [40, 0, 1, "coq:exn.The-\u2018natural\u2019-th-argument-of-\u2018ident\u2019-must-be-\u2018ident\u2019-in-\u2018type\u2019", "The \u2018natural\u2019 th argument of \u2018ident\u2019 must be \u2018ident\u2019 in \u2018type\u2019"], [32, 3, 1, "coq:cmd.Theorem", "Theorem"], [54, 0, 1, "coq:exn.There-is-already-an-Ltac-named-\u2018qualid\u2019", "There is already an Ltac named \u2018qualid\u2019"], [54, 0, 1, "coq:exn.There-is-no-Ltac-named-\u2018qualid\u2019", "There is no Ltac named \u2018qualid\u2019"], [29, 2, 1, "coq:warn.There-is-no-flag-or-option-with-this-name:-\"\u2018setting_name\u2019\"", "There is no flag or option with this name: "\u2018setting_name\u2019""], [29, 0, 1, "coq:exn.There-is-no-flag,-option-or-table-with-this-name:-\"\u2018setting_name\u2019\"", "There is no flag, option or table with this name: "\u2018setting_name\u2019""], [29, 0, 1, "coq:exn.There-is-no-qualid-valued-table-with-this-name:-\"\u2018setting_name\u2019\"", "There is no qualid-valued table with this name: "\u2018setting_name\u2019""], [29, 0, 1, "coq:exn.There-is-no-string-valued-table-with-this-name:-\"\u2018setting_name\u2019\"", "There is no string-valued table with this name: "\u2018setting_name\u2019""], [38, 0, 1, "coq:exn.There-is-nothing-to-end", "There is nothing to end"], [29, 2, 1, "coq:warn.This-command-does-not-support-this-attribute", "This command does not support this attribute"], [59, 0, 1, "coq:exn.This-object-does-not-support-universe-names", "This object does not support universe names"], [66, 0, 1, "coq:exn.This-proof-is-focused,-but-cannot-be-unfocused-this-way", "This proof is focused, but cannot be unfocused this way"], [54, 0, 1, "coq:exn.This-tactic-has-more-than-one-success", "This tactic has more than one success"], [59, 3, 1, "coq:cmd.Time", "Time"], [59, 3, 1, "coq:cmd.Timeout", "Timeout"], [71, 2, 1, "coq:warn.To-avoid-stack-overflow,-large-numbers-in-\u2018type\u2019-are-interpreted-as-applications-of-\u2018qualid\u2019", "To avoid stack overflow, large numbers in \u2018type\u2019 are interpreted as applications of \u2018qualid\u2019"], [41, 0, 1, "coq:exn.To-rename-arguments-the-'rename'-flag-must-be-specified", "To rename arguments the 'rename' flag must be specified"], [64, 3, 1, "coq:cmd.Transparent", "Transparent"], [9, 4, 1, "coq:flag.Transparent-Obligations", "Transparent Obligations"], [35, 2, 1, "coq:warn.Trying-to-mask-the-absolute-name-\u2018qualid\u2019!", "Trying to mask the absolute name \u2018qualid\u2019!"], [59, 3, 1, "coq:cmd.Type", "Type"], [67, 0, 1, "coq:exn.Type-of-\u2018ident\u2019-is-not-an-equality-of-recognized-\u03a3-types:-expected-one-of-sig-sig2-sigT-sigT2-sigT2-ex-or-ex2-but-got-\u2018term\u2019", "Type of \u2018ident\u2019 is not an equality of recognized \u03a3 types: expected one of sig sig2 sigT sigT2 sigT2 ex or ex2 but got \u2018term\u2019"], [13, 4, 1, "coq:flag.Typeclass-Resolution-For-Conversion", "Typeclass Resolution For Conversion"], [13, 4, 1, "coq:flag.Typeclasses-Debug", "Typeclasses Debug"], [13, 6, 1, "coq:opt.Typeclasses-Debug-Verbosity", "Typeclasses Debug Verbosity"], [13, 6, 1, "coq:opt.Typeclasses-Default-Mode", "Typeclasses Default Mode"], [13, 4, 1, "coq:flag.Typeclasses-Dependency-Order", "Typeclasses Dependency Order"], [13, 6, 1, "coq:opt.Typeclasses-Depth", "Typeclasses Depth"], [13, 4, 1, "coq:flag.Typeclasses-Iterative-Deepening", "Typeclasses Iterative Deepening"], [13, 4, 1, "coq:flag.Typeclasses-Limit-Intros", "Typeclasses Limit Intros"], [13, 3, 1, "coq:cmd.Typeclasses-Opaque", "Typeclasses Opaque"], [13, 4, 1, "coq:flag.Typeclasses-Strict-Resolution", "Typeclasses Strict Resolution"], [13, 3, 1, "coq:cmd.Typeclasses-Transparent", "Typeclasses Transparent"], [13, 4, 1, "coq:flag.Typeclasses-Unique-Instances", "Typeclasses Unique Instances"], [13, 4, 1, "coq:flag.Typeclasses-Unique-Solutions", "Typeclasses Unique Solutions"], [13, 3, 1, "coq:cmd.Typeclasses-eauto", "Typeclasses eauto"], [67, 0, 1, "coq:exn.Unable-to-find-an-instance-for-the-variables-\u2018ident\u2019-\u2026-\u2018ident\u2019", "Unable to find an instance for the variables \u2018ident\u2019 \u2026 \u2018ident\u2019"], [58, 0, 1, "coq:exn.Unable-to-find-an-instance-for-the-variables-\u2018ident\u2019\u2026\u2018ident\u2019", "Unable to find an instance for the variables \u2018ident\u2019\u2026\u2018ident\u2019"], [46, 0, 1, "coq:exn.Unable-to-infer-a-match-predicate", "Unable to infer a match predicate"], [3, 0, 1, "coq:exn.Unable-to-satisfy-the-rewriting-constraints", "Unable to satisfy the rewriting constraints"], [58, 0, 1, "coq:exn.Unable-to-unify-\u2018one_term\u2019-with-\u2018one_term\u2019", "Unable to unify \u2018one_term\u2019 with \u2018one_term\u2019"], [55, 0, 1, "coq:exn.Unbound-[value|constructor]-X", "Unbound [value|constructor] X"], [54, 0, 1, "coq:exn.Unbound-context-identifier-\u2018ident\u2019", "Unbound context identifier \u2018ident\u2019"], [14, 0, 1, "coq:exn.Undeclared-universe-\u2018ident\u2019", "Undeclared universe \u2018ident\u2019"], [71, 3, 1, "coq:cmd.Undelimit-Scope", "Undelimit Scope"], [66, 3, 1, "coq:cmd.Undo", "Undo"], [71, 0, 1, "coq:exn.Unexpected-non-option-term-\u2018term\u2019-while-parsing-a-number-notation", "Unexpected non-option term \u2018term\u2019 while parsing a number notation"], [71, 0, 1, "coq:exn.Unexpected-non-option-term-\u2018term\u2019-while-parsing-a-string-notation", "Unexpected non-option term \u2018term\u2019 while parsing a string notation"], [71, 0, 1, "coq:exn.Unexpected-only-parsing-for-an-only-printing-notation", "Unexpected only parsing for an only printing notation"], [71, 0, 1, "coq:exn.Unexpected-only-printing-for-an-only-parsing-notation", "Unexpected only printing for an only parsing notation"], [71, 0, 1, "coq:exn.Unexpected-term-\u2018term\u2019-while-parsing-a-number-notation", "Unexpected term \u2018term\u2019 while parsing a number notation"], [71, 0, 1, "coq:exn.Unexpected-term-\u2018term\u2019-while-parsing-a-string-notation", "Unexpected term \u2018term\u2019 while parsing a string notation"], [66, 3, 1, "coq:cmd.Unfocus", "Unfocus"], [66, 3, 1, "coq:cmd.Unfocused", "Unfocused"], [34, 4, 1, "coq:flag.Uniform-Inductive-Parameters", "Uniform Inductive Parameters"], [14, 3, 1, "coq:cmd.Universe", "Universe"], [59, 4, 1, "coq:flag.Universe-Checking", "Universe Checking"], [14, 4, 1, "coq:flag.Universe-Minimization-ToSet", "Universe Minimization ToSet"], [14, 4, 1, "coq:flag.Universe-Polymorphism", "Universe Polymorphism"], [14, 0, 1, "coq:exn.Universe-inconsistency", "Universe inconsistency"], [59, 0, 1, "coq:exn.Universe-instance-length-is-\u2018natural\u2019-but-should-be-\u2018natural\u2019", "Universe instance length is \u2018natural\u2019 but should be \u2018natural\u2019"], [14, 3, 1, "coq:cmd.Universes", "Universes"], [71, 0, 1, "coq:exn.Unknown-custom-entry", "Unknown custom entry"], [71, 0, 1, "coq:exn.Unknown-custom-entry:-\u2018ident\u2019", "Unknown custom entry: \u2018ident\u2019"], [66, 0, 1, "coq:exn.Unknown-inductive-type", "Unknown inductive type"], [29, 3, 1, "coq:cmd.Unset", "Unset"], [66, 3, 1, "coq:cmd.Unshelve", "Unshelve"], [71, 0, 1, "coq:exn.Unterminated-string-in-notation", "Unterminated string in notation"], [28, 2, 1, "coq:warn.Use-of-\"Variable\"-or-\"Hypothesis\"-outside-sections-behaves-as-\"#[local]-Parameter\"-or-\"#[local]-Axiom\"", "Use of "Variable" or "Hypothesis" outside sections behaves as "#[local] Parameter" or "#[local] Axiom""], [71, 2, 1, "coq:warn.Use-of-\u2018string\u2019-Notation-is-deprecated-as-it-is-inconsistent-with-pattern-syntax", "Use of \u2018string\u2019 Notation is deprecated as it is inconsistent with pattern syntax"], [13, 2, 1, "coq:warn.Using-inferred-default-mode:-\u201cmode\u201d-for-\u201c\u2018ident\u2019\u201d", "Using inferred default mode: \u201cmode\u201d for \u201c\u2018ident\u2019\u201d"], [66, 3, 1, "coq:cmd.Validate-Proof", "Validate Proof"], [28, 3, 1, "coq:cmd.Variable", "Variable"], [66, 2, 1, "coq:warn.Variable-All-is-shadowed-by-Collection-named-All-containing-all-variables", "Variable All is shadowed by Collection named All containing all variables"], [28, 3, 1, "coq:cmd.Variables", "Variables"], [40, 3, 1, "coq:cmd.Variant", "Variant"], [59, 6, 1, "coq:opt.Warnings", "Warnings"], [44, 0, 1, "coq:exn.Wrong-argument-name", "Wrong argument name"], [44, 0, 1, "coq:exn.Wrong-argument-position", "Wrong argument position"], [66, 0, 1, "coq:exn.Wrong-bullet-\u2018bullet\u2019:-Bullet-\u2018bullet\u2019-is-mandatory-here", "Wrong bullet \u2018bullet\u2019: Bullet \u2018bullet\u2019 is mandatory here"], [66, 0, 1, "coq:exn.Wrong-bullet-\u2018bullet\u2019:-Current-bullet-\u2018bullet\u2019-is-not-finished", "Wrong bullet \u2018bullet\u2019: Current bullet \u2018bullet\u2019 is not finished"], [54, 1, 1, "coq:tacn.[-\u2026-|-\u2026-|-\u2026-]-(dispatch)", "[ \u2026 | \u2026 | \u2026 ] (dispatch)"], [54, 1, 1, "coq:tacn.[>-\u2026-|-\u2026-|-\u2026-]-(dispatch)", "[> \u2026 | \u2026 | \u2026 ] (dispatch)"], [55, 7, 1, "coq:attr.abstract", "abstract"], [66, 1, 1, "coq:tacn.abstract", "abstract"], [57, 1, 1, "coq:tacn.abstract-(ssreflect)", "abstract (ssreflect)"], [58, 1, 1, "coq:tacn.absurd", "absurd"], [71, 7, 1, "coq:attr.add_bottom", "add_bottom"], [71, 7, 1, "coq:attr.add_top", "add_top"], [66, 1, 1, "coq:tacn.admit", "admit"], [58, 1, 1, "coq:tacn.apply", "apply"], [57, 1, 1, "coq:tacn.apply-(ssreflect)", "apply (ssreflect)"], [58, 1, 1, "coq:tacn.assert", "assert"], [54, 1, 1, "coq:tacn.assert_fails", "assert_fails"], [54, 1, 1, "coq:tacn.assert_succeeds", "assert_succeeds"], [58, 1, 1, "coq:tacn.assumption", "assumption"], [60, 1, 1, "coq:tacn.auto", "auto"], [13, 1, 1, "coq:tacn.autoapply", "autoapply"], [60, 1, 1, "coq:tacn.autorewrite", "autorewrite"], [60, 1, 1, "coq:tacn.autounfold", "autounfold"], [60, 1, 1, "coq:tacn.autounfold_one", "autounfold_one"], [62, 1, 1, "coq:tacn.btauto", "btauto"], [66, 1, 1, "coq:tacn.bullet-(--+-*)", "bullet (- + *)"], [57, 1, 1, "coq:tacn.by", "by"], [59, 7, 1, "coq:attr.bypass_check(guard)", "bypass_check(guard)"], [59, 7, 1, "coq:attr.bypass_check(positivity)", "bypass_check(positivity)"], [59, 7, 1, "coq:attr.bypass_check(universes)", "bypass_check(universes)"], [42, 7, 1, "coq:attr.canonical", "canonical"], [67, 1, 1, "coq:tacn.case", "case"], [57, 1, 1, "coq:tacn.case-(ssreflect)", "case (ssreflect)"], [67, 1, 1, "coq:tacn.case_eq", "case_eq"], [64, 1, 1, "coq:tacn.cbn", "cbn"], [64, 1, 1, "coq:tacn.cbv", "cbv"], [64, 1, 1, "coq:tacn.change", "change"], [64, 1, 1, "coq:tacn.change_no_check", "change_no_check"], [58, 1, 1, "coq:tacn.classical_left", "classical_left"], [58, 1, 1, "coq:tacn.classical_right", "classical_right"], [58, 1, 1, "coq:tacn.clear", "clear"], [58, 1, 1, "coq:tacn.clear-dependent", "clear dependent"], [38, 7, 1, "coq:attr.clearbody", "clearbody"], [58, 1, 1, "coq:tacn.clearbody", "clearbody"], [71, 2, 1, "coq:warn.closed-notation-not-level-0", "closed-notation-not-level-0"], [67, 1, 1, "coq:tacn.cofix", "cofix"], [67, 1, 1, "coq:tacn.compare", "compare"], [64, 1, 1, "coq:tacn.compute", "compute"], [57, 1, 1, "coq:tacn.congr", "congr"], [62, 1, 1, "coq:tacn.congruence", "congruence"], [54, 1, 1, "coq:tacn.constr_eq", "constr_eq"], [54, 1, 1, "coq:tacn.constr_eq_nounivs", "constr_eq_nounivs"], [54, 1, 1, "coq:tacn.constr_eq_strict", "constr_eq_strict"], [67, 1, 1, "coq:tacn.constructor", "constructor"], [54, 1, 1, "coq:tacn.context", "context"], [58, 1, 1, "coq:tacn.contradict", "contradict"], [58, 1, 1, "coq:tacn.contradiction", "contradiction"], [54, 1, 1, "coq:tacn.convert", "convert"], [58, 1, 1, "coq:tacn.cut", "cut"], [66, 1, 1, "coq:tacn.cycle", "cycle"], [60, 1, 1, "coq:tacn.debug-auto", "debug auto"], [60, 1, 1, "coq:tacn.debug-eauto", "debug eauto"], [60, 1, 1, "coq:tacn.debug-trivial", "debug trivial"], [67, 1, 1, "coq:tacn.decide", "decide"], [67, 1, 1, "coq:tacn.decide-equality", "decide equality"], [67, 1, 1, "coq:tacn.decompose", "decompose"], [67, 1, 1, "coq:tacn.decompose-record", "decompose record"], [67, 1, 1, "coq:tacn.decompose-sum", "decompose sum"], [67, 1, 1, "coq:tacn.dependent-destruction", "dependent destruction"], [58, 1, 1, "coq:tacn.dependent-generalize_eqs", "dependent generalize_eqs"], [58, 1, 1, "coq:tacn.dependent-generalize_eqs_vars", "dependent generalize_eqs_vars"], [67, 1, 1, "coq:tacn.dependent-induction", "dependent induction"], [67, 1, 1, "coq:tacn.dependent-inversion", "dependent inversion"], [67, 1, 1, "coq:tacn.dependent-inversion_clear", "dependent inversion_clear"], [67, 1, 1, "coq:tacn.dependent-rewrite", "dependent rewrite"], [67, 1, 1, "coq:tacn.dependent-simple-inversion", "dependent simple inversion"], [74, 7, 1, "coq:attr.deprecated", "deprecated"], [67, 1, 1, "coq:tacn.destauto", "destauto"], [67, 1, 1, "coq:tacn.destruct", "destruct"], [62, 1, 1, "coq:tacn.dintuition", "dintuition"], [67, 1, 1, "coq:tacn.discriminate", "discriminate"], [54, 1, 1, "coq:tacn.do", "do"], [57, 1, 1, "coq:tacn.do-(ssreflect)", "do (ssreflect)"], [57, 1, 1, "coq:tacn.done", "done"], [62, 1, 1, "coq:tacn.dtauto", "dtauto"], [58, 1, 1, "coq:tacn.eapply", "eapply"], [58, 1, 1, "coq:tacn.eassert", "eassert"], [58, 1, 1, "coq:tacn.eassumption", "eassumption"], [60, 1, 1, "coq:tacn.easy", "easy"], [60, 1, 1, "coq:tacn.eauto", "eauto"], [67, 1, 1, "coq:tacn.ecase", "ecase"], [67, 1, 1, "coq:tacn.econstructor", "econstructor"], [67, 1, 1, "coq:tacn.edestruct", "edestruct"], [67, 1, 1, "coq:tacn.ediscriminate", "ediscriminate"], [67, 1, 1, "coq:tacn.eelim", "eelim"], [58, 1, 1, "coq:tacn.eenough", "eenough"], [58, 1, 1, "coq:tacn.eexact", "eexact"], [67, 1, 1, "coq:tacn.eexists", "eexists"], [67, 1, 1, "coq:tacn.einduction", "einduction"], [67, 1, 1, "coq:tacn.einjection", "einjection"], [58, 1, 1, "coq:tacn.eintros", "eintros"], [67, 1, 1, "coq:tacn.eleft", "eleft"], [67, 1, 1, "coq:tacn.elim", "elim"], [57, 1, 1, "coq:tacn.elim-(ssreflect)", "elim (ssreflect)"], [58, 1, 1, "coq:tacn.enough", "enough"], [58, 1, 1, "coq:tacn.epose", "epose"], [58, 1, 1, "coq:tacn.epose-proof", "epose proof"], [58, 1, 1, "coq:tacn.eremember", "eremember"], [64, 1, 1, "coq:tacn.erewrite", "erewrite"], [67, 1, 1, "coq:tacn.eright", "eright"], [58, 1, 1, "coq:tacn.eset", "eset"], [67, 1, 1, "coq:tacn.esimplify_eq", "esimplify_eq"], [67, 1, 1, "coq:tacn.esplit", "esplit"], [64, 1, 1, "coq:tacn.etransitivity", "etransitivity"], [64, 1, 1, "coq:tacn.eval", "eval"], [58, 1, 1, "coq:tacn.evar", "evar"], [58, 1, 1, "coq:tacn.exact", "exact"], [57, 1, 1, "coq:tacn.exact-(ssreflect)", "exact (ssreflect)"], [58, 1, 1, "coq:tacn.exact_no_check", "exact_no_check"], [54, 1, 1, "coq:tacn.exactly_once", "exactly_once"], [58, 1, 1, "coq:tacn.exfalso", "exfalso"], [67, 1, 1, "coq:tacn.exists", "exists"], [35, 7, 1, "coq:attr.export", "export"], [64, 1, 1, "coq:tacn.f_equal", "f_equal"], [54, 1, 1, "coq:tacn.fail", "fail"], [11, 1, 1, "coq:tacn.field", "field"], [11, 1, 1, "coq:tacn.field_lookup", "field_lookup"], [11, 1, 1, "coq:tacn.field_simplify", "field_simplify"], [11, 1, 1, "coq:tacn.field_simplify_eq", "field_simplify_eq"], [54, 1, 1, "coq:tacn.finish_timing", "finish_timing"], [54, 1, 1, "coq:tacn.first", "first"], [57, 1, 1, "coq:tacn.first-(ssreflect)", "first (ssreflect)"], [57, 9, 1, "coq:tacv.first-last", "first last"], [62, 1, 1, "coq:tacn.firstorder", "firstorder"], [67, 1, 1, "coq:tacn.fix", "fix"], [64, 1, 1, "coq:tacn.fold", "fold"], [54, 1, 1, "coq:tacn.fresh", "fresh"], [54, 1, 1, "coq:tacn.fun", "fun"], [72, 1, 1, "coq:tacn.functional-induction", "functional induction"], [72, 1, 1, "coq:tacn.functional-inversion", "functional inversion"], [58, 1, 1, "coq:tacn.generalize", "generalize"], [58, 1, 1, "coq:tacn.generalize-dependent", "generalize dependent"], [58, 1, 1, "coq:tacn.generalize_eqs", "generalize_eqs"], [58, 1, 1, "coq:tacn.generalize_eqs_vars", "generalize_eqs_vars"], [57, 1, 1, "coq:tacn.generally-have", "generally have"], [54, 1, 1, "coq:tacn.gfail", "gfail"], [66, 1, 1, "coq:tacn.give_up", "give_up"], [35, 7, 1, "coq:attr.global", "global"], [54, 1, 1, "coq:tacn.guard", "guard"], [54, 1, 1, "coq:tacn.has_evar", "has_evar"], [57, 1, 1, "coq:tacn.have", "have"], [3, 1, 1, "coq:tacn.head_of_constr", "head_of_constr"], [64, 1, 1, "coq:tacn.hnf", "hnf"], [54, 1, 1, "coq:tacn.idtac", "idtac"], [55, 1, 1, "coq:tacn.if-then-else-(Ltac2)", "if-then-else (Ltac2)"], [57, 1, 1, "coq:tacn.in", "in"], [67, 1, 1, "coq:tacn.induction", "induction"], [54, 3, 1, "coq:cmd.infoH", "infoH"], [60, 1, 1, "coq:tacn.info_auto", "info_auto"], [60, 1, 1, "coq:tacn.info_eauto", "info_eauto"], [60, 1, 1, "coq:tacn.info_trivial", "info_trivial"], [67, 1, 1, "coq:tacn.injection", "injection"], [58, 1, 1, "coq:tacn.instantiate", "instantiate"], [58, 1, 1, "coq:tacn.intro", "intro"], [58, 1, 1, "coq:tacn.intros", "intros"], [58, 1, 1, "coq:tacn.intros-until", "intros until"], [62, 1, 1, "coq:tacn.intuition", "intuition"], [67, 1, 1, "coq:tacn.inversion", "inversion"], [67, 1, 1, "coq:tacn.inversion_clear", "inversion_clear"], [67, 1, 1, "coq:tacn.inversion_sigma", "inversion_sigma"], [54, 1, 1, "coq:tacn.is_cofix", "is_cofix"], [54, 1, 1, "coq:tacn.is_const", "is_const"], [54, 1, 1, "coq:tacn.is_constructor", "is_constructor"], [54, 1, 1, "coq:tacn.is_evar", "is_evar"], [54, 1, 1, "coq:tacn.is_fix", "is_fix"], [54, 1, 1, "coq:tacn.is_ground", "is_ground"], [54, 1, 1, "coq:tacn.is_ind", "is_ind"], [54, 1, 1, "coq:tacn.is_proj", "is_proj"], [54, 1, 1, "coq:tacn.is_var", "is_var"], [58, 1, 1, "coq:tacn.lapply", "lapply"], [58, 0, 1, "coq:exn.lapply-needs-a-non-dependent-product", "lapply needs a non-dependent product"], [57, 1, 1, "coq:tacn.last", "last"], [57, 9, 1, "coq:tacv.last-first", "last first"], [64, 1, 1, "coq:tacn.lazy", "lazy"], [55, 1, 1, "coq:tacn.lazy_match!", "lazy_match!"], [55, 1, 1, "coq:tacn.lazy_match!-goal", "lazy_match! goal"], [54, 1, 1, "coq:tacn.lazymatch", "lazymatch"], [54, 1, 1, "coq:tacn.lazymatch-goal", "lazymatch goal"], [67, 1, 1, "coq:tacn.left", "left"], [54, 1, 1, "coq:tacn.let", "let"], [5, 1, 1, "coq:tacn.lia", "lia"], [35, 7, 1, "coq:attr.local", "local"], [5, 1, 1, "coq:tacn.lra", "lra"], [54, 1, 1, "coq:tacn.ltac-seq", "ltac-seq"], [54, 1, 1, "coq:tacn.match", "match"], [55, 1, 1, "coq:tacn.match-(Ltac2)", "match (Ltac2)"], [54, 1, 1, "coq:tacn.match-goal", "match goal"], [55, 1, 1, "coq:tacn.match!", "match!"], [55, 1, 1, "coq:tacn.match!-goal", "match! goal"], [60, 2, 1, "coq:warn.mismatched-hint-db", "mismatched-hint-db"], [13, 7, 1, "coq:attr.mode", "mode"], [58, 1, 1, "coq:tacn.move", "move"], [57, 1, 1, "coq:tacn.move-(ssreflect)", "move (ssreflect)"], [55, 1, 1, "coq:tacn.multi_match!", "multi_match!"], [55, 1, 1, "coq:tacn.multi_match!-goal", "multi_match! goal"], [54, 1, 1, "coq:tacn.multimatch", "multimatch"], [54, 1, 1, "coq:tacn.multimatch-goal", "multimatch goal"], [58, 1, 1, "coq:tacn.native_cast_no_check", "native_cast_no_check"], [64, 1, 1, "coq:tacn.native_compute", "native_compute"], [5, 1, 1, "coq:tacn.nia", "nia"], [4, 7, 1, "coq:attr.nonuniform", "nonuniform"], [54, 0, 1, "coq:exn.not-a-cofix-definition", "not a cofix definition"], [54, 0, 1, "coq:exn.not-a-constant", "not a constant"], [54, 0, 1, "coq:exn.not-a-constructor", "not a constructor"], [54, 0, 1, "coq:exn.not-a-fix-definition", "not a fix definition"], [54, 0, 1, "coq:exn.not-a-primitive-projection", "not a primitive projection"], [54, 0, 1, "coq:exn.not-an-(co)inductive-datatype", "not an (co)inductive datatype"], [54, 1, 1, "coq:tacn.not_evar", "not_evar"], [71, 2, 1, "coq:warn.notation-incompatible-prefix", "notation-incompatible-prefix"], [60, 1, 1, "coq:tacn.now", "now"], [64, 1, 1, "coq:tacn.now_show", "now_show"], [5, 1, 1, "coq:tacn.nra", "nra"], [7, 1, 1, "coq:tacn.nsatz", "nsatz"], [7, 1, 1, "coq:tacn.nsatz_compute", "nsatz_compute"], [54, 1, 1, "coq:tacn.numgoals", "numgoals"], [54, 1, 1, "coq:tacn.once", "once"], [54, 1, 1, "coq:tacn.only", "only"], [54, 1, 1, "coq:tacn.optimize_heap", "optimize_heap"], [57, 1, 1, "coq:tacn.over", "over"], [71, 0, 1, "coq:exn.overflow-in-int63-literal-\u2018bigint\u2019", "overflow in int63 literal \u2018bigint\u2019"], [64, 1, 1, "coq:tacn.pattern", "pattern"], [58, 1, 1, "coq:tacn.pose", "pose"], [57, 1, 1, "coq:tacn.pose-(ssreflect)", "pose (ssreflect)"], [58, 1, 1, "coq:tacn.pose-proof", "pose proof"], [71, 2, 1, "coq:warn.postfix-notation-not-level-1", "postfix-notation-not-level-1"], [40, 7, 1, "coq:attr.private(matching)", "private(matching)"], [9, 7, 1, "coq:attr.program", "program"], [54, 1, 1, "coq:tacn.progress", "progress"], [37, 7, 1, "coq:attr.projections(primitive)", "projections(primitive)"], [11, 1, 1, "coq:tacn.protect_fv", "protect_fv"], [5, 1, 1, "coq:tacn.psatz", "psatz"], [59, 0, 1, "coq:exn.public-name-according-to-findlib,-for-example", "public name according to findlib, for example"], [58, 1, 1, "coq:tacn.rapply", "rapply"], [64, 1, 1, "coq:tacn.red", "red"], [13, 7, 1, "coq:attr.refine", "refine"], [58, 1, 1, "coq:tacn.refine", "refine"], [64, 1, 1, "coq:tacn.reflexivity", "reflexivity"], [58, 1, 1, "coq:tacn.remember", "remember"], [58, 1, 1, "coq:tacn.rename", "rename"], [54, 1, 1, "coq:tacn.repeat", "repeat"], [64, 1, 1, "coq:tacn.replace", "replace"], [54, 1, 1, "coq:tacn.reset-ltac-profile", "reset ltac profile"], [54, 1, 1, "coq:tacn.restart_timer", "restart_timer"], [4, 7, 1, "coq:attr.reversible", "reversible"], [58, 1, 1, "coq:tacn.revert", "revert"], [58, 1, 1, "coq:tacn.revert-dependent", "revert dependent"], [66, 1, 1, "coq:tacn.revgoals", "revgoals"], [64, 1, 1, "coq:tacn.rewrite", "rewrite"], [57, 1, 1, "coq:tacn.rewrite-(ssreflect)", "rewrite (ssreflect)"], [64, 1, 1, "coq:tacn.rewrite-*", "rewrite *"], [3, 1, 1, "coq:tacn.rewrite_db", "rewrite_db"], [3, 1, 1, "coq:tacn.rewrite_strat", "rewrite_strat"], [67, 1, 1, "coq:tacn.right", "right"], [11, 1, 1, "coq:tacn.ring", "ring"], [11, 1, 1, "coq:tacn.ring_lookup", "ring_lookup"], [11, 1, 1, "coq:tacn.ring_simplify", "ring_simplify"], [62, 1, 1, "coq:tacn.rtauto", "rtauto"], [58, 1, 1, "coq:tacn.set", "set"], [57, 1, 1, "coq:tacn.set-(ssreflect)", "set (ssreflect)"], [3, 1, 1, "coq:tacn.setoid_etransitivity", "setoid_etransitivity"], [3, 1, 1, "coq:tacn.setoid_reflexivity", "setoid_reflexivity"], [3, 1, 1, "coq:tacn.setoid_replace", "setoid_replace"], [3, 1, 1, "coq:tacn.setoid_rewrite", "setoid_rewrite"], [3, 1, 1, "coq:tacn.setoid_symmetry", "setoid_symmetry"], [3, 1, 1, "coq:tacn.setoid_transitivity", "setoid_transitivity"], [59, 0, 1, "coq:exn.shared-library-failed:-Coq-Error:-\u2018string\u2019-is-not-a-valid", "shared library failed: Coq Error: \u2018string\u2019 is not a valid"], [66, 1, 1, "coq:tacn.shelve", "shelve"], [66, 1, 1, "coq:tacn.shelve_unifiable", "shelve_unifiable"], [54, 1, 1, "coq:tacn.show-ltac-profile", "show ltac profile"], [64, 1, 1, "coq:tacn.simpl", "simpl"], [58, 1, 1, "coq:tacn.simple-apply", "simple apply"], [62, 1, 1, "coq:tacn.simple-congruence", "simple congruence"], [67, 1, 1, "coq:tacn.simple-destruct", "simple destruct"], [58, 1, 1, "coq:tacn.simple-eapply", "simple eapply"], [67, 1, 1, "coq:tacn.simple-induction", "simple induction"], [67, 1, 1, "coq:tacn.simple-injection", "simple injection"], [67, 1, 1, "coq:tacn.simple-inversion", "simple inversion"], [64, 1, 1, "coq:tacn.simple-subst", "simple subst"], [67, 1, 1, "coq:tacn.simplify_eq", "simplify_eq"], [72, 1, 1, "coq:tacn.soft-functional-induction", "soft functional induction"], [54, 1, 1, "coq:tacn.solve", "solve"], [66, 1, 1, "coq:tacn.solve_constraints", "solve_constraints"], [58, 1, 1, "coq:tacn.specialize", "specialize"], [58, 1, 1, "coq:tacn.specialize_eqs", "specialize_eqs"], [67, 1, 1, "coq:tacn.split", "split"], [54, 1, 1, "coq:tacn.start-ltac-profiling", "start ltac profiling"], [64, 1, 1, "coq:tacn.stepl", "stepl"], [64, 1, 1, "coq:tacn.stepr", "stepr"], [54, 1, 1, "coq:tacn.stop-ltac-profiling", "stop ltac profiling"], [64, 1, 1, "coq:tacn.subst", "subst"], [64, 1, 1, "coq:tacn.substitute", "substitute"], [57, 1, 1, "coq:tacn.suff", "suff"], [57, 1, 1, "coq:tacn.suffices", "suffices"], [66, 1, 1, "coq:tacn.swap", "swap"], [64, 1, 1, "coq:tacn.symmetry", "symmetry"], [62, 1, 1, "coq:tacn.tauto", "tauto"], [34, 0, 1, "coq:exn.template-and-polymorphism-not-compatible", "template and polymorphism not compatible"], [54, 1, 1, "coq:tacn.time", "time"], [54, 1, 1, "coq:tacn.time_constr", "time_constr"], [54, 1, 1, "coq:tacn.timeout", "timeout"], [64, 1, 1, "coq:tacn.transitivity", "transitivity"], [66, 1, 1, "coq:tacn.transparent_abstract", "transparent_abstract"], [60, 1, 1, "coq:tacn.trivial", "trivial"], [54, 1, 1, "coq:tacn.try", "try"], [54, 1, 1, "coq:tacn.tryif", "tryif"], [54, 1, 1, "coq:tacn.type-of", "type of"], [54, 1, 1, "coq:tacn.type_term", "type_term"], [13, 1, 1, "coq:tacn.typeclasses-eauto", "typeclasses eauto"], [57, 1, 1, "coq:tacn.under", "under"], [64, 1, 1, "coq:tacn.unfold", "unfold"], [54, 1, 1, "coq:tacn.unify", "unify"], [14, 7, 1, "coq:attr.universes(cumulative)", "universes(cumulative)"], [14, 7, 1, "coq:attr.universes(polymorphic)", "universes(polymorphic)"], [34, 7, 1, "coq:attr.universes(template)", "universes(template)"], [57, 1, 1, "coq:tacn.unlock", "unlock"], [66, 1, 1, "coq:tacn.unshelve", "unshelve"], [66, 7, 1, "coq:attr.using", "using"], [58, 1, 1, "coq:tacn.vm_cast_no_check", "vm_cast_no_check"], [64, 1, 1, "coq:tacn.vm_compute", "vm_compute"], [74, 7, 1, "coq:attr.warn", "warn"], [29, 7, 1, "coq:attr.warning", "warning"], [29, 7, 1, "coq:attr.warnings", "warnings"], [64, 1, 1, "coq:tacn.with_strategy", "with_strategy"], [57, 1, 1, "coq:tacn.without-loss", "without loss"], [5, 1, 1, "coq:tacn.wlia", "wlia"], [57, 1, 1, "coq:tacn.wlog", "wlog"], [5, 1, 1, "coq:tacn.wlra_Q", "wlra_Q"], [5, 1, 1, "coq:tacn.wnia", "wnia"], [5, 1, 1, "coq:tacn.wnra_Q", "wnra_Q"], [5, 1, 1, "coq:tacn.wpsatz_Q", "wpsatz_Q"], [5, 1, 1, "coq:tacn.wpsatz_Z", "wpsatz_Z"], [5, 1, 1, "coq:tacn.wsos_Q", "wsos_Q"], [5, 1, 1, "coq:tacn.wsos_Z", "wsos_Z"], [5, 1, 1, "coq:tacn.xlia", "xlia"], [5, 1, 1, "coq:tacn.xlra_Q", "xlra_Q"], [5, 1, 1, "coq:tacn.xlra_R", "xlra_R"], [5, 1, 1, "coq:tacn.xnia", "xnia"], [5, 1, 1, "coq:tacn.xnra_Q", "xnra_Q"], [5, 1, 1, "coq:tacn.xnra_R", "xnra_R"], [5, 1, 1, "coq:tacn.xpsatz_Q", "xpsatz_Q"], [5, 1, 1, "coq:tacn.xpsatz_R", "xpsatz_R"], [5, 1, 1, "coq:tacn.xpsatz_Z", "xpsatz_Z"], [5, 1, 1, "coq:tacn.xsos_Q", "xsos_Q"], [5, 1, 1, "coq:tacn.xsos_R", "xsos_R"], [5, 1, 1, "coq:tacn.xsos_Z", "xsos_Z"], [5, 1, 1, "coq:tacn.zify", "zify"], [5, 1, 1, "coq:tacn.zify_elim_let", "zify_elim_let"], [5, 1, 1, "coq:tacn.zify_iter_let", "zify_iter_let"], [5, 1, 1, "coq:tacn.zify_iter_specs", "zify_iter_specs"], [5, 1, 1, "coq:tacn.zify_op", "zify_op"], [5, 1, 1, "coq:tacn.zify_saturate", "zify_saturate"], [66, 1, 1, "coq:tacn.{", "{"], [54, 1, 1, "coq:tacn.||-(first-tactic-making-progress)", "|| (first tactic making progress)"], [66, 1, 1, "coq:tacn.}", "}"], [4, 0, 1, "coq:exn.\u2018coercion_class\u2019-must-be-a-transparent-constant", "\u2018coercion_class\u2019 must be a transparent constant"], [37, 0, 1, "coq:exn.\u2018ident\u2019-already-exists", "\u2018ident\u2019 already exists"], [37, 2, 1, "coq:warn.\u2018ident\u2019-cannot-be-defined", "\u2018ident\u2019 cannot be defined"], [37, 2, 1, "coq:warn.\u2018ident\u2019-cannot-be-defined-because-it-is-informative-and-\u2018ident\u2019-is-not", "\u2018ident\u2019 cannot be defined because it is informative and \u2018ident\u2019 is not"], [37, 2, 1, "coq:warn.\u2018ident\u2019-cannot-be-defined-because-the-projection-\u2018ident\u2019-was-not-defined", "\u2018ident\u2019 cannot be defined because the projection \u2018ident\u2019 was not defined"], [13, 2, 1, "coq:warn.\u2018ident\u2019-is-already-declared-as-a-typeclass", "\u2018ident\u2019 is already declared as a typeclass"], [58, 0, 1, "coq:exn.\u2018ident\u2019-is-already-used", "\u2018ident\u2019 is already used"], [66, 2, 1, "coq:warn.\u2018ident\u2019-is-both-name-of-a-Collection-and-Variable,-Collection-\u2018ident\u2019-takes-precedence-over-Variable", "\u2018ident\u2019 is both name of a Collection and Variable, Collection \u2018ident\u2019 takes precedence over Variable"], [58, 0, 1, "coq:exn.\u2018ident\u2019-is-not-a-local-definition", "\u2018ident\u2019 is not a local definition"], [67, 0, 1, "coq:exn.\u2018ident\u2019-is-not-an-equality-of-\u03a3-types", "\u2018ident\u2019 is not an equality of \u03a3 types"], [64, 0, 1, "coq:exn.\u2018ident\u2019-is-opaque", "\u2018ident\u2019 is opaque"], [58, 0, 1, "coq:exn.\u2018ident\u2019-is-used-in-the-conclusion", "\u2018ident\u2019 is used in the conclusion"], [58, 0, 1, "coq:exn.\u2018ident\u2019-is-used-in-the-hypothesis-\u2018ident\u2019", "\u2018ident\u2019 is used in the hypothesis \u2018ident\u2019"], [66, 2, 1, "coq:warn.\u2018ident\u2019-was-already-a-defined-Variable,-the-name-\u2018ident\u2019-will-refer-to-Collection-when-executing-\"Proof-using\"-command", "\u2018ident\u2019 was already a defined Variable, the name \u2018ident\u2019 will refer to Collection when executing "Proof using" command"], [60, 0, 1, "coq:exn.\u2018qualid\u2019-cannot-be-used-as-a-hint", "\u2018qualid\u2019 cannot be used as a hint"], [64, 0, 1, "coq:exn.\u2018qualid\u2019-does-not-occur", "\u2018qualid\u2019 does not occur"], [4, 2, 1, "coq:warn.\u2018qualid\u2019-does-not-respect-the-uniform-inheritance-condition", "\u2018qualid\u2019 does not respect the uniform inheritance condition"], [4, 0, 1, "coq:exn.\u2018qualid\u2019-is-already-a-coercion", "\u2018qualid\u2019 is already a coercion"], [71, 0, 1, "coq:exn.\u2018qualid\u2019-is-bound-to-a-notation-that-does-not-denote-a-reference", "\u2018qualid\u2019 is bound to a notation that does not denote a reference"], [4, 0, 1, "coq:exn.\u2018qualid\u2019-is-not-a-function", "\u2018qualid\u2019 is not a function"], [35, 0, 1, "coq:exn.\u2018qualid\u2019-is-not-a-module", "\u2018qualid\u2019 is not a module"], [60, 0, 1, "coq:exn.\u2018qualid\u2019-is-not-an-inductive-type", "\u2018qualid\u2019 is not an inductive type"], [59, 0, 1, "coq:exn.\u2018qualid\u2019-not-a-defined-object", "\u2018qualid\u2019 not a defined object"], [4, 0, 1, "coq:exn.\u2018qualid\u2019-not-declared", "\u2018qualid\u2019 not declared"], [71, 0, 1, "coq:exn.\u2018qualid\u2019-was-already-mapped-to-\u2018qualid\u2019-and-cannot-be-remapped-to-\u2018qualid\u2019", "\u2018qualid\u2019 was already mapped to \u2018qualid\u2019 and cannot be remapped to \u2018qualid\u2019"], [74, 2, 1, "coq:warn.\u2018string\u2019", "\u2018string\u2019"], [71, 0, 1, "coq:exn.\u2018type\u2019-is-not-an-inductive-type", "\u2018type\u2019 is not an inductive type"], [71, 2, 1, "coq:warn.\u2018type\u2019-was-already-mapped-to-\u2018type\u2019,-mapping-it-also-to-\u2018type\u2019-might-yield-ill-typed-terms-when-using-the-notation", "\u2018type\u2019 was already mapped to \u2018type\u2019, mapping it also to \u2018type\u2019 might yield ill typed terms when using the notation"], [54, 1, 1, "coq:tacn.\u2026-:-\u2026-(goal-selector)", "\u2026 : \u2026 (goal selector)"], [57, 1, 1, "coq:tacn.\u2026-:-\u2026-(ssreflect)", "\u2026 : \u2026 (ssreflect)"]], "..": [[4, 2, 1, "coq:warn....-is-not-definitionally-an-identity-function", " is not definitionally an identity function"]], "Argument \u2018name\u2019 is a trailing implicit, so it can't be declared non maximal": [[44, 0, 1, "coq:exn.Argument-\u2018name\u2019-is-a-trailing-implicit,-so-it-can't-be-declared-non-maximal.-Please-use-{-}-instead-of-[-]", " Please use { } instead of [ ]"]], "Cannot infer a term for this placeholder": [[44, 0, 1, "coq:exn.Cannot-infer-a-term-for-this-placeholder.-(Casual-use-of-implicit-arguments)", " (Casual use of implicit arguments)"], [58, 0, 1, "coq:exn.Cannot-infer-a-term-for-this-placeholder.-(refine)", " (refine)"]], "Compiled library \u2018ident\u2019": [[59, 0, 1, "coq:exn.Compiled-library-\u2018ident\u2019.vo-makes-inconsistent-assumptions-over-library-\u2018qualid\u2019", "vo makes inconsistent assumptions over library \u2018qualid\u2019"]], "Duplicate clear of H": [[57, 2, 1, "coq:warn.Duplicate-clear-of-H.-Use-{-}H-instead-of-{-H-}H", " Use { }H instead of { H }H"]], "File ... found twice in ..": [[59, 2, 1, "coq:warn.File-...-found-twice-in-...", ""]], "Goal is solvable by congruence but some arguments are missing": [[62, 0, 1, "coq:exn.Goal-is-solvable-by-congruence-but-some-arguments-are-missing.-Try-congruence-with-\u2018term\u2019\u2026\u2018term\u2019,-replacing-metavariables-by-arbitrary-terms", " Try congruence with \u2018term\u2019\u2026\u2018term\u2019, replacing metavariables by arbitrary terms"]], "Library File (transitively required) \u2018qualid\u2019 is deprecated since \u2018string\u2019. \u2018string\u2019": [[74, 2, 1, "coq:warn.Library-File-(transitively-required)-\u2018qualid\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019.-Use-\u2018qualid\u2019-instead", " Use \u2018qualid\u2019 instead"]], "Library File \u2018qualid\u2019 is deprecated since \u2018string\u2019. \u2018string\u2019": [[74, 2, 1, "coq:warn.Library-File-\u2018qualid\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019.-Use-\u2018qualid\u2019-instead", " Use \u2018qualid\u2019 instead"]], "Ltac Profiler encountered an invalid stack (no self node)": [[54, 2, 1, "coq:warn.Ltac-Profiler-encountered-an-invalid-stack-(no-self-node).-This-can-happen-if-you-reset-the-profile-during-tactic-execution", " This can happen if you reset the profile during tactic execution"]], "Ltac2 alias \u2018qualid\u2019 is deprecated since \u2018string\u2019": [[74, 2, 1, "coq:warn.Ltac2-alias-\u2018qualid\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019", " \u2018string\u2019"]], "Ltac2 constructor \u2018qualid\u2019 is deprecated since \u2018string\u2019": [[74, 2, 1, "coq:warn.Ltac2-constructor-\u2018qualid\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019", " \u2018string\u2019"]], "Ltac2 definition \u2018qualid\u2019 is deprecated since \u2018string\u2019": [[74, 2, 1, "coq:warn.Ltac2-definition-\u2018qualid\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019", " \u2018string\u2019"]], "Ltac2 notation \u2018ltac2_scope\u2019\u2026\u2018ltac2_scope\u2019 is deprecated since \u2018string\u2019": [[74, 2, 1, "coq:warn.Ltac2-notation-\u2018ltac2_scope\u2019\u2026\u2018ltac2_scope\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019", " \u2018string\u2019"]], "Nested proofs are discouraged and not allowed by default. This error probably means that you forgot to close the last "Proof." with "Qed." or "Defined."": [[32, 0, 1, "coq:exn.Nested-proofs-are-discouraged-and-not-allowed-by-default.-This-error-probably-means-that-you-forgot-to-close-the-last-\"Proof.\"-with-\"Qed.\"-or-\"Defined.\".-If-you-really-intended-to-use-nested-proofs,-you-can-do-so-by-turning-the-\"Nested-Proofs-Allowed\"-flag-on", " If you really intended to use nested proofs, you can do so by turning the "Nested Proofs Allowed" flag on"]], "New coercion path ... is ambiguous with existing ..": [[4, 2, 1, "coq:warn.New-coercion-path-...-is-ambiguous-with-existing-...", ""]], "No information can be deduced from this equality and the injectivity of constructors. This may be because the terms are convertible, or due to pattern matching restrictions in the sort Prop": [[67, 0, 1, "coq:exn.No-information-can-be-deduced-from-this-equality-and-the-injectivity-of-constructors.-This-may-be-because-the-terms-are-convertible,-or-due-to-pattern-matching-restrictions-in-the-sort-Prop.-You-can-try-to-use-option-Set-Keep-Proof-Equalities", " You can try to use option Set Keep Proof Equalities"]], "No such bound variable \u2018ident\u2019 (possible names are: \u2018ident\u2019 ..": [[58, 0, 1, "coq:exn.No-such-bound-variable-\u2018ident\u2019-(possible-names-are:-\u2018ident\u2019-...)", ")"]], "No such goal": [[54, 0, 1, "coq:exn.No-such-goal.-(Goal-selector)", " (Goal selector)"], [54, 0, 1, "coq:exn.No-such-goal.-(fail)", " (fail)"], [66, 0, 1, "coq:exn.No-such-goal.-Focus-next-goal-with-bullet-\u2018bullet\u2019", " Focus next goal with bullet \u2018bullet\u2019"], [66, 0, 1, "coq:exn.No-such-goal.-Try-unfocusing-with-}", " Try unfocusing with }"]], "Notation \u2018string\u2019 is deprecated since \u2018string\u2019. \u2018string\u2019": [[74, 2, 1, "coq:warn.Notation-\u2018string\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019.-Use-\u2018qualid\u2019-instead", " Use \u2018qualid\u2019 instead"]], "Proof is not complete": [[66, 0, 1, "coq:exn.Proof-is-not-complete.-(abstract)", " (abstract)"], [58, 0, 1, "coq:exn.Proof-is-not-complete.-(assert)", " (assert)"]], "Require inside a module is deprecated and strongly discouraged": [[59, 2, 1, "coq:warn.Require-inside-a-module-is-deprecated-and-strongly-discouraged.-You-can-Require-a-module-at-toplevel-and-optionally-Import-it-inside-another-one", " You can Require a module at toplevel and optionally Import it inside another one"]], "Required library \u2018qualid\u2019 matches several files in path (found file.vo, file.vo, ..": [[59, 0, 1, "coq:exn.Required-library-\u2018qualid\u2019-matches-several-files-in-path-(found-file.vo,-file.vo,-...)", ")"]], "SSReflect: cannot obtain new equations out of ..": [[57, 2, 1, "coq:warn.SSReflect:-cannot-obtain-new-equations-out-of-...", ""]], "Tactic Notation \u2018qualid\u2019 is deprecated since \u2018string\u2019": [[74, 2, 1, "coq:warn.Tactic-Notation-\u2018qualid\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019", " \u2018string\u2019"]], "Tactic \u2018qualid\u2019 is deprecated since \u2018string\u2019": [[74, 2, 1, "coq:warn.Tactic-\u2018qualid\u2019-is-deprecated-since-\u2018string\u2019.-\u2018string\u2019", " \u2018string\u2019"]], "The file \u2018ident\u2019": [[59, 0, 1, "coq:exn.The-file-\u2018ident\u2019.vo-contains-library-\u2018qualid\u2019-and-not-library-\u2018qualid\u2019", "vo contains library \u2018qualid\u2019 and not library \u2018qualid\u2019"]], "The relation \u2018ident\u2019 is not a declared reflexive relation. Maybe you need to require the Stdlib.Classes": [[64, 0, 1, "coq:exn.The-relation-\u2018ident\u2019-is-not-a-declared-reflexive-relation.-Maybe-you-need-to-require-the-Stdlib.Classes.RelationClasses-library", "RelationClasses library"]], "The relation \u2018ident\u2019 is not a declared symmetric relation. Maybe you need to require the Stdlib.Classes": [[64, 0, 1, "coq:exn.The-relation-\u2018ident\u2019-is-not-a-declared-symmetric-relation.-Maybe-you-need-to-require-the-Stdlib.Classes.RelationClasses-library", "RelationClasses library"]], "The relation \u2018ident\u2019 is not a declared transitive relation. Maybe you need to require the Stdlib.Classes": [[64, 0, 1, "coq:exn.The-relation-\u2018ident\u2019-is-not-a-declared-transitive-relation.-Maybe-you-need-to-require-the-Stdlib.Classes.RelationClasses-library", "RelationClasses library"]], "This command is just asserting the names of arguments of \u2018qualid\u2019. If this is what you want, add ': assert' to silence the warning. If you want to clear implicit arguments, add ': clear implicits'": [[41, 2, 1, "coq:warn.This-command-is-just-asserting-the-names-of-arguments-of-\u2018qualid\u2019.-If-this-is-what-you-want,-add-':-assert'-to-silence-the-warning.-If-you-want-to-clear-implicit-arguments,-add-':-clear-implicits'.-If-you-want-to-clear-notation-scopes,-add-':-clear-scopes'", " If you want to clear notation scopes, add ': clear scopes'"]], "This hint is not local but depends on a section variable": [[60, 2, 1, "coq:warn.This-hint-is-not-local-but-depends-on-a-section-variable.-It-will-disappear-when-the-section-is-closed", " It will disappear when the section is closed"]], "Type of \u2018qualid\u2019 seems incompatible with the type of \u2018qualid\u2019. Expected type is: \u2018type\u2019 instead of \u2018type\u2019": [[71, 2, 1, "coq:warn.Type-of-\u2018qualid\u2019-seems-incompatible-with-the-type-of-\u2018qualid\u2019.-Expected-type-is:-\u2018type\u2019-instead-of-\u2018type\u2019.-This-might-yield-ill-typed-terms-when-using-the-notation", " This might yield ill typed terms when using the notation"]], "Unable to apply lemma of type "..." on hypothesis of type "..": [[58, 0, 1, "coq:exn.Unable-to-apply-lemma-of-type-\"...\"-on-hypothesis-of-type-\"...\"", """]], "Unused variable \u2018ident\u2019 might be a misspelled constructor. Use _ or _\u2018ident\u2019 to silence this warning": [[46, 2, 1, "coq:warn.Unused-variable-\u2018ident\u2019-might-be-a-misspelled-constructor.-Use-_-or-_\u2018ident\u2019-to-silence-this-warning.", ""]], "package-name": [[59, 0, 1, "coq:exn.package-name.foo-and-not-foo_plugin", "foo and not foo_plugin"]], "plugin name anymore": [[59, 0, 1, "coq:exn.plugin-name-anymore.-Plugins-should-be-loaded-using-their", " Plugins should be loaded using their"]], "\u2018ident\u2019 already exists": [[28, 0, 1, "coq:exn.\u2018ident\u2019-already-exists.-(Axiom)", " (Axiom)"], [32, 0, 1, "coq:exn.\u2018ident\u2019-already-exists.-(Definition)", " (Definition)"], [32, 0, 1, "coq:exn.\u2018ident\u2019-already-exists.-(Theorem)", " (Theorem)"]], "\u2018qualid\u2019 should go from Byte.byte, (list Byte.byte), or PrimString": [[71, 0, 1, "coq:exn.\u2018qualid\u2019-should-go-from-Byte.byte,-(list-Byte.byte),-or-PrimString.string-to-\u2018type\u2019-or-(option-\u2018type\u2019)", "string to \u2018type\u2019 or (option \u2018type\u2019)"]], "\u2018qualid\u2019 should go from Number.int to \u2018type\u2019 or (option \u2018type\u2019). Instead of Number.int, the types Number.uint or Z or PrimInt63.pos_neg_int63 or PrimFloat.float or Number": [[71, 0, 1, "coq:exn.\u2018qualid\u2019-should-go-from-Number.int-to-\u2018type\u2019-or-(option-\u2018type\u2019).-Instead-of-Number.int,-the-types-Number.uint-or-Z-or-PrimInt63.pos_neg_int63-or-PrimFloat.float-or-Number.number-could-be-used-(you-may-need-to-require-BinNums-or-Number-or-PrimInt63-or-PrimFloat-first)", "number could be used (you may need to require BinNums or Number or PrimInt63 or PrimFloat first)"]], "\u2018qualid\u2019 should go from \u2018type\u2019 to Number.int or (option Number.int). Instead of Number.int, the types Number.uint or Z or PrimInt63.pos_neg_int63 or Number": [[71, 0, 1, "coq:exn.\u2018qualid\u2019-should-go-from-\u2018type\u2019-to-Number.int-or-(option-Number.int).-Instead-of-Number.int,-the-types-Number.uint-or-Z-or-PrimInt63.pos_neg_int63-or-Number.number-could-be-used-(you-may-need-to-require-BinNums-or-Number-or-PrimInt63-first)", "number could be used (you may need to require BinNums or Number or PrimInt63 first)"]], "\u2018qualid\u2019 should go from \u2018type\u2019 to T or (option T), where T is either Byte.byte, (list Byte.byte), or PrimString": [[71, 0, 1, "coq:exn.\u2018qualid\u2019-should-go-from-\u2018type\u2019-to-T-or-(option-T),-where-T-is-either-Byte.byte,-(list-Byte.byte),-or-PrimString.string", "string"]], "\u2018string\u2019 cannot be interpreted as a known notation in \u2018ident\u2019 entry": [[71, 0, 1, "coq:exn.\u2018string\u2019-cannot-be-interpreted-as-a-known-notation-in-\u2018ident\u2019-entry.-Make-sure-that-symbols-are-surrounded-by-spaces-and-that-holes-are-explicitly-denoted-by-\"_\"", " Make sure that symbols are surrounded by spaces and that holes are explicitly denoted by "_""]], "\u2018string\u2019 cannot be interpreted as a known notation": [[71, 0, 1, "coq:exn.\u2018string\u2019-cannot-be-interpreted-as-a-known-notation.-Make-sure-that-symbols-are-surrounded-by-spaces-and-that-holes-are-explicitly-denoted-by-\"_\"", " Make sure that symbols are surrounded by spaces and that holes are explicitly denoted by "_""]]}, "objtypes": {"0": "coq:exn", "1": "coq:tacn", "2": "coq:warn", "3": "coq:cmd", "4": "coq:flag", "5": "coq:thm", "6": "coq:opt", "7": "coq:attr", "8": "coq:table", "9": "coq:tacv"}, "objnames": {"0": ["coq", "exn", "Coq exn"], "1": ["coq", "tacn", "Coq tacn"], "2": ["coq", "warn", "Coq warn"], "3": ["coq", "cmd", "Coq cmd"], "4": ["coq", "flag", "Coq flag"], "5": ["coq", "thm", "Coq thm"], "6": ["coq", "opt", "Coq opt"], "7": ["coq", "attr", "Coq attr"], "8": ["coq", "table", "Coq table"], "9": ["coq", "tacv", "Coq tacv"]}, "titleterms": {"program": [2, 6, 9, 27, 55, 60], "extract": [2, 17, 24], "gener": [2, 3, 4, 11, 14, 23, 29, 44, 54, 55, 57, 67, 71, 72], "ml": [2, 55], "code": 2, "option": [2, 17, 21, 29, 51, 66, 75], "set": [2, 13, 26, 29, 37, 41, 57, 58, 60, 66], "target": [2, 53], "languag": [2, 17, 24, 25, 33, 45, 55, 57], "inlin": [2, 59], "optim": [2, 54], "extra": [2, 59], "elimin": [2, 46, 57], "useless": 2, "argument": [2, 37, 41, 44, 46, 53, 57, 67, 71], "realiz": 2, "axiom": 2, "induct": [2, 26, 34, 40, 46, 67, 71, 72], "type": [2, 3, 4, 10, 17, 26, 28, 30, 32, 34, 35, 37, 38, 40, 44, 46, 54, 55, 57, 59, 67, 71], "ffi": 2, "avoid": 2, "conflict": 2, "exist": [2, 24, 35], "filenam": [2, 53], "addit": [2, 57, 60], "differ": [2, 44, 66], "between": [2, 55, 59, 66], "rocq": [2, 25, 51, 53, 57, 60, 71, 74, 75], "system": [2, 35], "some": [2, 35], "exampl": [2, 3, 4, 5, 6, 11, 14, 17, 26, 27, 28, 29, 30, 31, 34, 35, 37, 38, 40, 41, 42, 43, 44, 46, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 71, 72, 74, 75], "A": [2, 14, 35, 58, 67], "detail": [2, 17, 24, 53], "euclidean": 2, "divis": 2, "": [2, 41, 67], "horror": 2, "museum": 2, "user": [2, 3, 10, 24, 27], "contribut": [2, 24, 27], "rewrit": [3, 10, 57, 64, 67], "introduct": [3, 25, 57], "relat": 3, "morphism": 3, "parametr": [3, 46, 57], "continu": [3, 41, 44], "contravari": 3, "ad": [3, 11, 52], "new": [3, 11, 17, 24, 35, 53, 57, 63], "nonreflex": 3, "nonsymmetr": 3, "covari": 3, "ambigu": 3, "setoid": [3, 64], "context": [3, 13, 54, 55, 57, 58], "valu": [3, 46, 54, 55], "declar": [3, 13, 38, 41, 42, 44, 55, 57, 66, 67], "command": [3, 13, 17, 19, 24, 35, 51, 52, 57, 59, 66, 67, 71, 75, 76], "tactic": [3, 5, 11, 17, 22, 24, 27, 43, 54, 55, 57, 58, 60, 61, 63, 64, 67, 71, 72, 74], "first": [3, 34, 46, 54, 57], "class": [3, 4, 37, 55, 71], "enabl": [3, 66, 71], "provid": [3, 46], "print": [3, 4, 14, 37, 43, 44, 46, 54, 55, 59, 71, 75], "deprec": [3, 74], "syntax": [3, 10, 17, 24, 29, 44, 46, 54, 55, 57, 71], "backward": [3, 58], "incompat": [3, 17], "extens": [3, 24, 45, 46, 57, 71], "under": [3, 57], "binder": [3, 28, 44, 57, 71], "subrel": 3, "constant": [3, 37, 59, 71], "unfold": [3, 41, 64], "dure": 3, "proper": 3, "instanc": [3, 13, 43], "search": [3, 59, 60], "strategi": [3, 46, 64], "usag": [3, 11, 57, 66, 75], "definit": [3, 9, 12, 14, 30, 32, 34, 37, 40, 46, 54, 55, 57, 64, 71], "innermost": 3, "outermost": 3, "implicit": [4, 41, 44, 46, 60, 71], "coercion": [4, 46, 71], "present": [4, 14], "revers": [4, 44, 54, 55, 64], "ident": [4, 54], "inherit": [4, 71], "graph": 4, "displai": [4, 43, 44, 52, 59, 71], "avail": 4, "activ": 4, "record": [4, 37], "section": [4, 13, 14, 38, 66, 75], "modul": [4, 35, 53], "function": [4, 28, 30, 34, 41, 44, 54, 60, 72], "applic": [4, 28, 44, 54, 58], "us": [4, 14, 25, 35, 37, 38, 43, 44, 46, 51, 52, 53, 54, 58, 64, 66, 67, 71], "attribut": [4, 17, 18, 29, 35, 38], "micromega": 5, "solver": [5, 7, 11, 61, 62], "arithmet": [5, 27], "goal": [5, 11, 54, 55, 57, 58, 66, 67], "over": [5, 9, 55, 57], "order": [5, 10, 58], "ring": [5, 11], "short": 5, "descript": 5, "positivstellensatz": 5, "refut": 5, "lra": 5, "decis": 5, "procedur": 5, "linear": 5, "real": [5, 17], "ration": [5, 11], "lia": 5, "integ": [5, 36, 71], "high": 5, "level": [5, 10, 29, 30, 32, 34, 55], "view": [5, 57], "cut": [5, 54], "plane": 5, "proof": [5, 8, 12, 14, 25, 31, 32, 46, 54, 57, 58, 60, 65, 66], "case": [5, 24, 40, 52, 57, 58, 67], "split": [5, 53], "nra": 5, "non": [5, 12, 34, 44, 54, 55, 58, 67, 71], "nia": 5, "psatz": 5, "zifi": 5, "pre": 5, "process": [5, 8, 54], "deriv": [6, 42, 67], "nsatz": 7, "equal": [7, 9, 27, 62, 64, 67], "integr": 7, "domain": 7, "more": 7, "about": [7, 46, 71], "asynchron": [8, 52], "parallel": 8, "annot": 8, "automat": [8, 11, 34, 41, 43, 44, 61, 67], "suggest": 8, "block": [8, 57], "error": [8, 20, 54, 55], "resili": 8, "caveat": [8, 30], "interact": [8, 35, 44, 51, 54, 55, 57], "mode": [8, 44, 52, 55, 57, 66], "limit": [8, 67], "number": [8, 54, 60, 71], "worker": 8, "elabor": 9, "syntact": [9, 54, 55], "control": [9, 35, 44, 46, 54, 57, 58, 59, 64, 66], "fixpoint": [9, 34], "lemma": [9, 27, 66], "solv": [9, 43, 54, 66], "oblig": 9, "frequent": 9, "ask": 9, "question": 9, "defin": [10, 34, 35, 37, 54, 55, 60], "rule": [10, 26, 31, 34, 38, 57, 64, 71, 75], "symbol": [10, 52, 54], "pattern": [10, 44, 46, 54, 55, 57, 58, 59, 71], "higher": 10, "hole": [10, 54], "univers": [10, 14], "polymorph": [10, 14, 34, 57], "preserv": 10, "confluenc": 10, "termin": [10, 12, 57], "compat": [10, 17, 37, 55, 57, 74], "eta": 10, "law": 10, "support": [10, 29, 52], "field": [11, 35, 37], "polynomi": 11, "equat": [11, 57], "what": 11, "doe": [11, 46], "thi": 11, "do": [11, 54], "The": [11, 26, 27, 34, 35, 44, 51, 53, 57, 71, 75], "variabl": [11, 43, 44, 46, 51, 52, 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arguments": [[2, "extra-elimination-of-useless-arguments"]], "Realizing axioms": [[2, "realizing-axioms"]], "Realizing inductive types": [[2, "realizing-inductive-types"]], "Generating FFI Code": [[2, "generating-ffi-code"]], "Avoiding conflicts with existing filenames": [[2, "avoiding-conflicts-with-existing-filenames"]], "Additional settings": [[2, "additional-settings"]], "Differences between Rocq and ML type systems": [[2, "differences-between-rocq-and-ml-type-systems"]], "Some examples": [[2, "some-examples"]], "A detailed example: Euclidean division": [[2, "a-detailed-example-euclidean-division"]], "Extraction's horror museum": [[2, "extraction-s-horror-museum"]], "Users' Contributions": [[2, "users-contributions"]], "Generalized rewriting": [[3, "generalized-rewriting"]], "Introduction to generalized rewriting": [[3, "introduction-to-generalized-rewriting"]], "Relations and morphisms": [[3, "relations-and-morphisms"]], "Example: Parametric relation": [[3, null], [3, null]], "Example: Parametric relation (continued)": [[3, null]], "Example: Morphisms": [[3, null]], "Example: Contravariant morphisms": [[3, null]], "Example: Rewriting": [[3, null]], "Adding new relations and morphisms": [[3, "adding-new-relations-and-morphisms"]], "Example": [[3, null], [3, null], [3, null], [3, null], [3, null], [3, null], [6, null], [11, null], [11, null], [11, null], [17, null], [26, null], [27, null], [30, null], [30, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [34, null], [35, null], [35, null], [35, null], [35, null], [35, null], [37, null], [37, null], [40, null], [40, null], [41, null], [41, null], [41, null], [41, null], [41, null], [41, null], [42, null], [42, null], [42, null], [44, null], [44, 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relations": [[3, "rewriting-and-nonsymmetric-relations"]], "Example: Covariance and contravariance": [[3, null]], "Rewriting in ambiguous setoid contexts": [[3, "rewriting-in-ambiguous-setoid-contexts"]], "Rewriting with Type valued relations": [[3, "rewriting-with-type-valued-relations"]], "Declaring rewrite relations": [[3, "declaring-rewrite-relations"]], "Commands and tactics": [[3, "commands-and-tactics"]], "First class setoids and morphisms": [[3, "first-class-setoids-and-morphisms"]], "Example: First class setoids": [[3, null]], "Tactics enabled on user provided relations": [[3, "tactics-enabled-on-user-provided-relations"]], "Printing relations and morphisms": [[3, "printing-relations-and-morphisms"]], "Deprecated syntax and backward incompatibilities": [[3, "deprecated-syntax-and-backward-incompatibilities"]], "Extensions": [[3, "extensions"]], "Rewriting under binders": [[3, "rewriting-under-binders"], [57, "rewriting-under-binders"]], "Subrelations": [[3, "subrelations"]], "Constant unfolding during rewriting": [[3, "constant-unfolding-during-rewriting"]], "Constant unfolding during Proper-instance search": [[3, "constant-unfolding-during-proper-instance-search"]], "Strategies for rewriting": [[3, "strategies-for-rewriting"]], "Usage": [[3, "usage"], [57, "usage"], [75, "usage"]], "Definitions": [[3, "definitions"], [32, "definitions"], [57, "definitions"]], "Example: innermost and outermost": [[3, "rewrite-strat-innermost-outermost"]], "Implicit Coercions": [[4, "implicit-coercions"]], "General Presentation": [[4, "general-presentation"], [14, "general-presentation"]], "Coercion Classes": [[4, "coercion-classes"], [4, "id2"]], "Coercions": [[4, "id1"]], "Reversible Coercions": [[4, "reversible-coercions"]], "Identity Coercions": [[4, "identity-coercions"]], "Inheritance Graph": [[4, "inheritance-graph"]], "Displaying Available Coercions": [[4, "displaying-available-coercions"]], "Activating the Printing of Coercions": [[4, "activating-the-printing-of-coercions"]], "Classes as Records": [[4, "classes-as-records"]], "Coercions and Sections": [[4, "coercions-and-sections"]], "Coercions and Modules": [[4, "coercions-and-modules"]], "Examples": [[4, "examples"], [31, "examples"], [35, "examples"], [57, "examples"]], "Example: Coercion at function application": [[4, null]], "Example: Coercion to a type": [[4, null]], "Example: Coercion to a function": [[4, null]], "Example: Reversible coercions": [[4, "example-reversible-coercion"]], "Example: Reversible coercions using the reversible attribute": [[4, "example-reversible-coercion-attribute"]], "Example: Identity coercions.": [[4, "example-identity-coercion"]], "Example: Inheritance Graph": [[4, null]], "Micromega: solvers for arithmetic goals over ordered rings": [[5, "micromega-solvers-for-arithmetic-goals-over-ordered-rings"]], "Short description of the tactics": [[5, "short-description-of-the-tactics"]], "Positivstellensatz refutations": [[5, "positivstellensatz-refutations"]], "lra: a decision procedure for linear real and rational arithmetic": [[5, "lra-a-decision-procedure-for-linear-real-and-rational-arithmetic"]], "lia: a tactic for linear integer arithmetic": [[5, "lia-a-tactic-for-linear-integer-arithmetic"]], "High level view of lia": [[5, "high-level-view-of-lia"]], "Cutting plane proofs": [[5, "cutting-plane-proofs"]], "Example: Cutting plane": [[5, null]], "Case split": [[5, "case-split"]], "nra: a proof procedure for non-linear arithmetic": [[5, "nra-a-proof-procedure-for-non-linear-arithmetic"]], "nia: a proof procedure for non-linear integer arithmetic": [[5, "nia-a-proof-procedure-for-non-linear-integer-arithmetic"]], "psatz: a proof procedure for non-linear arithmetic": [[5, "psatz-a-proof-procedure-for-non-linear-arithmetic"]], "zify: pre-processing of arithmetic goals": [[5, "zify-pre-processing-of-arithmetic-goals"]], "Example: Lra": [[5, "lra-example"]], "Program derivation": [[6, "program-derivation"]], "Nsatz: a solver for equalities in integral domains": [[7, "nsatz-a-solver-for-equalities-in-integral-domains"]], "More about nsatz": [[7, "more-about-nsatz"]], "Asynchronous and Parallel Proof Processing": [[8, "asynchronous-and-parallel-proof-processing"]], "Proof annotations": [[8, "proof-annotations"]], "Automatic suggestion of proof annotations": [[8, "automatic-suggestion-of-proof-annotations"]], "Proof blocks and error resilience": [[8, "proof-blocks-and-error-resilience"]], "Caveats": [[8, "caveats"], [8, "id3"]], "Interactive mode": [[8, "interactive-mode"], [57, "interactive-mode"]], "Limiting the number of parallel workers": [[8, "limiting-the-number-of-parallel-workers"]], "Program": [[9, "program"]], "Elaborating programs": [[9, "elaborating-programs"]], "Syntactic control over equalities": [[9, "syntactic-control-over-equalities"]], "Program Definition": [[9, "program-definition"]], "Program Fixpoint": [[9, "program-fixpoint"]], "Program Lemma": [[9, "program-lemma"]], "Solving obligations": [[9, "solving-obligations"]], "Frequently Asked Questions": [[9, "frequently-asked-questions"]], "User-defined rewrite rules": [[10, "user-defined-rewrite-rules"]], "Symbols": [[10, "symbols"]], "Rewrite rules": [[10, "id1"]], "Pattern syntax": [[10, "pattern-syntax"]], "Higher-order pattern holes": [[10, "higher-order-pattern-holes"]], "Universe polymorphic rules": [[10, "universe-polymorphic-rules"]], "Rewrite rules, type preservation, confluence and termination": [[10, "rewrite-rules-type-preservation-confluence-and-termination"]], "Compatibility with the eta laws": [[10, "compatibility-with-the-eta-laws"]], "Level of support": [[10, "level-of-support"]], "ring and field: solvers for polynomial and rational equations": [[11, "ring-and-field-solvers-for-polynomial-and-rational-equations"]], "What does this tactic do?": [[11, "what-does-this-tactic-do"]], "The variables map": [[11, "the-variables-map"]], "Is it automatic?": [[11, "is-it-automatic"]], "Concrete usage": [[11, "concrete-usage"]], "Adding a ring structure": [[11, "adding-a-ring-structure"]], "How does it work?": [[11, "how-does-it-work"]], "Dealing with fields": [[11, "dealing-with-fields"]], "Example: field that generates side goals": [[11, null]], "Adding a new field structure": [[11, "adding-a-new-field-structure"]], "History of ring": [[11, "history-of-ring"]], "Discussion": [[11, "discussion"]], "SProp (proof irrelevant propositions)": [[12, "sprop-proof-irrelevant-propositions"]], "Basic constructs": [[12, "basic-constructs"]], "Encodings for strict propositions": [[12, "encodings-for-strict-propositions"]], "Definitional UIP": [[12, "definitional-uip"]], "Non Termination with UIP": [[12, "non-termination-with-uip"]], "Debugging \\SProp issues": [[12, "debugging-sprop-issues"]], "Typeclasses": [[13, "typeclasses"]], "Typeclass and instance declarations": [[13, "typeclass-and-instance-declarations"]], "Binding typeclasses": [[13, "binding-typeclasses"]], "Parameterized instances": [[13, "parameterized-instances"]], "Sections and contexts": [[13, "sections-and-contexts"]], "Building hierarchies": [[13, "building-hierarchies"]], "Superclasses": [[13, "superclasses"]], "Substructures": [[13, "substructures"]], "Command summary": [[13, "command-summary"]], "Typeclasses Transparent, Typeclasses Opaque": [[13, "typeclasses-transparent-typeclasses-opaque"]], "Settings": [[13, "settings"], [29, "settings"], [57, "settings"]], "Typeclasses eauto": [[13, "typeclasses-eauto"]], "Polymorphic Universes": [[14, "polymorphic-universes"]], "Polymorphic, Monomorphic": [[14, "polymorphic-monomorphic"]], "Cumulative, NonCumulative": [[14, "cumulative-noncumulative"]], "Specifying cumulativity": [[14, "specifying-cumulativity"]], "Example: Demonstration of universe variances": [[14, null]], "Example: A proof using cumulativity": [[14, null]], "Cumulativity Weak Constraints": [[14, "cumulativity-weak-constraints"]], "Global and local universes": [[14, "global-and-local-universes"]], "Conversion and unification": [[14, "conversion-and-unification"]], "Minimization": [[14, "minimization"]], "Explicit Universes": [[14, "explicit-universes"]], "Printing universes": [[14, "printing-universes"]], "Polymorphic definitions": [[14, "polymorphic-definitions"]], "Sort polymorphism": [[14, "sort-polymorphism"]], "Universe polymorphism and sections": [[14, "universe-polymorphism-and-sections"]], "History and recent changes": [[15, "history-and-recent-changes"]], "Indexes": [[16, "indexes"]], "Recent changes": [[17, "recent-changes"]], "Unreleased changes": [[17, "unreleased-changes"]], "Kernel": [[17, "kernel"], [17, "id102"], [17, "id305"], [17, "id456"], [17, "id500"], [17, "id646"], [17, "id807"], [17, "id948"], [17, "id970"], [17, "id1138"], [17, "id1198"], [17, "id1371"], [17, "id1392"], [17, "id1539"], [17, "id1543"], [17, "id1557"]], "Specification language, type inference": [[17, "specification-language-type-inference"], [17, 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8.1gamma": [[17, "details-of-changes-in-8-1gamma"]], "Details of changes in 8.1": [[17, "details-of-changes-in-8-1"]], "Version 8.0": [[17, "version-8-0"]], "Details of changes in 8.0beta old syntax": [[17, "details-of-changes-in-8-0beta-old-syntax"]], "Details of changes in 8.0beta new syntax": [[17, "details-of-changes-in-8-0beta-new-syntax"]], "Details of changes in 8.0": [[17, "details-of-changes-in-8-0"]], "Attribute index": [[18, "attribute-index"]], "Command index": [[19, "command-index"]], "Errors and warnings index": [[20, "errors-and-warnings-index"]], "Flags, options and tables index": [[21, "flags-options-and-tables-index"]], "Tactic index": [[22, "tactic-index"]], "General index": [[23, "general-index"]], "Early history of Coq": [[24, "early-history-of-coq"]], "Historical roots": [[24, "historical-roots"]], "Versions 1 to 5": [[24, "versions-1-to-5"]], "Version 1": [[24, "version-1"]], "Version 2": [[24, "version-2"]], "Version 3": [[24, "version-3"]], "Version 4": [[24, "version-4"]], "Version 5": [[24, "version-5"]], "Versions 6": [[24, "versions-6"]], "Version 6.1": [[24, "version-6-1"]], "Version 6.2": [[24, "version-6-2"]], "Version 6.3": [[24, "version-6-3"]], "Versions 7": [[24, "versions-7"]], "Details of changes in 7.0 and 7.1": [[24, "details-of-changes-in-7-0-and-7-1"]], "Main novelties": [[24, "main-novelties"]], "Language: new \"let-in\" construction": [[24, "language-new-let-in-construction"]], "Language: long names": [[24, "language-long-names"]], "Language: miscellaneous": [[24, "language-miscellaneous"]], "Language: Cases": [[24, "language-cases"]], "Reduction": [[24, "reduction"], [37, "reduction"], [55, "reduction"]], "New tactics": [[24, "new-tactics"]], "Changes in existing tactics": [[24, "changes-in-existing-tactics"]], "Efficiency": [[24, "efficiency"]], "Concrete syntax of constructions": [[24, "concrete-syntax-of-constructions"]], "Parsing and grammar extension": [[24, "parsing-and-grammar-extension"]], "New commands": [[24, "new-commands"]], "Changes in existing commands": [[24, "changes-in-existing-commands"]], "New user contributions": [[24, "new-user-contributions"]], "Details of changes in 7.2": [[24, "details-of-changes-in-7-2"]], "Details of changes in 7.3": [[24, "details-of-changes-in-7-3"]], "Changes in 7.3.1": [[24, "changes-in-7-3-1"]], "Details of changes in 7.4": [[24, "details-of-changes-in-7-4"]], "Introduction and Contents": [[25, "introduction-and-contents"]], "Contents": [[25, "contents"]], "Specification language": [[25, null]], "Proofs": [[25, null]], "Using the Rocq Prover": [[25, null]], "Appendix": [[25, null]], "Typing rules": [[26, "typing-rules"], [26, "id4"]], "The terms": [[26, "the-terms"]], "Subtyping rules": [[26, "subtyping-rules"]], "The Calculus of Inductive Constructions with impredicative Set": [[26, "the-calculus-of-inductive-constructions-with-impredicative-set"]], "The Coq libraries": [[27, "the-coq-libraries"]], "The prelude": [[27, "the-prelude"]], "Logic": [[27, "logic"]], "Propositional Connectives": [[27, "propositional-connectives"]], "Quantifiers": [[27, "quantifiers"]], "Equality": [[27, "equality"]], "Lemmas": [[27, "lemmas"]], "Datatypes": [[27, "datatypes"]], "Programming": [[27, "programming"]], "Specification": [[27, "specification"]], "Basic Arithmetic": [[27, "basic-arithmetic"]], "Well-founded recursion": [[27, "well-founded-recursion"]], "Users\u2019 contributions": [[27, "users-contributions"]], "Functions and assumptions": [[28, "functions-and-assumptions"]], "Binders": [[28, "binders"]], "Functions (fun) and function types (forall)": [[28, "functions-fun-and-function-types-forall"]], "Function application": [[28, "function-application"]], "Assumptions": [[28, "assumptions"]], "Example: Simple assumptions": [[28, null]], "Basic notions and conventions": [[29, "basic-notions-and-conventions"]], "Syntax and lexical conventions": [[29, "syntax-and-lexical-conventions"]], "Syntax conventions": [[29, "syntax-conventions"]], "Lexical conventions": [[29, "lexical-conventions"]], "Example: Stack overflow with nat": [[29, null]], "Essential vocabulary": [[29, "essential-vocabulary"]], "Attributes": [[29, "attributes"]], "Generic attributes": [[29, "generic-attributes"]], "Document-level attributes": [[29, "document-level-attributes"]], "Flags, Options and Tables": [[29, "flags-options-and-tables"]], "Locality attributes supported by Set and Unset": [[29, "locality-attributes-supported-by-set-and-unset"]], "Coinductive types and corecursive functions": [[30, "coinductive-types-and-corecursive-functions"]], "Coinductive types": [[30, "coinductive-types"]], "Caveat": [[30, "caveat"]], "Co-recursive functions: cofix": [[30, "co-recursive-functions-cofix"]], "Top-level definitions of corecursive functions": [[30, "top-level-definitions-of-corecursive-functions"]], "Conversion rules": [[31, "conversion-rules"]], "\u03b1-conversion": [[31, "conversion"]], "\u03b2-reduction": [[31, "reduction"]], "\u03b4-reduction": [[31, "delta-reduction-sect"]], "\u03b9-reduction": [[31, "id4"]], "\u03b6-reduction": [[31, "id6"]], "\u03b7-expansion": [[31, "expansion"]], "Example: Simple delta, fix, beta and match reductions": [[31, null]], "Proof Irrelevance": [[31, "proof-irrelevance"]], "Convertibility": [[31, "convertibility"]], "Let-in definitions": [[32, "let-in-definitions"]], "Type cast": [[32, "type-cast"]], "Top-level definitions": [[32, "top-level-definitions"]], "Assertions and proofs": [[32, "assertions-and-proofs"]], "Core language": [[33, "core-language"]], "Inductive types and recursive functions": [[34, "inductive-types-and-recursive-functions"]], "Inductive types": [[34, "inductive-types"]], "Simple inductive types": [[34, "simple-inductive-types"]], "Automatic Prop lowering": [[34, "automatic-prop-lowering"]], "Simple indexed inductive types": [[34, "simple-indexed-inductive-types"]], "Parameterized inductive types": [[34, "parameterized-inductive-types"]], "Mutually defined inductive types": [[34, "mutually-defined-inductive-types"]], "Example: Mutually defined inductive types": [[34, null]], "Recursive functions: fix": [[34, "recursive-functions-fix"]], "Top-level recursive functions": [[34, "top-level-recursive-functions"]], "Example: Mutual fixpoints": [[34, null]], "Theory of inductive definitions": [[34, "theory-of-inductive-definitions"]], "Types of inductive objects": [[34, "types-of-inductive-objects"]], "Well-formed inductive definitions": [[34, "well-formed-inductive-definitions"]], "Arity of a given sort": [[34, "arity-of-a-given-sort"]], "Arity": [[34, "arity"]], "Type of constructor": [[34, "type-of-constructor"]], "Positivity Condition": [[34, "positivity-condition"]], "Strict positivity": [[34, "strict-positivity"]], "Nested Positivity": [[34, "nested-positivity"]], "Correctness rules": [[34, "correctness-rules"]], "Example: Negative occurrence (first example)": [[34, null]], "Example: Negative occurrence (second example)": [[34, null]], "Example: Non strictly positive occurrence": [[34, null]], "Template polymorphism": [[34, "template-polymorphism"]], "Destructors": [[34, "destructors"]], "The match ... with ... end construction": [[34, "the-match-with-end-construction"]], "Fixpoint definitions": [[34, "fixpoint-definitions"]], "Typing rule": [[34, "id10"]], "Reduction rule": [[34, "reduction-rule"]], "The Module System": [[35, "the-module-system"]], "Modules and module types": [[35, "modules-and-module-types"]], "Using modules": [[35, "using-modules"]], "Example: Defining a simple module interactively": [[35, null]], "Example: Defining a simple module type interactively": [[35, "example-def-simple-module-type"]], "Example: Creating a new module that omits some items from an existing module": [[35, "example-filter-module"]], "Example: Creating a functor (a module with parameters)": [[35, null]], "Example: A module type with two sub-modules, sharing some fields": [[35, null]], "Qualified names": [[35, "qualified-names"]], "Controlling the scope of commands with locality attributes": [[35, "controlling-the-scope-of-commands-with-locality-attributes"]], "Summary of locality attributes in a module": [[35, "summary-of-locality-attributes-in-a-module"]], "Typing Modules": [[35, "typing-modules"]], "Primitive objects": [[36, "primitive-objects"]], "Primitive Integers": [[36, "primitive-integers"]], "Primitive Floats": [[36, "primitive-floats"]], "Primitive Arrays": [[36, "primitive-arrays"]], "Primitive (Byte-Based) Strings": [[36, "primitive-byte-based-strings"]], "Record types": [[37, "record-types"]], "Defining record types": [[37, "defining-record-types"]], "Example: Defining a record": [[37, null]], "Example: Reusing a field name in multiple records": [[37, null]], "Example: Using the \"as\" clause in a record definition": [[37, null]], "Example: Argument name for a record type created using Class": [[37, null]], "Constructing records": [[37, "constructing-records"]], "Example: Constructing 1/2 as a record": [[37, null]], "Accessing fields (projections)": [[37, "accessing-fields-projections"]], "Example: Accessing record fields": [[37, null]], "Example: Matching on records": [[37, null]], "Example: Accessing anonymous record fields with match": [[37, null]], "Settings for printing records": [[37, "settings-for-printing-records"]], "Primitive Projections": [[37, "primitive-projections"]], "Compatibility Constants for Projections": [[37, "compatibility-constants-for-projections"]], "Sections": [[38, "sections"], [75, "sections"]], "Using sections": [[38, "using-sections"]], "Example: Section-local declarations": [[38, "section-local-declarations"]], "Summary of locality attributes in a section": [[38, "summary-of-locality-attributes-in-a-section"]], "Typing rules used at the end of a section": [[38, "typing-rules-used-at-the-end-of-a-section"]], "Sorts": [[39, "sorts"]], "Variants and the match construct": [[40, "variants-and-the-match-construct"]], "Variants": [[40, "id1"]], "Private (matching) inductive types": [[40, "private-matching-inductive-types"]], "Definition by cases: match": [[40, "definition-by-cases-match"]], "Setting properties of a function's arguments": [[41, "setting-properties-of-a-function-s-arguments"]], "Manual declaration of implicit arguments": [[41, "manual-declaration-of-implicit-arguments"]], "Example: Multiple alternatives with implicits_alt": [[41, "example-more-implicits"]], "Automatic declaration of implicit arguments": [[41, "automatic-declaration-of-implicit-arguments"]], "Example: Default implicits": [[41, null]], "Renaming implicit arguments": [[41, "renaming-implicit-arguments"]], "Example: (continued) Renaming implicit arguments": [[41, null]], "Binding arguments to scopes": [[41, "binding-arguments-to-scopes"]], "Effects of Arguments on unfolding": [[41, "effects-of-arguments-on-unfolding"]], "Bidirectionality hints": [[41, "bidirectionality-hints"]], "Example: Bidirectionality hints": [[41, null]], "Canonical Structures": [[42, "canonical-structures"]], "Declaration of canonical structures": [[42, "declaration-of-canonical-structures"]], "Notation overloading": [[42, "notation-overloading"]], "Derived Canonical Structures": [[42, "derived-canonical-structures"]], "Hierarchy of structures": [[42, "hierarchy-of-structures"]], "Compact declaration of Canonical Structures": [[42, "compact-declaration-of-canonical-structures"]], "Existential variables": [[43, "existential-variables"]], "Inferable subterms": [[43, "inferable-subterms"]], "e* tactics that can create existential variables": [[43, "e-tactics-that-can-create-existential-variables"]], "Example: apply vs eapply": [[43, null]], "Automatic resolution of existential variables": [[43, "automatic-resolution-of-existential-variables"]], "Example: Automatic resolution of existential variables": [[43, "automatic-evar-resolution"]], "Explicit display of existential instances for pretty-printing": [[43, "explicit-display-of-existential-instances-for-pretty-printing"]], "Solving existential variables using tactics": [[43, "solving-existential-variables-using-tactics"]], "Implicit arguments": [[44, "implicit-arguments"]], "The different kinds of implicit arguments": [[44, "the-different-kinds-of-implicit-arguments"]], "Implicit arguments inferable from the knowledge of other arguments of a function": [[44, "implicit-arguments-inferable-from-the-knowledge-of-other-arguments-of-a-function"]], "Implicit arguments inferable by resolution": [[44, "implicit-arguments-inferable-by-resolution"]], "Maximal and non-maximal insertion of implicit arguments": [[44, "maximal-and-non-maximal-insertion-of-implicit-arguments"]], "Trailing Implicit Arguments": [[44, "trailing-implicit-arguments"]], "Casual use of implicit arguments": [[44, "casual-use-of-implicit-arguments"]], "Declaration of implicit arguments": [[44, "declaration-of-implicit-arguments"]], "Implicit Argument Binders": [[44, "implicit-argument-binders"]], "Mode for automatic declaration of implicit arguments": [[44, "mode-for-automatic-declaration-of-implicit-arguments"]], "Controlling strict implicit arguments": [[44, "controlling-strict-implicit-arguments"]], "Controlling contextual implicit arguments": [[44, "controlling-contextual-implicit-arguments"]], "Controlling reversible-pattern implicit arguments": [[44, "controlling-reversible-pattern-implicit-arguments"]], "Controlling the insertion of implicit arguments not followed by explicit arguments": [[44, "controlling-the-insertion-of-implicit-arguments-not-followed-by-explicit-arguments"]], "Combining manual declaration and automatic declaration": [[44, "combining-manual-declaration-and-automatic-declaration"]], "Explicit applications": [[44, "explicit-applications"]], "Example: Syntax for explicitly giving implicit arguments (continued)": [[44, null]], "Displaying implicit arguments": [[44, "displaying-implicit-arguments"]], "Displaying implicit arguments when pretty-printing": [[44, "displaying-implicit-arguments-when-pretty-printing"]], "Interaction with subtyping": [[44, "interaction-with-subtyping"]], "Deactivation of implicit arguments for parsing": [[44, "deactivation-of-implicit-arguments-for-parsing"]], "Implicit types of variables": [[44, "implicit-types-of-variables"]], "Implicit generalization": [[44, "implicit-generalization"]], "Language extensions": [[45, "language-extensions"]], "Extended pattern matching": [[46, "extended-pattern-matching"]], "Variants and extensions of match": [[46, "variants-and-extensions-of-match"]], "Multiple and nested pattern matching": [[46, "multiple-and-nested-pattern-matching"]], "Pattern-matching on boolean values: the if expression": [[46, "pattern-matching-on-boolean-values-the-if-expression"]], "Irrefutable patterns: the destructuring let variants": [[46, "irrefutable-patterns-the-destructuring-let-variants"]], "First destructuring let syntax": [[46, "first-destructuring-let-syntax"]], "Second destructuring let syntax": [[46, "second-destructuring-let-syntax"]], "Controlling pretty-printing of match expressions": [[46, "controlling-pretty-printing-of-match-expressions"]], "Printing nested patterns": [[46, "printing-nested-patterns"]], "Factorization of clauses with same right-hand side": [[46, "factorization-of-clauses-with-same-right-hand-side"]], "Use of a default clause": [[46, "use-of-a-default-clause"]], "Printing of wildcard patterns": [[46, "printing-of-wildcard-patterns"]], "Printing of the elimination predicate": [[46, "printing-of-the-elimination-predicate"]], "Printing of hidden subterms": [[46, "printing-of-hidden-subterms"]], "Printing matching on irrefutable patterns": [[46, "printing-matching-on-irrefutable-patterns"]], "Printing matching on booleans": [[46, "printing-matching-on-booleans"]], "Conventions about unused pattern-matching variables": [[46, "conventions-about-unused-pattern-matching-variables"]], "Patterns": [[46, "patterns"]], "Multiple patterns": [[46, "multiple-patterns"]], "Aliasing subpatterns": [[46, "aliasing-subpatterns"]], "Nested patterns": [[46, "nested-patterns"]], "Disjunctive patterns": [[46, "disjunctive-patterns"]], "About patterns of parametric types": [[46, "about-patterns-of-parametric-types"]], "Parameters in patterns": [[46, "parameters-in-patterns"]], "Implicit arguments in patterns": [[46, "implicit-arguments-in-patterns"]], "Matching objects of dependent types": [[46, "matching-objects-of-dependent-types"]], "Understanding dependencies in patterns": [[46, "understanding-dependencies-in-patterns"]], "When the elimination predicate must be provided": [[46, "when-the-elimination-predicate-must-be-provided"]], "Dependent pattern matching": [[46, "dependent-pattern-matching"]], "Multiple dependent pattern matching": [[46, "multiple-dependent-pattern-matching"]], "Patterns in in": [[46, "patterns-in-in"]], "Using pattern matching to write proofs": [[46, "using-pattern-matching-to-write-proofs"]], "Pattern-matching on inductive objects involving local definitions": [[46, "pattern-matching-on-inductive-objects-involving-local-definitions"]], "Pattern-matching and coercions": [[46, "pattern-matching-and-coercions"]], "When does the expansion strategy fail?": [[46, "when-does-the-expansion-strategy-fail"]], "The Rocq Prover commands": [[51, "the-rocq-prover-commands"]], "Interactive use (rocq repl)": [[51, "interactive-use-rocq-repl"]], "Batch compilation (rocq compile)": [[51, "batch-compilation-rocq-compile"]], "Example: Compiling and loading a single file": [[51, null]], "Customization at launch time": [[51, "customization-at-launch-time"]], "Command parameters": [[51, "command-parameters"]], "coqrc start up script": [[51, "coqrc-start-up-script"]], "Environment variables": [[51, "environment-variables"]], "Command line options": [[51, "command-line-options"], [75, "command-line-options"]], "Profiling": [[51, "profiling"], [55, "profiling"]], "Compiled interfaces (produced using -vos)": [[51, "compiled-interfaces-produced-using-vos"]], "Compiled libraries checker (rocqchk)": [[51, "compiled-libraries-checker-rocqchk"]], "Managing files and buffers, basic editing": [[52, "managing-files-and-buffers-basic-editing"]], "Running Coq scripts": [[52, "running-coq-scripts"]], "Asynchronous mode": [[52, "asynchronous-mode"]], "Commands and templates": [[52, "commands-and-templates"]], "Queries": [[52, "queries"]], "Compilation": [[52, "compilation"]], "Customizations": [[52, "customizations"]], "Preferences": [[52, "preferences"]], "Key bindings": [[52, "key-bindings"]], "Using Unicode symbols": [[52, "using-unicode-symbols"]], "Displaying Unicode symbols": [[52, "displaying-unicode-symbols"]], "Bindings for input of Unicode symbols": [[52, "bindings-for-input-of-unicode-symbols"]], "Adding custom bindings": [[52, "adding-custom-bindings"]], "Character encoding for saved files": [[52, "character-encoding-for-saved-files"]], "Debugger": [[52, "debugger"]], "Breakpoints": [[52, "breakpoints"]], "Call Stack and Variables": [[52, "call-stack-and-variables"]], "Supported use cases": [[52, "supported-use-cases"]], "Building Rocq Projects": [[53, "building-rocq-projects"]], "Rocq configuration basics": [[53, "rocq-configuration-basics"]], "Installing the Rocq Prover and Rocq packages with opam": [[53, "installing-the-rocq-prover-and-rocq-packages-with-opam"]], "Setup for working on your own projects": [[53, "setup-for-working-on-your-own-projects"]], "Building a project with _CoqProject (overview)": [[53, "building-a-project-with-coqproject-overview"]], "Logical paths and the load path": [[53, "logical-paths-and-the-load-path"]], "Modifying multiple interdependent projects at the same time": [[53, "modifying-multiple-interdependent-projects-at-the-same-time"]], "Installed and uninstalled packages": [[53, "installed-and-uninstalled-packages"]], "Upgrading to a new version of Rocq": [[53, "upgrading-to-a-new-version-of-rocq"]], "Building a Rocq project with rocq makefile (details)": [[53, "building-a-rocq-project-with-rocq-makefile-details"]], "Comments": [[53, "comments"]], "Quoting arguments to rocq c": [[53, "quoting-arguments-to-rocq-c"]], "Forbidden filenames": [[53, "forbidden-filenames"]], "Warning: No common logical root": [[53, "warning-no-common-logical-root"]], "CoqMakefile.local": [[53, "coqmakefile-local"]], "CoqMakefile.local-late": [[53, "coqmakefile-local-late"]], "Timing targets and performance testing": [[53, "timing-targets-and-performance-testing"]], "Building a subset of the targets with -j": [[53, "building-a-subset-of-the-targets-with-j"]], "Precompiling for native_compute": [[53, "precompiling-for-native-compute"]], "The grammar of _CoqProject": [[53, "the-grammar-of-coqproject"]], "Building a Rocq project with Dune": [[53, "building-a-rocq-project-with-dune"]], "rocq dep: Computing Module dependencies": [[53, "rocq-dep-computing-module-dependencies"]], "Split compilation of native computation files": [[53, "split-compilation-of-native-computation-files"]], "Using Rocq as a library": [[53, "using-rocq-as-a-library"]], "Embedded Rocq phrases inside LaTeX documents": [[53, "embedded-rocq-phrases-inside-latex-documents"]], "Man pages": [[53, "man-pages"]], "Ltac": [[54, "ltac"]], "Example: Basic tactic macros": [[54, null]], "Defects": [[54, "defects"]], "Syntax": [[54, "syntax"], [55, "syntax"], [57, "syntax"], [71, "syntax"]], "Values": [[54, "values"]], "Syntactic values": [[54, "syntactic-values"]], "Substitution": [[54, "substitution"]], "Example: Substitution of global and local symbols": [[54, null]], "Local definitions: let": [[54, "local-definitions-let"]], "Function construction and application": [[54, "function-construction-and-application"]], "Tactics in terms": [[54, "tactics-in-terms"]], "Goal selectors": [[54, "goal-selectors"]], "Example: Selector reordering goals": [[54, "reordering-goals-ex"]], "Processing multiple goals": [[54, "processing-multiple-goals"]], "Example: Multiple focused goals": [[54, null]], "Branching and backtracking": [[54, "branching-and-backtracking"]], "Example: Backtracking": [[54, null]], "Control flow": [[54, "control-flow"], [57, "control-flow"]], "Sequence: ;": [[54, "sequence"]], "Do loop": [[54, "do-loop"]], "Repeat loop": [[54, "repeat-loop"]], "Catching errors: try": [[54, "catching-errors-try"]], "Conditional branching: tryif": [[54, "conditional-branching-tryif"]], "Alternatives": [[54, "alternatives"]], "Branching with backtracking: +": [[54, "branching-with-backtracking"]], "Example: Backtracking branching with +": [[54, null]], "Local application of tactics: [> ... ]": [[54, "local-application-of-tactics"]], "First tactic to succeed": [[54, "first-tactic-to-succeed"]], "Example: Backtracking inside a non-backtracking construct": [[54, null]], "Example: Referring to a list of tactics in Tactic Notation": [[54, null]], "Solving": [[54, "solving"]], "First tactic to make progress: ||": [[54, "first-tactic-to-make-progress"]], "Detecting progress": [[54, "detecting-progress"]], "Success and failure": [[54, "success-and-failure"]], "Checking for success: assert_succeeds": [[54, "checking-for-success-assert-succeeds"]], "Checking for failure: assert_fails": [[54, "checking-for-failure-assert-fails"]], "Failing": [[54, "failing"]], "Soft cut: once": [[54, "soft-cut-once"]], "Checking for a single success: exactly_once": [[54, "checking-for-a-single-success-exactly-once"]], "Manipulating values": [[54, "manipulating-values"]], "Pattern matching on terms: match": [[54, "pattern-matching-on-terms-match"]], "Example: Comparison of lazymatch and match": [[54, null]], "Example: Comparison of match and multimatch": [[54, null]], "Example: Matching a pattern with holes": [[54, null]], "Example: Multiple matches for a \"context\" pattern.": [[54, null]], "Pattern matching on goals and hypotheses: match goal": [[54, "pattern-matching-on-goals-and-hypotheses-match-goal"]], "Example: Matching hypotheses": [[54, null]], "Example: Matching hypotheses with reverse": [[54, null], [55, "ltac2-match-goal-hyps-rev-ex"]], "Example: Multiple ways to match hypotheses": [[54, null]], "Filling a term context": [[54, "filling-a-term-context"]], "Example: Substituting a matched context": [[54, null]], "Generating fresh hypothesis names": [[54, "generating-fresh-hypothesis-names"]], "Computing in a term: eval": [[54, "computing-in-a-term-eval"]], "Getting the type of a term": [[54, "getting-the-type-of-a-term"]], "Manipulating untyped terms: type_term": [[54, "manipulating-untyped-terms-type-term"]], "Counting goals: numgoals": [[54, "counting-goals-numgoals"]], "Testing boolean expressions: guard": [[54, "testing-boolean-expressions-guard"]], "Example: guard": [[54, null]], "Checking properties of terms": [[54, "checking-properties-of-terms"]], "Example: is_fix": [[54, null]], "Example: is_cofix": [[54, null]], "Example: is_proj": [[54, null]], "Timing": [[54, "timing"]], "Timeout": [[54, "timeout"]], "Timing a tactic": [[54, "timing-a-tactic"]], "Timing a tactic that evaluates to a term: time_constr": [[54, "timing-a-tactic-that-evaluates-to-a-term-time-constr"]], "Print/identity tactic: idtac": [[54, "print-identity-tactic-idtac"]], "Tactic toplevel definitions": [[54, "tactic-toplevel-definitions"]], "Defining Ltac symbols": [[54, "defining-ltac-symbols"]], "Printing Ltac tactics": [[54, "printing-ltac-tactics"]], "Examples of using Ltac": [[54, "examples-of-using-ltac"]], "Proof that the natural numbers have at least two elements": [[54, "proof-that-the-natural-numbers-have-at-least-two-elements"]], "Example: Proof that the natural numbers have at least two elements": [[54, null]], "Proving that a list is a permutation of a second list": [[54, "proving-that-a-list-is-a-permutation-of-a-second-list"]], "Example: Proving that a list is a permutation of a second list": [[54, null]], "Deciding intuitionistic propositional logic": [[54, "deciding-intuitionistic-propositional-logic"]], "Deciding type isomorphisms": [[54, "deciding-type-isomorphisms"]], "Debugging Ltac tactics": [[54, "debugging-ltac-tactics"]], "Backtraces": [[54, "backtraces"]], "Tracing execution": [[54, "tracing-execution"]], "Interactive debugger": [[54, "interactive-debugger"]], "Profiling Ltac tactics": [[54, "profiling-ltac-tactics"]], "Run-time optimization tactic": [[54, "run-time-optimization-tactic"]], "Ltac2": [[55, "ltac2"]], "General design": [[55, "general-design"]], "ML component": [[55, "ml-component"]], "Overview": [[55, "overview"], [55, "id3"]], "Type Syntax": [[55, "type-syntax"]], "Type declarations": [[55, "type-declarations"]], "APIs": [[55, "apis"]], "Term Syntax": [[55, "term-syntax"]], "Ltac2 Definitions": [[55, "ltac2-definitions"]], "Example: Dynamic nature of mutable cells": [[55, null]], "Example: Interaction with recursive calls": [[55, null]], "Printing Ltac2 tactics": [[55, "printing-ltac2-tactics"]], "Typing": [[55, "typing"]], "Effects": [[55, "effects"]], "Standard IO": [[55, "standard-io"]], "Fatal errors": [[55, "fatal-errors"]], "Backtracking": [[55, "backtracking"], [59, "backtracking"]], "Goals": [[55, "goals"]], "Meta-programming": [[55, "meta-programming"]], "Quotations": [[55, "quotations"]], "Built-in quotations": [[55, "built-in-quotations"]], "Strict vs. non-strict mode": [[55, "strict-vs-non-strict-mode"]], "Term Antiquotations": [[55, "term-antiquotations"]], "Semantics": [[55, "semantics"]], "Static semantics": [[55, "static-semantics"]], "Dynamic semantics": [[55, "dynamic-semantics"]], "Match over terms": [[55, "match-over-terms"]], "Example: Ltac2 Comparison of lazy_match! and match!": [[55, "ltac2-match-vs-lazymatch-ex"]], "Example: Ltac2 Comparison of match! and multi_match!": [[55, "ltac2-match-vs-multimatch-ex"]], "Example: Ltac2 Multiple matches for a \"context\" pattern.": [[55, "ltac2-match-term-context-ex"]], "Match over goals": [[55, "match-over-goals"]], "Example: Ltac2 Matching hypotheses": [[55, "ltac2-match-goal-hyps-ex"]], "Example: Multiple ways to match a hypotheses": [[55, "ltac2-match-goal-multiple-hyps-ex"]], "Match on values": [[55, "match-on-values"]], "Example: Printing a term": [[55, null]], "Example: Parsing a list of terms": [[55, null]], "Abbreviations": [[55, "abbreviations"], [57, "abbreviations"], [71, "abbreviations"]], "Defining tactics": [[55, "defining-tactics"]], "Syntactic classes": [[55, "syntactic-classes"]], "Evaluation": [[55, "evaluation"]], "Debug": [[55, "debug"]], "Compatibility layer with Ltac1": [[55, "compatibility-layer-with-ltac1"]], "Ltac1 from Ltac2": [[55, "ltac1-from-ltac2"]], "Simple API": [[55, "simple-api"]], "Low-level API": [[55, "low-level-api"]], "Ltac2 from Ltac1": [[55, "ltac2-from-ltac1"]], "Switching between Ltac languages": [[55, "switching-between-ltac-languages"]], "Transition from Ltac1": [[55, "transition-from-ltac1"]], "Syntax changes": [[55, "syntax-changes"]], "Tactic delay": [[55, "tactic-delay"]], "Variable binding": [[55, "variable-binding"]], "In Ltac expressions": [[55, "in-ltac-expressions"]], "In quotations": [[55, "in-quotations"]], "Exception catching": [[55, "exception-catching"]], "The SSReflect proof language": [[57, "the-ssr-proof-language"]], "Introduction": [[57, "introduction"]], "Acknowledgments": [[57, "acknowledgments"]], "Getting started": [[57, "getting-started"]], "Compatibility issues": [[57, "compatibility-issues"]], "Gallina extensions": [[57, "gallina-extensions"]], "Pattern assignment": [[57, "pattern-assignment"]], "Pattern conditional": [[57, "pattern-conditional"]], "Parametric polymorphism": [[57, "parametric-polymorphism"]], "Anonymous arguments": [[57, "anonymous-arguments"]], "Wildcards": [[57, "wildcards"]], "Matching": [[57, "matching"]], "Occurrence selection": [[57, "occurrence-selection"]], "Basic localization": [[57, "basic-localization"]], "Basic tactics": [[57, "basic-tactics"]], "Bookkeeping": [[57, "bookkeeping"]], "The defective tactics": [[57, "the-defective-tactics"]], "The move tactic.": [[57, "the-move-tactic"]], "The case tactic": [[57, "the-case-tactic"]], "The elim tactic": [[57, "the-elim-tactic"]], "The apply tactic": [[57, "the-apply-tactic"]], "Discharge": [[57, "discharge"]], "Clear rules": [[57, "clear-rules"]], "Matching for apply and exact": [[57, "matching-for-apply-and-exact"]], "The abstract tactic": [[57, "the-abstract-tactic"]], "Introduction in the context": [[57, "introduction-in-the-context"]], "Simplification items": [[57, "simplification-items"]], "Views": [[57, "views"]], "Intro patterns": [[57, "intro-patterns"], [58, "intro-patterns"]], "Clear switch": [[57, "clear-switch"]], "Branching and destructuring": [[57, "branching-and-destructuring"]], "Block introduction": [[57, "block-introduction"]], "Generation of equations": [[57, "generation-of-equations"]], "Type families": [[57, "type-families"]], "Indentation and bullets": [[57, "indentation-and-bullets"]], "Terminators": [[57, "terminators"]], "Selectors": [[57, "selectors"]], "Iteration": [[57, "iteration"]], "Localization": [[57, "localization"]], "Structure": [[57, "structure"]], "The have tactic.": [[57, "the-have-tactic"]], "Generating let in context entries with have": [[57, "generating-let-in-context-entries-with-have"]], "The have tactic and typeclass resolution": [[57, "the-have-tactic-and-typeclass-resolution"]], "Variants: the suff and wlog tactics": [[57, "variants-the-suff-and-wlog-tactics"]], "Advanced generalization": [[57, "advanced-generalization"]], "Rewriting": [[57, "rewriting"]], "An extended rewrite tactic": [[57, "an-extended-rewrite-tactic"]], "Remarks and examples": [[57, "remarks-and-examples"]], "Rewrite redex selection": [[57, "rewrite-redex-selection"]], "Chained rewrite steps": [[57, "chained-rewrite-steps"]], "Explicit redex switches are matched first": [[57, "explicit-redex-switches-are-matched-first"]], "Occurrence switches and redex switches": [[57, "occurrence-switches-and-redex-switches"]], "Occurrence selection and repetition": [[57, "occurrence-selection-and-repetition"]], "Multi-rule rewriting": [[57, "multi-rule-rewriting"]], "Wildcards vs abstractions": [[57, "wildcards-vs-abstractions"]], "When SSReflect rewrite fails on standard Rocq licit rewrite": [[57, "when-ssr-rewrite-fails-on-standard-rocq-licit-rewrite"]], "Existential metavariables and rewriting": [[57, "existential-metavariables-and-rewriting"]], "The under tactic": [[57, "the-under-tactic"]], "The over tactic": [[57, "the-over-tactic"]], "One-liner mode": [[57, "one-liner-mode"]], "Locking, unlocking": [[57, "locking-unlocking"]], "Congruence": [[57, "congruence"]], "Contextual patterns": [[57, "contextual-patterns"]], "Matching contextual patterns": [[57, "matching-contextual-patterns"]], "Contextual pattern in set and the : tactical": [[57, "contextual-pattern-in-set-and-the-tactical"]], "Contextual patterns in rewrite": [[57, "contextual-patterns-in-rewrite"]], "Patterns for recurrent contexts": [[57, "patterns-for-recurrent-contexts"]], "Views and reflection": [[57, "views-and-reflection"]], "Interpreting eliminations": [[57, "interpreting-eliminations"]], "Interpreting assumptions": [[57, "interpreting-assumptions"], [57, "id16"]], "Specializing assumptions": [[57, "specializing-assumptions"], [57, "id15"]], "Interpreting goals": [[57, "interpreting-goals"], [57, "id17"]], "Boolean reflection": [[57, "boolean-reflection"]], "The reflect predicate": [[57, "the-reflect-predicate"]], "General mechanism for interpreting goals and assumptions": [[57, "general-mechanism-for-interpreting-goals-and-assumptions"]], "Interpreting equivalences": [[57, "interpreting-equivalences"]], "Declaring new Hint Views": [[57, "declaring-new-hint-views"]], "Multiple views": [[57, "multiple-views"]], "Additional view shortcuts": [[57, "additional-view-shortcuts"]], "Synopsis and Index": [[57, "synopsis-and-index"]], "Parameters": [[57, "parameters"]], "Items and switches": [[57, "items-and-switches"]], "Tacticals": [[57, "tacticals"]], "Common elements of tactics": [[58, "common-elements-of-tactics"]], "Reserved keywords": [[58, "reserved-keywords"]], "Invocation of tactics": [[58, "invocation-of-tactics"]], "Bindings": [[58, "bindings"]], "Example: intro pattern for /\\": [[58, null]], "Example: intro pattern for \\/": [[58, null]], "Example: -> intro pattern": [[58, null]], "Example: [=] intro pattern": [[58, null]], "Example: (A & B & \u2026) intro pattern": [[58, null]], "Example: * intro pattern": [[58, null]], "Example: ** pattern (\"intros **\" is equivalent to \"intros\")": [[58, null]], "Example: compound intro pattern": [[58, null]], "Example: combined intro pattern using [=] -> and %": [[58, null]], "Occurrence clauses": [[58, "occurrence-clauses"]], "Applying theorems": [[58, "applying-theorems"]], "Example: Backward reasoning in the goal with apply": [[58, "apply-backward"]], "Example: Backward reasoning in the goal with apply including a premise": [[58, "apply-backward-w-premises"]], "Example: Forward reasoning in hypotheses with apply": [[58, "apply-forward"]], "Example: Apply a theorem with a binding in a goal": [[58, "apply-with-binding-goal"]], "Example: Apply a theorem with a binding in a hypothesis": [[58, "apply-with-binding-hyp"]], "Example: Applying theorems with <->": [[58, "apply-with-iff"]], "Example: Special case of second-order unification in apply": [[58, "example-apply-pattern"]], "Managing the local context": [[58, "managing-the-local-context"]], "Example: intro and intros": [[58, "intro-examples"]], "Example: intros until": [[58, null]], "Example: move": [[58, null]], "Example: set with a simple_binder": [[58, null]], "Controlling the proof flow": [[58, "controlling-the-proof-flow"]], "Example: partial application in specialize": [[58, null]], "Example: specialize with a non-dependent product": [[58, null]], "Example: contradiction tactic": [[58, null]], "Classical tactics": [[58, "classical-tactics"]], "Performance-oriented tactic variants": [[58, "performance-oriented-tactic-variants"]], "Displaying": [[59, "displaying"]], "Query commands": [[59, "query-commands"]], "Example: Searching for a pattern": [[59, "search-pattern"]], "Example: Searching for part of an identifier": [[59, "search-part-ident"]], "Example: Searching for a reference by notation": [[59, "search-by-notation"]], "Example: Disambiguating between part of identifier and notation": [[59, "search-disambiguate-notation"]], "Example: Search in hypotheses": [[59, "search-hyp"]], "Example: Search in conclusion": [[59, "search-concl"]], "Example: Search by keyword or status": [[59, "search-by-keyword"]], "Example: SearchPattern examples": [[59, null]], "Example: SearchRewrite examples": [[59, null]], "Requests to the environment": [[59, "requests-to-the-environment"]], "Example: Locate examples": [[59, null]], "Printing flags": [[59, "printing-flags"]], "Loading files": [[59, "loading-files"]], "Compiled files": [[59, "compiled-files"]], "Load paths": [[59, "load-paths"]], "Extra Dependencies": [[59, "extra-dependencies"]], "Quitting and debugging": [[59, "quitting-and-debugging"]], "Controlling display": [[59, "controlling-display"]], "Printing constructions in full": [[59, "printing-constructions-in-full"]], "Controlling Typing Flags": [[59, "controlling-typing-flags"]], "Internal registration commands": [[59, "internal-registration-commands"]], "Exposing constants to OCaml libraries": [[59, "exposing-constants-to-ocaml-libraries"]], "Inlining hints for the fast reduction machines": [[59, "inlining-hints-for-the-fast-reduction-machines"]], "Registering primitive operations": [[59, "registering-primitive-operations"]], "Programmable proof search": [[60, "programmable-proof-search"]], "Example: Ackermann function": [[60, null]], "Example: MacCarthy function": [[60, null]], "Hint databases": [[60, "hint-databases"]], "Creating hint databases": [[60, "creating-hint-databases"]], "Hint databases defined in the Rocq standard library": [[60, "hint-databases-defined-in-the-rocq-standard-library"]], "Creating Hints": [[60, "creating-hints"]], "Example: Logic programming with addition on natural numbers": [[60, null]], "Hint locality": [[60, "hint-locality"]], "Setting implicit automation tactics": [[60, "setting-implicit-automation-tactics"]], "Automatic solvers and programmable tactics": [[61, "automatic-solvers-and-programmable-tactics"]], "Solvers for logic and equality": [[62, "solvers-for-logic-and-equality"]], "Creating new tactics": [[63, "creating-new-tactics"]], "Reasoning with equalities": [[64, "reasoning-with-equalities"]], "Tactics for simple equalities": [[64, "tactics-for-simple-equalities"]], "Rewriting with Leibniz and setoid equality": [[64, "rewriting-with-leibniz-and-setoid-equality"]], "Rewriting with definitional equality": [[64, "rewriting-with-definitional-equality"]], "Applying conversion rules": [[64, "applying-conversion-rules"]], "Example: fold doesn't always undo unfold": [[64, null]], "Example: Use fold to reverse unfolding of fold_right": [[64, null]], "Fast reduction tactics: vm_compute and native_compute": [[64, "fast-reduction-tactics-vm-compute-and-native-compute"]], "Computing in a term: eval and Eval": [[64, "computing-in-a-term-eval-and-eval"]], "Controlling reduction strategies and the conversion algorithm": [[64, "controlling-reduction-strategies-and-the-conversion-algorithm"]], "Basic proof writing": [[65, "basic-proof-writing"]], "Proof mode": [[66, "proof-mode"]], "Proof State": [[66, "proof-state"]], "Entering and exiting proof mode": [[66, "entering-and-exiting-proof-mode"]], "Example: Declaring section variables": [[66, null]], "Proof using options": [[66, "proof-using-options"]], "Name a set of section hypotheses for Proof using": [[66, "name-a-set-of-section-hypotheses-for-proof-using"]], "Proof modes": [[66, "proof-modes"]], "Managing goals": [[66, "managing-goals"]], "Focusing goals": [[66, "focusing-goals"]], "Curly braces": [[66, "curly-braces"]], "Example: Working with named goals": [[66, null]], "Bullets": [[66, "bullets"]], "Example: Use of bullets": [[66, null]], "Other focusing commands": [[66, "other-focusing-commands"]], "Shelving goals": [[66, "shelving-goals"]], "Example: shelve_unifiable": [[66, null]], "Reordering goals": [[66, "reordering-goals"]], "Example: cycle": [[66, null]], "Example: swap": [[66, null]], "Example: revgoals": [[66, null]], "Proving a subgoal as a separate lemma: abstract": [[66, "proving-a-subgoal-as-a-separate-lemma-abstract"]], "Requesting information": [[66, "requesting-information"]], "Showing differences between proof steps": [[66, "showing-differences-between-proof-steps"]], "How to enable diffs": [[66, "how-to-enable-diffs"]], "How diffs are calculated": [[66, "how-diffs-are-calculated"]], "\"Show Proof\" differences": [[66, "show-proof-differences"]], "Delaying solving unification constraints": [[66, "delaying-solving-unification-constraints"]], "Proof maintenance": [[66, "proof-maintenance"]], "Controlling proof mode": [[66, "controlling-proof-mode"]], "Controlling memory usage": [[66, "controlling-memory-usage"]], "Reasoning with inductive types": [[67, "reasoning-with-inductive-types"]], "Applying constructors": [[67, "applying-constructors"]], "Example: constructor, left and right": [[67, null]], "Case analysis": [[67, "case-analysis"]], "Example: Using destruct on an argument with premises": [[67, "example-destruct-ind-concl"]], "Induction": [[67, "induction"]], "Example: induction with occurrences": [[67, null]], "Equality of inductive types": [[67, "equality-of-inductive-types"]], "Example: Proving 1 <> 2": [[67, null]], "Example: discriminate limitation: proving n <> S n": [[67, null]], "Example: inversion with as or_and_intropattern": [[67, null]], "Example: Non-dependent inversion": [[67, null]], "Example: Dependent inversion": [[67, null]], "Example: Using inversion_sigma": [[67, null]], "Helper tactics": [[67, "helper-tactics"]], "Example: Using decide to rewrite the goal": [[67, null]], "Generation of induction principles with Scheme": [[67, "generation-of-induction-principles-with-scheme"]], "Example: Induction scheme for tree and forest": [[67, null]], "Example: Predicates odd and even on naturals": [[67, null]], "Example: Scheme commands with various scheme_types": [[67, null]], "Automatic declaration of schemes": [[67, "automatic-declaration-of-schemes"]], "Combined Scheme": [[67, "combined-scheme"]], "Generation of inversion principles with Derive Inversion": [[67, "generation-of-inversion-principles-with-derive-inversion"]], "Examples of dependent destruction / dependent induction": [[67, "examples-of-dependent-destruction-dependent-induction"]], "A larger example": [[67, "a-larger-example"]], "Glossary index": [[69, "glossary-index"]], "Syntax extensions and notation scopes": [[71, "syntax-extensions-and-notation-scopes"]], "Basic notations": [[71, "basic-notations"]], "Precedences and associativity": [[71, "precedences-and-associativity"]], "Complex notations": [[71, "complex-notations"]], "Simple factorization rules": [[71, "simple-factorization-rules"]], "Use of notations for printing": [[71, "use-of-notations-for-printing"]], "The Infix command": [[71, "the-infix-command"]], "Reserving notations": [[71, "reserving-notations"]], "Simultaneous definition of terms and notations": [[71, "simultaneous-definition-of-terms-and-notations"]], "Enabling and disabling notations": [[71, "enabling-and-disabling-notations"]], "Example: Enabling and disabling notations": [[71, null]], "Displaying information about notations": [[71, "displaying-information-about-notations"]], "Example: Print Notation": [[71, null]], "Locating notations": [[71, "locating-notations"]], "Inheritance of the properties of arguments of constants bound to a notation": [[71, "inheritance-of-the-properties-of-arguments-of-constants-bound-to-a-notation"]], "Notations and binders": [[71, "notations-and-binders"]], "Binders bound in the notation and parsed as identifiers": [[71, "binders-bound-in-the-notation-and-parsed-as-identifiers"]], "Binders bound in the notation and parsed as patterns": [[71, "binders-bound-in-the-notation-and-parsed-as-patterns"]], "Binders bound in the notation and parsed as terms": [[71, "binders-bound-in-the-notation-and-parsed-as-terms"]], "Binders bound in the notation and parsed as general binders": [[71, "binders-bound-in-the-notation-and-parsed-as-general-binders"]], "Binders not bound in the notation": [[71, "binders-not-bound-in-the-notation"]], "Notations with expressions used both as binder and term": [[71, "notations-with-expressions-used-both-as-binder-and-term"]], "Notations with recursive patterns": [[71, "notations-with-recursive-patterns"]], "Notations with recursive patterns involving binders": [[71, "notations-with-recursive-patterns-involving-binders"]], "Predefined entries": [[71, "predefined-entries"]], "Custom entries": [[71, "custom-entries"]], "Notation scopes": [[71, "notation-scopes"]], "Global interpretation rules for notations": [[71, "global-interpretation-rules-for-notations"]], "Local interpretation rules for notations": [[71, "local-interpretation-rules-for-notations"]], "Opening a notation scope locally": [[71, "opening-a-notation-scope-locally"]], "Binding types or coercion classes to notation scopes": [[71, "binding-types-or-coercion-classes-to-notation-scopes"]], "Example: Binding scopes to a type": [[71, null]], "The type_scope notation scope": [[71, "the-type-scope-notation-scope"]], "The function_scope notation scope": [[71, "the-function-scope-notation-scope"]], "Notation scopes used in the standard library of Rocq": [[71, "notation-scopes-used-in-the-standard-library-of-rocq"]], "Displaying information about scopes": [[71, "displaying-information-about-scopes"]], "Numbers and strings": [[71, "numbers-and-strings"]], "Number notations": [[71, "number-notations"]], "String notations": [[71, "string-notations"]], "Example: Number Notation for radix 3": [[71, null]], "Example: Number Notation for primitive integers": [[71, "example-number-notation-primitive-int"]], "Example: Number Notation for a non-inductive type": [[71, "example-number-notation-non-inductive"]], "Example: Number Notation with implicit arguments": [[71, "example-number-notation-implicit-args"]], "Example: String Notation with a parameterized inductive type": [[71, "example-string-notation-parameterized-inductive"]], "Tactic Notations": [[71, "tactic-notations"]], "Functional induction": [[72, "functional-induction"]], "Advanced recursive functions": [[72, "advanced-recursive-functions"]], "Generation of induction principles with Functional Scheme": [[72, "generation-of-induction-principles-with-functional-scheme"]], "Libraries and plugins": [[73, "libraries-and-plugins"]], "Writing Rocq libraries and plugins": [[74, "writing-rocq-libraries-and-plugins"]], "Deprecating library objects, tactics or library files": [[74, "deprecating-library-objects-tactics-or-library-files"]], "Triggering warning for library objects or library files": [[74, "triggering-warning-for-library-objects-or-library-files"]], "Example: Deprecating a tactic.": [[74, null]], "Example: Introducing a compatibility alias": [[74, "compatibility-alias"]], "Documenting Rocq files with rocq doc": [[75, "documenting-rocq-files-with-rocq-doc"]], "Principles": [[75, "principles"]], "Rocq material inside documentation.": [[75, "rocq-material-inside-documentation"]], "Pretty-printing.": [[75, "pretty-printing"]], "Lists.": [[75, "lists"]], "Rules.": [[75, "rules"]], "Emphasis.": [[75, "emphasis"]], "Escaping to LaTeX and HTML.": [[75, "escaping-to-latex-and-html"]], "Verbatim": [[75, "verbatim"]], "Hyperlinks": [[75, "hyperlinks"]], "Hiding / Showing parts of the source": [[75, "hiding-showing-parts-of-the-source"]], "The rocq doc LaTeX style file": [[75, "the-rocq-doc-latex-style-file"]], "Command-line and graphical tools": [[76, "command-line-and-graphical-tools"]], "Bibliography": [[77, "bibliography"]]}, "indexentries": {"cd (command)": [[2, "coq:cmd.Cd"]], "extract callback (command)": [[2, "coq:cmd.Extract-Callback"]], "extract callback is supported only for ocaml extraction (error)": [[2, "coq:exn.Extract-Callback-is-supported-only-for-OCaml-extraction"]], "extract constant (command)": [[2, "coq:cmd.Extract-Constant"]], "extract foreign constant (command)": [[2, "coq:cmd.Extract-Foreign-Constant"]], "extract foreign constant is supported only for ocaml extraction (error)": [[2, "coq:exn.Extract-Foreign-Constant-is-supported-only-for-OCaml-extraction"]], "extract foreign constant is supported only for functions (error)": [[2, "coq:exn.Extract-Foreign-Constant-is-supported-only-for-functions"]], "extract inductive (command)": [[2, "coq:cmd.Extract-Inductive"]], "extract inlined constant (command)": [[2, "coq:cmd.Extract-Inlined-Constant"]], "extraction (command)": [[2, "coq:cmd.Extraction"]], "extraction autoinline (flag)": [[2, "coq:flag.Extraction-AutoInline"]], "extraction blacklist (command)": [[2, "coq:cmd.Extraction-Blacklist"]], "extraction conservative types (flag)": [[2, "coq:flag.Extraction-Conservative-Types"]], "extraction file comment (option)": [[2, "coq:opt.Extraction-File-Comment"]], "extraction flag (option)": [[2, "coq:opt.Extraction-Flag"]], "extraction implicit (command)": [[2, "coq:cmd.Extraction-Implicit"]], "extraction inline (command)": [[2, "coq:cmd.Extraction-Inline"]], "extraction keepsingleton (flag)": [[2, "coq:flag.Extraction-KeepSingleton"]], "extraction language (command)": [[2, "coq:cmd.Extraction-Language"]], "extraction library (command)": [[2, "coq:cmd.Extraction-Library"]], "extraction noinline (command)": [[2, "coq:cmd.Extraction-NoInline"]], "extraction optimize (flag)": [[2, "coq:flag.Extraction-Optimize"]], "extraction output directory (option)": [[2, "coq:opt.Extraction-Output-Directory"]], "extraction safeimplicits (flag)": [[2, "coq:flag.Extraction-SafeImplicits"]], "extraction testcompile (command)": [[2, "coq:cmd.Extraction-TestCompile"]], "extraction typeexpand (flag)": [[2, "coq:flag.Extraction-TypeExpand"]], "print extraction blacklist (command)": [[2, "coq:cmd.Print-Extraction-Blacklist"]], "print extraction callback (command)": [[2, "coq:cmd.Print-Extraction-Callback"]], "print extraction foreign (command)": [[2, "coq:cmd.Print-Extraction-Foreign"]], "print extraction inline (command)": [[2, "coq:cmd.Print-Extraction-Inline"]], "pwd (command)": [[2, "coq:cmd.Pwd"]], "recursive extraction (command)": [[2, "coq:cmd.Recursive-Extraction"]], "recursive extraction library (command)": [[2, "coq:cmd.Recursive-Extraction-Library"]], "reset extraction blacklist (command)": [[2, "coq:cmd.Reset-Extraction-Blacklist"]], "reset extraction callback (command)": [[2, "coq:cmd.Reset-Extraction-Callback"]], "reset extraction inline (command)": [[2, "coq:cmd.Reset-Extraction-Inline"]], "separate extraction (command)": [[2, "coq:cmd.Separate-Extraction"]], "show extraction (command)": [[2, "coq:cmd.Show-Extraction"]], "the term \u2018qualid\u2019 is already defined as foreign custom constant (error)": [[2, "coq:exn.The-term-\u2018qualid\u2019-is-already-defined-as-foreign-custom-constant"]], "the term \u2018qualid\u2019 is already defined as inline custom constant (error)": [[2, "coq:exn.The-term-\u2018qualid\u2019-is-already-defined-as-inline-custom-constant"]], "add morphism (command)": [[3, "coq:cmd.Add-Morphism"]], "add parametric morphism (command)": [[3, "coq:cmd.Add-Parametric-Morphism"]], "add parametric relation (command)": [[3, "coq:cmd.Add-Parametric-Relation"]], "add parametric setoid (command)": [[3, "coq:cmd.Add-Parametric-Setoid"]], "add relation (command)": [[3, "coq:cmd.Add-Relation"]], "add setoid (command)": [[3, "coq:cmd.Add-Setoid"]], "declare morphism (command)": [[3, "coq:cmd.Declare-Morphism"]], "no progress made (error)": [[3, "coq:exn.No-progress-made"]], "nothing to rewrite (error)": [[3, "coq:exn.Nothing-to-rewrite"]], "unable to satisfy the rewriting constraints (error)": [[3, "coq:exn.Unable-to-satisfy-the-rewriting-constraints"]], "head_of_constr (tactic)": [[3, "coq:tacn.head_of_constr"]], "rewrite_db (tactic)": [[3, "coq:tacn.rewrite_db"]], "rewrite_strat (tactic)": [[3, "coq:tacn.rewrite_strat"]], "setoid_etransitivity (tactic)": [[3, "coq:tacn.setoid_etransitivity"]], "setoid_reflexivity (tactic)": [[3, "coq:tacn.setoid_reflexivity"]], "setoid_replace (tactic)": [[3, "coq:tacn.setoid_replace"]], "setoid_rewrite (tactic)": [[3, "coq:tacn.setoid_rewrite"]], "setoid_symmetry (tactic)": [[3, "coq:tacn.setoid_symmetry"]], "setoid_transitivity (tactic)": [[3, "coq:tacn.setoid_transitivity"]], "... is not definitionally an identity function (warning)": [[4, "coq:warn....-is-not-definitionally-an-identity-function"]], ":> (coercion)": [[4, "index-0"]], "cannot find the source class of \u2018qualid\u2019 (error)": [[4, "coq:exn.Cannot-find-the-source-class-of-\u2018qualid\u2019"]], "cannot find the target class (error)": [[4, "coq:exn.Cannot-find-the-target-class"]], "cannot recognize \u2018coercion_class\u2019 as a source class of \u2018qualid\u2019 (error)": [[4, "coq:exn.Cannot-recognize-\u2018coercion_class\u2019-as-a-source-class-of-\u2018qualid\u2019"]], "coercion (command)": [[4, "coq:cmd.Coercion"]], "found target class \u2018coercion_class\u2019 instead of \u2018coercion_class\u2019 (error)": [[4, "coq:exn.Found-target-class-\u2018coercion_class\u2019-instead-of-\u2018coercion_class\u2019"]], "funclass cannot be a source class (error)": [[4, "coq:exn.Funclass-cannot-be-a-source-class"]], "identity coercion (command)": [[4, "coq:cmd.Identity-Coercion"]], "new coercion path ... is ambiguous with existing ... (warning)": [[4, "coq:warn.New-coercion-path-...-is-ambiguous-with-existing-..."]], "print classes (command)": [[4, "coq:cmd.Print-Classes"]], "print coercion paths (command)": [[4, "coq:cmd.Print-Coercion-Paths"]], "print coercions (command)": [[4, "coq:cmd.Print-Coercions"]], "print graph (command)": [[4, "coq:cmd.Print-Graph"]], "printing coercion (table)": [[4, "coq:table.Printing-Coercion"]], "printing coercions (flag)": [[4, "coq:flag.Printing-Coercions"]], "subclass (command)": [[4, "coq:cmd.SubClass"]], "nonuniform (attribute)": [[4, "coq:attr.nonuniform"]], "reversible (attribute)": [[4, "coq:attr.reversible"]], "\u2018coercion_class\u2019 must be a transparent constant (error)": [[4, "coq:exn.\u2018coercion_class\u2019-must-be-a-transparent-constant"]], "\u2018qualid\u2019 does not respect the uniform inheritance condition (warning)": [[4, "coq:warn.\u2018qualid\u2019-does-not-respect-the-uniform-inheritance-condition"]], "\u2018qualid\u2019 is already a coercion (error)": [[4, "coq:exn.\u2018qualid\u2019-is-already-a-coercion"]], "\u2018qualid\u2019 is not a function (error)": [[4, "coq:exn.\u2018qualid\u2019-is-not-a-function"]], "\u2018qualid\u2019 not declared (error)": [[4, "coq:exn.\u2018qualid\u2019-not-declared"]], "add zify (command)": [[5, "coq:cmd.Add-Zify"]], "bound on the ceiling function (theorem)": [[5, "coq:thm.Bound-on-the-ceiling-function"]], "case split (theorem)": [[5, "coq:thm.Case-split"]], "dump arith (option)": [[5, "coq:opt.Dump-Arith"]], "info micromega (flag)": [[5, "coq:flag.Info-Micromega"]], "lia cache (flag)": [[5, "coq:flag.Lia-Cache"]], "nia cache (flag)": [[5, "coq:flag.Nia-Cache"]], "nra cache (flag)": [[5, "coq:flag.Nra-Cache"]], "psatz (theorem)": [[5, "coq:thm.Psatz"]], "show lia profile (command)": [[5, "coq:cmd.Show-Lia-Profile"]], "show zify (command)": [[5, "coq:cmd.Show-Zify"]], "lia (tactic)": [[5, "coq:tacn.lia"]], "lra (tactic)": [[5, "coq:tacn.lra"]], "nia (tactic)": [[5, "coq:tacn.nia"]], "nra (tactic)": [[5, "coq:tacn.nra"]], "psatz (tactic)": [[5, "coq:tacn.psatz"]], "wlia (tactic)": [[5, "coq:tacn.wlia"]], "wlra_q (tactic)": [[5, "coq:tacn.wlra_Q"]], "wnia (tactic)": [[5, "coq:tacn.wnia"]], "wnra_q (tactic)": [[5, "coq:tacn.wnra_Q"]], "wpsatz_q (tactic)": [[5, "coq:tacn.wpsatz_Q"]], "wpsatz_z (tactic)": [[5, "coq:tacn.wpsatz_Z"]], "wsos_q (tactic)": [[5, "coq:tacn.wsos_Q"]], "wsos_z (tactic)": [[5, "coq:tacn.wsos_Z"]], "xlia (tactic)": [[5, "coq:tacn.xlia"]], "xlra_q (tactic)": [[5, "coq:tacn.xlra_Q"]], "xlra_r (tactic)": [[5, "coq:tacn.xlra_R"]], "xnia (tactic)": [[5, "coq:tacn.xnia"]], "xnra_q (tactic)": [[5, "coq:tacn.xnra_Q"]], "xnra_r (tactic)": [[5, "coq:tacn.xnra_R"]], "xpsatz_q (tactic)": [[5, "coq:tacn.xpsatz_Q"]], "xpsatz_r (tactic)": [[5, "coq:tacn.xpsatz_R"]], "xpsatz_z (tactic)": [[5, "coq:tacn.xpsatz_Z"]], "xsos_q (tactic)": [[5, "coq:tacn.xsos_Q"]], "xsos_r (tactic)": [[5, "coq:tacn.xsos_R"]], "xsos_z (tactic)": [[5, "coq:tacn.xsos_Z"]], "zify (tactic)": [[5, "coq:tacn.zify"]], "zify_elim_let (tactic)": [[5, "coq:tacn.zify_elim_let"]], "zify_iter_let (tactic)": [[5, "coq:tacn.zify_iter_let"]], "zify_iter_specs (tactic)": [[5, "coq:tacn.zify_iter_specs"]], "zify_op (tactic)": [[5, "coq:tacn.zify_op"]], "zify_saturate (tactic)": [[5, "coq:tacn.zify_saturate"]], "derive (command)": [[6, "coq:cmd.Derive"]], "nsatz (tactic)": [[7, "coq:tacn.nsatz"]], "nsatz_compute (tactic)": [[7, "coq:tacn.nsatz_compute"]], "admit obligations (command)": [[9, "coq:cmd.Admit-Obligations"]], "final obligation (command)": [[9, "coq:cmd.Final-Obligation"]], "ill-formed recursive definition (error)": [[9, "coq:exn.Ill-formed-recursive-definition"]], "next obligation (command)": [[9, "coq:cmd.Next-Obligation"]], "non extensible universe declaration not supported with monomorphic program definition (error)": [[9, "coq:exn.Non-extensible-universe-declaration-not-supported-with-monomorphic-Program-Definition"]], "obligation (command)": [[9, "coq:cmd.Obligation"]], "obligation tactic (command)": [[9, "coq:cmd.Obligation-Tactic"]], "obligations (command)": [[9, "coq:cmd.Obligations"]], "preterm (command)": [[9, "coq:cmd.Preterm"]], "program (attribute)": [[9, "coq:attr.Program"], [9, "coq:attr.program"]], "program cases (flag)": [[9, "coq:flag.Program-Cases"]], "program generalized coercion (flag)": [[9, "coq:flag.Program-Generalized-Coercion"]], "program mode (flag)": [[9, "coq:flag.Program-Mode"]], "show obligation tactic (command)": [[9, "coq:cmd.Show-Obligation-Tactic"]], "solve all obligations (command)": [[9, "coq:cmd.Solve-All-Obligations"]], "solve obligations (command)": [[9, "coq:cmd.Solve-Obligations"]], "transparent obligations (flag)": [[9, "coq:flag.Transparent-Obligations"]], "rewrite rule (command)": [[10, "coq:cmd.Rewrite-Rule"]], "rewrite rules (command)": [[10, "coq:cmd.Rewrite-Rules"]], "rewrite rule declaration requires passing the flag \"-allow-rewrite-rules\" (error)": [[10, "coq:exn.Rewrite-rule-declaration-requires-passing-the-flag-\"-allow-rewrite-rules\""]], "symbol (command)": [[10, "coq:cmd.Symbol"]], "symbols (command)": [[10, "coq:cmd.Symbols"]], "add field (command)": [[11, "coq:cmd.Add-Field"]], "add ring (command)": [[11, "coq:cmd.Add-Ring"]], "arguments of ring_simplify do not have all the same type (error)": [[11, "coq:exn.Arguments-of-ring_simplify-do-not-have-all-the-same-type"]], "bad lemma for decidability of equality (error)": [[11, "coq:exn.Bad-lemma-for-decidability-of-equality"]], "bad ring structure (error)": [[11, "coq:exn.Bad-ring-structure"]], "cannot find a declared ring structure for equality \u2018term\u2019 (error)": [[11, "coq:exn.Cannot-find-a-declared-ring-structure-for-equality-\u2018term\u2019"]], "cannot find a declared ring structure over \u2018term\u2019 (error)": [[11, "coq:exn.Cannot-find-a-declared-ring-structure-over-\u2018term\u2019"]], "not a valid ring equation (error)": [[11, "coq:exn.Not-a-valid-ring-equation"]], "print fields (command)": [[11, "coq:cmd.Print-Fields"]], "print rings (command)": [[11, "coq:cmd.Print-Rings"]], "ring operation should be declared as a morphism (error)": [[11, "coq:exn.Ring-operation-should-be-declared-as-a-morphism"]], "field (tactic)": [[11, "coq:tacn.field"]], "field_lookup (tactic)": [[11, "coq:tacn.field_lookup"]], "field_simplify (tactic)": [[11, "coq:tacn.field_simplify"]], "field_simplify_eq (tactic)": [[11, "coq:tacn.field_simplify_eq"]], "protect_fv (tactic)": [[11, "coq:tacn.protect_fv"]], "ring (tactic)": [[11, "coq:tacn.ring"]], "ring_lookup (tactic)": [[11, "coq:tacn.ring_lookup"]], "ring_simplify (tactic)": [[11, "coq:tacn.ring_simplify"]], "allow strictprop (flag)": [[12, "coq:flag.Allow-StrictProp"]], "bad relevance (warning)": [[12, "coq:warn.Bad-relevance"]], "definitional uip (flag)": [[12, "coq:flag.Definitional-UIP"]], "printing relevance marks (flag)": [[12, "coq:flag.Printing-Relevance-Marks"]], "sprop is disallowed because the \"allow strictprop\" flag is off (error)": [[12, "coq:exn.SProp-is-disallowed-because-the-\"Allow-StrictProp\"-flag-is-off"]], ":: (substructure)": [[13, "index-0"]], "class (command)": [[13, "coq:cmd.Class"]], "declare instance (command)": [[13, "coq:cmd.Declare-Instance"]], "existing class (command)": [[13, "coq:cmd.Existing-Class"]], "existing instance (command)": [[13, "coq:cmd.Existing-Instance"]], "existing instances (command)": [[13, "coq:cmd.Existing-Instances"]], "ignored instance declaration for \u201c\u2018ident\u2019\u201d: \u201c\u2018term\u2019\u201d is not a class (warning)": [[13, "coq:warn.Ignored-instance-declaration-for-\u201c\u2018ident\u2019\u201d:-\u201c\u2018term\u2019\u201d-is-not-a-class"]], "instance (command)": [[13, "coq:cmd.Instance"]], "print instances (command)": [[13, "coq:cmd.Print-Instances"]], "print typeclasses (command)": [[13, "coq:cmd.Print-Typeclasses"]], "typeclass resolution for conversion (flag)": [[13, "coq:flag.Typeclass-Resolution-For-Conversion"]], "typeclasses debug (flag)": [[13, "coq:flag.Typeclasses-Debug"]], "typeclasses debug verbosity (option)": [[13, "coq:opt.Typeclasses-Debug-Verbosity"]], "typeclasses default mode (option)": [[13, "coq:opt.Typeclasses-Default-Mode"]], "typeclasses dependency order (flag)": [[13, "coq:flag.Typeclasses-Dependency-Order"]], "typeclasses depth (option)": [[13, "coq:opt.Typeclasses-Depth"]], "typeclasses iterative deepening (flag)": [[13, "coq:flag.Typeclasses-Iterative-Deepening"]], "typeclasses limit intros (flag)": [[13, "coq:flag.Typeclasses-Limit-Intros"]], "typeclasses opaque (command)": [[13, "coq:cmd.Typeclasses-Opaque"]], "typeclasses strict resolution (flag)": [[13, "coq:flag.Typeclasses-Strict-Resolution"]], "typeclasses transparent (command)": [[13, "coq:cmd.Typeclasses-Transparent"]], "typeclasses unique instances (flag)": [[13, "coq:flag.Typeclasses-Unique-Instances"]], "typeclasses unique solutions (flag)": [[13, "coq:flag.Typeclasses-Unique-Solutions"]], "typeclasses eauto (command)": [[13, "coq:cmd.Typeclasses-eauto"]], "using inferred default mode: \u201cmode\u201d for \u201c\u2018ident\u2019\u201d (warning)": [[13, "coq:warn.Using-inferred-default-mode:-\u201cmode\u201d-for-\u201c\u2018ident\u2019\u201d"]], "autoapply (tactic)": [[13, "coq:tacn.autoapply"]], "mode (attribute)": [[13, "coq:attr.mode"]], "refine (attribute)": [[13, "coq:attr.refine"]], "typeclasses eauto (tactic)": [[13, "coq:tacn.typeclasses-eauto"]], "\u2018ident\u2019 is already declared as a typeclass (warning)": [[13, "coq:warn.\u2018ident\u2019-is-already-declared-as-a-typeclass"]], "constraint (command)": [[14, "coq:cmd.Constraint"]], "cumulative (attribute)": [[14, "coq:attr.Cumulative"]], "cumulativity weak constraints (flag)": [[14, "coq:flag.Cumulativity-Weak-Constraints"]], "monomorphic (attribute)": [[14, "coq:attr.Monomorphic"]], "noncumulative (attribute)": [[14, "coq:attr.NonCumulative"]], "polymorphic (attribute)": [[14, "coq:attr.Polymorphic"]], "polymorphic inductive cumulativity (flag)": [[14, "coq:flag.Polymorphic-Inductive-Cumulativity"]], "polymorphic universe constraints can only be declared inside sections, use monomorphic constraint instead (error)": [[14, "coq:exn.Polymorphic-universe-constraints-can-only-be-declared-inside-sections,-use-Monomorphic-Constraint-instead"]], "polymorphic universes can only be declared inside sections, use monomorphic universe instead (error)": [[14, "coq:exn.Polymorphic-universes-can-only-be-declared-inside-sections,-use-Monomorphic-Universe-instead"]], "print universes (command)": [[14, "coq:cmd.Print-Universes"]], "printing universes (flag)": [[14, "coq:flag.Printing-Universes"]], "private polymorphic universes (flag)": [[14, "coq:flag.Private-Polymorphic-Universes"]], "strict universe declaration (flag)": [[14, "coq:flag.Strict-Universe-Declaration"]], "the cumulative attribute can only be used in a polymorphic context (error)": [[14, "coq:exn.The-cumulative-attribute-can-only-be-used-in-a-polymorphic-context"]], "undeclared universe \u2018ident\u2019 (error)": [[14, "coq:exn.Undeclared-universe-\u2018ident\u2019"]], "universe (command)": [[14, "coq:cmd.Universe"]], "universe minimization toset (flag)": [[14, "coq:flag.Universe-Minimization-ToSet"]], "universe polymorphism (flag)": [[14, "coq:flag.Universe-Polymorphism"]], "universe inconsistency (error)": [[14, "coq:exn.Universe-inconsistency"]], "universes (command)": [[14, "coq:cmd.Universes"]], "universes(cumulative) (attribute)": [[14, "coq:attr.universes(cumulative)"]], "universes(polymorphic) (attribute)": [[14, "coq:attr.universes(polymorphic)"]], "* (term)": [[27, "index-9"]], "+ (term)": [[27, "index-9"]], "a*b (term)": [[27, "index-9"]], "a+b (term)": [[27, "index-9"]], "a+{b} (term)": [[27, "index-13"]], "acc (term)": [[27, "index-20"]], "acc_inv (term)": [[27, "index-20"]], "acc_rect (term)": [[27, "index-20"]], "choice (term)": [[27, "index-14"]], "choice2 (term)": [[27, "index-14"]], "connectives": [[27, "index-1"]], "datatypes": [[27, "index-7"]], "equality": [[27, "index-4"]], "exc (term)": [[27, "index-15"]], "false (term)": [[27, "index-1"], [27, "index-8"]], "false_rec (term)": [[27, "index-16"]], "false_rect (term)": [[27, "index-16"]], "fix_f (term)": [[27, "index-21"]], "fix_f_eq (term)": [[27, "index-21"]], "fix_f_inv (term)": [[27, "index-21"]], "fix_eq (term)": [[27, "index-21"]], "i (term)": [[27, "index-1"]], "issucc (term)": [[27, "index-17"]], "none (term)": [[27, "index-8"]], "o (term)": [[27, "index-8"]], "o_s (term)": [[27, "index-17"]], "programming": [[27, "index-8"]], "quantifiers": [[27, "index-3"]], "recursion": [[27, "index-20"]], "s (term)": [[27, "index-8"]], "some (term)": [[27, "index-8"]], "theories": [[27, "index-0"]], "true (term)": [[27, "index-1"], [27, "index-8"]], "well founded induction": [[27, "index-20"]], "well foundedness": [[27, "index-20"]], "absurd (term)": [[27, "index-5"]], "absurd_set (term)": [[27, "index-16"]], "all (term)": [[27, "index-3"]], "and (term)": [[27, "index-1"]], "and_rect (term)": [[27, "index-16"]], "bool (term)": [[27, "index-8"]], "bool_choice (term)": [[27, "index-14"]], "conj (term)": [[27, "index-1"]], "eq (term)": [[27, "index-4"]], "eq_s (term)": [[27, "index-17"]], "eq_add_s (term)": [[27, "index-17"]], "eq_ind_r (term)": [[27, "index-5"]], "eq_rec_r (term)": [[27, "index-5"]], "eq_rect (term)": [[27, "index-16"], [27, "index-5"]], "eq_rect_r (term)": [[27, "index-5"]], "eq_refl (term)": [[27, "index-4"]], "eq_sym (term)": [[27, "index-5"]], "eq_trans (term)": [[27, "index-5"]], "error (term)": [[27, "index-15"]], "ex (term)": [[27, "index-3"]], "ex2 (term)": [[27, "index-3"]], "ex_intro (term)": [[27, "index-3"]], "ex_intro2 (term)": [[27, "index-3"]], "exist (term)": [[27, "index-10"]], "exist2 (term)": [[27, "index-10"]], "existt (term)": [[27, "index-11"]], "existt2 (term)": [[27, "index-11"]], "exists (term)": [[27, "index-3"]], "exists2 (term)": [[27, "index-3"]], "f_equal (term)": [[27, "index-5"]], "f_equal2 ... f_equal5 (term)": [[27, "index-6"]], "fst (term)": [[27, "index-9"]], "ge (term)": [[27, "index-18"]], "gt (term)": [[27, "index-18"]], "identity (term)": [[27, "index-8"]], "iff (term)": [[27, "index-1"]], "inl (term)": [[27, "index-9"]], "inleft (term)": [[27, "index-13"]], "inr (term)": [[27, "index-9"]], "inright (term)": [[27, "index-13"]], "le (term)": [[27, "index-18"]], "le_s (term)": [[27, "index-18"]], "le_n (term)": [[27, "index-18"]], "left (term)": [[27, "index-12"]], "lt (term)": [[27, "index-18"]], "mult (term)": [[27, "index-17"]], "mult_n_o (term)": [[27, "index-17"]], "mult_n_sm (term)": [[27, "index-17"]], "n_sn (term)": [[27, "index-17"]], "nat (term)": [[27, "index-8"]], "nat_case (term)": [[27, "index-19"]], "nat_double_ind (term)": [[27, "index-19"]], "not (term)": [[27, "index-1"]], "nott (term)": [[27, "index-2"]], "not_eq_s (term)": [[27, "index-17"]], "option (term)": [[27, "index-8"]], "or (term)": [[27, "index-1"]], "or_introl (term)": [[27, "index-1"]], "or_intror (term)": [[27, "index-1"]], "pair (term)": [[27, "index-9"]], "plus (term)": [[27, "index-17"]], "plus_n_o (term)": [[27, "index-17"]], "plus_n_sm (term)": [[27, "index-17"]], "pred (term)": [[27, "index-17"]], "pred_sn (term)": [[27, "index-17"]], "prod (term)": [[27, "index-9"]], "proj1 (term)": [[27, "index-1"]], "proj2 (term)": [[27, "index-1"]], "projt1 (term)": [[27, "index-11"]], "projt2 (term)": [[27, "index-11"]], "refl_identity (term)": [[27, "index-8"]], "right (term)": [[27, "index-12"]], "sig (term)": [[27, "index-10"]], "sig2 (term)": [[27, "index-10"]], "sigt (term)": [[27, "index-11"]], "sigt2 (term)": [[27, "index-11"]], "snd (term)": [[27, "index-9"]], "sum (term)": [[27, "index-9"]], "sumbool (term)": [[27, "index-12"]], "sumor (term)": [[27, "index-13"]], "sym_not_eq (term)": [[27, "index-5"]], "tt (term)": [[27, "index-8"]], "unit (term)": [[27, "index-8"]], "value (term)": [[27, "index-15"]], "well_founded (term)": [[27, "index-20"]], "{a}+{b} (term)": [[27, "index-12"]], "{x:a & p x} (term)": [[27, "index-11"]], "{x:a | p x} (term)": [[27, "index-10"]], "axiom (command)": [[28, "coq:cmd.Axiom"]], "axioms (command)": [[28, "coq:cmd.Axioms"]], "conjecture (command)": [[28, "coq:cmd.Conjecture"]], "conjectures (command)": [[28, "coq:cmd.Conjectures"]], "hypotheses (command)": [[28, "coq:cmd.Hypotheses"]], "hypothesis (command)": [[28, "coq:cmd.Hypothesis"]], "parameter (command)": [[28, "coq:cmd.Parameter"]], "parameters (command)": [[28, "coq:cmd.Parameters"]], "use of \"variable\" or \"hypothesis\" outside sections behaves as \"#[local] parameter\" or \"#[local] axiom\" (warning)": [[28, "coq:warn.Use-of-\"Variable\"-or-\"Hypothesis\"-outside-sections-behaves-as-\"#[local]-Parameter\"-or-\"#[local]-Axiom\""]], "variable (command)": [[28, "coq:cmd.Variable"]], "variables (command)": [[28, "coq:cmd.Variables"]], "forall": [[28, "index-1"]], "fun": [[28, "index-0"]], "\u2018ident\u2019 already exists. (axiom) (error)": [[28, "coq:exn.\u2018ident\u2019-already-exists.-(Axiom)"]], "add (command)": [[29, "coq:cmd.Add"]], "attributes (command)": [[29, "coq:cmd.Attributes"]], "comments (command)": [[29, "coq:cmd.Comments"]], "print options (command)": [[29, "coq:cmd.Print-Options"]], "print table (command)": [[29, "coq:cmd.Print-Table"]], "print tables (command)": [[29, "coq:cmd.Print-Tables"]], "remove (command)": [[29, "coq:cmd.Remove"]], "set (command)": [[29, "coq:cmd.Set"]], "test (command)": [[29, "coq:cmd.Test"]], "there is no flag or option with this name: \"\u2018setting_name\u2019\" (warning)": [[29, "coq:warn.There-is-no-flag-or-option-with-this-name:-\"\u2018setting_name\u2019\""]], "there is no flag, option or table with this name: \"\u2018setting_name\u2019\" (error)": [[29, "coq:exn.There-is-no-flag,-option-or-table-with-this-name:-\"\u2018setting_name\u2019\""]], "there is no qualid-valued table with this name: \"\u2018setting_name\u2019\" (error)": [[29, "coq:exn.There-is-no-qualid-valued-table-with-this-name:-\"\u2018setting_name\u2019\""]], "there is no string-valued table with this name: \"\u2018setting_name\u2019\" (error)": [[29, "coq:exn.There-is-no-string-valued-table-with-this-name:-\"\u2018setting_name\u2019\""]], "this command does not support this attribute (warning)": [[29, "coq:warn.This-command-does-not-support-this-attribute"]], "unset (command)": [[29, "coq:cmd.Unset"]], "command": [[29, "term-command"]], "sentence": [[29, "term-sentence"]], "tactic": [[29, "term-tactic"]], "term": [[29, "term-term"]], "type": [[29, "term-type"], [39, "index-0"]], "warning (attribute)": [[29, "coq:attr.warning"]], "warnings (attribute)": [[29, "coq:attr.warnings"]], "cofixpoint (command)": [[30, "coq:cmd.CoFixpoint"]], "coinductive (command)": [[30, "coq:cmd.CoInductive"]], "cofix": [[30, "index-0"]], "... : ... (type cast)": [[32, "index-1"]], "... :> ... (volatile type cast)": [[32, "index-1"]], "... <: ... (vm type cast)": [[32, "index-1"]], "... <<: ... (native compute type cast)": [[32, "index-1"]], "corollary (command)": [[32, "coq:cmd.Corollary"]], "definition (command)": [[32, "coq:cmd.Definition"]], "example (command)": [[32, "coq:cmd.Example"]], "fact (command)": [[32, "coq:cmd.Fact"]], "lemma (command)": [[32, "coq:cmd.Lemma"]], "nested proofs are discouraged and not allowed by default. this error probably means that you forgot to close the last \"proof.\" with \"qed.\" or \"defined.\". if you really intended to use nested proofs, you can do so by turning the \"nested proofs allowed\" flag on (error)": [[32, "coq:exn.Nested-proofs-are-discouraged-and-not-allowed-by-default.-This-error-probably-means-that-you-forgot-to-close-the-last-\"Proof.\"-with-\"Qed.\"-or-\"Defined.\".-If-you-really-intended-to-use-nested-proofs,-you-can-do-so-by-turning-the-\"Nested-Proofs-Allowed\"-flag-on"]], "property (command)": [[32, "coq:cmd.Property"]], "proposition (command)": [[32, "coq:cmd.Proposition"]], "remark (command)": [[32, "coq:cmd.Remark"]], "the term \u2018term\u2019 has type \u2018type\u2019 which should be set, prop or type (error)": [[32, "coq:exn.The-term-\u2018term\u2019-has-type-\u2018type\u2019-which-should-be-Set,-Prop-or-Type"]], "the term \u2018term\u2019 has type \u2018type\u2019 while it is expected to have type \u2018type\u2019' (error)": [[32, "coq:exn.The-term-\u2018term\u2019-has-type-\u2018type\u2019-while-it-is-expected-to-have-type-\u2018type\u2019'"]], "theorem (command)": [[32, "coq:cmd.Theorem"]], "let ... := ... (term)": [[32, "index-0"]], "\u2018ident\u2019 already exists. (definition) (error)": [[32, "coq:exn.\u2018ident\u2019-already-exists.-(Definition)"]], "\u2018ident\u2019 already exists. (theorem) (error)": [[32, "coq:exn.\u2018ident\u2019-already-exists.-(Theorem)"]], "auto template polymorphism (flag)": [[34, "coq:flag.Auto-Template-Polymorphism"]], "automatically declaring \u2018ident\u2019 as template polymorphic (warning)": [[34, "coq:warn.Automatically-declaring-\u2018ident\u2019-as-template-polymorphic"]], "dependent proposition eliminators (flag)": [[34, "coq:flag.Dependent-Proposition-Eliminators"]], "fixpoint (command)": [[34, "coq:cmd.Fixpoint"]], "ill-formed template inductive declaration: not polymorphic on any universe (error)": [[34, "coq:exn.Ill-formed-template-inductive-declaration:-not-polymorphic-on-any-universe"]], "inductive (command)": [[34, "coq:cmd.Inductive"]], "non strictly positive occurrence of \u2018ident\u2019 in \u2018type\u2019 (error)": [[34, "coq:exn.Non-strictly-positive-occurrence-of-\u2018ident\u2019-in-\u2018type\u2019"]], "the conclusion of \u2018type\u2019 is not valid": [[34, "coq:exn.The-conclusion-of-\u2018type\u2019-is-not-valid;-it-must-be-built-from-\u2018ident\u2019"]], "uniform inductive parameters (flag)": [[34, "coq:flag.Uniform-Inductive-Parameters"]], "fix": [[34, "index-0"]], "it must be built from \u2018ident\u2019 (error)": [[34, "coq:exn.The-conclusion-of-\u2018type\u2019-is-not-valid;-it-must-be-built-from-\u2018ident\u2019"]], "template and polymorphism not compatible (error)": [[34, "coq:exn.template-and-polymorphism-not-compatible"]], "universes(template) (attribute)": [[34, "coq:attr.universes(template)"]], "cannot import local constant, it will be ignored (warning)": [[35, "coq:warn.Cannot-import-local-constant,-it-will-be-ignored"]], "declare module (command)": [[35, "coq:cmd.Declare-Module"]], "export (command)": [[35, "coq:cmd.Export"]], "import (command)": [[35, "coq:cmd.Import"]], "include (command)": [[35, "coq:cmd.Include"]], "include type (command)": [[35, "coq:cmd.Include-Type"]], "module (command)": [[35, "coq:cmd.Module"]], "module type (command)": [[35, "coq:cmd.Module-Type"]], "no field named \u2018ident\u2019 in \u2018qualid\u2019 (error)": [[35, "coq:exn.No-field-named-\u2018ident\u2019-in-\u2018qualid\u2019"]], "print module (command)": [[35, "coq:cmd.Print-Module"]], "print module type (command)": [[35, "coq:cmd.Print-Module-Type"]], "print namespace (command)": [[35, "coq:cmd.Print-Namespace"]], "short module printing (flag)": [[35, "coq:flag.Short-Module-Printing"]], "signature components for field \u2018ident\u2019 do not match (error)": [[35, "coq:exn.Signature-components-for-field-\u2018ident\u2019-do-not-match"]], "the field \u2018ident\u2019 is missing in \u2018qualid\u2019 (error)": [[35, "coq:exn.The-field-\u2018ident\u2019-is-missing-in-\u2018qualid\u2019"]], "trying to mask the absolute name \u2018qualid\u2019! (warning)": [[35, "coq:warn.Trying-to-mask-the-absolute-name-\u2018qualid\u2019!"]], "export (attribute)": [[35, "coq:attr.export"]], "global (attribute)": [[35, "coq:attr.global"]], "local (attribute)": [[35, "coq:attr.local"]], "\u2018qualid\u2019 is not a module (error)": [[35, "coq:exn.\u2018qualid\u2019-is-not-a-module"]], "primitive projections (flag)": [[37, "coq:flag.Primitive-Projections"]], "printing constructor (table)": [[37, "coq:table.Printing-Constructor"]], "printing primitive projection parameters (flag)": [[37, "coq:flag.Printing-Primitive-Projection-Parameters"]], "printing projections (flag)": [[37, "coq:flag.Printing-Projections"]], "printing record (table)": [[37, "coq:table.Printing-Record"]], "printing records (flag)": [[37, "coq:flag.Printing-Records"]], "printing unfolded projection as match (flag)": [[37, "coq:flag.Printing-Unfolded-Projection-As-Match"]], "record (command)": [[37, "coq:cmd.Record"]], "records declared with the keyword record or structure cannot be recursive (error)": [[37, "coq:exn.Records-declared-with-the-keyword-Record-or-Structure-cannot-be-recursive"]], "structure (command)": [[37, "coq:cmd.Structure"]], "projections(primitive) (attribute)": [[37, "coq:attr.projections(primitive)"]], "\u2018ident\u2019 already exists (error)": [[37, "coq:exn.\u2018ident\u2019-already-exists"]], "\u2018ident\u2019 cannot be defined (warning)": [[37, "coq:warn.\u2018ident\u2019-cannot-be-defined"]], "\u2018ident\u2019 cannot be defined because it is informative and \u2018ident\u2019 is not (warning)": [[37, "coq:warn.\u2018ident\u2019-cannot-be-defined-because-it-is-informative-and-\u2018ident\u2019-is-not"]], "\u2018ident\u2019 cannot be defined because the projection \u2018ident\u2019 was not defined (warning)": [[37, "coq:warn.\u2018ident\u2019-cannot-be-defined-because-the-projection-\u2018ident\u2019-was-not-defined"]], "context (command)": [[38, "coq:cmd.Context"]], "end (command)": [[38, "coq:cmd.End"]], "last block to end has name \u2018ident\u2019 (error)": [[38, "coq:exn.Last-block-to-end-has-name-\u2018ident\u2019"]], "let (command)": [[38, "coq:cmd.Let"]], "let cofixpoint (command)": [[38, "coq:cmd.Let-CoFixpoint"]], "let fixpoint (command)": [[38, "coq:cmd.Let-Fixpoint"]], "section (command)": [[38, "coq:cmd.Section"]], "there is nothing to end (error)": [[38, "coq:exn.There-is-nothing-to-end"]], "clearbody (attribute)": [[38, "coq:attr.clearbody"]], "prop": [[39, "index-0"]], "sprop": [[39, "index-0"]], "set (sort)": [[39, "index-0"]], "casts are not supported in this pattern (error)": [[40, "coq:exn.Casts-are-not-supported-in-this-pattern"]], "private (attribute)": [[40, "coq:attr.Private"]], "the \u2018natural\u2019 th argument of \u2018ident\u2019 must be \u2018ident\u2019 in \u2018type\u2019 (error)": [[40, "coq:exn.The-\u2018natural\u2019-th-argument-of-\u2018ident\u2019-must-be-\u2018ident\u2019-in-\u2018type\u2019"]], "variant (command)": [[40, "coq:cmd.Variant"]], "match ... with ...": [[40, "index-0"]], "private(matching) (attribute)": [[40, "coq:attr.private(matching)"]], "arguments (command)": [[41, "coq:cmd.Arguments"]], "arguments of section variables such as \u2018name\u2019 may not be renamed (error)": [[41, "coq:exn.Arguments-of-section-variables-such-as-\u2018name\u2019-may-not-be-renamed"]], "flag 'rename' expected to rename \u2018name\u2019 into \u2018name\u2019 (error)": [[41, "coq:exn.Flag-'rename'-expected-to-rename-\u2018name\u2019-into-\u2018name\u2019"]], "the & modifier may only occur once (error)": [[41, "coq:exn.The-&-modifier-may-only-occur-once"]], "the 'clear implicits' flag must be omitted if implicit annotations are given (error)": [[41, "coq:exn.The-'clear-implicits'-flag-must-be-omitted-if-implicit-annotations-are-given"]], "the 'default implicits' flag is incompatible with implicit annotations (error)": [[41, "coq:exn.The-'default-implicits'-flag-is-incompatible-with-implicit-annotations"]], "the / modifier may only occur once (error)": [[41, "coq:exn.The-/-modifier-may-only-occur-once"]], "this command is just asserting the names of arguments of \u2018qualid\u2019. if this is what you want, add ': assert' to silence the warning. if you want to clear implicit arguments, add ': clear implicits'. if you want to clear notation scopes, add ': clear scopes' (warning)": [[41, "coq:warn.This-command-is-just-asserting-the-names-of-arguments-of-\u2018qualid\u2019.-If-this-is-what-you-want,-add-':-assert'-to-silence-the-warning.-If-you-want-to-clear-implicit-arguments,-add-':-clear-implicits'.-If-you-want-to-clear-notation-scopes,-add-':-clear-scopes'"]], "to rename arguments the 'rename' flag must be specified (error)": [[41, "coq:exn.To-rename-arguments-the-'rename'-flag-must-be-specified"]], "canonical structure (command)": [[42, "coq:cmd.Canonical-Structure"]], "print canonical projections (command)": [[42, "coq:cmd.Print-Canonical-Projections"]], "canonical (attribute)": [[42, "coq:attr.canonical"]], "printing existential instances (flag)": [[43, "coq:flag.Printing-Existential-Instances"]], "_": [[43, "index-0"]], "argument at position \u2018natural\u2019 is mentioned more than once (error)": [[44, "coq:exn.Argument-at-position-\u2018natural\u2019-is-mentioned-more-than-once"]], "argument \u2018name\u2019 is a trailing implicit, so it can't be declared non maximal. please use { } instead of [ ] (error)": [[44, "coq:exn.Argument-\u2018name\u2019-is-a-trailing-implicit,-so-it-can't-be-declared-non-maximal.-Please-use-{-}-instead-of-[-]"]], "arguments given by name or position not supported in explicit mode (error)": [[44, "coq:exn.Arguments-given-by-name-or-position-not-supported-in-explicit-mode"]], "cannot infer a term for this placeholder. (casual use of implicit arguments) (error)": [[44, "coq:exn.Cannot-infer-a-term-for-this-placeholder.-(Casual-use-of-implicit-arguments)"]], "contextual implicit (flag)": [[44, "coq:flag.Contextual-Implicit"]], "generalizable (command)": [[44, "coq:cmd.Generalizable"]], "ignoring implicit binder declaration in unexpected position (warning)": [[44, "coq:warn.Ignoring-implicit-binder-declaration-in-unexpected-position"]], "implicit arguments (flag)": [[44, "coq:flag.Implicit-Arguments"]], "implicit type (command)": [[44, "coq:cmd.Implicit-Type"]], "implicit types (command)": [[44, "coq:cmd.Implicit-Types"]], "making shadowed name of implicit argument accessible by position (warning)": [[44, "coq:warn.Making-shadowed-name-of-implicit-argument-accessible-by-position"]], "maximal implicit insertion (flag)": [[44, "coq:flag.Maximal-Implicit-Insertion"]], "not enough non implicit arguments to accept the argument bound to \u2018ident\u2019 (error)": [[44, "coq:exn.Not-enough-non-implicit-arguments-to-accept-the-argument-bound-to-\u2018ident\u2019"]], "not enough non implicit arguments to accept the argument bound to \u2018natural\u2019 (error)": [[44, "coq:exn.Not-enough-non-implicit-arguments-to-accept-the-argument-bound-to-\u2018natural\u2019"]], "parsing explicit (flag)": [[44, "coq:flag.Parsing-Explicit"]], "print implicit (command)": [[44, "coq:cmd.Print-Implicit"]], "printing implicit (flag)": [[44, "coq:flag.Printing-Implicit"]], "printing implicit defensive (flag)": [[44, "coq:flag.Printing-Implicit-Defensive"]], "printing use implicit types (flag)": [[44, "coq:flag.Printing-Use-Implicit-Types"]], "reversible pattern implicit (flag)": [[44, "coq:flag.Reversible-Pattern-Implicit"]], "strict implicit (flag)": [[44, "coq:flag.Strict-Implicit"]], "strongly strict implicit (flag)": [[44, "coq:flag.Strongly-Strict-Implicit"]], "wrong argument name (error)": [[44, "coq:exn.Wrong-argument-name"]], "wrong argument position (error)": [[44, "coq:exn.Wrong-argument-position"]], "`( )": [[44, "index-2"]], "`(! )": [[44, "index-5"]], "`[ ]": [[44, "index-1"]], "`[! ]": [[44, "index-4"]], "`{ }": [[44, "index-0"]], "`{! }": [[44, "index-3"]], "asymmetric patterns (flag)": [[46, "coq:flag.Asymmetric-Patterns"]], "either there is a type incompatibility or the problem involves dependencies (error)": [[46, "coq:exn.Either-there-is-a-type-incompatibility-or-the-problem-involves-dependencies"]], "found a constructor of inductive type term while a constructor of term is expected (error)": [[46, "coq:exn.Found-a-constructor-of-inductive-type-term-while-a-constructor-of-term-is-expected"]], "non exhaustive pattern matching (error)": [[46, "coq:exn.Non-exhaustive-pattern-matching"]], "printing allow match default clause (flag)": [[46, "coq:flag.Printing-Allow-Match-Default-Clause"]], "printing factorizable match patterns (flag)": [[46, "coq:flag.Printing-Factorizable-Match-Patterns"]], "printing if (table)": [[46, "coq:table.Printing-If"]], "printing let (table)": [[46, "coq:table.Printing-Let"]], "printing match all subterms (flag)": [[46, "coq:flag.Printing-Match-All-Subterms"]], "printing matching (flag)": [[46, "coq:flag.Printing-Matching"]], "printing synth (flag)": [[46, "coq:flag.Printing-Synth"]], "printing wildcard (flag)": [[46, "coq:flag.Printing-Wildcard"]], "the constructor \u2018ident\u2019 expects \u2018natural\u2019 arguments (error)": [[46, "coq:exn.The-constructor-\u2018ident\u2019-expects-\u2018natural\u2019-arguments"]], "the elimination predicate term should be of arity \u2018natural\u2019 (for non dependent case) or \u2018natural\u2019 (for dependent case) (error)": [[46, "coq:exn.The-elimination-predicate-term-should-be-of-arity-\u2018natural\u2019-(for-non-dependent-case)-or-\u2018natural\u2019-(for-dependent-case)"]], "the variable ident is bound several times in pattern term (error)": [[46, "coq:exn.The-variable-ident-is-bound-several-times-in-pattern-term"]], "unable to infer a match predicate (error)": [[46, "coq:exn.Unable-to-infer-a-match-predicate"]], "unused variable \u2018ident\u2019 might be a misspelled constructor. use _ or _\u2018ident\u2019 to silence this warning (warning)": [[46, "coq:warn.Unused-variable-\u2018ident\u2019-might-be-a-misspelled-constructor.-Use-_-or-_\u2018ident\u2019-to-silence-this-warning."]], "coqtop exit on error (flag)": [[51, "coq:flag.Coqtop-Exit-On-Error"]], "+ (backtracking branching) (tactic)": [[54, "coq:tacn.+-(backtracking-branching)"]], "::=": [[54, "index-0"]], "argument of match does not evaluate to a term (error)": [[54, "coq:exn.Argument-of-match-does-not-evaluate-to-a-term"]], "condition not satisfied (error)": [[54, "coq:exn.Condition-not-satisfied"]], "debug (command)": [[54, "coq:cmd.Debug"]], "debug mode not available in the ide (error)": [[54, "coq:exn.Debug-mode-not-available-in-the-IDE"]], "expression does not evaluate to a tactic (error)": [[54, "coq:exn.Expression-does-not-evaluate-to-a-tactic"]], "failed to progress (error)": [[54, "coq:exn.Failed-to-progress"]], "info (command)": [[54, "coq:cmd.Info"]], "info level (option)": [[54, "coq:opt.Info-Level"]], "ltac (command)": [[54, "coq:cmd.Ltac"]], "ltac backtrace (flag)": [[54, "coq:flag.Ltac-Backtrace"]], "ltac batch debug (flag)": [[54, "coq:flag.Ltac-Batch-Debug"]], "ltac debug (flag)": [[54, "coq:flag.Ltac-Debug"]], "ltac profiler encountered an invalid stack (no self node). this can happen if you reset the profile during tactic execution (warning)": [[54, "coq:warn.Ltac-Profiler-encountered-an-invalid-stack-(no-self-node).-This-can-happen-if-you-reset-the-profile-during-tactic-execution"]], "ltac profiling (flag)": [[54, "coq:flag.Ltac-Profiling"]], "no applicable tactic (error)": [[54, "coq:exn.No-applicable-tactic"]], "no evars (error)": [[54, "coq:exn.No-evars"]], "no matching clauses for match (error)": [[54, "coq:exn.No-matching-clauses-for-match"]], "no matching clauses for match goal (error)": [[54, "coq:exn.No-matching-clauses-for-match-goal"]], "no such goal. (goal selector) (error)": [[54, "coq:exn.No-such-goal.-(Goal-selector)"]], "no such goal. (fail) (error)": [[54, "coq:exn.No-such-goal.-(fail)"]], "not a context variable (error)": [[54, "coq:exn.Not-a-context-variable"]], "not a variable or hypothesis (error)": [[54, "coq:exn.Not-a-variable-or-hypothesis"]], "not an evar (error)": [[54, "coq:exn.Not-an-evar"]], "not equal (due to universes) (error)": [[54, "coq:exn.Not-equal-(due-to-universes)"]], "not equal (error)": [[54, "coq:exn.Not-equal"]], "not ground (error)": [[54, "coq:exn.Not-ground"]], "print ltac (command)": [[54, "coq:cmd.Print-Ltac"]], "print ltac signatures (command)": [[54, "coq:cmd.Print-Ltac-Signatures"]], "reset ltac profile (command)": [[54, "coq:cmd.Reset-Ltac-Profile"]], "show ltac profile (command)": [[54, "coq:cmd.Show-Ltac-Profile"]], "tactic failure (error)": [[54, "coq:exn.Tactic-failure"]], "tactic failure (level \u2018natural\u2019) (error)": [[54, "coq:exn.Tactic-failure-(level-\u2018natural\u2019)"]], "tactic failure: succeeds (error)": [[54, "coq:exn.Tactic-failure:--succeeds"]], "there is already an ltac named \u2018qualid\u2019 (error)": [[54, "coq:exn.There-is-already-an-Ltac-named-\u2018qualid\u2019"]], "there is no ltac named \u2018qualid\u2019 (error)": [[54, "coq:exn.There-is-no-Ltac-named-\u2018qualid\u2019"]], "this tactic has more than one success (error)": [[54, "coq:exn.This-tactic-has-more-than-one-success"]], "unbound context identifier \u2018ident\u2019 (error)": [[54, "coq:exn.Unbound-context-identifier-\u2018ident\u2019"]], "[ \u2026 | \u2026 | \u2026 ] (dispatch) (tactic)": [[54, "coq:tacn.[-\u2026-|-\u2026-|-\u2026-]-(dispatch)"]], "[> \u2026 | \u2026 | \u2026 ] (dispatch) (tactic)": [[54, "coq:tacn.[>-\u2026-|-\u2026-|-\u2026-]-(dispatch)"]], "assert_fails (tactic)": [[54, "coq:tacn.assert_fails"]], "assert_succeeds (tactic)": [[54, "coq:tacn.assert_succeeds"]], "constr_eq (tactic)": [[54, "coq:tacn.constr_eq"]], "constr_eq_nounivs (tactic)": [[54, "coq:tacn.constr_eq_nounivs"]], "constr_eq_strict (tactic)": [[54, "coq:tacn.constr_eq_strict"]], "context (tactic)": [[54, "coq:tacn.context"]], "convert (tactic)": [[54, "coq:tacn.convert"]], "do (tactic)": [[54, "coq:tacn.do"]], "exactly_once (tactic)": [[54, "coq:tacn.exactly_once"]], "fail (tactic)": [[54, "coq:tacn.fail"]], "finish_timing (tactic)": [[54, "coq:tacn.finish_timing"]], "first (tactic)": [[54, "coq:tacn.first"]], "fresh (tactic)": [[54, "coq:tacn.fresh"]], "fun (tactic)": [[54, "coq:tacn.fun"]], "gfail (tactic)": [[54, "coq:tacn.gfail"]], "guard (tactic)": [[54, "coq:tacn.guard"]], "has_evar (tactic)": [[54, "coq:tacn.has_evar"]], "idtac (tactic)": [[54, "coq:tacn.idtac"]], "infoh (command)": [[54, "coq:cmd.infoH"]], "is_cofix (tactic)": [[54, "coq:tacn.is_cofix"]], "is_const (tactic)": [[54, "coq:tacn.is_const"]], "is_constructor (tactic)": [[54, "coq:tacn.is_constructor"]], "is_evar (tactic)": [[54, "coq:tacn.is_evar"]], "is_fix (tactic)": [[54, "coq:tacn.is_fix"]], "is_ground (tactic)": [[54, "coq:tacn.is_ground"]], "is_ind (tactic)": [[54, "coq:tacn.is_ind"]], "is_proj (tactic)": [[54, "coq:tacn.is_proj"]], "is_var (tactic)": [[54, "coq:tacn.is_var"]], "lazymatch (tactic)": [[54, "coq:tacn.lazymatch"]], "lazymatch goal (tactic)": [[54, "coq:tacn.lazymatch-goal"]], "let (tactic)": [[54, "coq:tacn.let"]], "ltac-seq (tactic)": [[54, "coq:tacn.ltac-seq"]], "match (tactic)": [[54, "coq:tacn.match"]], "match goal (tactic)": [[54, "coq:tacn.match-goal"]], "multimatch (tactic)": [[54, "coq:tacn.multimatch"]], "multimatch goal (tactic)": [[54, "coq:tacn.multimatch-goal"]], "not a cofix definition (error)": [[54, "coq:exn.not-a-cofix-definition"]], "not a constant (error)": [[54, "coq:exn.not-a-constant"]], "not a constructor (error)": [[54, "coq:exn.not-a-constructor"]], "not a fix definition (error)": [[54, "coq:exn.not-a-fix-definition"]], "not a primitive projection (error)": [[54, "coq:exn.not-a-primitive-projection"]], "not an (co)inductive datatype (error)": [[54, "coq:exn.not-an-(co)inductive-datatype"]], "not_evar (tactic)": [[54, "coq:tacn.not_evar"]], "numgoals (tactic)": [[54, "coq:tacn.numgoals"]], "once (tactic)": [[54, "coq:tacn.once"]], "only (tactic)": [[54, "coq:tacn.only"]], "optimize_heap (tactic)": [[54, "coq:tacn.optimize_heap"]], "progress (tactic)": [[54, "coq:tacn.progress"]], "repeat (tactic)": [[54, "coq:tacn.repeat"]], "reset ltac profile (tactic)": [[54, "coq:tacn.reset-ltac-profile"]], "restart_timer (tactic)": [[54, "coq:tacn.restart_timer"]], "show ltac profile (tactic)": [[54, "coq:tacn.show-ltac-profile"]], "solve (tactic)": [[54, "coq:tacn.solve"]], "start ltac profiling (tactic)": [[54, "coq:tacn.start-ltac-profiling"]], "stop ltac profiling (tactic)": [[54, "coq:tacn.stop-ltac-profiling"]], "time (tactic)": [[54, "coq:tacn.time"]], "time_constr (tactic)": [[54, "coq:tacn.time_constr"]], "timeout (tactic)": [[54, "coq:tacn.timeout"]], "try (tactic)": [[54, "coq:tacn.try"]], "tryif (tactic)": [[54, "coq:tacn.tryif"]], "type of (tactic)": [[54, "coq:tacn.type-of"]], "type_term (tactic)": [[54, "coq:tacn.type_term"]], "unify (tactic)": [[54, "coq:tacn.unify"]], "|| (first tactic making progress) (tactic)": [[54, "coq:tacn.||-(first-tactic-making-progress)"]], "\u2026 : \u2026 (goal selector) (tactic)": [[54, "coq:tacn.\u2026-:-\u2026-(goal-selector)"]], "ltac2 (command)": [[55, "coq:cmd.Ltac2"]], "ltac2 backtrace (flag)": [[55, "coq:flag.Ltac2-Backtrace"]], "ltac2 check (command)": [[55, "coq:cmd.Ltac2-Check"]], "ltac2 eval (command)": [[55, "coq:cmd.Ltac2-Eval"]], "ltac2 globalize (command)": [[55, "coq:cmd.Ltac2-Globalize"]], "ltac2 in ltac1 profiling (flag)": [[55, "coq:flag.Ltac2-In-Ltac1-Profiling"]], "ltac2 notation (abbreviation) (command)": [[55, "coq:cmd.Ltac2-Notation-(abbreviation)"]], "ltac2 notation (command)": [[55, "coq:cmd.Ltac2-Notation"]], "ltac2 set (command)": [[55, "coq:cmd.Ltac2-Set"]], "ltac2 type (command)": [[55, "coq:cmd.Ltac2-Type"]], "ltac2 typed notations (flag)": [[55, "coq:flag.Ltac2-Typed-Notations"]], "ltac2 external (command)": [[55, "coq:cmd.Ltac2-external"]], "notation levels must range between 0 and 6 (error)": [[55, "coq:exn.Notation-levels-must-range-between-0-and-6"]], "print ltac2 (command)": [[55, "coq:cmd.Print-Ltac2"]], "print ltac2 signatures (command)": [[55, "coq:cmd.Print-Ltac2-Signatures"]], "print ltac2 type (command)": [[55, "coq:cmd.Print-Ltac2-Type"]], "the reference x was not found in the current environment (error)": [[55, "coq:exn.The-reference-X-was-not-found-in-the-current-environment"]], "unbound [value|constructor] x (error)": [[55, "coq:exn.Unbound-[value|constructor]-X"]], "abstract (attribute)": [[55, "coq:attr.abstract"]], "if-then-else (ltac2) (tactic)": [[55, "coq:tacn.if-then-else-(Ltac2)"]], "lazy_match! (tactic)": [[55, "coq:tacn.lazy_match!"]], "lazy_match! goal (tactic)": [[55, "coq:tacn.lazy_match!-goal"]], "match (ltac2) (tactic)": [[55, "coq:tacn.match-(Ltac2)"]], "match! (tactic)": [[55, "coq:tacn.match!"]], "match! goal (tactic)": [[55, "coq:tacn.match!-goal"]], "multi_match! (tactic)": [[55, "coq:tacn.multi_match!"]], "multi_match! goal (tactic)": [[55, "coq:tacn.multi_match!-goal"]], "=> (tactic)": [[57, "coq:tacn.=>"]], "debug ssrmatching (flag)": [[57, "coq:flag.Debug-SsrMatching"]], "debug ssreflect (flag)": [[57, "coq:flag.Debug-Ssreflect"]], "duplicate clear of h. use { }h instead of { h }h (warning)": [[57, "coq:warn.Duplicate-clear-of-H.-Use-{-}H-instead-of-{-H-}H"]], "hint view for (command)": [[57, "coq:cmd.Hint-View-for"]], "hint view for apply (command)": [[57, "coq:cmd.Hint-View-for-apply"]], "hint view for move (command)": [[57, "coq:cmd.Hint-View-for-move"]], "incorrect number of tactics (expected n tactics, was given m) (error)": [[57, "coq:exn.Incorrect-number-of-tactics-(expected-N-tactics,-was-given-M)"]], "prenex implicits (command)": [[57, "coq:cmd.Prenex-Implicits"]], "ssreflect: cannot obtain new equations out of ... (warning)": [[57, "coq:warn.SSReflect:-cannot-obtain-new-equations-out-of-..."]], "ssrhave notcresolution (flag)": [[57, "coq:flag.SsrHave-NoTCResolution"]], "ssridents (flag)": [[57, "coq:flag.SsrIdents"]], "ssroldrewritegoalsorder (flag)": [[57, "coq:flag.SsrOldRewriteGoalsOrder"]], "ssrrewrite (flag)": [[57, "coq:flag.SsrRewrite"]], "abstract (ssreflect) (tactic)": [[57, "coq:tacn.abstract-(ssreflect)"]], "apply (ssreflect) (tactic)": [[57, "coq:tacn.apply-(ssreflect)"]], "by (tactic)": [[57, "coq:tacn.by"]], "case (ssreflect) (tactic)": [[57, "coq:tacn.case-(ssreflect)"]], "congr (tactic)": [[57, "coq:tacn.congr"]], "do (ssreflect) (tactic)": [[57, "coq:tacn.do-(ssreflect)"]], "done (tactic)": [[57, "coq:tacn.done"]], "elim (ssreflect) (tactic)": [[57, "coq:tacn.elim-(ssreflect)"]], "exact (ssreflect) (tactic)": [[57, "coq:tacn.exact-(ssreflect)"]], "first (ssreflect) (tactic)": [[57, "coq:tacn.first-(ssreflect)"]], "first last (tactic variant)": [[57, "coq:tacv.first-last"]], "generally have (tactic)": [[57, "coq:tacn.generally-have"]], "have (tactic)": [[57, "coq:tacn.have"]], "in (tactic)": [[57, "coq:tacn.in"]], "last (tactic)": [[57, "coq:tacn.last"]], "last first (tactic variant)": [[57, "coq:tacv.last-first"]], "move (ssreflect) (tactic)": [[57, "coq:tacn.move-(ssreflect)"]], "over (tactic)": [[57, "coq:tacn.over"]], "pose (ssreflect) (tactic)": [[57, "coq:tacn.pose-(ssreflect)"]], "rewrite (ssreflect) (tactic)": [[57, "coq:tacn.rewrite-(ssreflect)"]], "set (ssreflect) (tactic)": [[57, "coq:tacn.set-(ssreflect)"]], "suff (tactic)": [[57, "coq:tacn.suff"]], "suffices (tactic)": [[57, "coq:tacn.suffices"]], "under (tactic)": [[57, "coq:tacn.under"]], "unlock (tactic)": [[57, "coq:tacn.unlock"]], "without loss (tactic)": [[57, "coq:tacn.without-loss"]], "wlog (tactic)": [[57, "coq:tacn.wlog"]], "\u2026 : \u2026 (ssreflect) (tactic)": [[57, "coq:tacn.\u2026-:-\u2026-(ssreflect)"]], "cannot change \u2018ident\u2019, it is used in conclusion (error)": [[58, "coq:exn.Cannot-change-\u2018ident\u2019,-it-is-used-in-conclusion"]], "cannot change \u2018ident\u2019, it is used in hypothesis \u2018ident\u2019 (error)": [[58, "coq:exn.Cannot-change-\u2018ident\u2019,-it-is-used-in-hypothesis-\u2018ident\u2019"]], "cannot infer a term for this placeholder. (refine) (error)": [[58, "coq:exn.Cannot-infer-a-term-for-this-placeholder.-(refine)"]], "cannot move \u2018ident\u2019 after \u2018ident\u2019: it depends on \u2018ident\u2019 (error)": [[58, "coq:exn.Cannot-move-\u2018ident\u2019-after-\u2018ident\u2019:-it-depends-on-\u2018ident\u2019"]], "cannot move \u2018ident\u2019 after \u2018ident\u2019: it occurs in the type of \u2018ident\u2019 (error)": [[58, "coq:exn.Cannot-move-\u2018ident\u2019-after-\u2018ident\u2019:-it-occurs-in-the-type-of-\u2018ident\u2019"]], "default goal selector (option)": [[58, "coq:opt.Default-Goal-Selector"]], "no product even after head-reduction (error)": [[58, "coq:exn.No-product-even-after-head-reduction"]], "no quantified hypothesis named \u2018ident\u2019 in current goal even after head-reduction (error)": [[58, "coq:exn.No-quantified-hypothesis-named-\u2018ident\u2019-in-current-goal-even-after-head-reduction"]], "no such assumption (error)": [[58, "coq:exn.No-such-assumption"]], "no such binder (error)": [[58, "coq:exn.No-such-binder"]], "no such bound variable \u2018ident\u2019 (no bound variables at all in the expression) (error)": [[58, "coq:exn.No-such-bound-variable-\u2018ident\u2019-(no-bound-variables-at-all-in-the-expression)"]], "no such bound variable \u2018ident\u2019 (possible names are: \u2018ident\u2019 ...) (error)": [[58, "coq:exn.No-such-bound-variable-\u2018ident\u2019-(possible-names-are:-\u2018ident\u2019-...)"]], "no such hypothesis: \u2018ident\u2019 (error)": [[58, "coq:exn.No-such-hypothesis:-\u2018ident\u2019"]], "no \u2018natural\u2019-th non dependent hypothesis in current goal even after head-reduction (error)": [[58, "coq:exn.No-\u2018natural\u2019-th-non-dependent-hypothesis-in-current-goal-even-after-head-reduction"]], "not an exact proof (error)": [[58, "coq:exn.Not-an-exact-proof"]], "not the right number of missing arguments (expected \u2018natural\u2019) (error)": [[58, "coq:exn.Not-the-right-number-of-missing-arguments-(expected-\u2018natural\u2019)"]], "proof is not complete. (assert) (error)": [[58, "coq:exn.Proof-is-not-complete.-(assert)"]], "the term \"\u2018type\u2019\" has type \"\u2018type\u2019\" which should be set, prop or type (error)": [[58, "coq:exn.The-term-\"\u2018type\u2019\"-has-type-\"\u2018type\u2019\"-which-should-be-Set,-Prop-or-Type"]], "the variable \u2018ident\u2019 is already declared (error)": [[58, "coq:exn.The-variable-\u2018ident\u2019-is-already-declared"]], "unable to apply lemma of type \"...\" on hypothesis of type \"...\" (error)": [[58, "coq:exn.Unable-to-apply-lemma-of-type-\"...\"-on-hypothesis-of-type-\"...\""]], "unable to find an instance for the variables \u2018ident\u2019\u2026\u2018ident\u2019 (error)": [[58, "coq:exn.Unable-to-find-an-instance-for-the-variables-\u2018ident\u2019\u2026\u2018ident\u2019"]], "unable to unify \u2018one_term\u2019 with \u2018one_term\u2019 (error)": [[58, "coq:exn.Unable-to-unify-\u2018one_term\u2019-with-\u2018one_term\u2019"]], "absurd (tactic)": [[58, "coq:tacn.absurd"]], "apply (tactic)": [[58, "coq:tacn.apply"]], "assert (tactic)": [[58, "coq:tacn.assert"]], "assumption (tactic)": [[58, "coq:tacn.assumption"]], "classical_left (tactic)": [[58, "coq:tacn.classical_left"]], "classical_right (tactic)": [[58, "coq:tacn.classical_right"]], "clear (tactic)": [[58, "coq:tacn.clear"]], "clear dependent (tactic)": [[58, "coq:tacn.clear-dependent"]], "clearbody (tactic)": [[58, "coq:tacn.clearbody"]], "contradict (tactic)": [[58, "coq:tacn.contradict"]], "contradiction (tactic)": [[58, "coq:tacn.contradiction"]], "cut (tactic)": [[58, "coq:tacn.cut"]], "dependent generalize_eqs (tactic)": [[58, "coq:tacn.dependent-generalize_eqs"]], "dependent generalize_eqs_vars (tactic)": [[58, "coq:tacn.dependent-generalize_eqs_vars"]], "eapply (tactic)": [[58, "coq:tacn.eapply"]], "eassert (tactic)": [[58, "coq:tacn.eassert"]], "eassumption (tactic)": [[58, "coq:tacn.eassumption"]], "eenough (tactic)": [[58, "coq:tacn.eenough"]], "eexact (tactic)": [[58, "coq:tacn.eexact"]], "eintros (tactic)": [[58, "coq:tacn.eintros"]], "enough (tactic)": [[58, "coq:tacn.enough"]], "epose (tactic)": [[58, "coq:tacn.epose"]], "epose proof (tactic)": [[58, "coq:tacn.epose-proof"]], "eremember (tactic)": [[58, "coq:tacn.eremember"]], "eset (tactic)": [[58, "coq:tacn.eset"]], "evar (tactic)": [[58, "coq:tacn.evar"]], "exact (tactic)": [[58, "coq:tacn.exact"]], "exact_no_check (tactic)": [[58, "coq:tacn.exact_no_check"]], "exfalso (tactic)": [[58, "coq:tacn.exfalso"]], "generalize (tactic)": [[58, "coq:tacn.generalize"]], "generalize dependent (tactic)": [[58, "coq:tacn.generalize-dependent"]], "generalize_eqs (tactic)": [[58, "coq:tacn.generalize_eqs"]], "generalize_eqs_vars (tactic)": [[58, "coq:tacn.generalize_eqs_vars"]], "instantiate (tactic)": [[58, "coq:tacn.instantiate"]], "intro (tactic)": [[58, "coq:tacn.intro"]], "intros (tactic)": [[58, "coq:tacn.intros"]], "intros until (tactic)": [[58, "coq:tacn.intros-until"]], "lapply (tactic)": [[58, "coq:tacn.lapply"]], "lapply needs a non-dependent product (error)": [[58, "coq:exn.lapply-needs-a-non-dependent-product"]], "move (tactic)": [[58, "coq:tacn.move"]], "native_cast_no_check (tactic)": [[58, "coq:tacn.native_cast_no_check"]], "pose (tactic)": [[58, "coq:tacn.pose"]], "pose proof (tactic)": [[58, "coq:tacn.pose-proof"]], "rapply (tactic)": [[58, "coq:tacn.rapply"]], "refine (tactic)": [[58, "coq:tacn.refine"]], "remember (tactic)": [[58, "coq:tacn.remember"]], "rename (tactic)": [[58, "coq:tacn.rename"]], "revert (tactic)": [[58, "coq:tacn.revert"]], "revert dependent (tactic)": [[58, "coq:tacn.revert-dependent"]], "set (tactic)": [[58, "coq:tacn.set"]], "simple apply (tactic)": [[58, "coq:tacn.simple-apply"]], "simple eapply (tactic)": [[58, "coq:tacn.simple-eapply"]], "specialize (tactic)": [[58, "coq:tacn.specialize"]], "specialize_eqs (tactic)": [[58, "coq:tacn.specialize_eqs"]], "vm_cast_no_check (tactic)": [[58, "coq:tacn.vm_cast_no_check"]], "\u2018ident\u2019 is already used (error)": [[58, "coq:exn.\u2018ident\u2019-is-already-used"]], "\u2018ident\u2019 is not a local definition (error)": [[58, "coq:exn.\u2018ident\u2019-is-not-a-local-definition"]], "\u2018ident\u2019 is used in the conclusion (error)": [[58, "coq:exn.\u2018ident\u2019-is-used-in-the-conclusion"]], "\u2018ident\u2019 is used in the hypothesis \u2018ident\u2019 (error)": [[58, "coq:exn.\u2018ident\u2019-is-used-in-the-hypothesis-\u2018ident\u2019"]], "about (command)": [[59, "coq:cmd.About"]], "back (command)": [[59, "coq:cmd.Back"]], "backto (command)": [[59, "coq:cmd.BackTo"]], "bad magic number (error)": [[59, "coq:exn.Bad-magic-number"]], "cannot find library foo in loadpath (error)": [[59, "coq:exn.Cannot-find-library-foo-in-loadpath"]], "cannot load \u2018qualid\u2019: no physical path bound to \u2018dirpath\u2019 (error)": [[59, "coq:exn.Cannot-load-\u2018qualid\u2019:-no-physical-path-bound-to-\u2018dirpath\u2019"]], "can\u2019t find file \u2018ident\u2019 on loadpath (error)": [[59, "coq:exn.Can\u2019t-find-file-\u2018ident\u2019-on-loadpath"]], "check (command)": [[59, "coq:cmd.Check"]], "compiled library \u2018ident\u2019.vo makes inconsistent assumptions over library \u2018qualid\u2019 (error)": [[59, "coq:exn.Compiled-library-\u2018ident\u2019.vo-makes-inconsistent-assumptions-over-library-\u2018qualid\u2019"]], "debug (option)": [[59, "coq:opt.Debug"]], "declare ml module (command)": [[59, "coq:cmd.Declare-ML-Module"]], "default timeout (option)": [[59, "coq:opt.Default-Timeout"]], "drop (command)": [[59, "coq:cmd.Drop"]], "dynlink error: execution of module initializers in the (error)": [[59, "coq:exn.Dynlink-error:-execution-of-module-initializers-in-the"]], "fail (command)": [[59, "coq:cmd.Fail"]], "fast name printing (flag)": [[59, "coq:flag.Fast-Name-Printing"]], "file ... found twice in ... (warning)": [[59, "coq:warn.File-...-found-twice-in-..."]], "file not found on loadpath: \u2018string\u2019 (error)": [[59, "coq:exn.File-not-found-on-loadpath:-\u2018string\u2019"]], "files processed by load cannot leave open proofs (error)": [[59, "coq:exn.Files-processed-by-Load-cannot-leave-open-proofs"]], "from \u2026 dependency (command)": [[59, "coq:cmd.From-\u2026-Dependency"]], "from \u2026 require (command)": [[59, "coq:cmd.From-\u2026-Require"]], "guard checking (flag)": [[59, "coq:flag.Guard-Checking"]], "inspect (command)": [[59, "coq:cmd.Inspect"]], "instructions (command)": [[59, "coq:cmd.Instructions"]], "invalid backtrack (error)": [[59, "coq:exn.Invalid-backtrack"]], "load (command)": [[59, "coq:cmd.Load"]], "load is not supported inside proofs (error)": [[59, "coq:exn.Load-is-not-supported-inside-proofs"]], "locate (command)": [[59, "coq:cmd.Locate"]], "locate file (command)": [[59, "coq:cmd.Locate-File"]], "locate library (command)": [[59, "coq:cmd.Locate-Library"]], "locate ltac (command)": [[59, "coq:cmd.Locate-Ltac"]], "locate ltac2 (command)": [[59, "coq:cmd.Locate-Ltac2"]], "locate module (command)": [[59, "coq:cmd.Locate-Module"]], "locate term (command)": [[59, "coq:cmd.Locate-Term"]], "module/section \u2018qualid\u2019 not found (error)": [[59, "coq:exn.Module/section-\u2018qualid\u2019-not-found"]], "positivity checking (flag)": [[59, "coq:flag.Positivity-Checking"]], "primitive (command)": [[59, "coq:cmd.Primitive"]], "print (command)": [[59, "coq:cmd.Print"]], "print all (command)": [[59, "coq:cmd.Print-All"]], "print all dependencies (command)": [[59, "coq:cmd.Print-All-Dependencies"]], "print assumptions (command)": [[59, "coq:cmd.Print-Assumptions"]], "print libraries (command)": [[59, "coq:cmd.Print-Libraries"]], "print loadpath (command)": [[59, "coq:cmd.Print-LoadPath"]], "print ml modules (command)": [[59, "coq:cmd.Print-ML-Modules"]], "print ml path (command)": [[59, "coq:cmd.Print-ML-Path"]], "print opaque dependencies (command)": [[59, "coq:cmd.Print-Opaque-Dependencies"]], "print registered (command)": [[59, "coq:cmd.Print-Registered"]], "print registered schemes (command)": [[59, "coq:cmd.Print-Registered-Schemes"]], "print section (command)": [[59, "coq:cmd.Print-Section"]], "print transparent dependencies (command)": [[59, "coq:cmd.Print-Transparent-Dependencies"]], "print typing flags (command)": [[59, "coq:cmd.Print-Typing-Flags"]], "printing all (flag)": [[59, "coq:flag.Printing-All"]], "printing compact contexts (flag)": [[59, "coq:flag.Printing-Compact-Contexts"]], "printing dependent evars line (flag)": [[59, "coq:flag.Printing-Dependent-Evars-Line"]], "printing depth (option)": [[59, "coq:opt.Printing-Depth"]], "printing unfocused (flag)": [[59, "coq:flag.Printing-Unfocused"]], "printing width (option)": [[59, "coq:opt.Printing-Width"]], "profile (command)": [[59, "coq:cmd.Profile"]], "quit (command)": [[59, "coq:cmd.Quit"]], "redirect (command)": [[59, "coq:cmd.Redirect"]], "register (command)": [[59, "coq:cmd.Register"]], "register inline (command)": [[59, "coq:cmd.Register-Inline"]], "register scheme (command)": [[59, "coq:cmd.Register-Scheme"]], "require (command)": [[59, "coq:cmd.Require"]], "require export (command)": [[59, "coq:cmd.Require-Export"]], "require import (command)": [[59, "coq:cmd.Require-Import"]], "require inside a module is deprecated and strongly discouraged. you can require a module at toplevel and optionally import it inside another one (warning)": [[59, "coq:warn.Require-inside-a-module-is-deprecated-and-strongly-discouraged.-You-can-Require-a-module-at-toplevel-and-optionally-Import-it-inside-another-one"]], "required library \u2018qualid\u2019 matches several files in path (found file.vo, file.vo, ...) (error)": [[59, "coq:exn.Required-library-\u2018qualid\u2019-matches-several-files-in-path-(found-file.vo,-file.vo,-...)"]], "reset (command)": [[59, "coq:cmd.Reset"]], "reset initial (command)": [[59, "coq:cmd.Reset-Initial"]], "search (command)": [[59, "coq:cmd.Search"]], "search blacklist (table)": [[59, "coq:table.Search-Blacklist"]], "search output name only (flag)": [[59, "coq:flag.Search-Output-Name-Only"]], "searchpattern (command)": [[59, "coq:cmd.SearchPattern"]], "searchrewrite (command)": [[59, "coq:cmd.SearchRewrite"]], "silent (flag)": [[59, "coq:flag.Silent"]], "succeed (command)": [[59, "coq:cmd.Succeed"]], "the command has not failed! (error)": [[59, "coq:exn.The-command-has-not-failed!"]], "the file \u2018ident\u2019.vo contains library \u2018qualid\u2019 and not library \u2018qualid\u2019 (error)": [[59, "coq:exn.The-file-\u2018ident\u2019.vo-contains-library-\u2018qualid\u2019-and-not-library-\u2018qualid\u2019"]], "the type \u2018ident\u2019 must be registered before this construction can be typechecked (error)": [[59, "coq:exn.The-type-\u2018ident\u2019-must-be-registered-before-this-construction-can-be-typechecked"]], "this object does not support universe names (error)": [[59, "coq:exn.This-object-does-not-support-universe-names"]], "time (command)": [[59, "coq:cmd.Time"]], "timeout (command)": [[59, "coq:cmd.Timeout"]], "type (command)": [[59, "coq:cmd.Type"]], "universe checking (flag)": [[59, "coq:flag.Universe-Checking"]], "universe instance length is \u2018natural\u2019 but should be \u2018natural\u2019 (error)": [[59, "coq:exn.Universe-instance-length-is-\u2018natural\u2019-but-should-be-\u2018natural\u2019"]], "warnings (option)": [[59, "coq:opt.Warnings"]], "bypass_check(guard) (attribute)": [[59, "coq:attr.bypass_check(guard)"]], "bypass_check(positivity) (attribute)": [[59, "coq:attr.bypass_check(positivity)"]], "bypass_check(universes) (attribute)": [[59, "coq:attr.bypass_check(universes)"]], "package-name.foo and not foo_plugin (error)": [[59, "coq:exn.package-name.foo-and-not-foo_plugin"]], "plugin name anymore. plugins should be loaded using their (error)": [[59, "coq:exn.plugin-name-anymore.-Plugins-should-be-loaded-using-their"]], "public name according to findlib, for example (error)": [[59, "coq:exn.public-name-according-to-findlib,-for-example"]], "shared library failed: coq error: \u2018string\u2019 is not a valid (error)": [[59, "coq:exn.shared-library-failed:-Coq-Error:-\u2018string\u2019-is-not-a-valid"]], "\u2018qualid\u2019 not a defined object (error)": [[59, "coq:exn.\u2018qualid\u2019-not-a-defined-object"]], "cannot coerce \u2018qualid\u2019 to an evaluable reference (error)": [[60, "coq:exn.Cannot-coerce-\u2018qualid\u2019-to-an-evaluable-reference"]], "create hintdb (command)": [[60, "coq:cmd.Create-HintDb"]], "debug auto (flag)": [[60, "coq:flag.Debug-Auto"]], "debug eauto (flag)": [[60, "coq:flag.Debug-Eauto"]], "debug trivial (flag)": [[60, "coq:flag.Debug-Trivial"]], "declaring arbitrary terms as hints is fragile and deprecated": [[60, "coq:warn.Declaring-arbitrary-terms-as-hints-is-fragile-and-deprecated;-it-is-recommended-to-declare-a-toplevel-constant-instead"]], "hint constants (command)": [[60, "coq:cmd.Hint-Constants"]], "hint constructors (command)": [[60, "coq:cmd.Hint-Constructors"]], "hint cut (command)": [[60, "coq:cmd.Hint-Cut"]], "hint extern (command)": [[60, "coq:cmd.Hint-Extern"]], "hint immediate (command)": [[60, "coq:cmd.Hint-Immediate"]], "hint mode (command)": [[60, "coq:cmd.Hint-Mode"]], "hint opaque (command)": [[60, "coq:cmd.Hint-Opaque"]], "hint projections (command)": [[60, "coq:cmd.Hint-Projections"]], "hint resolve (command)": [[60, "coq:cmd.Hint-Resolve"]], "hint rewrite (command)": [[60, "coq:cmd.Hint-Rewrite"]], "hint transparent (command)": [[60, "coq:cmd.Hint-Transparent"]], "hint unfold (command)": [[60, "coq:cmd.Hint-Unfold"]], "hint variables (command)": [[60, "coq:cmd.Hint-Variables"]], "info auto (flag)": [[60, "coq:flag.Info-Auto"]], "info eauto (flag)": [[60, "coq:flag.Info-Eauto"]], "info trivial (flag)": [[60, "coq:flag.Info-Trivial"]], "loose hint behavior (option)": [[60, "coq:opt.Loose-Hint-Behavior"]], "print hint (command)": [[60, "coq:cmd.Print-Hint"]], "print hintdb (command)": [[60, "coq:cmd.Print-HintDb"]], "print rewrite hintdb (command)": [[60, "coq:cmd.Print-Rewrite-HintDb"]], "proof with (command)": [[60, "coq:cmd.Proof-with"]], "remove hints (command)": [[60, "coq:cmd.Remove-Hints"]], "the \"at\" syntax isn't available yet for the autorewrite tactic (error)": [[60, "coq:exn.The-\"at\"-syntax-isn't-available-yet-for-the-autorewrite-tactic"]], "this hint is not local but depends on a section variable. it will disappear when the section is closed (warning)": [[60, "coq:warn.This-hint-is-not-local-but-depends-on-a-section-variable.-It-will-disappear-when-the-section-is-closed"]], "auto (tactic)": [[60, "coq:tacn.auto"]], "autorewrite (tactic)": [[60, "coq:tacn.autorewrite"]], "autounfold (tactic)": [[60, "coq:tacn.autounfold"]], "autounfold_one (tactic)": [[60, "coq:tacn.autounfold_one"]], "debug auto (tactic)": [[60, "coq:tacn.debug-auto"]], "debug eauto (tactic)": [[60, "coq:tacn.debug-eauto"]], "debug trivial (tactic)": [[60, "coq:tacn.debug-trivial"]], "easy (tactic)": [[60, "coq:tacn.easy"]], "eauto (tactic)": [[60, "coq:tacn.eauto"]], "info_auto (tactic)": [[60, "coq:tacn.info_auto"]], "info_eauto (tactic)": [[60, "coq:tacn.info_eauto"]], "info_trivial (tactic)": [[60, "coq:tacn.info_trivial"]], "it is recommended to declare a toplevel constant instead (warning)": [[60, "coq:warn.Declaring-arbitrary-terms-as-hints-is-fragile-and-deprecated;-it-is-recommended-to-declare-a-toplevel-constant-instead"]], "mismatched-hint-db (warning)": [[60, "coq:warn.mismatched-hint-db"]], "now (tactic)": [[60, "coq:tacn.now"]], "trivial (tactic)": [[60, "coq:tacn.trivial"]], "\u2018qualid\u2019 cannot be used as a hint (error)": [[60, "coq:exn.\u2018qualid\u2019-cannot-be-used-as-a-hint"]], "\u2018qualid\u2019 is not an inductive type (error)": [[60, "coq:exn.\u2018qualid\u2019-is-not-an-inductive-type"]], "cannot recognize a boolean equality (error)": [[62, "coq:exn.Cannot-recognize-a-boolean-equality"]], "firstorder depth (option)": [[62, "coq:opt.Firstorder-Depth"]], "firstorder solver (option)": [[62, "coq:opt.Firstorder-Solver"]], "goal is solvable by congruence but some arguments are missing. try congruence with \u2018term\u2019\u2026\u2018term\u2019, replacing metavariables by arbitrary terms (error)": [[62, "coq:exn.Goal-is-solvable-by-congruence-but-some-arguments-are-missing.-Try-congruence-with-\u2018term\u2019\u2026\u2018term\u2019,-replacing-metavariables-by-arbitrary-terms"]], "i don\u2019t know how to handle dependent equality (error)": [[62, "coq:exn.I-don\u2019t-know-how-to-handle-dependent-equality"]], "intuition negation unfolding (flag)": [[62, "coq:flag.Intuition-Negation-Unfolding"]], "print firstorder solver (command)": [[62, "coq:cmd.Print-Firstorder-Solver"]], "btauto (tactic)": [[62, "coq:tacn.btauto"]], "congruence (tactic)": [[62, "coq:tacn.congruence"]], "dintuition (tactic)": [[62, "coq:tacn.dintuition"]], "dtauto (tactic)": [[62, "coq:tacn.dtauto"]], "firstorder (tactic)": [[62, "coq:tacn.firstorder"]], "intuition (tactic)": [[62, "coq:tacn.intuition"]], "rtauto (tactic)": [[62, "coq:tacn.rtauto"]], "simple congruence (tactic)": [[62, "coq:tacn.simple-congruence"]], "tauto (tactic)": [[62, "coq:tacn.tauto"]], "bad occurrence number of \u2018qualid\u2019 (error)": [[64, "coq:exn.Bad-occurrence-number-of-\u2018qualid\u2019"]], "cannot find a relation to rewrite (error)": [[64, "coq:exn.Cannot-find-a-relation-to-rewrite"]], "cannot find any non-recursive equality over \u2018ident\u2019 (error)": [[64, "coq:exn.Cannot-find-any-non-recursive-equality-over-\u2018ident\u2019"]], "cannot turn [inductive|constructor] into an evaluable reference (error)": [[64, "coq:exn.Cannot-turn-[inductive|constructor]-into-an-evaluable-reference"]], "compute (command)": [[64, "coq:cmd.Compute"]], "declare equivalent keys (command)": [[64, "coq:cmd.Declare-Equivalent-Keys"]], "declare left step (command)": [[64, "coq:cmd.Declare-Left-Step"]], "declare reduction (command)": [[64, "coq:cmd.Declare-Reduction"]], "declare right step (command)": [[64, "coq:cmd.Declare-Right-Step"]], "eval (command)": [[64, "coq:cmd.Eval"]], "found an \"at\" clause without \"with\" clause (error)": [[64, "coq:exn.Found-an-\"at\"-clause-without-\"with\"-clause"]], "found no subterm matching \u2018term\u2019 in the current goal (error)": [[64, "coq:exn.Found-no-subterm-matching-\u2018term\u2019-in-the-current-goal"]], "found no subterm matching \u2018term\u2019 in \u2018ident\u2019 (error)": [[64, "coq:exn.Found-no-subterm-matching-\u2018term\u2019-in-\u2018ident\u2019"]], "kernel term sharing (flag)": [[64, "coq:flag.Kernel-Term-Sharing"]], "keyed unification (flag)": [[64, "coq:flag.Keyed-Unification"]], "nativecompute profile filename (option)": [[64, "coq:opt.NativeCompute-Profile-Filename"]], "nativecompute profiling (flag)": [[64, "coq:flag.NativeCompute-Profiling"]], "nativecompute timing (flag)": [[64, "coq:flag.NativeCompute-Timing"]], "no head constant to reduce (error)": [[64, "coq:exn.No-head-constant-to-reduce"]], "not convertible (error)": [[64, "coq:exn.Not-convertible"]], "opaque (command)": [[64, "coq:cmd.Opaque"]], "print equivalent keys (command)": [[64, "coq:cmd.Print-Equivalent-Keys"]], "print strategies (command)": [[64, "coq:cmd.Print-Strategies"]], "print strategy (command)": [[64, "coq:cmd.Print-Strategy"]], "regular subst tactic (flag)": [[64, "coq:flag.Regular-Subst-Tactic"]], "section variable \u2018ident\u2019 occurs implicitly in global declaration \u2018qualid\u2019 present in hypothesis \u2018ident\u2019 (error)": [[64, "coq:exn.Section-variable-\u2018ident\u2019-occurs-implicitly-in-global-declaration-\u2018qualid\u2019-present-in-hypothesis-\u2018ident\u2019"]], "section variable \u2018ident\u2019 occurs implicitly in global declaration \u2018qualid\u2019 present in the conclusion (error)": [[64, "coq:exn.Section-variable-\u2018ident\u2019-occurs-implicitly-in-global-declaration-\u2018qualid\u2019-present-in-the-conclusion"]], "strategy (command)": [[64, "coq:cmd.Strategy"]], "tactic failure: setoid library not loaded (error)": [[64, "coq:exn.Tactic-failure:-Setoid-library-not-loaded"]], "tactic generated a subgoal identical to the original goal (error)": [[64, "coq:exn.Tactic-generated-a-subgoal-identical-to-the-original-goal"]], "terms do not have convertible types (error)": [[64, "coq:exn.Terms-do-not-have-convertible-types"]], "the reference is not unfoldable (error)": [[64, "coq:exn.The-reference-is-not-unfoldable"]], "the reference \u2018qualid\u2019 was not found in the current environment (error)": [[64, "coq:exn.The-reference-\u2018qualid\u2019-was-not-found-in-the-current-environment"]], "the relation \u2018ident\u2019 is not a declared reflexive relation. maybe you need to require the stdlib.classes.relationclasses library (error)": [[64, "coq:exn.The-relation-\u2018ident\u2019-is-not-a-declared-reflexive-relation.-Maybe-you-need-to-require-the-Stdlib.Classes.RelationClasses-library"]], "the relation \u2018ident\u2019 is not a declared symmetric relation. maybe you need to require the stdlib.classes.relationclasses library (error)": [[64, "coq:exn.The-relation-\u2018ident\u2019-is-not-a-declared-symmetric-relation.-Maybe-you-need-to-require-the-Stdlib.Classes.RelationClasses-library"]], "the relation \u2018ident\u2019 is not a declared transitive relation. maybe you need to require the stdlib.classes.relationclasses library (error)": [[64, "coq:exn.The-relation-\u2018ident\u2019-is-not-a-declared-transitive-relation.-Maybe-you-need-to-require-the-Stdlib.Classes.RelationClasses-library"]], "transparent (command)": [[64, "coq:cmd.Transparent"]], "cbn (tactic)": [[64, "coq:tacn.cbn"]], "cbv (tactic)": [[64, "coq:tacn.cbv"]], "change (tactic)": [[64, "coq:tacn.change"]], "change_no_check (tactic)": [[64, "coq:tacn.change_no_check"]], "compute (tactic)": [[64, "coq:tacn.compute"]], "erewrite (tactic)": [[64, "coq:tacn.erewrite"]], "etransitivity (tactic)": [[64, "coq:tacn.etransitivity"]], "eval (tactic)": [[64, "coq:tacn.eval"]], "f_equal (tactic)": [[64, "coq:tacn.f_equal"]], "fold (tactic)": [[64, "coq:tacn.fold"]], "hnf (tactic)": [[64, "coq:tacn.hnf"]], "lazy (tactic)": [[64, "coq:tacn.lazy"]], "native_compute (tactic)": [[64, "coq:tacn.native_compute"]], "now_show (tactic)": [[64, "coq:tacn.now_show"]], "pattern (tactic)": [[64, "coq:tacn.pattern"]], "red (tactic)": [[64, "coq:tacn.red"]], "reflexivity (tactic)": [[64, "coq:tacn.reflexivity"]], "replace (tactic)": [[64, "coq:tacn.replace"]], "rewrite (tactic)": [[64, "coq:tacn.rewrite"]], "rewrite * (tactic)": [[64, "coq:tacn.rewrite-*"]], "simpl (tactic)": [[64, "coq:tacn.simpl"]], "simple subst (tactic)": [[64, "coq:tacn.simple-subst"]], "stepl (tactic)": [[64, "coq:tacn.stepl"]], "stepr (tactic)": [[64, "coq:tacn.stepr"]], "subst (tactic)": [[64, "coq:tacn.subst"]], "substitute (tactic)": [[64, "coq:tacn.substitute"]], "symmetry (tactic)": [[64, "coq:tacn.symmetry"]], "transitivity (tactic)": [[64, "coq:tacn.transitivity"]], "unfold (tactic)": [[64, "coq:tacn.unfold"]], "vm_compute (tactic)": [[64, "coq:tacn.vm_compute"]], "with_strategy (tactic)": [[64, "coq:tacn.with_strategy"]], "\u2018ident\u2019 is opaque (error)": [[64, "coq:exn.\u2018ident\u2019-is-opaque"]], "\u2018qualid\u2019 does not occur (error)": [[64, "coq:exn.\u2018qualid\u2019-does-not-occur"]], "\"all\" is a predefined collection containing all variables. it can't be redefined (error)": [[66, "coq:exn.\"All\"-is-a-predefined-collection-containing-all-variables.-It-can't-be-redefined"]], "abort (command)": [[66, "coq:cmd.Abort"]], "admitted (command)": [[66, "coq:cmd.Admitted"]], "attempt to save an incomplete proof (error)": [[66, "coq:exn.Attempt-to-save-an-incomplete-proof"]], "brackets do not support multi-goal selectors (error)": [[66, "coq:exn.Brackets-do-not-support-multi-goal-selectors"]], "bullet behavior (option)": [[66, "coq:opt.Bullet-Behavior"]], "collection (command)": [[66, "coq:cmd.Collection"]], "default proof mode (option)": [[66, "coq:opt.Default-Proof-Mode"]], "default proof using (option)": [[66, "coq:opt.Default-Proof-Using"]], "defined (command)": [[66, "coq:cmd.Defined"]], "diffs (option)": [[66, "coq:opt.Diffs"]], "focus (command)": [[66, "coq:cmd.Focus"]], "goal (command)": [[66, "coq:cmd.Goal"]], "guarded (command)": [[66, "coq:cmd.Guarded"]], "hyps limit (option)": [[66, "coq:opt.Hyps-Limit"]], "mangle names (flag)": [[66, "coq:flag.Mangle-Names"]], "mangle names light (flag)": [[66, "coq:flag.Mangle-Names-Light"]], "mangle names prefix (option)": [[66, "coq:opt.Mangle-Names-Prefix"]], "nested proofs allowed (flag)": [[66, "coq:flag.Nested-Proofs-Allowed"]], "new collection definition of \u2018ident\u2019 shadows the previous one (warning)": [[66, "coq:warn.New-Collection-definition-of-\u2018ident\u2019-shadows-the-previous-one"]], "no focused proof (no proof-editing in progress) (error)": [[66, "coq:exn.No-focused-proof-(No-proof-editing-in-progress)"]], "no focused proof (error)": [[66, "coq:exn.No-focused-proof"]], "no focused proof to restart (error)": [[66, "coq:exn.No-focused-proof-to-restart"]], "no such goal (error)": [[66, "coq:exn.No-such-goal"]], "no such goal (\u2018ident\u2019) (error)": [[66, "coq:exn.No-such-goal-(\u2018ident\u2019)"]], "no such goal (\u2018natural\u2019) (error)": [[66, "coq:exn.No-such-goal-(\u2018natural\u2019)"]], "no such goal. focus next goal with bullet \u2018bullet\u2019 (error)": [[66, "coq:exn.No-such-goal.-Focus-next-goal-with-bullet-\u2018bullet\u2019"]], "no such goal. try unfocusing with } (error)": [[66, "coq:exn.No-such-goal.-Try-unfocusing-with-}"]], "optimize heap (command)": [[66, "coq:cmd.Optimize-Heap"]], "optimize proof (command)": [[66, "coq:cmd.Optimize-Proof"]], "print debug gc (command)": [[66, "coq:cmd.Print-Debug-GC"]], "printing goal names (flag)": [[66, "coq:flag.Printing-Goal-Names"]], "printing goal tags (flag)": [[66, "coq:flag.Printing-Goal-Tags"]], "proof (command)": [[66, "coq:cmd.Proof"]], "proof mode (command)": [[66, "coq:cmd.Proof-Mode"]], "proof `term` (command)": [[66, "coq:cmd.Proof-`term`"]], "proof is not complete. (abstract) (error)": [[66, "coq:exn.Proof-is-not-complete.-(abstract)"]], "proof using (command)": [[66, "coq:cmd.Proof-using"]], "qed (command)": [[66, "coq:cmd.Qed"]], "restart (command)": [[66, "coq:cmd.Restart"]], "save (command)": [[66, "coq:cmd.Save"]], "show (command)": [[66, "coq:cmd.Show"]], "show conjectures (command)": [[66, "coq:cmd.Show-Conjectures"]], "show existentials (command)": [[66, "coq:cmd.Show-Existentials"]], "show goal (command)": [[66, "coq:cmd.Show-Goal"]], "show intro (command)": [[66, "coq:cmd.Show-Intro"]], "show intros (command)": [[66, "coq:cmd.Show-Intros"]], "show match (command)": [[66, "coq:cmd.Show-Match"]], "show proof (command)": [[66, "coq:cmd.Show-Proof"]], "show universes (command)": [[66, "coq:cmd.Show-Universes"]], "solve unification constraints (flag)": [[66, "coq:flag.Solve-Unification-Constraints"]], "suggest proof using (flag)": [[66, "coq:flag.Suggest-Proof-Using"]], "this proof is focused, but cannot be unfocused this way (error)": [[66, "coq:exn.This-proof-is-focused,-but-cannot-be-unfocused-this-way"]], "undo (command)": [[66, "coq:cmd.Undo"]], "unfocus (command)": [[66, "coq:cmd.Unfocus"]], "unfocused (command)": [[66, "coq:cmd.Unfocused"]], "unknown inductive type (error)": [[66, "coq:exn.Unknown-inductive-type"]], "unshelve (command)": [[66, "coq:cmd.Unshelve"]], "validate proof (command)": [[66, "coq:cmd.Validate-Proof"]], "variable all is shadowed by collection named all containing all variables (warning)": [[66, "coq:warn.Variable-All-is-shadowed-by-Collection-named-All-containing-all-variables"]], "wrong bullet \u2018bullet\u2019: bullet \u2018bullet\u2019 is mandatory here (error)": [[66, "coq:exn.Wrong-bullet-\u2018bullet\u2019:-Bullet-\u2018bullet\u2019-is-mandatory-here"]], "wrong bullet \u2018bullet\u2019: current bullet \u2018bullet\u2019 is not finished (error)": [[66, "coq:exn.Wrong-bullet-\u2018bullet\u2019:-Current-bullet-\u2018bullet\u2019-is-not-finished"]], "abstract (tactic)": [[66, "coq:tacn.abstract"]], "admit (tactic)": [[66, "coq:tacn.admit"]], "bullet (- + *) (tactic)": [[66, "coq:tacn.bullet-(--+-*)"]], "cycle (tactic)": [[66, "coq:tacn.cycle"]], "give_up (tactic)": [[66, "coq:tacn.give_up"]], "revgoals (tactic)": [[66, "coq:tacn.revgoals"]], "shelve (tactic)": [[66, "coq:tacn.shelve"]], "shelve_unifiable (tactic)": [[66, "coq:tacn.shelve_unifiable"]], "solve_constraints (tactic)": [[66, "coq:tacn.solve_constraints"]], "swap (tactic)": [[66, "coq:tacn.swap"]], "transparent_abstract (tactic)": [[66, "coq:tacn.transparent_abstract"]], "unshelve (tactic)": [[66, "coq:tacn.unshelve"]], "using (attribute)": [[66, "coq:attr.using"]], "{ (tactic)": [[66, "coq:tacn.{"]], "} (tactic)": [[66, "coq:tacn.}"]], "\u2018ident\u2019 is both name of a collection and variable, collection \u2018ident\u2019 takes precedence over variable (warning)": [[66, "coq:warn.\u2018ident\u2019-is-both-name-of-a-Collection-and-Variable,-Collection-\u2018ident\u2019-takes-precedence-over-Variable"]], "\u2018ident\u2019 was already a defined variable, the name \u2018ident\u2019 will refer to collection when executing \"proof using\" command (warning)": [[66, "coq:warn.\u2018ident\u2019-was-already-a-defined-Variable,-the-name-\u2018ident\u2019-will-refer-to-Collection-when-executing-\"Proof-using\"-command"]], "boolean equality schemes (flag)": [[67, "coq:flag.Boolean-Equality-Schemes"]], "cannot recognize a statement based on \u2018reference\u2019 (error)": [[67, "coq:exn.Cannot-recognize-a-statement-based-on-\u2018reference\u2019"]], "case analysis schemes (flag)": [[67, "coq:flag.Case-Analysis-Schemes"]], "combined scheme (command)": [[67, "coq:cmd.Combined-Scheme"]], "decidable equality schemes (flag)": [[67, "coq:flag.Decidable-Equality-Schemes"]], "derive dependent inversion (command)": [[67, "coq:cmd.Derive-Dependent-Inversion"]], "derive dependent inversion_clear (command)": [[67, "coq:cmd.Derive-Dependent-Inversion_clear"]], "derive inversion (command)": [[67, "coq:cmd.Derive-Inversion"]], "derive inversion_clear (command)": [[67, "coq:cmd.Derive-Inversion_clear"]], "elimination schemes (flag)": [[67, "coq:flag.Elimination-Schemes"]], "keep equalities (table)": [[67, "coq:table.Keep-Equalities"]], "keep proof equalities (flag)": [[67, "coq:flag.Keep-Proof-Equalities"]], "no information can be deduced from this equality and the injectivity of constructors. this may be because the terms are convertible, or due to pattern matching restrictions in the sort prop. you can try to use option set keep proof equalities (error)": [[67, "coq:exn.No-information-can-be-deduced-from-this-equality-and-the-injectivity-of-constructors.-This-may-be-because-the-terms-are-convertible,-or-due-to-pattern-matching-restrictions-in-the-sort-Prop.-You-can-try-to-use-option-Set-Keep-Proof-Equalities"]], "no primitive equality found (error)": [[67, "coq:exn.No-primitive-equality-found"]], "nonrecursive elimination schemes (flag)": [[67, "coq:flag.Nonrecursive-Elimination-Schemes"]], "not a discriminable equality (error)": [[67, "coq:exn.Not-a-discriminable-equality"]], "not a negated primitive equality (error)": [[67, "coq:exn.Not-a-negated-primitive-equality"]], "not an inductive goal with 1 constructor (error)": [[67, "coq:exn.Not-an-inductive-goal-with-1-constructor"]], "not an inductive goal with 2 constructors (error)": [[67, "coq:exn.Not-an-inductive-goal-with-2-constructors"]], "not an inductive product (error)": [[67, "coq:exn.Not-an-inductive-product"]], "not enough constructors (error)": [[67, "coq:exn.Not-enough-constructors"]], "nothing to inject (error)": [[67, "coq:exn.Nothing-to-inject"]], "rewriting schemes (flag)": [[67, "coq:flag.Rewriting-Schemes"]], "scheme (command)": [[67, "coq:cmd.Scheme"]], "scheme boolean equality (command)": [[67, "coq:cmd.Scheme-Boolean-Equality"]], "scheme equality (command)": [[67, "coq:cmd.Scheme-Equality"]], "structural injection (flag)": [[67, "coq:flag.Structural-Injection"]], "the type has no constructors (error)": [[67, "coq:exn.The-type-has-no-constructors"]], "type of \u2018ident\u2019 is not an equality of recognized \u03c3 types: expected one of sig sig2 sigt sigt2 sigt2 ex or ex2 but got \u2018term\u2019 (error)": [[67, "coq:exn.Type-of-\u2018ident\u2019-is-not-an-equality-of-recognized-\u03a3-types:-expected-one-of-sig-sig2-sigT-sigT2-sigT2-ex-or-ex2-but-got-\u2018term\u2019"]], "unable to find an instance for the variables \u2018ident\u2019 \u2026 \u2018ident\u2019 (error)": [[67, "coq:exn.Unable-to-find-an-instance-for-the-variables-\u2018ident\u2019-\u2026-\u2018ident\u2019"]], "case (tactic)": [[67, "coq:tacn.case"]], "case_eq (tactic)": [[67, "coq:tacn.case_eq"]], "cofix (tactic)": [[67, "coq:tacn.cofix"]], "compare (tactic)": [[67, "coq:tacn.compare"]], "constructor (tactic)": [[67, "coq:tacn.constructor"]], "decide (tactic)": [[67, "coq:tacn.decide"]], "decide equality (tactic)": [[67, "coq:tacn.decide-equality"]], "decompose (tactic)": [[67, "coq:tacn.decompose"]], "decompose record (tactic)": [[67, "coq:tacn.decompose-record"]], "decompose sum (tactic)": [[67, "coq:tacn.decompose-sum"]], "dependent destruction (tactic)": [[67, "coq:tacn.dependent-destruction"]], "dependent induction (tactic)": [[67, "coq:tacn.dependent-induction"]], "dependent inversion (tactic)": [[67, "coq:tacn.dependent-inversion"]], "dependent inversion_clear (tactic)": [[67, "coq:tacn.dependent-inversion_clear"]], "dependent rewrite (tactic)": [[67, "coq:tacn.dependent-rewrite"]], "dependent simple inversion (tactic)": [[67, "coq:tacn.dependent-simple-inversion"]], "destauto (tactic)": [[67, "coq:tacn.destauto"]], "destruct (tactic)": [[67, "coq:tacn.destruct"]], "discriminate (tactic)": [[67, "coq:tacn.discriminate"]], "ecase (tactic)": [[67, "coq:tacn.ecase"]], "econstructor (tactic)": [[67, "coq:tacn.econstructor"]], "edestruct (tactic)": [[67, "coq:tacn.edestruct"]], "ediscriminate (tactic)": [[67, "coq:tacn.ediscriminate"]], "eelim (tactic)": [[67, "coq:tacn.eelim"]], "eexists (tactic)": [[67, "coq:tacn.eexists"]], "einduction (tactic)": [[67, "coq:tacn.einduction"]], "einjection (tactic)": [[67, "coq:tacn.einjection"]], "eleft (tactic)": [[67, "coq:tacn.eleft"]], "elim (tactic)": [[67, "coq:tacn.elim"]], "eright (tactic)": [[67, "coq:tacn.eright"]], "esimplify_eq (tactic)": [[67, "coq:tacn.esimplify_eq"]], "esplit (tactic)": [[67, "coq:tacn.esplit"]], "exists (tactic)": [[67, "coq:tacn.exists"]], "fix (tactic)": [[67, "coq:tacn.fix"]], "induction (tactic)": [[67, "coq:tacn.induction"]], "injection (tactic)": [[67, "coq:tacn.injection"]], "inversion (tactic)": [[67, "coq:tacn.inversion"]], "inversion_clear (tactic)": [[67, "coq:tacn.inversion_clear"]], "inversion_sigma (tactic)": [[67, "coq:tacn.inversion_sigma"]], "left (tactic)": [[67, "coq:tacn.left"]], "right (tactic)": [[67, "coq:tacn.right"]], "simple destruct (tactic)": [[67, "coq:tacn.simple-destruct"]], "simple induction (tactic)": [[67, "coq:tacn.simple-induction"]], "simple injection (tactic)": [[67, "coq:tacn.simple-injection"]], "simple inversion (tactic)": [[67, "coq:tacn.simple-inversion"]], "simplify_eq (tactic)": [[67, "coq:tacn.simplify_eq"]], "split (tactic)": [[67, "coq:tacn.split"]], "\u2018ident\u2019 is not an equality of \u03c3 types (error)": [[67, "coq:exn.\u2018ident\u2019-is-not-an-equality-of-\u03a3-types"]], "'via' and 'abstract' cannot be used together (error)": [[71, "coq:exn.'via'-and-'abstract'-cannot-be-used-together"]], "activation of abbreviations does not expect mentioning a grammar entry (warning)": [[71, "coq:warn.Activation-of-abbreviations-does-not-expect-mentioning-a-grammar-entry"]], "activation of abbreviations does not expect mentioning a scope (warning)": [[71, "coq:warn.Activation-of-abbreviations-does-not-expect-mentioning-a-scope"]], "bind scope (command)": [[71, "coq:cmd.Bind-Scope"]], "cannot interpret in \u2018scope_name\u2019 because \u2018qualid\u2019 could not be found in the current environment (error)": [[71, "coq:exn.Cannot-interpret-in-\u2018scope_name\u2019-because-\u2018qualid\u2019-could-not-be-found-in-the-current-environment"]], "cannot interpret this number as a value of type \u2018type\u2019 (error)": [[71, "coq:exn.Cannot-interpret-this-number-as-a-value-of-type-\u2018type\u2019"]], "cannot interpret this string as a value of type \u2018type\u2019 (error)": [[71, "coq:exn.Cannot-interpret-this-string-as-a-value-of-type-\u2018type\u2019"]], "close scope (command)": [[71, "coq:cmd.Close-Scope"]], "declare custom entry (command)": [[71, "coq:cmd.Declare-Custom-Entry"]], "declare scope (command)": [[71, "coq:cmd.Declare-Scope"]], "delimit scope (command)": [[71, "coq:cmd.Delimit-Scope"]], "disable notation (command)": [[71, "coq:cmd.Disable-Notation"]], "enable notation (command)": [[71, "coq:cmd.Enable-Notation"]], "end of quoted string not followed by a space in notation (error)": [[71, "coq:exn.End-of-quoted-string-not-followed-by-a-space-in-notation"]], "found no matching notation to enable or disable (warning)": [[71, "coq:warn.Found-no-matching-notation-to-enable-or-disable"]], "infix (command)": [[71, "coq:cmd.Infix"]], "missing mapping for constructor \u2018qualid\u2019 (error)": [[71, "coq:exn.Missing-mapping-for-constructor-\u2018qualid\u2019"]], "more than one interpretation bound to this notation, confirm with the \"all\" modifier (error)": [[71, "coq:exn.More-than-one-interpretation-bound-to-this-notation,-confirm-with-the-\"all\"-modifier"]], "multiple 'via' options (error)": [[71, "coq:exn.Multiple-'via'-options"]], "multiple 'warning after' or 'abstract after' options (error)": [[71, "coq:exn.Multiple-'warning-after'-or-'abstract-after'-options"]], "no notation provided (error)": [[71, "coq:exn.No-notation-provided"]], "notation (abbreviation) (command)": [[71, "coq:cmd.Notation-(abbreviation)"]], "notation (command)": [[71, "coq:cmd.Notation"]], "number notation (command)": [[71, "coq:cmd.Number-Notation"]], "open scope (command)": [[71, "coq:cmd.Open-Scope"]], "print custom grammar (command)": [[71, "coq:cmd.Print-Custom-Grammar"]], "print grammar (command)": [[71, "coq:cmd.Print-Grammar"]], "print keywords (command)": [[71, "coq:cmd.Print-Keywords"]], "print notation (command)": [[71, "coq:cmd.Print-Notation"]], "print scope (command)": [[71, "coq:cmd.Print-Scope"]], "print scopes (command)": [[71, "coq:cmd.Print-Scopes"]], "print visibility (command)": [[71, "coq:cmd.Print-Visibility"]], "printing notations (flag)": [[71, "coq:flag.Printing-Notations"]], "printing parentheses (flag)": [[71, "coq:flag.Printing-Parentheses"]], "printing raw literals (flag)": [[71, "coq:flag.Printing-Raw-Literals"]], "reserved infix (command)": [[71, "coq:cmd.Reserved-Infix"]], "reserved notation (command)": [[71, "coq:cmd.Reserved-Notation"]], "scope delimiters should not start with an underscore (error)": [[71, "coq:exn.Scope-delimiters-should-not-start-with-an-underscore"]], "scope names should not start with an underscore (error)": [[71, "coq:exn.Scope-names-should-not-start-with-an-underscore"]], "stack overflow or segmentation fault happens when working with large numbers in \u2018type\u2019 (threshold may vary depending on your system limits and on the command executed) (warning)": [[71, "coq:warn.Stack-overflow-or-segmentation-fault-happens-when-working-with-large-numbers-in-\u2018type\u2019-(threshold-may-vary-depending-on-your-system-limits-and-on-the-command-executed)"]], "string notation (command)": [[71, "coq:cmd.String-Notation"]], "syntax error: [prim:reference] expected after 'notation' (in [vernac:command]) (error)": [[71, "coq:exn.Syntax-error:-[prim:reference]-expected-after-'Notation'-(in-[vernac:command])"]], "syntax error: [prim:reference] expected after [prim:reference] (in [vernac:command]) (error)": [[71, "coq:exn.Syntax-error:-[prim:reference]-expected-after-[prim:reference]-(in-[vernac:command])"]], "tactic notation (command)": [[71, "coq:cmd.Tactic-Notation"]], "the 'abstract after' directive has no effect when the parsing function (\u2018qualid\u2019) targets an option type (warning)": [[71, "coq:warn.The-'abstract-after'-directive-has-no-effect-when-the-parsing-function-(\u2018qualid\u2019)-targets-an-option-type"]], "to avoid stack overflow, large numbers in \u2018type\u2019 are interpreted as applications of \u2018qualid\u2019 (warning)": [[71, "coq:warn.To-avoid-stack-overflow,-large-numbers-in-\u2018type\u2019-are-interpreted-as-applications-of-\u2018qualid\u2019"]], "type of \u2018qualid\u2019 seems incompatible with the type of \u2018qualid\u2019. expected type is: \u2018type\u2019 instead of \u2018type\u2019. this might yield ill typed terms when using the notation (warning)": [[71, "coq:warn.Type-of-\u2018qualid\u2019-seems-incompatible-with-the-type-of-\u2018qualid\u2019.-Expected-type-is:-\u2018type\u2019-instead-of-\u2018type\u2019.-This-might-yield-ill-typed-terms-when-using-the-notation"]], "undelimit scope (command)": [[71, "coq:cmd.Undelimit-Scope"]], "unexpected non-option term \u2018term\u2019 while parsing a number notation (error)": [[71, "coq:exn.Unexpected-non-option-term-\u2018term\u2019-while-parsing-a-number-notation"]], "unexpected non-option term \u2018term\u2019 while parsing a string notation (error)": [[71, "coq:exn.Unexpected-non-option-term-\u2018term\u2019-while-parsing-a-string-notation"]], "unexpected only parsing for an only printing notation (error)": [[71, "coq:exn.Unexpected-only-parsing-for-an-only-printing-notation"]], "unexpected only printing for an only parsing notation (error)": [[71, "coq:exn.Unexpected-only-printing-for-an-only-parsing-notation"]], "unexpected term \u2018term\u2019 while parsing a number notation (error)": [[71, "coq:exn.Unexpected-term-\u2018term\u2019-while-parsing-a-number-notation"]], "unexpected term \u2018term\u2019 while parsing a string notation (error)": [[71, "coq:exn.Unexpected-term-\u2018term\u2019-while-parsing-a-string-notation"]], "unknown custom entry (error)": [[71, "coq:exn.Unknown-custom-entry"]], "unknown custom entry: \u2018ident\u2019 (error)": [[71, "coq:exn.Unknown-custom-entry:-\u2018ident\u2019"]], "unterminated string in notation (error)": [[71, "coq:exn.Unterminated-string-in-notation"]], "use of \u2018string\u2019 notation is deprecated as it is inconsistent with pattern syntax (warning)": [[71, "coq:warn.Use-of-\u2018string\u2019-Notation-is-deprecated-as-it-is-inconsistent-with-pattern-syntax"]], "add_bottom (attribute)": [[71, "coq:attr.add_bottom"]], "add_top (attribute)": [[71, "coq:attr.add_top"]], "closed-notation-not-level-0 (warning)": [[71, "coq:warn.closed-notation-not-level-0"]], "function_scope": [[71, "index-1"]], "notation-incompatible-prefix (warning)": [[71, "coq:warn.notation-incompatible-prefix"]], "overflow in int63 literal \u2018bigint\u2019 (error)": [[71, "coq:exn.overflow-in-int63-literal-\u2018bigint\u2019"]], "postfix-notation-not-level-1 (warning)": [[71, "coq:warn.postfix-notation-not-level-1"]], "type_scope": [[71, "index-0"]], "\u2018qualid\u2019 is bound to a notation that does not denote a reference (error)": [[71, "coq:exn.\u2018qualid\u2019-is-bound-to-a-notation-that-does-not-denote-a-reference"]], "\u2018qualid\u2019 should go from byte.byte, (list byte.byte), or primstring.string to \u2018type\u2019 or (option \u2018type\u2019) (error)": [[71, "coq:exn.\u2018qualid\u2019-should-go-from-Byte.byte,-(list-Byte.byte),-or-PrimString.string-to-\u2018type\u2019-or-(option-\u2018type\u2019)"]], "\u2018qualid\u2019 should go from number.int to \u2018type\u2019 or (option \u2018type\u2019). instead of number.int, the types number.uint or z or primint63.pos_neg_int63 or primfloat.float or number.number could be used (you may need to require binnums or number or primint63 or primfloat first) (error)": [[71, "coq:exn.\u2018qualid\u2019-should-go-from-Number.int-to-\u2018type\u2019-or-(option-\u2018type\u2019).-Instead-of-Number.int,-the-types-Number.uint-or-Z-or-PrimInt63.pos_neg_int63-or-PrimFloat.float-or-Number.number-could-be-used-(you-may-need-to-require-BinNums-or-Number-or-PrimInt63-or-PrimFloat-first)"]], "\u2018qualid\u2019 should go from \u2018type\u2019 to number.int or (option number.int). instead of number.int, the types number.uint or z or primint63.pos_neg_int63 or number.number could be used (you may need to require binnums or number or primint63 first) (error)": [[71, "coq:exn.\u2018qualid\u2019-should-go-from-\u2018type\u2019-to-Number.int-or-(option-Number.int).-Instead-of-Number.int,-the-types-Number.uint-or-Z-or-PrimInt63.pos_neg_int63-or-Number.number-could-be-used-(you-may-need-to-require-BinNums-or-Number-or-PrimInt63-first)"]], "\u2018qualid\u2019 should go from 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"coq:warn.\u2018string\u2019"]], "coqdoc": [[75, "index-0"]]}}) \ No newline at end of file diff --git a/master/refman/std-glossindex.html b/master/refman/std-glossindex.html index 4dba9e50f0..3b9b59cea3 100644 --- a/master/refman/std-glossindex.html +++ b/master/refman/std-glossindex.html @@ -1826,51 +1826,53 @@

Glossary

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Numbers and stringsdev +
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Tacticsdev +
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diff --git a/master/refman/using/libraries/writing.html b/master/refman/using/libraries/writing.html index 167f50f39a..97421a4747 100644 --- a/master/refman/using/libraries/writing.html +++ b/master/refman/using/libraries/writing.html @@ -1470,51 +1470,53 @@

Triggering warning for library objects or library files
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The rocq doc LaTeX style filedev +
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diff --git a/master/stdlib/Stdlib.Arith.Arith_base.html b/master/stdlib/Stdlib.Arith.Arith_base.html index 371c26a5b8..3325c32515 100644 --- a/master/stdlib/Stdlib.Arith.Arith_base.html +++ b/master/stdlib/Stdlib.Arith.Arith_base.html @@ -57,7 +57,7 @@

Library Stdlib.Arith.Arith_base

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arith hint database

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arith hint database

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Library Stdlib.Arith.Arith_base

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lt and le

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lt and le

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Library Stdlib.Arith.EqNat

Equality on natural numbers
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Propositional equality

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Propositional equality

diff --git a/master/stdlib/Stdlib.Arith.PeanoNat.html b/master/stdlib/Stdlib.Arith.PeanoNat.html index 11a6c51483..78476a44f5 100644 --- a/master/stdlib/Stdlib.Arith.PeanoNat.html +++ b/master/stdlib/Stdlib.Arith.PeanoNat.html @@ -148,7 +148,7 @@

Library Stdlib.Arith.PeanoNat

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Remaining constants not defined in Stdlib.Init.Nat

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Remaining constants not defined in Stdlib.Init.Nat

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Library Stdlib.Arith.PeanoNat

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Basic specifications : pred add sub mul

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Library Stdlib.Arith.PeanoNat

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Boolean comparisons

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Boolean comparisons

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Library Stdlib.Arith.PeanoNat

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Decidability of equality over nat.

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Decidability of equality over nat.

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Library Stdlib.Arith.PeanoNat

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Ternary comparison

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Library Stdlib.Arith.PeanoNat

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Minimum, maximum

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Library Stdlib.Arith.PeanoNat

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Power

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Power

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Library Stdlib.Arith.PeanoNat

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Square

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Square

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Parity

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Library Stdlib.Arith.PeanoNat

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Division

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Square root

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Library Stdlib.Arith.PeanoNat

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Logarithm

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Library Stdlib.Arith.PeanoNat

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Properties of iter

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Gcd

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Gcd

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Library Stdlib.Arith.PeanoNat

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Bitwise operations

+

Bitwise operations

diff --git a/master/stdlib/Stdlib.Bool.Bool.html b/master/stdlib/Stdlib.Bool.Bool.html index 644421fa51..5edac25b66 100644 --- a/master/stdlib/Stdlib.Bool.Bool.html +++ b/master/stdlib/Stdlib.Bool.Bool.html @@ -89,7 +89,7 @@

Library Stdlib.Bool.Bool

-

Decidability

+

Decidability

@@ -101,7 +101,7 @@

Library Stdlib.Bool.Bool

-

Discrimination

+

Discrimination

@@ -137,7 +137,7 @@

Library Stdlib.Bool.Bool

-

Order on booleans

+

Order on booleans

@@ -179,7 +179,7 @@

Library Stdlib.Bool.Bool

-

Equality

+

Equality

@@ -222,7 +222,7 @@

Library Stdlib.Bool.Bool

-

A synonym of if on bool

+

A synonym of if on bool

@@ -241,7 +241,7 @@

Library Stdlib.Bool.Bool

-

De Morgan laws

+

De Morgan laws

@@ -256,7 +256,7 @@

Library Stdlib.Bool.Bool

-

Properties of negb

+

Properties of negb

@@ -298,7 +298,7 @@

Library Stdlib.Bool.Bool

-

Properties of orb

+

Properties of orb

@@ -426,7 +426,7 @@

Library Stdlib.Bool.Bool

-

Properties of andb

+

Properties of andb

@@ -543,7 +543,7 @@

Library Stdlib.Bool.Bool

-

Properties mixing andb and orb

+

Properties mixing andb and orb

@@ -593,7 +593,7 @@

Library Stdlib.Bool.Bool

-

Properties of implb

+

Properties of implb

@@ -647,7 +647,7 @@

Library Stdlib.Bool.Bool

-

Properties of xorb

+

Properties of xorb

@@ -809,7 +809,7 @@

Library Stdlib.Bool.Bool

-

Reflection of bool into Prop

+

Reflection of bool into Prop

@@ -923,7 +923,7 @@

Library Stdlib.Bool.Bool

-

Alternative versions of andb and orb

+

Alternative versions of andb and orb

with lazy behavior (for vm_compute)
@@ -951,7 +951,7 @@

Library Stdlib.Bool.Bool

-

Reflect: a specialized inductive type for

+

Reflect: a specialized inductive type for

relating propositions and booleans, as popularized by the Ssreflect library. diff --git a/master/stdlib/Stdlib.Bool.BoolOrder.html b/master/stdlib/Stdlib.Bool.BoolOrder.html index 91dd601d0f..372fcf3960 100644 --- a/master/stdlib/Stdlib.Bool.BoolOrder.html +++ b/master/stdlib/Stdlib.Bool.BoolOrder.html @@ -65,7 +65,7 @@

Library Stdlib.Bool.BoolOrder

-

Order le

+

Order le

@@ -91,7 +91,7 @@

Library Stdlib.Bool.BoolOrder

-

Strict order lt

+

Strict order lt

@@ -126,7 +126,7 @@

Library Stdlib.Bool.BoolOrder

-

Order structures

+

Order structures

diff --git a/master/stdlib/Stdlib.Classes.CEquivalence.html b/master/stdlib/Stdlib.Classes.CEquivalence.html index 8c8e12b16f..890dd540c0 100644 --- a/master/stdlib/Stdlib.Classes.CEquivalence.html +++ b/master/stdlib/Stdlib.Classes.CEquivalence.html @@ -48,7 +48,7 @@

Library Stdlib.Classes.CEquivalence

-

Typeclass-based setoids. Definitions on Equivalence.

+

Typeclass-based setoids. Definitions on Equivalence.

diff --git a/master/stdlib/Stdlib.Classes.DecidableClass.html b/master/stdlib/Stdlib.Classes.DecidableClass.html index 0f7055266c..ecf3963026 100644 --- a/master/stdlib/Stdlib.Classes.DecidableClass.html +++ b/master/stdlib/Stdlib.Classes.DecidableClass.html @@ -48,7 +48,7 @@

Library Stdlib.Classes.DecidableClass

-

A typeclass to ease the handling of decidable properties.

+

A typeclass to ease the handling of decidable properties.

diff --git a/master/stdlib/Stdlib.Classes.EquivDec.html b/master/stdlib/Stdlib.Classes.EquivDec.html index 4d543bec04..ecb7c5819f 100644 --- a/master/stdlib/Stdlib.Classes.EquivDec.html +++ b/master/stdlib/Stdlib.Classes.EquivDec.html @@ -48,7 +48,7 @@

Library Stdlib.Classes.EquivDec

-

Decidable equivalences.

+

Decidable equivalences.

diff --git a/master/stdlib/Stdlib.Classes.Morphisms_Relations.html b/master/stdlib/Stdlib.Classes.Morphisms_Relations.html index 9170e1ba06..d3effadfa2 100644 --- a/master/stdlib/Stdlib.Classes.Morphisms_Relations.html +++ b/master/stdlib/Stdlib.Classes.Morphisms_Relations.html @@ -48,7 +48,7 @@

Library Stdlib.Classes.Morphisms_Relations

-

Morphism instances for relations.

+

Morphism instances for relations.

diff --git a/master/stdlib/Stdlib.Classes.RelationPairs.html b/master/stdlib/Stdlib.Classes.RelationPairs.html index 3f321f31b7..6ad6a472da 100644 --- a/master/stdlib/Stdlib.Classes.RelationPairs.html +++ b/master/stdlib/Stdlib.Classes.RelationPairs.html @@ -48,7 +48,7 @@

Library Stdlib.Classes.RelationPairs

-

Relations over pairs

+

Relations over pairs

diff --git a/master/stdlib/Stdlib.Classes.SetoidClass.html b/master/stdlib/Stdlib.Classes.SetoidClass.html index 9a6fc4df4a..fec32facb1 100644 --- a/master/stdlib/Stdlib.Classes.SetoidClass.html +++ b/master/stdlib/Stdlib.Classes.SetoidClass.html @@ -48,7 +48,7 @@

Library Stdlib.Classes.SetoidClass

-

Typeclass-based setoids, tactics and standard instances.

+

Typeclass-based setoids, tactics and standard instances.

diff --git a/master/stdlib/Stdlib.Classes.SetoidDec.html b/master/stdlib/Stdlib.Classes.SetoidDec.html index 2f08f41ee1..82c3b37a97 100644 --- a/master/stdlib/Stdlib.Classes.SetoidDec.html +++ b/master/stdlib/Stdlib.Classes.SetoidDec.html @@ -48,7 +48,7 @@

Library Stdlib.Classes.SetoidDec

-

Decidable setoid equality theory.

+

Decidable setoid equality theory.

diff --git a/master/stdlib/Stdlib.FSets.FMapAVL.html b/master/stdlib/Stdlib.FSets.FMapAVL.html index 25ee22cade..12317fe5cc 100644 --- a/master/stdlib/Stdlib.FSets.FMapAVL.html +++ b/master/stdlib/Stdlib.FSets.FMapAVL.html @@ -50,7 +50,7 @@

Library Stdlib.FSets.FMapAVL

-

FMapAVL

+

FMapAVL

@@ -87,7 +87,7 @@

Library Stdlib.FSets.FMapAVL

-

The Raw functor

+

The Raw functor

@@ -113,11 +113,11 @@

Library Stdlib.FSets.FMapAVL

-

Trees

+

Trees

-

Trees

+

Trees

@@ -149,7 +149,7 @@

Library Stdlib.FSets.FMapAVL

-

Basic functions on trees: height and cardinal

+

Basic functions on trees: height and cardinal

@@ -172,7 +172,7 @@

Library Stdlib.FSets.FMapAVL

-

Empty Map

+

Empty Map

@@ -184,7 +184,7 @@

Library Stdlib.FSets.FMapAVL

-

Emptyness test

+

Emptyness test

@@ -196,7 +196,7 @@

Library Stdlib.FSets.FMapAVL

-

Membership

+

Membership

@@ -231,7 +231,7 @@

Library Stdlib.FSets.FMapAVL

-

Helper functions

+

Helper functions

@@ -294,7 +294,7 @@

Library Stdlib.FSets.FMapAVL

-

Insertion

+

Insertion

@@ -315,7 +315,7 @@

Library Stdlib.FSets.FMapAVL

-

Extraction of minimum binding

+

Extraction of minimum binding

@@ -340,7 +340,7 @@

Library Stdlib.FSets.FMapAVL

-

Merging two trees

+

Merging two trees

@@ -366,7 +366,7 @@

Library Stdlib.FSets.FMapAVL

-

Deletion

+

Deletion

@@ -386,7 +386,7 @@

Library Stdlib.FSets.FMapAVL

-

join

+

join

@@ -415,7 +415,7 @@

Library Stdlib.FSets.FMapAVL

-

Splitting

+

Splitting

@@ -455,7 +455,7 @@

Library Stdlib.FSets.FMapAVL

-

Concatenation

+

Concatenation

@@ -479,7 +479,7 @@

Library Stdlib.FSets.FMapAVL

-

Elements

+

Elements

@@ -510,7 +510,7 @@

Library Stdlib.FSets.FMapAVL

-

Fold

+

Fold

@@ -526,7 +526,7 @@

Library Stdlib.FSets.FMapAVL

-

Comparison

+

Comparison

@@ -538,7 +538,7 @@

Library Stdlib.FSets.FMapAVL

-

Enumeration of the elements of a tree

+

Enumeration of the elements of a tree

@@ -637,7 +637,7 @@

Library Stdlib.FSets.FMapAVL

-

Map

+

Map

@@ -662,7 +662,7 @@

Library Stdlib.FSets.FMapAVL

-

Map with removal

+

Map with removal

@@ -683,7 +683,7 @@

Library Stdlib.FSets.FMapAVL

-

Optimized map2

+

Optimized map2

@@ -739,7 +739,7 @@

Library Stdlib.FSets.FMapAVL

-

Map2

+

Map2

@@ -769,7 +769,7 @@

Library Stdlib.FSets.FMapAVL

-

Invariants

+

Invariants

@@ -782,7 +782,7 @@

Library Stdlib.FSets.FMapAVL

-

Occurrence in a tree

+

Occurrence in a tree

@@ -812,7 +812,7 @@

Library Stdlib.FSets.FMapAVL

-

Binary search trees

+

Binary search trees

@@ -846,7 +846,7 @@

Library Stdlib.FSets.FMapAVL

-

Correctness proofs, isolated in a sub-module

+

Correctness proofs, isolated in a sub-module

@@ -1138,7 +1138,7 @@

Library Stdlib.FSets.FMapAVL

-

Automation and dedicated tactics.

+

Automation and dedicated tactics.

@@ -1249,7 +1249,7 @@

Library Stdlib.FSets.FMapAVL

-

Basic results about MapsTo, In, lt_tree, gt_tree, height

+

Basic results about MapsTo, In, lt_tree, gt_tree, height

@@ -1353,7 +1353,7 @@

Library Stdlib.FSets.FMapAVL

-

Empty map

+

Empty map

@@ -1371,7 +1371,7 @@

Library Stdlib.FSets.FMapAVL

-

Emptyness test

+

Emptyness test

@@ -1386,7 +1386,7 @@

Library Stdlib.FSets.FMapAVL

-

Membership

+

Membership

@@ -1440,7 +1440,7 @@

Library Stdlib.FSets.FMapAVL

-

Helper functions

+

Helper functions

@@ -1480,7 +1480,7 @@

Library Stdlib.FSets.FMapAVL

-

Insertion

+

Insertion

@@ -1514,7 +1514,7 @@

Library Stdlib.FSets.FMapAVL

-

Extraction of minimum binding

+

Extraction of minimum binding

@@ -1557,7 +1557,7 @@

Library Stdlib.FSets.FMapAVL

-

Merging two trees

+

Merging two trees

@@ -1579,7 +1579,7 @@

Library Stdlib.FSets.FMapAVL

-

Deletion

+

Deletion

@@ -1606,7 +1606,7 @@

Library Stdlib.FSets.FMapAVL

-

join

+

join

@@ -1630,7 +1630,7 @@

Library Stdlib.FSets.FMapAVL

-

split

+

split

@@ -1669,7 +1669,7 @@

Library Stdlib.FSets.FMapAVL

-

Concatenation

+

Concatenation

@@ -1695,7 +1695,7 @@

Library Stdlib.FSets.FMapAVL

-

Elements

+

Elements

@@ -1749,7 +1749,7 @@

Library Stdlib.FSets.FMapAVL

-

Fold

+

Fold

@@ -1777,7 +1777,7 @@

Library Stdlib.FSets.FMapAVL

-

Comparison

+

Comparison

@@ -2004,7 +2004,7 @@

Library Stdlib.FSets.FMapAVL

-

Encapsulation

+

Encapsulation

diff --git a/master/stdlib/Stdlib.FSets.FMapFacts.html b/master/stdlib/Stdlib.FSets.FMapFacts.html index ba3d3b13c6..54c36833bd 100644 --- a/master/stdlib/Stdlib.FSets.FMapFacts.html +++ b/master/stdlib/Stdlib.FSets.FMapFacts.html @@ -48,7 +48,7 @@

Library Stdlib.FSets.FMapFacts

-

Finite maps library

+

Finite maps library

@@ -75,7 +75,7 @@

Library Stdlib.FSets.FMapFacts

-

Facts about weak maps

+

Facts about weak maps

@@ -102,7 +102,7 @@

Library Stdlib.FSets.FMapFacts

-

Specifications written using equivalences

+

Specifications written using equivalences

@@ -259,7 +259,7 @@

Library Stdlib.FSets.FMapFacts

-

Specifications written using boolean predicates

+

Specifications written using boolean predicates

@@ -398,7 +398,7 @@

Library Stdlib.FSets.FMapFacts

-

Relations between Equal, Equiv and Equivb.

+

Relations between Equal, Equiv and Equivb.

@@ -460,7 +460,7 @@

Library Stdlib.FSets.FMapFacts

-

Equal is a setoid equality.

+

Equal is a setoid equality.

@@ -544,7 +544,7 @@

Library Stdlib.FSets.FMapFacts

-

Same facts for self-contained weak sets and for full maps

+

Same facts for self-contained weak sets and for full maps

@@ -557,7 +557,7 @@

Library Stdlib.FSets.FMapFacts

-

Additional Properties for weak maps

+

Additional Properties for weak maps

@@ -617,7 +617,7 @@

Library Stdlib.FSets.FMapFacts

-

Elements

+

Elements

@@ -632,7 +632,7 @@

Library Stdlib.FSets.FMapFacts

-

Conversions between maps and association lists.

+

Conversions between maps and association lists.

@@ -669,7 +669,7 @@

Library Stdlib.FSets.FMapFacts

-

Fold

+

Fold

@@ -685,7 +685,7 @@

Library Stdlib.FSets.FMapFacts

-

Induction principles about fold contributed by S. Lescuyer

+

Induction principles about fold contributed by S. Lescuyer

@@ -798,7 +798,7 @@

Library Stdlib.FSets.FMapFacts

-

Additional properties of fold

+

Additional properties of fold

@@ -893,7 +893,7 @@

Library Stdlib.FSets.FMapFacts

-

Cardinal

+

Cardinal

@@ -939,7 +939,7 @@

Library Stdlib.FSets.FMapFacts

-

Additional notions over maps

+

Additional notions over maps

@@ -957,7 +957,7 @@

Library Stdlib.FSets.FMapFacts

-

Emulation of some functions lacking in the interface

+

Emulation of some functions lacking in the interface

@@ -1184,7 +1184,7 @@

Library Stdlib.FSets.FMapFacts

-

Same Properties for self-contained weak maps and for full maps

+

Same Properties for self-contained weak maps and for full maps

@@ -1197,7 +1197,7 @@

Library Stdlib.FSets.FMapFacts

-

Properties specific to maps with ordered keys

+

Properties specific to maps with ordered keys

diff --git a/master/stdlib/Stdlib.FSets.FMapFullAVL.html b/master/stdlib/Stdlib.FSets.FMapFullAVL.html index 3d02336c3e..26c45256fb 100644 --- a/master/stdlib/Stdlib.FSets.FMapFullAVL.html +++ b/master/stdlib/Stdlib.FSets.FMapFullAVL.html @@ -50,7 +50,7 @@

Library Stdlib.FSets.FMapFullAVL

-

FMapFullAVL

+

FMapFullAVL

@@ -119,7 +119,7 @@

Library Stdlib.FSets.FMapFullAVL

-

AVL trees

+

AVL trees

@@ -143,7 +143,7 @@

Library Stdlib.FSets.FMapFullAVL

-

Automation and dedicated tactics about avl.

+

Automation and dedicated tactics about avl.

@@ -181,7 +181,7 @@

Library Stdlib.FSets.FMapFullAVL

-

Basic results about avl, height

+

Basic results about avl, height

@@ -209,7 +209,7 @@

Library Stdlib.FSets.FMapFullAVL

-

Empty map

+

Empty map

@@ -221,7 +221,7 @@

Library Stdlib.FSets.FMapFullAVL

-

Helper functions

+

Helper functions

@@ -261,7 +261,7 @@

Library Stdlib.FSets.FMapFullAVL

-

Insertion

+

Insertion

@@ -279,7 +279,7 @@

Library Stdlib.FSets.FMapFullAVL

-

Extraction of minimum binding

+

Extraction of minimum binding

@@ -297,7 +297,7 @@

Library Stdlib.FSets.FMapFullAVL

-

Merging two trees

+

Merging two trees

@@ -316,7 +316,7 @@

Library Stdlib.FSets.FMapFullAVL

-

Deletion

+

Deletion

@@ -334,7 +334,7 @@

Library Stdlib.FSets.FMapFullAVL

-

Join

+

Join

@@ -453,7 +453,7 @@

Library Stdlib.FSets.FMapFullAVL

-

Encapsulation

+

Encapsulation

@@ -652,7 +652,7 @@

Library Stdlib.FSets.FMapFullAVL

-

As comparison function, we propose here a non-structural

+

As comparison function, we propose here a non-structural

version faithful to the code of Ocaml's Map library, instead of the structural version of FMapAVL diff --git a/master/stdlib/Stdlib.FSets.FMapInterface.html b/master/stdlib/Stdlib.FSets.FMapInterface.html index 43feb09942..2c3dc3a7aa 100644 --- a/master/stdlib/Stdlib.FSets.FMapInterface.html +++ b/master/stdlib/Stdlib.FSets.FMapInterface.html @@ -48,7 +48,7 @@

Library Stdlib.FSets.FMapInterface

-

Finite map library

+

Finite map library

@@ -134,7 +134,7 @@

Library Stdlib.FSets.FMapInterface

-

Weak signature for maps

+

Weak signature for maps

@@ -555,7 +555,7 @@

Library Stdlib.FSets.FMapInterface

-

Static signature for Weak Maps

+

Static signature for Weak Maps

@@ -574,7 +574,7 @@

Library Stdlib.FSets.FMapInterface

-

Maps on ordered keys, functorial signature

+

Maps on ordered keys, functorial signature

@@ -601,7 +601,7 @@

Library Stdlib.FSets.FMapInterface

-

Maps on ordered keys, self-contained signature

+

Maps on ordered keys, self-contained signature

@@ -616,7 +616,7 @@

Library Stdlib.FSets.FMapInterface

-

Maps with ordering both on keys and datas

+

Maps with ordering both on keys and datas

diff --git a/master/stdlib/Stdlib.FSets.FMapList.html b/master/stdlib/Stdlib.FSets.FMapList.html index fbdb062837..c84781e8aa 100644 --- a/master/stdlib/Stdlib.FSets.FMapList.html +++ b/master/stdlib/Stdlib.FSets.FMapList.html @@ -48,7 +48,7 @@

Library Stdlib.FSets.FMapList

-

Finite map library

+

Finite map library

@@ -92,7 +92,7 @@

Library Stdlib.FSets.FMapList

-

empty

+

empty

@@ -115,7 +115,7 @@

Library Stdlib.FSets.FMapList

-

is_empty

+

is_empty

@@ -133,7 +133,7 @@

Library Stdlib.FSets.FMapList

-

mem

+

mem

@@ -160,7 +160,7 @@

Library Stdlib.FSets.FMapList

-

find

+

find

@@ -187,7 +187,7 @@

Library Stdlib.FSets.FMapList

-

add

+

add

@@ -228,7 +228,7 @@

Library Stdlib.FSets.FMapList

-

remove

+

remove

@@ -269,7 +269,7 @@

Library Stdlib.FSets.FMapList

-

elements

+

elements

@@ -295,7 +295,7 @@

Library Stdlib.FSets.FMapList

-

fold

+

fold

@@ -315,7 +315,7 @@

Library Stdlib.FSets.FMapList

-

equal

+

equal

@@ -365,7 +365,7 @@

Library Stdlib.FSets.FMapList

-

map and mapi

+

map and mapi

@@ -458,7 +458,7 @@

Library Stdlib.FSets.FMapList

-

map2

+

map2

diff --git a/master/stdlib/Stdlib.FSets.FMapPositive.html b/master/stdlib/Stdlib.FSets.FMapPositive.html index fd9a863e86..1b20fd2891 100644 --- a/master/stdlib/Stdlib.FSets.FMapPositive.html +++ b/master/stdlib/Stdlib.FSets.FMapPositive.html @@ -48,7 +48,7 @@

Library Stdlib.FSets.FMapPositive

-

FMapPositive : an implementation of FMapInterface for positive keys.

+

FMapPositive : an implementation of FMapInterface for positive keys.

diff --git a/master/stdlib/Stdlib.FSets.FMapWeakList.html b/master/stdlib/Stdlib.FSets.FMapWeakList.html index 4197d88392..8c4a8def97 100644 --- a/master/stdlib/Stdlib.FSets.FMapWeakList.html +++ b/master/stdlib/Stdlib.FSets.FMapWeakList.html @@ -48,7 +48,7 @@

Library Stdlib.FSets.FMapWeakList

-

Finite map library

+

Finite map library

@@ -90,7 +90,7 @@

Library Stdlib.FSets.FMapWeakList

-

empty

+

empty

@@ -115,7 +115,7 @@

Library Stdlib.FSets.FMapWeakList

-

is_empty

+

is_empty

@@ -133,7 +133,7 @@

Library Stdlib.FSets.FMapWeakList

-

mem

+

mem

@@ -155,7 +155,7 @@

Library Stdlib.FSets.FMapWeakList

-

find

+

find

@@ -184,7 +184,7 @@

Library Stdlib.FSets.FMapWeakList

-

add

+

add

@@ -228,7 +228,7 @@

Library Stdlib.FSets.FMapWeakList

-

remove

+

remove

@@ -262,7 +262,7 @@

Library Stdlib.FSets.FMapWeakList

-

elements

+

elements

@@ -283,7 +283,7 @@

Library Stdlib.FSets.FMapWeakList

-

fold

+

fold

@@ -303,7 +303,7 @@

Library Stdlib.FSets.FMapWeakList

-

equal

+

equal

@@ -364,7 +364,7 @@

Library Stdlib.FSets.FMapWeakList

-

map and mapi

+

map and mapi

diff --git a/master/stdlib/Stdlib.FSets.FSetAVL.html b/master/stdlib/Stdlib.FSets.FSetAVL.html index 852f2563ec..759b6336fd 100644 --- a/master/stdlib/Stdlib.FSets.FSetAVL.html +++ b/master/stdlib/Stdlib.FSets.FSetAVL.html @@ -48,7 +48,7 @@

Library Stdlib.FSets.FSetAVL

-

FSetAVL : Implementation of FSetInterface via AVL trees

+

FSetAVL : Implementation of FSetInterface via AVL trees

diff --git a/master/stdlib/Stdlib.FSets.FSetBridge.html b/master/stdlib/Stdlib.FSets.FSetBridge.html index ed37302cb2..0ed157a221 100644 --- a/master/stdlib/Stdlib.FSets.FSetBridge.html +++ b/master/stdlib/Stdlib.FSets.FSetBridge.html @@ -48,7 +48,7 @@

Library Stdlib.FSets.FSetBridge

-

Finite sets library

+

Finite sets library

@@ -65,7 +65,7 @@

Library Stdlib.FSets.FSetBridge

-

From non-dependent signature S to dependent signature Sdep.

+

From non-dependent signature S to dependent signature Sdep.

@@ -243,7 +243,7 @@

Library Stdlib.FSets.FSetBridge

-

From dependent signature Sdep to non-dependent signature S.

+

From dependent signature Sdep to non-dependent signature S.

diff --git a/master/stdlib/Stdlib.FSets.FSetCompat.html b/master/stdlib/Stdlib.FSets.FSetCompat.html index f927245e96..819df14c1a 100644 --- a/master/stdlib/Stdlib.FSets.FSetCompat.html +++ b/master/stdlib/Stdlib.FSets.FSetCompat.html @@ -48,7 +48,7 @@

Library Stdlib.FSets.FSetCompat

-

Compatibility functors between FSetInterface and MSetInterface.

+

Compatibility functors between FSetInterface and MSetInterface.

@@ -64,7 +64,7 @@

Library Stdlib.FSets.FSetCompat

-

From new Weak Sets to old ones

+

From new Weak Sets to old ones

@@ -227,7 +227,7 @@

Library Stdlib.FSets.FSetCompat

-

From new Sets to new ones

+

From new Sets to new ones

@@ -285,7 +285,7 @@

Library Stdlib.FSets.FSetCompat

-

From old Weak Sets to new ones.

+

From old Weak Sets to new ones.

@@ -428,7 +428,7 @@

Library Stdlib.FSets.FSetCompat

-

From old Sets to new ones.

+

From old Sets to new ones.

diff --git a/master/stdlib/Stdlib.FSets.FSetDecide.html b/master/stdlib/Stdlib.FSets.FSetDecide.html index 60848b967e..40ce0a939e 100644 --- a/master/stdlib/Stdlib.FSets.FSetDecide.html +++ b/master/stdlib/Stdlib.FSets.FSetDecide.html @@ -74,7 +74,7 @@

Library Stdlib.FSets.FSetDecide

-

Overview

+

Overview

This functor defines the tactic fsetdec, which will solve any valid goal of the form @@ -180,7 +180,7 @@

Library Stdlib.FSets.FSetDecide

-

Facts and Tactics for Propositional Logic

+

Facts and Tactics for Propositional Logic

These lemmas and tactics are in a module so that they do not affect the namespace if you import the enclosing @@ -195,18 +195,18 @@

Library Stdlib.FSets.FSetDecide

-

Lemmas and Tactics About Decidable Propositions

+

Lemmas and Tactics About Decidable Propositions

-

Propositional Equivalences Involving Negation

+

Propositional Equivalences Involving Negation

These are all written with the unfolded form of negation, since I am not sure if setoid rewriting will always perform conversion.
-

Tactics for Negations

+

Tactics for Negations

@@ -457,7 +457,7 @@

Library Stdlib.FSets.FSetDecide

-

Auxiliary Tactics

+

Auxiliary Tactics

Again, these lemmas and tactics are in a module so that they do not affect the namespace if you import the @@ -470,7 +470,7 @@

Library Stdlib.FSets.FSetDecide

-

Generic Tactics

+

Generic Tactics

We begin by defining a few generic, useful tactics.
@@ -587,7 +587,7 @@

Library Stdlib.FSets.FSetDecide

-

Discarding Irrelevant Hypotheses

+

Discarding Irrelevant Hypotheses

We will want to clear the context of any non-FSet-related hypotheses in order to increase the @@ -667,7 +667,7 @@

Library Stdlib.FSets.FSetDecide

-

Turning Set Operators into Propositional Connectives

+

Turning Set Operators into Propositional Connectives

The lemmas from FSetFacts will be used to break down set operations into propositional formulas built over @@ -693,7 +693,7 @@

Library Stdlib.FSets.FSetDecide

-

Decidability of FSet Propositions

+

Decidability of FSet Propositions

@@ -728,7 +728,7 @@

Library Stdlib.FSets.FSetDecide

-

Normalizing Propositions About Equality

+

Normalizing Propositions About Equality

We have to deal with the fact that E.eq may be convertible with Coq's equality. Thus, we will find the @@ -811,7 +811,7 @@

Library Stdlib.FSets.FSetDecide

-

Considering Decidability of Base Propositions

+

Considering Decidability of Base Propositions

This tactic adds assertions about the decidability of E.eq and In to the context. This is necessary for @@ -860,7 +860,7 @@

Library Stdlib.FSets.FSetDecide

-

Handling Empty, Subset, and Equal

+

Handling Empty, Subset, and Equal

This tactic instantiates universally quantified hypotheses (which arise from the unfolding of Empty, @@ -908,7 +908,7 @@

Library Stdlib.FSets.FSetDecide

-

The Core fsetdec Auxiliary Tactics

+

The Core fsetdec Auxiliary Tactics

@@ -950,7 +950,7 @@

Library Stdlib.FSets.FSetDecide

-

The fsetdec Tactic

+

The fsetdec Tactic

Here is the top-level tactic (the only one intended for clients of this library). It's specification is given at @@ -1064,7 +1064,7 @@

Library Stdlib.FSets.FSetDecide

-

Examples

+

Examples

diff --git a/master/stdlib/Stdlib.FSets.FSetEqProperties.html b/master/stdlib/Stdlib.FSets.FSetEqProperties.html index 26dc68e223..41fb57af56 100644 --- a/master/stdlib/Stdlib.FSets.FSetEqProperties.html +++ b/master/stdlib/Stdlib.FSets.FSetEqProperties.html @@ -48,7 +48,7 @@

Library Stdlib.FSets.FSetEqProperties

-

Finite sets library

+

Finite sets library

diff --git a/master/stdlib/Stdlib.FSets.FSetFacts.html b/master/stdlib/Stdlib.FSets.FSetFacts.html index 2e7e53e577..cc9a91e830 100644 --- a/master/stdlib/Stdlib.FSets.FSetFacts.html +++ b/master/stdlib/Stdlib.FSets.FSetFacts.html @@ -48,7 +48,7 @@

Library Stdlib.FSets.FSetFacts

-

Finite sets library

+

Finite sets library

@@ -84,7 +84,7 @@

Library Stdlib.FSets.FSetFacts

-

Specifications written using equivalences

+

Specifications written using equivalences

@@ -178,7 +178,7 @@

Library Stdlib.FSets.FSetFacts

-

Specifications written using boolean predicates

+

Specifications written using boolean predicates

@@ -242,7 +242,7 @@

Library Stdlib.FSets.FSetFacts

-

E.eq and Equal are setoid equalities

+

E.eq and Equal are setoid equalities

diff --git a/master/stdlib/Stdlib.FSets.FSetInterface.html b/master/stdlib/Stdlib.FSets.FSetInterface.html index 426ffd0d29..1eb231e7ae 100644 --- a/master/stdlib/Stdlib.FSets.FSetInterface.html +++ b/master/stdlib/Stdlib.FSets.FSetInterface.html @@ -48,7 +48,7 @@

Library Stdlib.FSets.FSetInterface

-

Finite set library

+

Finite set library

@@ -104,7 +104,7 @@

Library Stdlib.FSets.FSetInterface

-

Non-dependent signatures

+

Non-dependent signatures

@@ -113,7 +113,7 @@

Library Stdlib.FSets.FSetInterface

programs together with axioms
-

Functorial signature for weak sets

+

Functorial signature for weak sets

@@ -618,7 +618,7 @@

Library Stdlib.FSets.FSetInterface

-

Static signature for weak sets

+

Static signature for weak sets

@@ -638,7 +638,7 @@

Library Stdlib.FSets.FSetInterface

-

Functorial signature for sets on ordered elements

+

Functorial signature for sets on ordered elements

@@ -765,7 +765,7 @@

Library Stdlib.FSets.FSetInterface

-

Static signature for sets on ordered elements

+

Static signature for sets on ordered elements

@@ -785,7 +785,7 @@

Library Stdlib.FSets.FSetInterface

-

Some subtyping tests

+

Some subtyping tests

 WSfun ---> WS
@@ -802,7 +802,7 @@ 
Library Stdlib.FSets.FSetInterface

 
 
 

 
-
Dependent signature

+
Dependent signature

 
 
 
 

diff --git a/master/stdlib/Stdlib.FSets.FSetList.html b/master/stdlib/Stdlib.FSets.FSetList.html
index c57f2be5f1..1ed974abb6 100644
--- a/master/stdlib/Stdlib.FSets.FSetList.html
+++ b/master/stdlib/Stdlib.FSets.FSetList.html
@@ -48,7 +48,7 @@ 
Library Stdlib.FSets.FSetList
-

Finite sets library

+

Finite sets library

diff --git a/master/stdlib/Stdlib.FSets.FSetProperties.html b/master/stdlib/Stdlib.FSets.FSetProperties.html index b81eeceb1c..25c32ef5ee 100644 --- a/master/stdlib/Stdlib.FSets.FSetProperties.html +++ b/master/stdlib/Stdlib.FSets.FSetProperties.html @@ -48,7 +48,7 @@

Library Stdlib.FSets.FSetProperties

-

Finite sets library

+

Finite sets library

@@ -340,7 +340,7 @@

Library Stdlib.FSets.FSetProperties

-

Properties of elements

+

Properties of elements

@@ -355,7 +355,7 @@

Library Stdlib.FSets.FSetProperties

-

Conversions between lists and sets

+

Conversions between lists and sets

@@ -379,7 +379,7 @@

Library Stdlib.FSets.FSetProperties

-

Fold

+

Fold

@@ -407,7 +407,7 @@

Library Stdlib.FSets.FSetProperties

-

Induction principles for fold (contributed by S. Lescuyer)

+

Induction principles for fold (contributed by S. Lescuyer)

@@ -513,7 +513,7 @@

Library Stdlib.FSets.FSetProperties

-

Alternative (weaker) specifications for fold

+

Alternative (weaker) specifications for fold

@@ -585,7 +585,7 @@

Library Stdlib.FSets.FSetProperties

-

Fold is a morphism

+

Fold is a morphism

@@ -602,7 +602,7 @@

Library Stdlib.FSets.FSetProperties

-

Fold and other set operators

+

Fold and other set operators

@@ -654,11 +654,11 @@

Library Stdlib.FSets.FSetProperties

-

Cardinal

+

Cardinal

-

Characterization of cardinal in terms of fold

+

Characterization of cardinal in terms of fold

@@ -670,7 +670,7 @@

Library Stdlib.FSets.FSetProperties

-

Old specifications for cardinal.

+

Old specifications for cardinal.

@@ -693,7 +693,7 @@

Library Stdlib.FSets.FSetProperties

-

Cardinal and (non-)emptiness

+

Cardinal and (non-)emptiness

@@ -718,7 +718,7 @@

Library Stdlib.FSets.FSetProperties

-

Cardinal is a morphism

+

Cardinal is a morphism

@@ -737,7 +737,7 @@

Library Stdlib.FSets.FSetProperties

-

Cardinal and set operators

+

Cardinal and set operators

diff --git a/master/stdlib/Stdlib.FSets.FSetToFiniteSet.html b/master/stdlib/Stdlib.FSets.FSetToFiniteSet.html index c36957c45b..0d26665329 100644 --- a/master/stdlib/Stdlib.FSets.FSetToFiniteSet.html +++ b/master/stdlib/Stdlib.FSets.FSetToFiniteSet.html @@ -48,7 +48,7 @@

Library Stdlib.FSets.FSetToFiniteSet

-

Finite sets library : conversion to old Finite_sets

+

Finite sets library : conversion to old Finite_sets

@@ -61,7 +61,7 @@

Library Stdlib.FSets.FSetToFiniteSet

-

Going from FSets with usual Leibniz equality

+

Going from FSets with usual Leibniz equality

to the good old Ensembles and Finite_sets theory.
diff --git a/master/stdlib/Stdlib.FSets.FSetWeakList.html b/master/stdlib/Stdlib.FSets.FSetWeakList.html index b6983f8e10..304982c970 100644 --- a/master/stdlib/Stdlib.FSets.FSetWeakList.html +++ b/master/stdlib/Stdlib.FSets.FSetWeakList.html @@ -48,7 +48,7 @@

Library Stdlib.FSets.FSetWeakList

-

Finite sets library

+

Finite sets library

diff --git a/master/stdlib/Stdlib.Floats.FloatLemmas.html b/master/stdlib/Stdlib.Floats.FloatLemmas.html index 5bc077109e..03e3fdce32 100644 --- a/master/stdlib/Stdlib.Floats.FloatLemmas.html +++ b/master/stdlib/Stdlib.Floats.FloatLemmas.html @@ -52,7 +52,7 @@

Library Stdlib.Floats.FloatLemmas

-

Support results involving frexp and ldexp

+

Support results involving frexp and ldexp

diff --git a/master/stdlib/Stdlib.Lists.List.html b/master/stdlib/Stdlib.Lists.List.html index c339aa99a2..6eb733f673 100644 --- a/master/stdlib/Stdlib.Lists.List.html +++ b/master/stdlib/Stdlib.Lists.List.html @@ -56,7 +56,7 @@

Library Stdlib.Lists.List

-

Basics: definition of polymorphic lists and some operations

+

Basics: definition of polymorphic lists and some operations

@@ -148,7 +148,7 @@

Library Stdlib.Lists.List

-

Generic facts

+

Generic facts

@@ -183,7 +183,7 @@

Library Stdlib.Lists.List

-

Head and tail

+

Head and tail

@@ -198,7 +198,7 @@

Library Stdlib.Lists.List

-

Facts about app

+

Facts about app

@@ -316,7 +316,7 @@

Library Stdlib.Lists.List

-

Facts about In

+

Facts about In

@@ -403,7 +403,7 @@

Library Stdlib.Lists.List

-

Operations on the elements of a list

+

Operations on the elements of a list

@@ -418,7 +418,7 @@

Library Stdlib.Lists.List

-

Nth element of a list

+

Nth element of a list

@@ -614,7 +614,7 @@

Library Stdlib.Lists.List

-

Last element of a list

+

Last element of a list

@@ -669,7 +669,7 @@

Library Stdlib.Lists.List

-

Remove

+

Remove

@@ -720,7 +720,7 @@

Library Stdlib.Lists.List

-

Counting occurrences of an element

+

Counting occurrences of an element

@@ -784,7 +784,7 @@

Library Stdlib.Lists.List

-

Manipulating whole lists

+

Manipulating whole lists

@@ -799,7 +799,7 @@

Library Stdlib.Lists.List

-

Reverse

+

Reverse

@@ -896,7 +896,7 @@

Library Stdlib.Lists.List

-

Concatenation

+

Concatenation

@@ -925,7 +925,7 @@

Library Stdlib.Lists.List

-

Decidable equality on lists

+

Decidable equality on lists

@@ -946,11 +946,11 @@

Library Stdlib.Lists.List

-

Applying functions to the elements of a list

+

Applying functions to the elements of a list

-

Map

+

Map

@@ -1038,7 +1038,7 @@

Library Stdlib.Lists.List

-

Flat Map

+

Flat Map

@@ -1220,7 +1220,7 @@

Library Stdlib.Lists.List

-

Boolean operations over lists

+

Boolean operations over lists

@@ -1387,7 +1387,7 @@

Library Stdlib.Lists.List

-

Further filtering facts

+

Further filtering facts

@@ -1481,7 +1481,7 @@

Library Stdlib.Lists.List

-

Operations on lists of pairs or lists of lists

+

Operations on lists of pairs or lists of lists

@@ -1613,11 +1613,11 @@

Library Stdlib.Lists.List

-

Miscellaneous operations on lists

+

Miscellaneous operations on lists

-

Length order of lists

+

Length order of lists

@@ -1661,7 +1661,7 @@

Library Stdlib.Lists.List

-

Set inclusion on list

+

Set inclusion on list

@@ -1751,7 +1751,7 @@

Library Stdlib.Lists.List

-

Cutting a list at some position

+

Cutting a list at some position

@@ -1916,7 +1916,7 @@

Library Stdlib.Lists.List

-

Combining pairs of lists of possibly-different lengths

+

Combining pairs of lists of possibly-different lengths

@@ -1948,7 +1948,7 @@

Library Stdlib.Lists.List

-

Predicate for List addition/removal (no need for decidability)

+

Predicate for List addition/removal (no need for decidability)

@@ -1992,7 +1992,7 @@

Library Stdlib.Lists.List

-

Lists without redundancy

+

Lists without redundancy

@@ -2144,7 +2144,7 @@

Library Stdlib.Lists.List

-

Sequence of natural numbers

+

Sequence of natural numbers

@@ -2196,7 +2196,7 @@

Library Stdlib.Lists.List

-

List comparison

+

List comparison

@@ -2333,7 +2333,7 @@

Library Stdlib.Lists.List

-

Existential and universal predicates over lists

+

Existential and universal predicates over lists

@@ -2866,7 +2866,7 @@

Library Stdlib.Lists.List

-

Inversion of predicates over lists based on head symbol

+

Inversion of predicates over lists based on head symbol

@@ -2894,7 +2894,7 @@

Library Stdlib.Lists.List

-

Exporting hints and tactics

+

Exporting hints and tactics

diff --git a/master/stdlib/Stdlib.Lists.SetoidList.html b/master/stdlib/Stdlib.Lists.SetoidList.html index 5bab0d0f9b..d9d0416e15 100644 --- a/master/stdlib/Stdlib.Lists.SetoidList.html +++ b/master/stdlib/Stdlib.Lists.SetoidList.html @@ -52,7 +52,7 @@

Library Stdlib.Lists.SetoidList

-

Logical relations over lists with respect to a setoid equality

+

Logical relations over lists with respect to a setoid equality

or ordering.
diff --git a/master/stdlib/Stdlib.Lists.StreamMemo.html b/master/stdlib/Stdlib.Lists.StreamMemo.html index 8018eef4ec..415d55ae66 100644 --- a/master/stdlib/Stdlib.Lists.StreamMemo.html +++ b/master/stdlib/Stdlib.Lists.StreamMemo.html @@ -52,7 +52,7 @@

Library Stdlib.Lists.StreamMemo

-

Memoization

+

Memoization

diff --git a/master/stdlib/Stdlib.Logic.ChoiceFacts.html b/master/stdlib/Stdlib.Logic.ChoiceFacts.html index eee74c80b1..bf80283a52 100644 --- a/master/stdlib/Stdlib.Logic.ChoiceFacts.html +++ b/master/stdlib/Stdlib.Logic.ChoiceFacts.html @@ -49,7 +49,7 @@

Library Stdlib.Logic.ChoiceFacts

Some facts and definitions concerning choice and description in - intuitionistic logic.

References:

+ intuitionistic logic.

References:

@@ -88,7 +88,7 @@

Library Stdlib.Logic.ChoiceFacts

-

Definitions

+

Definitions

@@ -115,7 +115,7 @@

Library Stdlib.Logic.ChoiceFacts

-

Constructive choice and description

+

Constructive choice and description

@@ -345,7 +345,7 @@

Library Stdlib.Logic.ChoiceFacts

-

Weakly classical choice and description

+

Weakly classical choice and description

@@ -624,7 +624,7 @@

Library Stdlib.Logic.ChoiceFacts

-

Table of contents

+

Table of contents

@@ -681,7 +681,7 @@

Library Stdlib.Logic.ChoiceFacts

-

AC_rel + AC! = AC_fun

+

AC_rel + AC! = AC_fun

@@ -721,7 +721,7 @@

Library Stdlib.Logic.ChoiceFacts

-

Connection between the guarded, non guarded and omniscient choices

+

Connection between the guarded, non guarded and omniscient choices

@@ -732,7 +732,7 @@

Library Stdlib.Logic.ChoiceFacts

irrelevance)
-

AC_rel + PI -> GAC_rel and AC_rel + IGP -> GAC_rel and GAC_rel = OAC_rel

+

AC_rel + PI -> GAC_rel and AC_rel + IGP -> GAC_rel and GAC_rel = OAC_rel

@@ -770,7 +770,7 @@

Library Stdlib.Logic.ChoiceFacts

-

AC_fun + IGP = GAC_fun = OAC_fun = AC_fun + Drinker

+

AC_fun + IGP = GAC_fun = OAC_fun = AC_fun + Drinker

@@ -845,7 +845,7 @@

Library Stdlib.Logic.ChoiceFacts

-

D_iota -> ID_iota and D_epsilon <-> ID_epsilon + Drinker

+

D_iota -> ID_iota and D_epsilon <-> ID_epsilon + Drinker

@@ -889,7 +889,7 @@

Library Stdlib.Logic.ChoiceFacts

-

Derivability of choice for decidable relations with well-ordered codomain

+

Derivability of choice for decidable relations with well-ordered codomain

@@ -922,11 +922,11 @@

Library Stdlib.Logic.ChoiceFacts

-

AC_fun = AC_fun_dep = AC_trunc

+

AC_fun = AC_fun_dep = AC_trunc

-

Choice on dependent and non dependent function types are equivalent

+

Choice on dependent and non dependent function types are equivalent

@@ -965,7 +965,7 @@

Library Stdlib.Logic.ChoiceFacts

-

Functional choice and truncation choice are equivalent

+

Functional choice and truncation choice are equivalent

@@ -982,7 +982,7 @@

Library Stdlib.Logic.ChoiceFacts

-

Reification of dependent and non dependent functional relation are equivalent

+

Reification of dependent and non dependent functional relation are equivalent

@@ -1017,11 +1017,11 @@

Library Stdlib.Logic.ChoiceFacts

-

Non contradiction of constructive descriptions wrt functional axioms of choice

+

Non contradiction of constructive descriptions wrt functional axioms of choice

-

Non contradiction of indefinite description

+

Non contradiction of indefinite description

@@ -1039,7 +1039,7 @@

Library Stdlib.Logic.ChoiceFacts

-

Non contradiction of definite description

+

Non contradiction of definite description

@@ -1083,7 +1083,7 @@

Library Stdlib.Logic.ChoiceFacts

-

Excluded-middle + definite description => computational excluded-middle

+

Excluded-middle + definite description => computational excluded-middle

@@ -1127,7 +1127,7 @@

Library Stdlib.Logic.ChoiceFacts

-

Choice => Dependent choice => Countable choice

+

Choice => Dependent choice => Countable choice

@@ -1147,7 +1147,7 @@

Library Stdlib.Logic.ChoiceFacts

-

About the axiom of choice over setoids

+

About the axiom of choice over setoids

@@ -1159,7 +1159,7 @@

Library Stdlib.Logic.ChoiceFacts

-

Consequences of the choice of a representative in an equivalence class

+

Consequences of the choice of a representative in an equivalence class

@@ -1180,7 +1180,7 @@

Library Stdlib.Logic.ChoiceFacts

-

This is a variant of Diaconescu and Goodman-Myhill theorems

+

This is a variant of Diaconescu and Goodman-Myhill theorems

@@ -1197,7 +1197,7 @@

Library Stdlib.Logic.ChoiceFacts

-

AC_fun_setoid = AC_fun_setoid_gen = AC_fun_setoid_simple

+

AC_fun_setoid = AC_fun_setoid_gen = AC_fun_setoid_simple

@@ -1230,7 +1230,7 @@

Library Stdlib.Logic.ChoiceFacts

-

AC_fun_setoid = AC! + AC_fun_repr

+

AC_fun_setoid = AC! + AC_fun_repr

@@ -1266,7 +1266,7 @@

Library Stdlib.Logic.ChoiceFacts

functional forms, SetoidFunctionalChoice seems strictly stronger
-

AC_fun_setoid = AC_fun + Ext_fun_repr + EM

+

AC_fun_setoid = AC_fun + Ext_fun_repr + EM

@@ -1278,7 +1278,7 @@

Library Stdlib.Logic.ChoiceFacts

-

This is the main theorem in [Carlström04]

+

This is the main theorem in [Carlström04]

@@ -1302,7 +1302,7 @@

Library Stdlib.Logic.ChoiceFacts

-

AC_fun_setoid = AC_fun + Ext_pred_repr + PI

+

AC_fun_setoid = AC_fun + Ext_pred_repr + PI

@@ -1326,7 +1326,7 @@

Library Stdlib.Logic.ChoiceFacts

-

Compatibility notations

+

Compatibility notations

diff --git a/master/stdlib/Stdlib.Logic.ClassicalEpsilon.html b/master/stdlib/Stdlib.Logic.ClassicalEpsilon.html index 001ba67426..ce4c2b6699 100644 --- a/master/stdlib/Stdlib.Logic.ClassicalEpsilon.html +++ b/master/stdlib/Stdlib.Logic.ClassicalEpsilon.html @@ -132,7 +132,7 @@

Library Stdlib.Logic.ClassicalEpsilon

-

Weaker lemmas (compatibility lemmas)

+

Weaker lemmas (compatibility lemmas)

diff --git a/master/stdlib/Stdlib.Logic.ClassicalFacts.html b/master/stdlib/Stdlib.Logic.ClassicalFacts.html index 72c8f40ce6..7ab0754f6a 100644 --- a/master/stdlib/Stdlib.Logic.ClassicalFacts.html +++ b/master/stdlib/Stdlib.Logic.ClassicalFacts.html @@ -117,7 +117,7 @@

Library Stdlib.Logic.ClassicalFacts

-

Prop degeneracy = excluded-middle + prop extensionality

+

Prop degeneracy = excluded-middle + prop extensionality

@@ -193,11 +193,11 @@

Library Stdlib.Logic.ClassicalFacts

-

Classical logic and proof-irrelevance

+

Classical logic and proof-irrelevance

-

CC |- prop ext + A inhabited -> (A = A->A) -> A has fixpoint

+

CC |- prop ext + A inhabited -> (A = A->A) -> A has fixpoint

@@ -250,7 +250,7 @@

Library Stdlib.Logic.ClassicalFacts

-

CC |- prop_ext /\ dep elim on bool -> proof-irrelevance

+

CC |- prop_ext /\ dep elim on bool -> proof-irrelevance

@@ -347,7 +347,7 @@

Library Stdlib.Logic.ClassicalFacts

-

CIC |- prop. ext. -> proof-irrelevance

+

CIC |- prop. ext. -> proof-irrelevance

@@ -401,7 +401,7 @@

Library Stdlib.Logic.ClassicalFacts

-

CC |- excluded-middle + dep elim on bool -> proof-irrelevance

+

CC |- excluded-middle + dep elim on bool -> proof-irrelevance

@@ -573,7 +573,7 @@

Library Stdlib.Logic.ClassicalFacts

-

CIC |- excluded-middle -> proof-irrelevance

+

CIC |- excluded-middle -> proof-irrelevance

@@ -638,7 +638,7 @@

Library Stdlib.Logic.ClassicalFacts

-

Weak classical axioms

+

Weak classical axioms

@@ -660,7 +660,7 @@

Library Stdlib.Logic.ClassicalFacts

-

Weak excluded-middle

+

Weak excluded-middle

@@ -715,7 +715,7 @@

Library Stdlib.Logic.ClassicalFacts

-

Gödel-Dummett axiom

+

Gödel-Dummett axiom

@@ -786,7 +786,7 @@

Library Stdlib.Logic.ClassicalFacts

-

Independence of general premises and drinker's paradox

+

Independence of general premises and drinker's paradox

@@ -962,11 +962,11 @@

Library Stdlib.Logic.ClassicalFacts

-

Axioms equivalent to classical logic

+

Axioms equivalent to classical logic

-

Principle of unrestricted minimization

+

Principle of unrestricted minimization

@@ -1039,7 +1039,7 @@

Library Stdlib.Logic.ClassicalFacts

-

Choice of representatives in a partition of bool

+

Choice of representatives in a partition of bool

diff --git a/master/stdlib/Stdlib.Logic.Diaconescu.html b/master/stdlib/Stdlib.Logic.Diaconescu.html index 9454016b2f..8ec0fb4778 100644 --- a/master/stdlib/Stdlib.Logic.Diaconescu.html +++ b/master/stdlib/Stdlib.Logic.Diaconescu.html @@ -107,7 +107,7 @@

Library Stdlib.Logic.Diaconescu

-

Pred. Ext. + Rel. Axiom of Choice -> Excluded-Middle

+

Pred. Ext. + Rel. Axiom of Choice -> Excluded-Middle

@@ -203,7 +203,7 @@

Library Stdlib.Logic.Diaconescu

-

Proof-Irrel. + Rel. Axiom of Choice -> Excl.-Middle for Equality

+

Proof-Irrel. + Rel. Axiom of Choice -> Excl.-Middle for Equality

@@ -310,7 +310,7 @@

Library Stdlib.Logic.Diaconescu

-

Extensional Hilbert's epsilon description operator -> Excluded-Middle

+

Extensional Hilbert's epsilon description operator -> Excluded-Middle

diff --git a/master/stdlib/Stdlib.Logic.EqdepFacts.html b/master/stdlib/Stdlib.Logic.EqdepFacts.html index bd349727ff..7ec5df6f08 100644 --- a/master/stdlib/Stdlib.Logic.EqdepFacts.html +++ b/master/stdlib/Stdlib.Logic.EqdepFacts.html @@ -115,7 +115,7 @@

Library Stdlib.Logic.EqdepFacts

-

Definition of dependent equality and equivalence with equality of dependent pairs

+

Definition of dependent equality and equivalence with equality of dependent pairs

@@ -283,7 +283,7 @@

Library Stdlib.Logic.EqdepFacts

-

Eq_rect_eq <-> Eq_dep_eq <-> UIP <-> UIP_refl <-> K

+

Eq_rect_eq <-> Eq_dep_eq <-> UIP <-> UIP_refl <-> K

@@ -509,7 +509,7 @@

Library Stdlib.Logic.EqdepFacts

-

Definition of the functor that builds properties of dependent equalities assuming axiom eq_rect_eq

+

Definition of the functor that builds properties of dependent equalities assuming axiom eq_rect_eq

diff --git a/master/stdlib/Stdlib.Logic.Eqdep_dec.html b/master/stdlib/Stdlib.Logic.Eqdep_dec.html index 85d6cc56a5..7659d6e466 100644 --- a/master/stdlib/Stdlib.Logic.Eqdep_dec.html +++ b/master/stdlib/Stdlib.Logic.Eqdep_dec.html @@ -87,7 +87,7 @@

Library Stdlib.Logic.Eqdep_dec

-

Streicher's K and injectivity of dependent pair hold on decidable types

+

Streicher's K and injectivity of dependent pair hold on decidable types

@@ -245,7 +245,7 @@

Library Stdlib.Logic.Eqdep_dec

-

Definition of the functor that builds properties of dependent equalities on decidable sets in Type

+

Definition of the functor that builds properties of dependent equalities on decidable sets in Type

@@ -369,7 +369,7 @@

Library Stdlib.Logic.Eqdep_dec

-

Definition of the functor that builds properties of dependent equalities on decidable sets in Set

+

Definition of the functor that builds properties of dependent equalities on decidable sets in Set

diff --git a/master/stdlib/Stdlib.Logic.ExtensionalityFacts.html b/master/stdlib/Stdlib.Logic.ExtensionalityFacts.html index 37bff157cd..55847d769d 100644 --- a/master/stdlib/Stdlib.Logic.ExtensionalityFacts.html +++ b/master/stdlib/Stdlib.Logic.ExtensionalityFacts.html @@ -104,7 +104,7 @@

Library Stdlib.Logic.ExtensionalityFacts

-

Definitions

+

Definitions

@@ -196,7 +196,7 @@

Library Stdlib.Logic.ExtensionalityFacts

-

Functional extensionality <-> Equality of projections from diagonal

+

Functional extensionality <-> Equality of projections from diagonal

@@ -208,7 +208,7 @@

Library Stdlib.Logic.ExtensionalityFacts

-

Functional extensionality <-> Unicity of bijection inverse

+

Functional extensionality <-> Unicity of bijection inverse

@@ -226,7 +226,7 @@

Library Stdlib.Logic.ExtensionalityFacts

-

Functional extensionality <-> Bijectivity of bijective composition

+

Functional extensionality <-> Bijectivity of bijective composition

diff --git a/master/stdlib/Stdlib.Logic.FinFun.html b/master/stdlib/Stdlib.Logic.FinFun.html index 8805a4f05a..ba6715e455 100644 --- a/master/stdlib/Stdlib.Logic.FinFun.html +++ b/master/stdlib/Stdlib.Logic.FinFun.html @@ -48,7 +48,7 @@

Library Stdlib.Logic.FinFun

-

Functions on finite domains

+

Functions on finite domains

diff --git a/master/stdlib/Stdlib.Logic.Hurkens.html b/master/stdlib/Stdlib.Logic.Hurkens.html index caf34a4cc9..0ff9ff8c14 100644 --- a/master/stdlib/Stdlib.Logic.Hurkens.html +++ b/master/stdlib/Stdlib.Logic.Hurkens.html @@ -175,7 +175,7 @@

Library Stdlib.Logic.Hurkens

-

A modular proof of Hurkens's paradox.

+

A modular proof of Hurkens's paradox.

@@ -202,7 +202,7 @@

Library Stdlib.Logic.Hurkens

-

Axiomatisation of impredicative universes in a Martin-Löf style

+

Axiomatisation of impredicative universes in a Martin-Löf style

@@ -213,7 +213,7 @@

Library Stdlib.Logic.Hurkens

actual system U-.
-

Large universe

+

Large universe

@@ -222,7 +222,7 @@

Library Stdlib.Logic.Hurkens

-

Closure by small product

+

Closure by small product

@@ -238,7 +238,7 @@

Library Stdlib.Logic.Hurkens

-

Closure by large products

+

Closure by large products

U1 only needs to quantify over itself.
@@ -255,7 +255,7 @@

Library Stdlib.Logic.Hurkens

-

Small universe

+

Small universe

The small universe is an element of the large one.
@@ -265,7 +265,7 @@

Library Stdlib.Logic.Hurkens

-

Closure by small product

+

Closure by small product

U0 does not need reduction rules
@@ -279,7 +279,7 @@

Library Stdlib.Logic.Hurkens

-

Closure by large products

+

Closure by large products

@@ -294,7 +294,7 @@

Library Stdlib.Logic.Hurkens

-

Automating the rewrite rules of our encoding.

+

Automating the rewrite rules of our encoding.

@@ -312,7 +312,7 @@

Library Stdlib.Logic.Hurkens

-

Hurkens's paradox.

+

Hurkens's paradox.

@@ -325,7 +325,7 @@

Library Stdlib.Logic.Hurkens

-

Preliminary definitions

+

Preliminary definitions

@@ -354,7 +354,7 @@

Library Stdlib.Logic.Hurkens

-

Proof

+

Proof

@@ -439,7 +439,7 @@

Library Stdlib.Logic.Hurkens

-

Impredicative universes are not retracts.

+

Impredicative universes are not retracts.

@@ -466,7 +466,7 @@

Library Stdlib.Logic.Hurkens

-

U1 is impredicative

+

U1 is impredicative

@@ -493,7 +493,7 @@

Library Stdlib.Logic.Hurkens

-

U0 is a retract of U1

+

U0 is a retract of U1

@@ -506,7 +506,7 @@

Library Stdlib.Logic.Hurkens

-

Paradox

+

Paradox

@@ -570,7 +570,7 @@

Library Stdlib.Logic.Hurkens

-

Modal fragments of Prop are not retracts

+

Modal fragments of Prop are not retracts

@@ -589,7 +589,7 @@

Library Stdlib.Logic.Hurkens

-

Monadic modality

+

Monadic modality

@@ -612,7 +612,7 @@

Library Stdlib.Logic.Hurkens

-

The universe of modal propositions

+

The universe of modal propositions

@@ -642,7 +642,7 @@

Library Stdlib.Logic.Hurkens

-

Retract of the modal fragment of Prop in a small type

+

Retract of the modal fragment of Prop in a small type

@@ -662,7 +662,7 @@

Library Stdlib.Logic.Hurkens

-

Paradox

+

Paradox

@@ -721,7 +721,7 @@

Library Stdlib.Logic.Hurkens

-

The negative fragment of Prop is not a retract

+

The negative fragment of Prop is not a retract

@@ -738,7 +738,7 @@

Library Stdlib.Logic.Hurkens

-

The universe of negative propositions.

+

The universe of negative propositions.

@@ -754,7 +754,7 @@

Library Stdlib.Logic.Hurkens

-

Retract of the negative fragment of Prop in a small type

+

Retract of the negative fragment of Prop in a small type

@@ -774,7 +774,7 @@

Library Stdlib.Logic.Hurkens

-

Paradox

+

Paradox

@@ -805,7 +805,7 @@

Library Stdlib.Logic.Hurkens

-

Prop is not a retract

+

Prop is not a retract

@@ -822,7 +822,7 @@

Library Stdlib.Logic.Hurkens

-

The universe of propositions.

+

The universe of propositions.

@@ -838,7 +838,7 @@

Library Stdlib.Logic.Hurkens

-

Retract of Prop in a small type, using the identity modality.

+

Retract of Prop in a small type, using the identity modality.

@@ -854,7 +854,7 @@

Library Stdlib.Logic.Hurkens

-

Paradox

+

Paradox

@@ -885,7 +885,7 @@

Library Stdlib.Logic.Hurkens

-

Retract of Prop in a small type

+

Retract of Prop in a small type

@@ -903,7 +903,7 @@

Library Stdlib.Logic.Hurkens

-

Paradox

+

Paradox

@@ -930,7 +930,7 @@

Library Stdlib.Logic.Hurkens

-

Large universes are not retracts of Prop.

+

Large universes are not retracts of Prop.

@@ -955,7 +955,7 @@

Library Stdlib.Logic.Hurkens

-

Assumption of a retract from Type into Prop

+

Assumption of a retract from Type into Prop

@@ -969,7 +969,7 @@

Library Stdlib.Logic.Hurkens

-

Paradox

+

Paradox

@@ -1024,7 +1024,7 @@

Library Stdlib.Logic.Hurkens

-

A<>Type

+

A<>Type

@@ -1045,7 +1045,7 @@

Library Stdlib.Logic.Hurkens

-

Universe U is equal to one of its elements.

+

Universe U is equal to one of its elements.

@@ -1059,7 +1059,7 @@

Library Stdlib.Logic.Hurkens

-

Universe U is a retract of A

+

Universe U is a retract of A

@@ -1149,7 +1149,7 @@

Library Stdlib.Logic.Hurkens

-

Prop<>Type.

+

Prop<>Type.

diff --git a/master/stdlib/Stdlib.Logic.PropExtensionalityFacts.html b/master/stdlib/Stdlib.Logic.PropExtensionalityFacts.html index 0ecf6efd9b..0a666c42fa 100644 --- a/master/stdlib/Stdlib.Logic.PropExtensionalityFacts.html +++ b/master/stdlib/Stdlib.Logic.PropExtensionalityFacts.html @@ -116,7 +116,7 @@

Library Stdlib.Logic.PropExtensionalityFacts

-

Definitions

+

Definitions

@@ -180,11 +180,11 @@

Library Stdlib.Logic.PropExtensionalityFacts

-

Propositional and predicate extensionality

+

Propositional and predicate extensionality

-

Predicate extensionality <-> Propositional extensionality + Propositional functional extensionality

+

Predicate extensionality <-> Propositional extensionality + Propositional functional extensionality

@@ -207,7 +207,7 @@

Library Stdlib.Logic.PropExtensionalityFacts

-

Propositional extensionality and provable proposition extensionality

+

Propositional extensionality and provable proposition extensionality

@@ -219,7 +219,7 @@

Library Stdlib.Logic.PropExtensionalityFacts

-

Propositional extensionality and refutable proposition extensionality

+

Propositional extensionality and refutable proposition extensionality

diff --git a/master/stdlib/Stdlib.Logic.PropFacts.html b/master/stdlib/Stdlib.Logic.PropFacts.html index 60eb9bf9de..bf3c0cb486 100644 --- a/master/stdlib/Stdlib.Logic.PropFacts.html +++ b/master/stdlib/Stdlib.Logic.PropFacts.html @@ -48,7 +48,7 @@

Library Stdlib.Logic.PropFacts

-

Basic facts about Prop as a type

+

Basic facts about Prop as a type

diff --git a/master/stdlib/Stdlib.Logic.SetIsType.html b/master/stdlib/Stdlib.Logic.SetIsType.html index e9147ec2d0..51e960e3fb 100644 --- a/master/stdlib/Stdlib.Logic.SetIsType.html +++ b/master/stdlib/Stdlib.Logic.SetIsType.html @@ -48,7 +48,7 @@

Library Stdlib.Logic.SetIsType

-

The Set universe seen as a synonym for Type

+

The Set universe seen as a synonym for Type

diff --git a/master/stdlib/Stdlib.MSets.MSetAVL.html b/master/stdlib/Stdlib.MSets.MSetAVL.html index 9259d67043..c28abef8fe 100644 --- a/master/stdlib/Stdlib.MSets.MSetAVL.html +++ b/master/stdlib/Stdlib.MSets.MSetAVL.html @@ -48,7 +48,7 @@

Library Stdlib.MSets.MSetAVL

-

MSetAVL : Implementation of MSetInterface via AVL trees

+

MSetAVL : Implementation of MSetInterface via AVL trees

@@ -90,7 +90,7 @@

Library Stdlib.MSets.MSetAVL

-

Ops : the pure functions

+

Ops : the pure functions

@@ -104,7 +104,7 @@

Library Stdlib.MSets.MSetAVL

-

Generic trees instantiated with integer height

+

Generic trees instantiated with integer height

@@ -124,7 +124,7 @@

Library Stdlib.MSets.MSetAVL

-

Height of trees

+

Height of trees

@@ -140,7 +140,7 @@

Library Stdlib.MSets.MSetAVL

-

Singleton set

+

Singleton set

@@ -152,7 +152,7 @@

Library Stdlib.MSets.MSetAVL

-

Helper functions

+

Helper functions

@@ -215,7 +215,7 @@

Library Stdlib.MSets.MSetAVL

-

Insertion

+

Insertion

@@ -235,7 +235,7 @@

Library Stdlib.MSets.MSetAVL

-

Join

+

Join

@@ -264,7 +264,7 @@

Library Stdlib.MSets.MSetAVL

-

Extraction of minimum element

+

Extraction of minimum element

@@ -288,7 +288,7 @@

Library Stdlib.MSets.MSetAVL

-

Merging two trees

+

Merging two trees

@@ -312,7 +312,7 @@

Library Stdlib.MSets.MSetAVL

-

Deletion

+

Deletion

@@ -332,7 +332,7 @@

Library Stdlib.MSets.MSetAVL

-

Concatenation

+

Concatenation

@@ -356,7 +356,7 @@

Library Stdlib.MSets.MSetAVL

-

Splitting

+

Splitting

@@ -396,7 +396,7 @@

Library Stdlib.MSets.MSetAVL

-

Intersection

+

Intersection

@@ -415,7 +415,7 @@

Library Stdlib.MSets.MSetAVL

-

Difference

+

Difference

@@ -434,7 +434,7 @@

Library Stdlib.MSets.MSetAVL

-

Union

+

Union

@@ -465,7 +465,7 @@

Library Stdlib.MSets.MSetAVL

-

Filter

+

Filter

@@ -483,7 +483,7 @@

Library Stdlib.MSets.MSetAVL

-

Partition

+

Partition

@@ -506,7 +506,7 @@

Library Stdlib.MSets.MSetAVL

-

MakeRaw

+

MakeRaw

@@ -779,7 +779,7 @@

Library Stdlib.MSets.MSetAVL

-

Singleton set

+

Singleton set

@@ -795,7 +795,7 @@

Library Stdlib.MSets.MSetAVL

-

Helper functions

+

Helper functions

@@ -822,7 +822,7 @@

Library Stdlib.MSets.MSetAVL

-

Insertion

+

Insertion

@@ -846,7 +846,7 @@

Library Stdlib.MSets.MSetAVL

-

Join

+

Join

@@ -885,7 +885,7 @@

Library Stdlib.MSets.MSetAVL

-

Extraction of minimum element

+

Extraction of minimum element

@@ -909,7 +909,7 @@

Library Stdlib.MSets.MSetAVL

-

Merging two trees

+

Merging two trees

@@ -928,7 +928,7 @@

Library Stdlib.MSets.MSetAVL

-

Deletion

+

Deletion

@@ -945,7 +945,7 @@

Library Stdlib.MSets.MSetAVL

-

Concatenation

+

Concatenation

@@ -964,7 +964,7 @@

Library Stdlib.MSets.MSetAVL

-

Splitting

+

Splitting

@@ -996,7 +996,7 @@

Library Stdlib.MSets.MSetAVL

-

Intersection

+

Intersection

@@ -1026,7 +1026,7 @@

Library Stdlib.MSets.MSetAVL

-

Difference

+

Difference

@@ -1047,7 +1047,7 @@

Library Stdlib.MSets.MSetAVL

-

Union

+

Union

@@ -1064,7 +1064,7 @@

Library Stdlib.MSets.MSetAVL

-

Filter

+

Filter

@@ -1086,7 +1086,7 @@

Library Stdlib.MSets.MSetAVL

-

Partition

+

Partition

@@ -1123,7 +1123,7 @@

Library Stdlib.MSets.MSetAVL

-

Encapsulation

+

Encapsulation

diff --git a/master/stdlib/Stdlib.MSets.MSetDecide.html b/master/stdlib/Stdlib.MSets.MSetDecide.html index 8f3b6749af..8953ea7717 100644 --- a/master/stdlib/Stdlib.MSets.MSetDecide.html +++ b/master/stdlib/Stdlib.MSets.MSetDecide.html @@ -74,7 +74,7 @@

Library Stdlib.MSets.MSetDecide

-

Overview

+

Overview

This functor defines the tactic fsetdec, which will solve any valid goal of the form @@ -180,7 +180,7 @@

Library Stdlib.MSets.MSetDecide

-

Facts and Tactics for Propositional Logic

+

Facts and Tactics for Propositional Logic

These lemmas and tactics are in a module so that they do not affect the namespace if you import the enclosing @@ -195,18 +195,18 @@

Library Stdlib.MSets.MSetDecide

-

Lemmas and Tactics About Decidable Propositions

+

Lemmas and Tactics About Decidable Propositions

-

Propositional Equivalences Involving Negation

+

Propositional Equivalences Involving Negation

These are all written with the unfolded form of negation, since I am not sure if setoid rewriting will always perform conversion.
-

Tactics for Negations

+

Tactics for Negations

@@ -457,7 +457,7 @@

Library Stdlib.MSets.MSetDecide

-

Auxiliary Tactics

+

Auxiliary Tactics

Again, these lemmas and tactics are in a module so that they do not affect the namespace if you import the @@ -470,7 +470,7 @@

Library Stdlib.MSets.MSetDecide

-

Generic Tactics

+

Generic Tactics

We begin by defining a few generic, useful tactics.
@@ -587,7 +587,7 @@

Library Stdlib.MSets.MSetDecide

-

Discarding Irrelevant Hypotheses

+

Discarding Irrelevant Hypotheses

We will want to clear the context of any non-MSet-related hypotheses in order to increase the @@ -667,7 +667,7 @@

Library Stdlib.MSets.MSetDecide

-

Turning Set Operators into Propositional Connectives

+

Turning Set Operators into Propositional Connectives

The lemmas from MSetFacts will be used to break down set operations into propositional formulas built over @@ -693,7 +693,7 @@

Library Stdlib.MSets.MSetDecide

-

Decidability of MSet Propositions

+

Decidability of MSet Propositions

@@ -728,7 +728,7 @@

Library Stdlib.MSets.MSetDecide

-

Normalizing Propositions About Equality

+

Normalizing Propositions About Equality

We have to deal with the fact that E.eq may be convertible with Coq's equality. Thus, we will find the @@ -811,7 +811,7 @@

Library Stdlib.MSets.MSetDecide

-

Considering Decidability of Base Propositions

+

Considering Decidability of Base Propositions

This tactic adds assertions about the decidability of E.eq and In to the context. This is necessary for @@ -860,7 +860,7 @@

Library Stdlib.MSets.MSetDecide

-

Handling Empty, Subset, and Equal

+

Handling Empty, Subset, and Equal

This tactic instantiates universally quantified hypotheses (which arise from the unfolding of Empty, @@ -908,7 +908,7 @@

Library Stdlib.MSets.MSetDecide

-

The Core fsetdec Auxiliary Tactics

+

The Core fsetdec Auxiliary Tactics

@@ -950,7 +950,7 @@

Library Stdlib.MSets.MSetDecide

-

The fsetdec Tactic

+

The fsetdec Tactic

Here is the top-level tactic (the only one intended for clients of this library). It's specification is given at @@ -1064,7 +1064,7 @@

Library Stdlib.MSets.MSetDecide

-

Examples

+

Examples

diff --git a/master/stdlib/Stdlib.MSets.MSetEqProperties.html b/master/stdlib/Stdlib.MSets.MSetEqProperties.html index d0574e6dd2..23e441d6e0 100644 --- a/master/stdlib/Stdlib.MSets.MSetEqProperties.html +++ b/master/stdlib/Stdlib.MSets.MSetEqProperties.html @@ -48,7 +48,7 @@

Library Stdlib.MSets.MSetEqProperties

-

Finite sets library

+

Finite sets library

diff --git a/master/stdlib/Stdlib.MSets.MSetFacts.html b/master/stdlib/Stdlib.MSets.MSetFacts.html index 8a7e1e72f3..776796e556 100644 --- a/master/stdlib/Stdlib.MSets.MSetFacts.html +++ b/master/stdlib/Stdlib.MSets.MSetFacts.html @@ -48,7 +48,7 @@

Library Stdlib.MSets.MSetFacts

-

Finite sets library

+

Finite sets library

@@ -87,7 +87,7 @@

Library Stdlib.MSets.MSetFacts

-

Specifications written using implications :

+

Specifications written using implications :

this used to be the default interface.
@@ -204,7 +204,7 @@

Library Stdlib.MSets.MSetFacts

-

Specifications written using equivalences :

+

Specifications written using equivalences :

this is now provided by the default interface.
@@ -293,7 +293,7 @@

Library Stdlib.MSets.MSetFacts

-

Specifications written using boolean predicates

+

Specifications written using boolean predicates

@@ -357,7 +357,7 @@

Library Stdlib.MSets.MSetFacts

-

Declarations of morphisms with respects to E.eq and Equal

+

Declarations of morphisms with respects to E.eq and Equal

diff --git a/master/stdlib/Stdlib.MSets.MSetGenTree.html b/master/stdlib/Stdlib.MSets.MSetGenTree.html index 4a9e20a624..0ce3933557 100644 --- a/master/stdlib/Stdlib.MSets.MSetGenTree.html +++ b/master/stdlib/Stdlib.MSets.MSetGenTree.html @@ -48,7 +48,7 @@

Library Stdlib.MSets.MSetGenTree

-

MSetGenTree : sets via generic trees

+

MSetGenTree : sets via generic trees

@@ -106,7 +106,7 @@

Library Stdlib.MSets.MSetGenTree

-

Ops : the pure functions

+

Ops : the pure functions

@@ -128,7 +128,7 @@

Library Stdlib.MSets.MSetGenTree

-

The empty set and emptyness test

+

The empty set and emptyness test

@@ -147,7 +147,7 @@

Library Stdlib.MSets.MSetGenTree

-

Membership test

+

Membership test

@@ -172,7 +172,7 @@

Library Stdlib.MSets.MSetGenTree

-

Minimal, maximal, arbitrary elements

+

Minimal, maximal, arbitrary elements

@@ -200,7 +200,7 @@

Library Stdlib.MSets.MSetGenTree

-

Iteration on elements

+

Iteration on elements

@@ -257,7 +257,7 @@

Library Stdlib.MSets.MSetGenTree

-

Testing universal or existential properties.

+

Testing universal or existential properties.

@@ -282,7 +282,7 @@

Library Stdlib.MSets.MSetGenTree

-

Comparison of trees

+

Comparison of trees

@@ -389,7 +389,7 @@

Library Stdlib.MSets.MSetGenTree

-

Subset test

+

Subset test

@@ -448,7 +448,7 @@

Library Stdlib.MSets.MSetGenTree

-

Props : correctness proofs of these generic operations

+

Props : correctness proofs of these generic operations

@@ -460,7 +460,7 @@

Library Stdlib.MSets.MSetGenTree

-

Occurrence in a tree

+

Occurrence in a tree

@@ -478,7 +478,7 @@

Library Stdlib.MSets.MSetGenTree

-

Some shortcuts

+

Some shortcuts

@@ -494,7 +494,7 @@

Library Stdlib.MSets.MSetGenTree

-

Binary search trees

+

Binary search trees

@@ -572,7 +572,7 @@

Library Stdlib.MSets.MSetGenTree

-

Known facts about ordered types

+

Known facts about ordered types

@@ -584,7 +584,7 @@

Library Stdlib.MSets.MSetGenTree

-

Automation and dedicated tactics

+

Automation and dedicated tactics

@@ -691,7 +691,7 @@

Library Stdlib.MSets.MSetGenTree

-

Basic results about In

+

Basic results about In

@@ -789,7 +789,7 @@

Library Stdlib.MSets.MSetGenTree

-

Empty set

+

Empty set

@@ -805,7 +805,7 @@

Library Stdlib.MSets.MSetGenTree

-

Emptyness test

+

Emptyness test

@@ -817,7 +817,7 @@

Library Stdlib.MSets.MSetGenTree

-

Membership

+

Membership

@@ -829,7 +829,7 @@

Library Stdlib.MSets.MSetGenTree

-

Minimal and maximal elements

+

Minimal and maximal elements

@@ -869,7 +869,7 @@

Library Stdlib.MSets.MSetGenTree

-

Elements

+

Elements

@@ -945,7 +945,7 @@

Library Stdlib.MSets.MSetGenTree

-

for_all and exists

+

for_all and exists

@@ -962,7 +962,7 @@

Library Stdlib.MSets.MSetGenTree

-

Fold

+

Fold

@@ -979,7 +979,7 @@

Library Stdlib.MSets.MSetGenTree

-

Subset

+

Subset

@@ -1004,7 +1004,7 @@

Library Stdlib.MSets.MSetGenTree

-

Comparison

+

Comparison

@@ -1106,7 +1106,7 @@

Library Stdlib.MSets.MSetGenTree

-

Equality test

+

Equality test

@@ -1119,7 +1119,7 @@

Library Stdlib.MSets.MSetGenTree

-

A few results about mindepth and maxdepth

+

A few results about mindepth and maxdepth

diff --git a/master/stdlib/Stdlib.MSets.MSetInterface.html b/master/stdlib/Stdlib.MSets.MSetInterface.html index 75af5f633e..eca37f0b50 100644 --- a/master/stdlib/Stdlib.MSets.MSetInterface.html +++ b/master/stdlib/Stdlib.MSets.MSetInterface.html @@ -48,7 +48,7 @@

Library Stdlib.MSets.MSetInterface

-

Finite set library

+

Finite set library

@@ -317,7 +317,7 @@

Library Stdlib.MSets.MSetInterface

-

Functorial signature for weak sets

+

Functorial signature for weak sets

@@ -431,7 +431,7 @@

Library Stdlib.MSets.MSetInterface

-

Static signature for weak sets

+

Static signature for weak sets

@@ -451,7 +451,7 @@

Library Stdlib.MSets.MSetInterface

-

Functorial signature for sets on ordered elements

+

Functorial signature for sets on ordered elements

@@ -563,7 +563,7 @@

Library Stdlib.MSets.MSetInterface

-

Static signature for sets on ordered elements

+

Static signature for sets on ordered elements

@@ -586,7 +586,7 @@

Library Stdlib.MSets.MSetInterface

-

Some subtyping tests

+

Some subtyping tests

 WSetsOn ---> WSets
@@ -603,7 +603,7 @@ 
Library Stdlib.MSets.MSetInterface

 
 
 

 
-
Signatures for set representations with ill-formed values.

+
Signatures for set representations with ill-formed values.

 
 
 
 

diff --git a/master/stdlib/Stdlib.MSets.MSetList.html b/master/stdlib/Stdlib.MSets.MSetList.html
index f64d248ae8..9ce804c7ce 100644
--- a/master/stdlib/Stdlib.MSets.MSetList.html
+++ b/master/stdlib/Stdlib.MSets.MSetList.html
@@ -48,7 +48,7 @@ 
Library Stdlib.MSets.MSetList
-

Finite sets library

+

Finite sets library

@@ -65,7 +65,7 @@

Library Stdlib.MSets.MSetList

-

Functions over lists

+

Functions over lists

@@ -93,7 +93,7 @@

Library Stdlib.MSets.MSetList

-

The set operations.

+

The set operations.

@@ -301,7 +301,7 @@

Library Stdlib.MSets.MSetList

-

Proofs of set operation specifications.

+

Proofs of set operation specifications.

@@ -642,7 +642,7 @@

Library Stdlib.MSets.MSetList

-

Encapsulation

+

Encapsulation

diff --git a/master/stdlib/Stdlib.MSets.MSetProperties.html b/master/stdlib/Stdlib.MSets.MSetProperties.html index c28db6a480..6fe3df8b53 100644 --- a/master/stdlib/Stdlib.MSets.MSetProperties.html +++ b/master/stdlib/Stdlib.MSets.MSetProperties.html @@ -48,7 +48,7 @@

Library Stdlib.MSets.MSetProperties

-

Finite sets library

+

Finite sets library

@@ -341,7 +341,7 @@

Library Stdlib.MSets.MSetProperties

-

Properties of elements

+

Properties of elements

@@ -356,7 +356,7 @@

Library Stdlib.MSets.MSetProperties

-

Conversions between lists and sets

+

Conversions between lists and sets

@@ -380,7 +380,7 @@

Library Stdlib.MSets.MSetProperties

-

Fold

+

Fold

@@ -408,7 +408,7 @@

Library Stdlib.MSets.MSetProperties

-

Induction principles for fold (contributed by S. Lescuyer)

+

Induction principles for fold (contributed by S. Lescuyer)

@@ -514,7 +514,7 @@

Library Stdlib.MSets.MSetProperties

-

Alternative (weaker) specifications for fold

+

Alternative (weaker) specifications for fold

@@ -586,7 +586,7 @@

Library Stdlib.MSets.MSetProperties

-

Fold is a morphism

+

Fold is a morphism

@@ -603,7 +603,7 @@

Library Stdlib.MSets.MSetProperties

-

Fold and other set operators

+

Fold and other set operators

@@ -655,11 +655,11 @@

Library Stdlib.MSets.MSetProperties

-

Cardinal

+

Cardinal

-

Characterization of cardinal in terms of fold

+

Characterization of cardinal in terms of fold

@@ -671,7 +671,7 @@

Library Stdlib.MSets.MSetProperties

-

Old specifications for cardinal.

+

Old specifications for cardinal.

@@ -694,7 +694,7 @@

Library Stdlib.MSets.MSetProperties

-

Cardinal and (non-)emptiness

+

Cardinal and (non-)emptiness

@@ -719,7 +719,7 @@

Library Stdlib.MSets.MSetProperties

-

Cardinal is a morphism

+

Cardinal is a morphism

@@ -739,7 +739,7 @@

Library Stdlib.MSets.MSetProperties

-

Cardinal and set operators

+

Cardinal and set operators

diff --git a/master/stdlib/Stdlib.MSets.MSetRBT.html b/master/stdlib/Stdlib.MSets.MSetRBT.html index 34adbdbf6c..780de61749 100644 --- a/master/stdlib/Stdlib.MSets.MSetRBT.html +++ b/master/stdlib/Stdlib.MSets.MSetRBT.html @@ -48,7 +48,7 @@

Library Stdlib.MSets.MSetRBT

-

MSetRBT : Implementation of MSetInterface via Red-Black trees

+

MSetRBT : Implementation of MSetInterface via Red-Black trees

@@ -152,7 +152,7 @@

Library Stdlib.MSets.MSetRBT

-

Ops : the pure functions

+

Ops : the pure functions

@@ -164,7 +164,7 @@

Library Stdlib.MSets.MSetRBT

-

Generic trees instantiated with color

+

Generic trees instantiated with color

@@ -186,7 +186,7 @@

Library Stdlib.MSets.MSetRBT

-

Basic tree

+

Basic tree

@@ -198,7 +198,7 @@

Library Stdlib.MSets.MSetRBT

-

Changing root color

+

Changing root color

@@ -221,7 +221,7 @@

Library Stdlib.MSets.MSetRBT

-

Balancing

+

Balancing

@@ -302,7 +302,7 @@

Library Stdlib.MSets.MSetRBT

-

Insertion

+

Insertion

@@ -334,7 +334,7 @@

Library Stdlib.MSets.MSetRBT

-

Deletion

+

Deletion

@@ -394,7 +394,7 @@

Library Stdlib.MSets.MSetRBT

-

Removing minimal element

+

Removing minimal element

@@ -424,7 +424,7 @@

Library Stdlib.MSets.MSetRBT

-

Tree-ification

+

Tree-ification

@@ -487,7 +487,7 @@

Library Stdlib.MSets.MSetRBT

-

Filtering

+

Filtering

@@ -525,7 +525,7 @@

Library Stdlib.MSets.MSetRBT

-

Union, intersection, difference

+

Union, intersection, difference

@@ -685,7 +685,7 @@

Library Stdlib.MSets.MSetRBT

-

MakeRaw : the pure functions and their specifications

+

MakeRaw : the pure functions and their specifications

@@ -723,7 +723,7 @@

Library Stdlib.MSets.MSetRBT

-

Singleton set

+

Singleton set

@@ -739,7 +739,7 @@

Library Stdlib.MSets.MSetRBT

-

makeBlack, MakeRed

+

makeBlack, MakeRed

@@ -762,7 +762,7 @@

Library Stdlib.MSets.MSetRBT

-

Generic handling for red-matching and red-red-matching

+

Generic handling for red-matching and red-red-matching

@@ -887,7 +887,7 @@

Library Stdlib.MSets.MSetRBT

-

Balancing for insertion

+

Balancing for insertion

@@ -933,7 +933,7 @@

Library Stdlib.MSets.MSetRBT

-

Insertion

+

Insertion

@@ -966,7 +966,7 @@

Library Stdlib.MSets.MSetRBT

-

Balancing for deletion

+

Balancing for deletion

@@ -996,7 +996,7 @@

Library Stdlib.MSets.MSetRBT

-

Append for deletion

+

Append for deletion

@@ -1049,7 +1049,7 @@

Library Stdlib.MSets.MSetRBT

-

Deletion

+

Deletion

@@ -1080,7 +1080,7 @@

Library Stdlib.MSets.MSetRBT

-

Removing the minimal element

+

Removing the minimal element

@@ -1109,7 +1109,7 @@

Library Stdlib.MSets.MSetRBT

-

Treeify

+

Treeify

@@ -1161,7 +1161,7 @@

Library Stdlib.MSets.MSetRBT

-

Filter

+

Filter

@@ -1187,7 +1187,7 @@

Library Stdlib.MSets.MSetRBT

-

Partition

+

Partition

@@ -1223,7 +1223,7 @@

Library Stdlib.MSets.MSetRBT

-

An invariant for binary list functions with accumulator.

+

An invariant for binary list functions with accumulator.

@@ -1270,7 +1270,7 @@

Library Stdlib.MSets.MSetRBT

-

union

+

union

@@ -1318,7 +1318,7 @@

Library Stdlib.MSets.MSetRBT

-

inter

+

inter

@@ -1359,7 +1359,7 @@

Library Stdlib.MSets.MSetRBT

-

difference

+

difference

@@ -1408,7 +1408,7 @@

Library Stdlib.MSets.MSetRBT

-

Balancing properties

+

Balancing properties

@@ -1431,7 +1431,7 @@

Library Stdlib.MSets.MSetRBT

-

Red-Black invariants

+

Red-Black invariants

@@ -1502,7 +1502,7 @@

Library Stdlib.MSets.MSetRBT

-

Basic tactics and results about red-black

+

Basic tactics and results about red-black

@@ -1537,7 +1537,7 @@

Library Stdlib.MSets.MSetRBT

-

A Red-Black tree has indeed a logarithmic depth

+

A Red-Black tree has indeed a logarithmic depth

@@ -1563,7 +1563,7 @@

Library Stdlib.MSets.MSetRBT

-

Singleton

+

Singleton

@@ -1575,7 +1575,7 @@

Library Stdlib.MSets.MSetRBT

-

makeBlack and makeRed

+

makeBlack and makeRed

@@ -1591,7 +1591,7 @@

Library Stdlib.MSets.MSetRBT

-

Balancing

+

Balancing

@@ -1628,7 +1628,7 @@

Library Stdlib.MSets.MSetRBT

-

Insertion

+

Insertion

@@ -1661,7 +1661,7 @@

Library Stdlib.MSets.MSetRBT

-

Deletion

+

Deletion

@@ -1692,7 +1692,7 @@

Library Stdlib.MSets.MSetRBT

-

Treeify

+

Treeify

@@ -1739,7 +1739,7 @@

Library Stdlib.MSets.MSetRBT

-

Filtering

+

Filtering

@@ -1760,7 +1760,7 @@

Library Stdlib.MSets.MSetRBT

-

Union, intersection, difference

+

Union, intersection, difference

@@ -1789,7 +1789,7 @@

Library Stdlib.MSets.MSetRBT

-

Final Encapsulation

+

Final Encapsulation

diff --git a/master/stdlib/Stdlib.MSets.MSetToFiniteSet.html b/master/stdlib/Stdlib.MSets.MSetToFiniteSet.html index 761876f6ca..d9281f2e03 100644 --- a/master/stdlib/Stdlib.MSets.MSetToFiniteSet.html +++ b/master/stdlib/Stdlib.MSets.MSetToFiniteSet.html @@ -48,7 +48,7 @@

Library Stdlib.MSets.MSetToFiniteSet

-

Finite sets library : conversion to old Finite_sets

+

Finite sets library : conversion to old Finite_sets

@@ -61,7 +61,7 @@

Library Stdlib.MSets.MSetToFiniteSet

-

Going from MSets with usual Leibniz equality

+

Going from MSets with usual Leibniz equality

to the good old Ensembles and Finite_sets theory.
diff --git a/master/stdlib/Stdlib.MSets.MSetWeakList.html b/master/stdlib/Stdlib.MSets.MSetWeakList.html index 348e709453..e1faffd980 100644 --- a/master/stdlib/Stdlib.MSets.MSetWeakList.html +++ b/master/stdlib/Stdlib.MSets.MSetWeakList.html @@ -48,7 +48,7 @@

Library Stdlib.MSets.MSetWeakList

-

Finite sets library

+

Finite sets library

@@ -68,7 +68,7 @@

Library Stdlib.MSets.MSetWeakList

-

Functions over lists

+

Functions over lists

@@ -78,7 +78,7 @@

Library Stdlib.MSets.MSetWeakList

And the functions returning sets are proved to preserve this invariant.
-

The set operations.

+

The set operations.

@@ -193,7 +193,7 @@

Library Stdlib.MSets.MSetWeakList

-

Proofs of set operation specifications.

+

Proofs of set operation specifications.

@@ -425,7 +425,7 @@

Library Stdlib.MSets.MSetWeakList

-

Encapsulation

+

Encapsulation

diff --git a/master/stdlib/Stdlib.NArith.BinNat.html b/master/stdlib/Stdlib.NArith.BinNat.html index 29f82132f9..3cc3219168 100644 --- a/master/stdlib/Stdlib.NArith.BinNat.html +++ b/master/stdlib/Stdlib.NArith.BinNat.html @@ -54,7 +54,7 @@

Library Stdlib.NArith.BinNat

-

Binary natural numbers, operations and properties

+

Binary natural numbers, operations and properties

@@ -894,7 +894,7 @@

Library Stdlib.NArith.BinNat

-

Properties of iter

+

Properties of iter

diff --git a/master/stdlib/Stdlib.NArith.BinNatDef.html b/master/stdlib/Stdlib.NArith.BinNatDef.html index 7b0214d961..ef32f7c781 100644 --- a/master/stdlib/Stdlib.NArith.BinNatDef.html +++ b/master/stdlib/Stdlib.NArith.BinNatDef.html @@ -61,7 +61,7 @@

Library Stdlib.NArith.BinNatDef

-

Binary natural numbers, definitions of operations

+

Binary natural numbers, definitions of operations

@@ -79,7 +79,7 @@

Library Stdlib.NArith.BinNatDef

-

Nicer name N.pos for constructor Npos

+

Nicer name N.pos for constructor Npos

@@ -91,7 +91,7 @@

Library Stdlib.NArith.BinNatDef

-

Constants

+

Constants

@@ -105,7 +105,7 @@

Library Stdlib.NArith.BinNatDef

-

Successor

+

Successor

@@ -121,7 +121,7 @@

Library Stdlib.NArith.BinNatDef

-

Predecessor

+

Predecessor

@@ -137,7 +137,7 @@

Library Stdlib.NArith.BinNatDef

-

Addition

+

Addition

diff --git a/master/stdlib/Stdlib.NArith.Nnat.html b/master/stdlib/Stdlib.NArith.Nnat.html index ae6a442a25..70d4708adb 100644 --- a/master/stdlib/Stdlib.NArith.Nnat.html +++ b/master/stdlib/Stdlib.NArith.Nnat.html @@ -51,7 +51,7 @@

Library Stdlib.NArith.Nnat

-

Conversions from N to nat

+

Conversions from N to nat

@@ -167,7 +167,7 @@

Library Stdlib.NArith.Nnat

-

Conversions from nat to N

+

Conversions from nat to N

diff --git a/master/stdlib/Stdlib.Numbers.AltBinNotations.html b/master/stdlib/Stdlib.Numbers.AltBinNotations.html index deede5d023..a2f657c40c 100644 --- a/master/stdlib/Stdlib.Numbers.AltBinNotations.html +++ b/master/stdlib/Stdlib.Numbers.AltBinNotations.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.AltBinNotations

-

Alternative Binary Number Notations

+

Alternative Binary Number Notations

diff --git a/master/stdlib/Stdlib.Numbers.Cyclic.Abstract.CyclicAxioms.html b/master/stdlib/Stdlib.Numbers.Cyclic.Abstract.CyclicAxioms.html index c047598d04..62265c7fd3 100644 --- a/master/stdlib/Stdlib.Numbers.Cyclic.Abstract.CyclicAxioms.html +++ b/master/stdlib/Stdlib.Numbers.Cyclic.Abstract.CyclicAxioms.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.Cyclic.Abstract.CyclicAxioms

-

Signature and specification of bounded integers

+

Signature and specification of bounded integers

diff --git a/master/stdlib/Stdlib.Numbers.Cyclic.Abstract.NZCyclic.html b/master/stdlib/Stdlib.Numbers.Cyclic.Abstract.NZCyclic.html index 8a887e2157..f8eb7aae6e 100644 --- a/master/stdlib/Stdlib.Numbers.Cyclic.Abstract.NZCyclic.html +++ b/master/stdlib/Stdlib.Numbers.Cyclic.Abstract.NZCyclic.html @@ -56,7 +56,7 @@

Library Stdlib.Numbers.Cyclic.Abstract.NZCyclic

-

From CyclicType to NZAxiomsSig

+

From CyclicType to NZAxiomsSig

diff --git a/master/stdlib/Stdlib.Numbers.Cyclic.Int63.Cyclic63.html b/master/stdlib/Stdlib.Numbers.Cyclic.Int63.Cyclic63.html index b1343d6fa1..f2bb9fe700 100644 --- a/master/stdlib/Stdlib.Numbers.Cyclic.Int63.Cyclic63.html +++ b/master/stdlib/Stdlib.Numbers.Cyclic.Int63.Cyclic63.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.Cyclic.Int63.Cyclic63

-

Uint63 numbers defines indeed a cyclic structure : Z/(2^63)Z

+

Uint63 numbers defines indeed a cyclic structure : Z/(2^63)Z

diff --git a/master/stdlib/Stdlib.Numbers.Cyclic.Int63.Ring63.html b/master/stdlib/Stdlib.Numbers.Cyclic.Int63.Ring63.html index 9b51c60126..e1063e17ce 100644 --- a/master/stdlib/Stdlib.Numbers.Cyclic.Int63.Ring63.html +++ b/master/stdlib/Stdlib.Numbers.Cyclic.Int63.Ring63.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.Cyclic.Int63.Ring63

-

Uint63 numbers defines Z/(2^63)Z, and can hence be equipped

+

Uint63 numbers defines Z/(2^63)Z, and can hence be equipped

with a ring structure and a ring tactic
diff --git a/master/stdlib/Stdlib.Numbers.DecimalFacts.html b/master/stdlib/Stdlib.Numbers.DecimalFacts.html index dba7c47a88..7983087980 100644 --- a/master/stdlib/Stdlib.Numbers.DecimalFacts.html +++ b/master/stdlib/Stdlib.Numbers.DecimalFacts.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.DecimalFacts

-

DecimalFacts : some facts about Decimal numbers

+

DecimalFacts : some facts about Decimal numbers

diff --git a/master/stdlib/Stdlib.Numbers.DecimalN.html b/master/stdlib/Stdlib.Numbers.DecimalN.html index 987e5eadc0..d4cb4de3c3 100644 --- a/master/stdlib/Stdlib.Numbers.DecimalN.html +++ b/master/stdlib/Stdlib.Numbers.DecimalN.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.DecimalN

-

DecimalN

+

DecimalN

diff --git a/master/stdlib/Stdlib.Numbers.DecimalNat.html b/master/stdlib/Stdlib.Numbers.DecimalNat.html index 13ce7a8d4b..615ad91a3b 100644 --- a/master/stdlib/Stdlib.Numbers.DecimalNat.html +++ b/master/stdlib/Stdlib.Numbers.DecimalNat.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.DecimalNat

-

DecimalNat

+

DecimalNat

diff --git a/master/stdlib/Stdlib.Numbers.DecimalPos.html b/master/stdlib/Stdlib.Numbers.DecimalPos.html index 01a300905f..fe21963782 100644 --- a/master/stdlib/Stdlib.Numbers.DecimalPos.html +++ b/master/stdlib/Stdlib.Numbers.DecimalPos.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.DecimalPos

-

DecimalPos

+

DecimalPos

diff --git a/master/stdlib/Stdlib.Numbers.DecimalQ.html b/master/stdlib/Stdlib.Numbers.DecimalQ.html index 1e0bc3512b..4d729be4c2 100644 --- a/master/stdlib/Stdlib.Numbers.DecimalQ.html +++ b/master/stdlib/Stdlib.Numbers.DecimalQ.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.DecimalQ

-

DecimalQ

+

DecimalQ

diff --git a/master/stdlib/Stdlib.Numbers.DecimalR.html b/master/stdlib/Stdlib.Numbers.DecimalR.html index 7af563fbc2..094b7b215d 100644 --- a/master/stdlib/Stdlib.Numbers.DecimalR.html +++ b/master/stdlib/Stdlib.Numbers.DecimalR.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.DecimalR

-

DecimalR

+

DecimalR

diff --git a/master/stdlib/Stdlib.Numbers.DecimalString.html b/master/stdlib/Stdlib.Numbers.DecimalString.html index 6db432a6e6..335307a6f6 100644 --- a/master/stdlib/Stdlib.Numbers.DecimalString.html +++ b/master/stdlib/Stdlib.Numbers.DecimalString.html @@ -51,7 +51,7 @@

Library Stdlib.Numbers.DecimalString

-

Conversion between decimal numbers and Coq strings

+

Conversion between decimal numbers and Coq strings

diff --git a/master/stdlib/Stdlib.Numbers.DecimalZ.html b/master/stdlib/Stdlib.Numbers.DecimalZ.html index 0956350ae5..e84c00503d 100644 --- a/master/stdlib/Stdlib.Numbers.DecimalZ.html +++ b/master/stdlib/Stdlib.Numbers.DecimalZ.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.DecimalZ

-

DecimalZ

+

DecimalZ

diff --git a/master/stdlib/Stdlib.Numbers.HexadecimalFacts.html b/master/stdlib/Stdlib.Numbers.HexadecimalFacts.html index a080027202..7862d746b9 100644 --- a/master/stdlib/Stdlib.Numbers.HexadecimalFacts.html +++ b/master/stdlib/Stdlib.Numbers.HexadecimalFacts.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.HexadecimalFacts

-

HexadecimalFacts : some facts about Hexadecimal numbers

+

HexadecimalFacts : some facts about Hexadecimal numbers

diff --git a/master/stdlib/Stdlib.Numbers.HexadecimalN.html b/master/stdlib/Stdlib.Numbers.HexadecimalN.html index 536bddb106..53aa14380b 100644 --- a/master/stdlib/Stdlib.Numbers.HexadecimalN.html +++ b/master/stdlib/Stdlib.Numbers.HexadecimalN.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.HexadecimalN

-

HexadecimalN

+

HexadecimalN

diff --git a/master/stdlib/Stdlib.Numbers.HexadecimalNat.html b/master/stdlib/Stdlib.Numbers.HexadecimalNat.html index 0caa21a7b2..7979e0df35 100644 --- a/master/stdlib/Stdlib.Numbers.HexadecimalNat.html +++ b/master/stdlib/Stdlib.Numbers.HexadecimalNat.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.HexadecimalNat

-

HexadecimalNat

+

HexadecimalNat

diff --git a/master/stdlib/Stdlib.Numbers.HexadecimalPos.html b/master/stdlib/Stdlib.Numbers.HexadecimalPos.html index 06c9de085f..0159ea88b0 100644 --- a/master/stdlib/Stdlib.Numbers.HexadecimalPos.html +++ b/master/stdlib/Stdlib.Numbers.HexadecimalPos.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.HexadecimalPos

-

HexadecimalPos

+

HexadecimalPos

diff --git a/master/stdlib/Stdlib.Numbers.HexadecimalQ.html b/master/stdlib/Stdlib.Numbers.HexadecimalQ.html index 43c3b9e8e3..0a4401241a 100644 --- a/master/stdlib/Stdlib.Numbers.HexadecimalQ.html +++ b/master/stdlib/Stdlib.Numbers.HexadecimalQ.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.HexadecimalQ

-

HexadecimalQ

+

HexadecimalQ

diff --git a/master/stdlib/Stdlib.Numbers.HexadecimalR.html b/master/stdlib/Stdlib.Numbers.HexadecimalR.html index 04b0103431..132278eea7 100644 --- a/master/stdlib/Stdlib.Numbers.HexadecimalR.html +++ b/master/stdlib/Stdlib.Numbers.HexadecimalR.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.HexadecimalR

-

HexadecimalR

+

HexadecimalR

diff --git a/master/stdlib/Stdlib.Numbers.HexadecimalString.html b/master/stdlib/Stdlib.Numbers.HexadecimalString.html index 79949dae2d..adda766bd2 100644 --- a/master/stdlib/Stdlib.Numbers.HexadecimalString.html +++ b/master/stdlib/Stdlib.Numbers.HexadecimalString.html @@ -51,7 +51,7 @@

Library Stdlib.Numbers.HexadecimalString

-

Conversion between hexadecimal numbers and Coq strings

+

Conversion between hexadecimal numbers and Coq strings

diff --git a/master/stdlib/Stdlib.Numbers.HexadecimalZ.html b/master/stdlib/Stdlib.Numbers.HexadecimalZ.html index 81813b403a..b35edf4797 100644 --- a/master/stdlib/Stdlib.Numbers.HexadecimalZ.html +++ b/master/stdlib/Stdlib.Numbers.HexadecimalZ.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.HexadecimalZ

-

HexadecimalZ

+

HexadecimalZ

diff --git a/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZBits.html b/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZBits.html index 75de367515..59534cae9f 100644 --- a/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZBits.html +++ b/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZBits.html @@ -472,7 +472,7 @@

Library Stdlib.Numbers.Integer.Abstract.ZBits

-

Properties of shifts

+

Properties of shifts

diff --git a/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZDivEucl.html b/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZDivEucl.html index 813c2ea49c..11f0f2ef4f 100644 --- a/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZDivEucl.html +++ b/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZDivEucl.html @@ -54,7 +54,7 @@

Library Stdlib.Numbers.Integer.Abstract.ZDivEucl

-

Euclidean Division for integers, Euclid convention

+

Euclidean Division for integers, Euclid convention

@@ -245,7 +245,7 @@

Library Stdlib.Numbers.Integer.Abstract.ZDivEucl

-

Basic values of divisions and modulo.

+

Basic values of divisions and modulo.

@@ -281,7 +281,7 @@

Library Stdlib.Numbers.Integer.Abstract.ZDivEucl

-

Order results about mod and div

+

Order results about mod and div

@@ -410,7 +410,7 @@

Library Stdlib.Numbers.Integer.Abstract.ZDivEucl

-

Relations between usual operations and mod and div

+

Relations between usual operations and mod and div

diff --git a/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZDivFloor.html b/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZDivFloor.html index a94d0f9e8a..e9ade89428 100644 --- a/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZDivFloor.html +++ b/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZDivFloor.html @@ -51,7 +51,7 @@

Library Stdlib.Numbers.Integer.Abstract.ZDivFloor

-

Euclidean Division for integers (Floor convention)

+

Euclidean Division for integers (Floor convention)

@@ -283,7 +283,7 @@

Library Stdlib.Numbers.Integer.Abstract.ZDivFloor

-

Basic values of divisions and modulo.

+

Basic values of divisions and modulo.

@@ -319,7 +319,7 @@

Library Stdlib.Numbers.Integer.Abstract.ZDivFloor

-

Order results about mod and div

+

Order results about mod and div

@@ -456,7 +456,7 @@

Library Stdlib.Numbers.Integer.Abstract.ZDivFloor

-

Relations between usual operations and mod and div

+

Relations between usual operations and mod and div

diff --git a/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZDivTrunc.html b/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZDivTrunc.html index b9fccf11c5..3c1518fba2 100644 --- a/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZDivTrunc.html +++ b/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZDivTrunc.html @@ -51,7 +51,7 @@

Library Stdlib.Numbers.Integer.Abstract.ZDivTrunc

-

Euclidean Division for integers (Trunc convention)

+

Euclidean Division for integers (Trunc convention)

@@ -208,7 +208,7 @@

Library Stdlib.Numbers.Integer.Abstract.ZDivTrunc

-

Basic values of divisions and modulo.

+

Basic values of divisions and modulo.

@@ -306,7 +306,7 @@

Library Stdlib.Numbers.Integer.Abstract.ZDivTrunc

-

Order results about rem and quot

+

Order results about rem and quot

@@ -441,7 +441,7 @@

Library Stdlib.Numbers.Integer.Abstract.ZDivTrunc

-

Relations between usual operations and rem and quot

+

Relations between usual operations and rem and quot

diff --git a/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZLcm.html b/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZLcm.html index 9ad29fe5ab..3cc7a7a0ad 100644 --- a/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZLcm.html +++ b/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZLcm.html @@ -51,7 +51,7 @@

Library Stdlib.Numbers.Integer.Abstract.ZLcm

-

Least Common Multiple

+

Least Common Multiple

diff --git a/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZMaxMin.html b/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZMaxMin.html index be37264416..aa7abf492b 100644 --- a/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZMaxMin.html +++ b/master/stdlib/Stdlib.Numbers.Integer.Abstract.ZMaxMin.html @@ -51,7 +51,7 @@

Library Stdlib.Numbers.Integer.Abstract.ZMaxMin

-

Properties of minimum and maximum specific to integer numbers

+

Properties of minimum and maximum specific to integer numbers

diff --git a/master/stdlib/Stdlib.Numbers.Integer.Binary.ZBinary.html b/master/stdlib/Stdlib.Numbers.Integer.Binary.ZBinary.html index 4de3319cc2..81f309ac09 100644 --- a/master/stdlib/Stdlib.Numbers.Integer.Binary.ZBinary.html +++ b/master/stdlib/Stdlib.Numbers.Integer.Binary.ZBinary.html @@ -70,7 +70,7 @@

Library Stdlib.Numbers.Integer.Binary.ZBinary

-

An order tactic for integers

+

An order tactic for integers

diff --git a/master/stdlib/Stdlib.Numbers.NaryFunctions.html b/master/stdlib/Stdlib.Numbers.NaryFunctions.html index ab1ac94e03..1d8da946e7 100644 --- a/master/stdlib/Stdlib.Numbers.NaryFunctions.html +++ b/master/stdlib/Stdlib.Numbers.NaryFunctions.html @@ -56,7 +56,7 @@

Library Stdlib.Numbers.NaryFunctions

-

Generic dependently-typed operators about n-ary functions

+

Generic dependently-typed operators about n-ary functions

diff --git a/master/stdlib/Stdlib.Numbers.NatInt.NZAdd.html b/master/stdlib/Stdlib.Numbers.NatInt.NZAdd.html index bb2111e366..4a73756a26 100644 --- a/master/stdlib/Stdlib.Numbers.NatInt.NZAdd.html +++ b/master/stdlib/Stdlib.Numbers.NatInt.NZAdd.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.NatInt.NZAdd

-

Some properties of the addition for modules implementing NZBasicFunsSig'

+

Some properties of the addition for modules implementing NZBasicFunsSig'

diff --git a/master/stdlib/Stdlib.Numbers.NatInt.NZAddOrder.html b/master/stdlib/Stdlib.Numbers.NatInt.NZAddOrder.html index d85b44ce55..0214a5110f 100644 --- a/master/stdlib/Stdlib.Numbers.NatInt.NZAddOrder.html +++ b/master/stdlib/Stdlib.Numbers.NatInt.NZAddOrder.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.NatInt.NZAddOrder

-

Properties of orders and addition for modules implementing NZOrdAxiomsSig'

+

Properties of orders and addition for modules implementing NZOrdAxiomsSig'

diff --git a/master/stdlib/Stdlib.Numbers.NatInt.NZAxioms.html b/master/stdlib/Stdlib.Numbers.NatInt.NZAxioms.html index 30fbf4698f..c9f81aa379 100644 --- a/master/stdlib/Stdlib.Numbers.NatInt.NZAxioms.html +++ b/master/stdlib/Stdlib.Numbers.NatInt.NZAxioms.html @@ -51,7 +51,7 @@

Library Stdlib.Numbers.NatInt.NZAxioms

Initial Author : Evgeny Makarov, INRIA, 2007
-

Axioms for a domain with zero, succ, pred.

+

Axioms for a domain with zero, succ, pred.

@@ -144,7 +144,7 @@

Library Stdlib.Numbers.NatInt.NZAxioms

-

Axiomatization of a domain with zero, succ, pred and a bi-directional induction principle.

+

Axiomatization of a domain with zero, succ, pred and a bi-directional induction principle.

@@ -226,7 +226,7 @@

Library Stdlib.Numbers.NatInt.NZAxioms

-

Axiomatization of some more constants

+

Axiomatization of some more constants

@@ -283,7 +283,7 @@

Library Stdlib.Numbers.NatInt.NZAxioms

-

Axiomatization of basic operations : + - *

+

Axiomatization of basic operations : + - *

@@ -339,7 +339,7 @@

Library Stdlib.Numbers.NatInt.NZAxioms

-

Axiomatization of order

+

Axiomatization of order

diff --git a/master/stdlib/Stdlib.Numbers.NatInt.NZBase.html b/master/stdlib/Stdlib.Numbers.NatInt.NZBase.html index 9596f619b7..93d5cad5c8 100644 --- a/master/stdlib/Stdlib.Numbers.NatInt.NZBase.html +++ b/master/stdlib/Stdlib.Numbers.NatInt.NZBase.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.NatInt.NZBase

-

Basic lemmas about modules implementing NZDomainSig'

+

Basic lemmas about modules implementing NZDomainSig'

diff --git a/master/stdlib/Stdlib.Numbers.NatInt.NZDiv.html b/master/stdlib/Stdlib.Numbers.NatInt.NZDiv.html index 158fcdfa00..1e23ebe97f 100644 --- a/master/stdlib/Stdlib.Numbers.NatInt.NZDiv.html +++ b/master/stdlib/Stdlib.Numbers.NatInt.NZDiv.html @@ -189,7 +189,7 @@

Library Stdlib.Numbers.NatInt.NZDiv

-

Basic values of divisions and modulo.

+

Basic values of divisions and modulo.

@@ -222,7 +222,7 @@

Library Stdlib.Numbers.NatInt.NZDiv

-

Order results about mod and div

+

Order results about mod and div

@@ -334,7 +334,7 @@

Library Stdlib.Numbers.NatInt.NZDiv

-

Relations between usual operations and mod and div

+

Relations between usual operations and mod and div

diff --git a/master/stdlib/Stdlib.Numbers.NatInt.NZDomain.html b/master/stdlib/Stdlib.Numbers.NatInt.NZDomain.html index 1997781b99..b26eb3b52a 100644 --- a/master/stdlib/Stdlib.Numbers.NatInt.NZDomain.html +++ b/master/stdlib/Stdlib.Numbers.NatInt.NZDomain.html @@ -77,7 +77,7 @@

Library Stdlib.Numbers.NatInt.NZDomain

-

Relationship between points thanks to succ and pred.

+

Relationship between points thanks to succ and pred.

@@ -128,7 +128,7 @@

Library Stdlib.Numbers.NatInt.NZDomain

-

Study of initial point w.r.t. succ (if any).

+

Study of initial point w.r.t. succ (if any).

@@ -252,7 +252,7 @@

Library Stdlib.Numbers.NatInt.NZDomain

-

An alternative induction principle using S and P.

+

An alternative induction principle using S and P.

diff --git a/master/stdlib/Stdlib.Numbers.NatInt.NZLog.html b/master/stdlib/Stdlib.Numbers.NatInt.NZLog.html index bb4922b64c..8c21530d37 100644 --- a/master/stdlib/Stdlib.Numbers.NatInt.NZLog.html +++ b/master/stdlib/Stdlib.Numbers.NatInt.NZLog.html @@ -417,7 +417,7 @@

Library Stdlib.Numbers.NatInt.NZLog

-

log2_up : a binary logarithm that rounds up instead of down

+

log2_up : a binary logarithm that rounds up instead of down

diff --git a/master/stdlib/Stdlib.Numbers.NatInt.NZMul.html b/master/stdlib/Stdlib.Numbers.NatInt.NZMul.html index 4688b8a38c..d4e04a9d16 100644 --- a/master/stdlib/Stdlib.Numbers.NatInt.NZMul.html +++ b/master/stdlib/Stdlib.Numbers.NatInt.NZMul.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.NatInt.NZMul

-

Some properties of the multiplication for modules implementing NZBasicFunsSig'

+

Some properties of the multiplication for modules implementing NZBasicFunsSig'

diff --git a/master/stdlib/Stdlib.Numbers.NatInt.NZMulOrder.html b/master/stdlib/Stdlib.Numbers.NatInt.NZMulOrder.html index 6bdcfdd62b..d76168c42c 100644 --- a/master/stdlib/Stdlib.Numbers.NatInt.NZMulOrder.html +++ b/master/stdlib/Stdlib.Numbers.NatInt.NZMulOrder.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.NatInt.NZMulOrder

-

Properties of orders and multiplication for modules implementing NZOrdAxiomsSig'

+

Properties of orders and multiplication for modules implementing NZOrdAxiomsSig'

diff --git a/master/stdlib/Stdlib.Numbers.NatInt.NZOrder.html b/master/stdlib/Stdlib.Numbers.NatInt.NZOrder.html index eae5142592..54ee8eb09c 100644 --- a/master/stdlib/Stdlib.Numbers.NatInt.NZOrder.html +++ b/master/stdlib/Stdlib.Numbers.NatInt.NZOrder.html @@ -48,7 +48,7 @@

Library Stdlib.Numbers.NatInt.NZOrder

-

Lemmas about orders for modules implementing NZOrdSig'

+

Lemmas about orders for modules implementing NZOrdSig'

@@ -104,11 +104,11 @@

Library Stdlib.Numbers.NatInt.NZOrder

-

Basic facts about le, lt, eq and succ

+

Basic facts about le, lt, eq and succ

-

Direct consequences of the specifications of lt and le

+

Direct consequences of the specifications of lt and le

@@ -166,7 +166,7 @@

Library Stdlib.Numbers.NatInt.NZOrder

-

Asymmetry and transitivity.

+

Asymmetry and transitivity.

@@ -187,7 +187,7 @@

Library Stdlib.Numbers.NatInt.NZOrder

-

Some type classes about order

+

Some type classes about order

@@ -208,7 +208,7 @@

Library Stdlib.Numbers.NatInt.NZOrder

-

Making the generic order tactic

+

Making the generic order tactic

@@ -235,7 +235,7 @@

Library Stdlib.Numbers.NatInt.NZOrder

-

Some direct consequences of order

+

Some direct consequences of order

@@ -280,7 +280,7 @@

Library Stdlib.Numbers.NatInt.NZOrder

-

More properties of < and <= with respect to S and 0

+

More properties of < and <= with respect to S and 0

@@ -336,7 +336,7 @@

Library Stdlib.Numbers.NatInt.NZOrder

-

More Trichotomy, decidability and double negation elimination

+

More Trichotomy, decidability and double negation elimination

@@ -447,7 +447,7 @@

Library Stdlib.Numbers.NatInt.NZOrder

-

Order-based induction principles

+

Order-based induction principles

diff --git a/master/stdlib/Stdlib.Numbers.NatInt.NZSqrt.html b/master/stdlib/Stdlib.Numbers.NatInt.NZSqrt.html index 765b3aa688..989112098d 100644 --- a/master/stdlib/Stdlib.Numbers.NatInt.NZSqrt.html +++ b/master/stdlib/Stdlib.Numbers.NatInt.NZSqrt.html @@ -347,7 +347,7 @@

Library Stdlib.Numbers.NatInt.NZSqrt

-

sqrt_up : a square root that rounds up instead of down

+

sqrt_up : a square root that rounds up instead of down

diff --git a/master/stdlib/Stdlib.Numbers.Natural.Abstract.NDiv.html b/master/stdlib/Stdlib.Numbers.Natural.Abstract.NDiv.html index 96053fbe8c..cf9bfde679 100644 --- a/master/stdlib/Stdlib.Numbers.Natural.Abstract.NDiv.html +++ b/master/stdlib/Stdlib.Numbers.Natural.Abstract.NDiv.html @@ -157,7 +157,7 @@

Library Stdlib.Numbers.Natural.Abstract.NDiv

-

Basic values of divisions and modulo.

+

Basic values of divisions and modulo.

@@ -190,7 +190,7 @@

Library Stdlib.Numbers.Natural.Abstract.NDiv

-

Order results about mod and div

+

Order results about mod and div

@@ -288,7 +288,7 @@

Library Stdlib.Numbers.Natural.Abstract.NDiv

-

Relations between usual operations and mod and div

+

Relations between usual operations and mod and div

diff --git a/master/stdlib/Stdlib.Numbers.Natural.Abstract.NLcm.html b/master/stdlib/Stdlib.Numbers.Natural.Abstract.NLcm.html index 81ae95c37a..ce7f83fc77 100644 --- a/master/stdlib/Stdlib.Numbers.Natural.Abstract.NLcm.html +++ b/master/stdlib/Stdlib.Numbers.Natural.Abstract.NLcm.html @@ -51,7 +51,7 @@

Library Stdlib.Numbers.Natural.Abstract.NLcm

-

Least Common Multiple

+

Least Common Multiple

diff --git a/master/stdlib/Stdlib.Numbers.Natural.Abstract.NMaxMin.html b/master/stdlib/Stdlib.Numbers.Natural.Abstract.NMaxMin.html index 151645ebca..701b191a3c 100644 --- a/master/stdlib/Stdlib.Numbers.Natural.Abstract.NMaxMin.html +++ b/master/stdlib/Stdlib.Numbers.Natural.Abstract.NMaxMin.html @@ -51,7 +51,7 @@

Library Stdlib.Numbers.Natural.Abstract.NMaxMin

-

Properties of minimum and maximum specific to natural numbers

+

Properties of minimum and maximum specific to natural numbers

diff --git a/master/stdlib/Stdlib.Numbers.Natural.Binary.NBinary.html b/master/stdlib/Stdlib.Numbers.Natural.Binary.NBinary.html index e911a47378..ba8a3ca7d5 100644 --- a/master/stdlib/Stdlib.Numbers.Natural.Binary.NBinary.html +++ b/master/stdlib/Stdlib.Numbers.Natural.Binary.NBinary.html @@ -58,7 +58,7 @@

Library Stdlib.Numbers.Natural.Binary.NBinary

-

BinNat.N already implements NAxiomSig

+

BinNat.N already implements NAxiomSig

diff --git a/master/stdlib/Stdlib.PArith.BinPos.html b/master/stdlib/Stdlib.PArith.BinPos.html index c07a60cae3..c7597e1add 100644 --- a/master/stdlib/Stdlib.PArith.BinPos.html +++ b/master/stdlib/Stdlib.PArith.BinPos.html @@ -56,7 +56,7 @@

Library Stdlib.PArith.BinPos

-

Binary positive numbers, operations and properties

+

Binary positive numbers, operations and properties

@@ -90,7 +90,7 @@

Library Stdlib.PArith.BinPos

-

Definitions of operations, now in a separate file

+

Definitions of operations, now in a separate file

@@ -112,7 +112,7 @@

Library Stdlib.PArith.BinPos

-

Logical Predicates

+

Logical Predicates

@@ -144,11 +144,11 @@

Library Stdlib.PArith.BinPos

-

Properties of operations over positive numbers

+

Properties of operations over positive numbers

-

Decidability of equality on binary positive numbers

+

Decidability of equality on binary positive numbers

@@ -160,11 +160,11 @@

Library Stdlib.PArith.BinPos

-

Properties of successor on binary positive numbers

+

Properties of successor on binary positive numbers

-

Specification of xI in term of succ and xO

+

Specification of xI in term of succ and xO

@@ -179,7 +179,7 @@

Library Stdlib.PArith.BinPos

-

Successor and double

+

Successor and double

@@ -203,7 +203,7 @@

Library Stdlib.PArith.BinPos

-

Successor and predecessor

+

Successor and predecessor

@@ -224,7 +224,7 @@

Library Stdlib.PArith.BinPos

-

Injectivity of successor

+

Injectivity of successor

@@ -236,7 +236,7 @@

Library Stdlib.PArith.BinPos

-

Predecessor to N

+

Predecessor to N

@@ -248,11 +248,11 @@

Library Stdlib.PArith.BinPos

-

Properties of addition on binary positive numbers

+

Properties of addition on binary positive numbers

-

Specification of succ in term of add

+

Specification of succ in term of add

@@ -267,7 +267,7 @@

Library Stdlib.PArith.BinPos

-

Specification of add_carry

+

Specification of add_carry

@@ -279,7 +279,7 @@

Library Stdlib.PArith.BinPos

-

Commutativity

+

Commutativity

@@ -291,7 +291,7 @@

Library Stdlib.PArith.BinPos

-

Permutation of add and succ

+

Permutation of add and succ

@@ -306,7 +306,7 @@

Library Stdlib.PArith.BinPos

-

No neutral elements for addition

+

No neutral elements for addition

@@ -316,7 +316,7 @@

Library Stdlib.PArith.BinPos

-

Simplification

+

Simplification

@@ -349,7 +349,7 @@

Library Stdlib.PArith.BinPos

-

Addition is associative

+

Addition is associative

@@ -361,7 +361,7 @@

Library Stdlib.PArith.BinPos

-

Commutation of addition and double

+

Commutation of addition and double

@@ -381,7 +381,7 @@

Library Stdlib.PArith.BinPos

-

Miscellaneous

+

Miscellaneous

@@ -393,7 +393,7 @@

Library Stdlib.PArith.BinPos

-

Peano induction and recursion on binary positive positive numbers

+

Peano induction and recursion on binary positive positive numbers

@@ -511,11 +511,11 @@

Library Stdlib.PArith.BinPos

-

Properties of multiplication on binary positive numbers

+

Properties of multiplication on binary positive numbers

-

One is neutral for multiplication

+

One is neutral for multiplication

@@ -530,7 +530,7 @@

Library Stdlib.PArith.BinPos

-

Right reduction properties for multiplication

+

Right reduction properties for multiplication

@@ -545,7 +545,7 @@

Library Stdlib.PArith.BinPos

-

Commutativity of multiplication

+

Commutativity of multiplication

@@ -557,7 +557,7 @@

Library Stdlib.PArith.BinPos

-

Distributivity of multiplication over addition

+

Distributivity of multiplication over addition

@@ -574,7 +574,7 @@

Library Stdlib.PArith.BinPos

-

Associativity of multiplication

+

Associativity of multiplication

@@ -586,7 +586,7 @@

Library Stdlib.PArith.BinPos

-

Successor and multiplication

+

Successor and multiplication

@@ -601,7 +601,7 @@

Library Stdlib.PArith.BinPos

-

Parity properties of multiplication

+

Parity properties of multiplication

@@ -616,7 +616,7 @@

Library Stdlib.PArith.BinPos

-

Simplification properties of multiplication

+

Simplification properties of multiplication

@@ -637,7 +637,7 @@

Library Stdlib.PArith.BinPos

-

Inversion of multiplication

+

Inversion of multiplication

@@ -655,7 +655,7 @@

Library Stdlib.PArith.BinPos

-

Square

+

Square

@@ -670,7 +670,7 @@

Library Stdlib.PArith.BinPos

-

Properties of iter

+

Properties of iter

@@ -716,7 +716,7 @@

Library Stdlib.PArith.BinPos

-

Properties of power

+

Properties of power

@@ -731,7 +731,7 @@

Library Stdlib.PArith.BinPos

-

Properties of square

+

Properties of square

@@ -743,7 +743,7 @@

Library Stdlib.PArith.BinPos

-

Properties of sub_mask

+

Properties of sub_mask

@@ -790,7 +790,7 @@

Library Stdlib.PArith.BinPos

-

Properties of boolean comparisons

+

Properties of boolean comparisons

@@ -819,7 +819,7 @@

Library Stdlib.PArith.BinPos

-

Properties of comparison on binary positive numbers

+

Properties of comparison on binary positive numbers

@@ -1013,7 +1013,7 @@

Library Stdlib.PArith.BinPos

-

Facts about gt and ge

+

Facts about gt and ge

@@ -1046,7 +1046,7 @@

Library Stdlib.PArith.BinPos

-

Comparison and the successor

+

Comparison and the successor

@@ -1072,7 +1072,7 @@

Library Stdlib.PArith.BinPos

-

1 is the least positive number

+

1 is the least positive number

@@ -1090,7 +1090,7 @@

Library Stdlib.PArith.BinPos

-

Properties of the order

+

Properties of the order

@@ -1163,7 +1163,7 @@

Library Stdlib.PArith.BinPos

-

Comparison and addition

+

Comparison and addition

@@ -1178,7 +1178,7 @@

Library Stdlib.PArith.BinPos

-

Order and addition

+

Order and addition

@@ -1208,7 +1208,7 @@

Library Stdlib.PArith.BinPos

-

Comparison and multiplication

+

Comparison and multiplication

@@ -1223,7 +1223,7 @@

Library Stdlib.PArith.BinPos

-

Order and multiplication

+

Order and multiplication

@@ -1259,7 +1259,7 @@

Library Stdlib.PArith.BinPos

-

Properties of subtraction on binary positive numbers

+

Properties of subtraction on binary positive numbers

@@ -1277,7 +1277,7 @@

Library Stdlib.PArith.BinPos

-

Properties of subtraction without underflow

+

Properties of subtraction without underflow

@@ -1375,7 +1375,7 @@

Library Stdlib.PArith.BinPos

-

Results concerning size and size_nat

+

Results concerning size and size_nat

@@ -1393,7 +1393,7 @@

Library Stdlib.PArith.BinPos

-

Properties of min and max

+

Properties of min and max

@@ -1489,7 +1489,7 @@

Library Stdlib.PArith.BinPos

-

Results concerning iter_op

+

Results concerning iter_op

@@ -1510,7 +1510,7 @@

Library Stdlib.PArith.BinPos

-

Results about of_nat and of_succ_nat

+

Results about of_nat and of_succ_nat

@@ -1528,7 +1528,7 @@

Library Stdlib.PArith.BinPos

-

Correctness proofs for the square root function

+

Correctness proofs for the square root function

@@ -1554,7 +1554,7 @@

Library Stdlib.PArith.BinPos

-

Correctness proofs for the gcd function

+

Correctness proofs for the gcd function

diff --git a/master/stdlib/Stdlib.PArith.BinPosDef.html b/master/stdlib/Stdlib.PArith.BinPosDef.html index 2e6416a6dc..05ebb58bba 100644 --- a/master/stdlib/Stdlib.PArith.BinPosDef.html +++ b/master/stdlib/Stdlib.PArith.BinPosDef.html @@ -48,7 +48,7 @@

Library Stdlib.PArith.BinPosDef

-

Binary positive numbers, operations

+

Binary positive numbers, operations

@@ -79,7 +79,7 @@

Library Stdlib.PArith.BinPosDef

-

Operations over positive numbers

+

Operations over positive numbers

@@ -91,7 +91,7 @@

Library Stdlib.PArith.BinPosDef

-

Predecessor

+

Predecessor

@@ -108,7 +108,7 @@

Library Stdlib.PArith.BinPosDef

-

Predecessor with mask

+

Predecessor with mask

@@ -132,7 +132,7 @@

Library Stdlib.PArith.BinPosDef

-

Power

+

Power

@@ -147,7 +147,7 @@

Library Stdlib.PArith.BinPosDef

-

Square

+

Square

@@ -164,7 +164,7 @@

Library Stdlib.PArith.BinPosDef

-

Number of digits in a positive number

+

Number of digits in a positive number

@@ -214,7 +214,7 @@

Library Stdlib.PArith.BinPosDef

-

Boolean equality and comparisons

+

Boolean equality and comparisons

@@ -232,7 +232,7 @@

Library Stdlib.PArith.BinPosDef

-

Greatest Common Divisor

+

Greatest Common Divisor

@@ -397,7 +397,7 @@

Library Stdlib.PArith.BinPosDef

-

From Peano natural numbers to binary positive numbers

+

From Peano natural numbers to binary positive numbers

@@ -417,7 +417,7 @@

Library Stdlib.PArith.BinPosDef

-

Conversion with a decimal representation for printing/parsing

+

Conversion with a decimal representation for printing/parsing

diff --git a/master/stdlib/Stdlib.PArith.POrderedType.html b/master/stdlib/Stdlib.PArith.POrderedType.html index f86c3fa804..1266851bcb 100644 --- a/master/stdlib/Stdlib.PArith.POrderedType.html +++ b/master/stdlib/Stdlib.PArith.POrderedType.html @@ -54,7 +54,7 @@

Library Stdlib.PArith.POrderedType

-

DecidableType structure for positive numbers

+

DecidableType structure for positive numbers

@@ -70,7 +70,7 @@

Library Stdlib.PArith.POrderedType

interfaces, such as DecidableType or EqualityType.
-

OrderedType structure for positive numbers

+

OrderedType structure for positive numbers

@@ -86,7 +86,7 @@

Library Stdlib.PArith.POrderedType

and a OrderedType (and also as a DecidableType).
-

An order tactic for positive numbers

+

An order tactic for positive numbers

diff --git a/master/stdlib/Stdlib.Program.Combinators.html b/master/stdlib/Stdlib.Program.Combinators.html index e5c95414fe..9b04cd4656 100644 --- a/master/stdlib/Stdlib.Program.Combinators.html +++ b/master/stdlib/Stdlib.Program.Combinators.html @@ -46,7 +46,7 @@

Library Stdlib.Program.Combinators

-

Proofs about standard combinators, exports functional extensionality.

+

Proofs about standard combinators, exports functional extensionality.

diff --git a/master/stdlib/Stdlib.QArith.QArith_base.html b/master/stdlib/Stdlib.QArith.QArith_base.html index 1095c70f07..e686a0aef2 100644 --- a/master/stdlib/Stdlib.QArith.QArith_base.html +++ b/master/stdlib/Stdlib.QArith.QArith_base.html @@ -58,7 +58,7 @@

Library Stdlib.QArith.QArith_base

-

Definition of Q and basic properties

+

Definition of Q and basic properties

@@ -201,7 +201,7 @@

Library Stdlib.QArith.QArith_base

-

Properties of equality.

+

Properties of equality.

@@ -293,7 +293,7 @@

Library Stdlib.QArith.QArith_base

-

Addition, multiplication and opposite

+

Addition, multiplication and opposite

@@ -560,7 +560,7 @@

Library Stdlib.QArith.QArith_base

-

Setoid compatibility results

+

Setoid compatibility results

@@ -634,7 +634,7 @@

Library Stdlib.QArith.QArith_base

-

Properties of Qadd

+

Properties of Qadd

@@ -674,7 +674,7 @@

Library Stdlib.QArith.QArith_base

-

Properties of Qopp

+

Properties of Qopp

@@ -705,7 +705,7 @@

Library Stdlib.QArith.QArith_base

-

Properties of Qmult

+

Properties of Qmult

@@ -787,7 +787,7 @@

Library Stdlib.QArith.QArith_base

-

inject_Z is a ring homomorphism:

+

inject_Z is a ring homomorphism:

@@ -805,7 +805,7 @@

Library Stdlib.QArith.QArith_base

-

Inverse and division.

+

Inverse and division.

@@ -857,11 +857,11 @@

Library Stdlib.QArith.QArith_base

-

Reduction and construction of Q

+

Reduction and construction of Q

-

Removal/introduction of common factor in both numerator and denominator.

+

Removal/introduction of common factor in both numerator and denominator.

@@ -906,7 +906,7 @@

Library Stdlib.QArith.QArith_base

-

Construction of a new rational by multiplication with an integer or pure fraction

+

Construction of a new rational by multiplication with an integer or pure fraction

@@ -932,7 +932,7 @@

Library Stdlib.QArith.QArith_base

-

Properties of order upon Q.

+

Properties of order upon Q.

@@ -1046,7 +1046,7 @@

Library Stdlib.QArith.QArith_base

-

Some decidability results about orders.

+

Some decidability results about orders.

@@ -1064,7 +1064,7 @@

Library Stdlib.QArith.QArith_base

-

Compatibility of addition with order

+

Compatibility of addition with order

@@ -1117,7 +1117,7 @@

Library Stdlib.QArith.QArith_base

-

Compatibility of multiplication with order.

+

Compatibility of multiplication with order.

@@ -1176,7 +1176,7 @@

Library Stdlib.QArith.QArith_base

-

Compatibility of inversion and division with order

+

Compatibility of inversion and division with order

@@ -1227,7 +1227,7 @@

Library Stdlib.QArith.QArith_base

-

Rational to the n-th power

+

Rational to the n-th power

diff --git a/master/stdlib/Stdlib.QArith.QOrderedType.html b/master/stdlib/Stdlib.QArith.QOrderedType.html index 800ec884af..9b3a5a37fb 100644 --- a/master/stdlib/Stdlib.QArith.QOrderedType.html +++ b/master/stdlib/Stdlib.QArith.QOrderedType.html @@ -54,7 +54,7 @@

Library Stdlib.QArith.QOrderedType

-

DecidableType structure for rational numbers

+

DecidableType structure for rational numbers

@@ -92,7 +92,7 @@

Library Stdlib.QArith.QOrderedType

interfaces, such as DecidableType or EqualityType.
-

OrderedType structure for rational numbers

+

OrderedType structure for rational numbers

@@ -123,7 +123,7 @@

Library Stdlib.QArith.QOrderedType

-

An order tactic for Q numbers

+

An order tactic for Q numbers

diff --git a/master/stdlib/Stdlib.QArith.Qcabs.html b/master/stdlib/Stdlib.QArith.Qcabs.html index 061d90cb79..d7de835fbd 100644 --- a/master/stdlib/Stdlib.QArith.Qcabs.html +++ b/master/stdlib/Stdlib.QArith.Qcabs.html @@ -48,7 +48,7 @@

Library Stdlib.QArith.Qcabs

-

An absolute value for normalized rational numbers.

+

An absolute value for normalized rational numbers.

diff --git a/master/stdlib/Stdlib.QArith.Qfield.html b/master/stdlib/Stdlib.QArith.Qfield.html index c83cbd7c2e..f0f98331df 100644 --- a/master/stdlib/Stdlib.QArith.Qfield.html +++ b/master/stdlib/Stdlib.QArith.Qfield.html @@ -53,7 +53,7 @@

Library Stdlib.QArith.Qfield

-

field and ring tactics for rational numbers

+

field and ring tactics for rational numbers

diff --git a/master/stdlib/Stdlib.QArith.Qminmax.html b/master/stdlib/Stdlib.QArith.Qminmax.html index eea40470f1..ed3e3cb6da 100644 --- a/master/stdlib/Stdlib.QArith.Qminmax.html +++ b/master/stdlib/Stdlib.QArith.Qminmax.html @@ -51,7 +51,7 @@

Library Stdlib.QArith.Qminmax

-

Maximum and Minimum of two rational numbers

+

Maximum and Minimum of two rational numbers

@@ -100,7 +100,7 @@

Library Stdlib.QArith.Qminmax

-

Properties specific to the Q domain

+

Properties specific to the Q domain

diff --git a/master/stdlib/Stdlib.QArith.Qpower.html b/master/stdlib/Stdlib.QArith.Qpower.html index 1a497302de..29f8a4fd52 100644 --- a/master/stdlib/Stdlib.QArith.Qpower.html +++ b/master/stdlib/Stdlib.QArith.Qpower.html @@ -51,11 +51,11 @@

Library Stdlib.QArith.Qpower

-

Properties of Qpower_positive

+

Properties of Qpower_positive

-

Values of Qpower_positive for specific arguments

+

Values of Qpower_positive for specific arguments

@@ -70,7 +70,7 @@

Library Stdlib.QArith.Qpower

-

Relation of Qpower_positive to zero

+

Relation of Qpower_positive to zero

@@ -85,7 +85,7 @@

Library Stdlib.QArith.Qpower

-

Qpower_positive and multiplication, exponent subtraction

+

Qpower_positive and multiplication, exponent subtraction

@@ -100,7 +100,7 @@

Library Stdlib.QArith.Qpower

-

Qpower_positive and inversion, division, exponent subtraction

+

Qpower_positive and inversion, division, exponent subtraction

@@ -117,7 +117,7 @@

Library Stdlib.QArith.Qpower

-

Qpower and exponent multiplication

+

Qpower and exponent multiplication

@@ -130,7 +130,7 @@

Library Stdlib.QArith.Qpower

-

Qpower_positive decomposition

+

Qpower_positive decomposition

@@ -146,11 +146,11 @@

Library Stdlib.QArith.Qpower

-

Properties of Qpower

+

Properties of Qpower

-

Values of Qpower for specific arguments

+

Values of Qpower for specific arguments

@@ -173,7 +173,7 @@

Library Stdlib.QArith.Qpower

-

Relation of Qpower to zero

+

Relation of Qpower to zero

@@ -195,7 +195,7 @@

Library Stdlib.QArith.Qpower

-

Relation of Qpower to 1

+

Relation of Qpower to 1

@@ -220,7 +220,7 @@

Library Stdlib.QArith.Qpower

-

Qpower and multiplication, exponent addition

+

Qpower and multiplication, exponent addition

@@ -238,7 +238,7 @@

Library Stdlib.QArith.Qpower

-

Qpower and inversion, division, exponent subtraction

+

Qpower and inversion, division, exponent subtraction

@@ -271,7 +271,7 @@

Library Stdlib.QArith.Qpower

-

Qpower and exponent multiplication

+

Qpower and exponent multiplication

@@ -283,7 +283,7 @@

Library Stdlib.QArith.Qpower

-

Qpower decomposition

+

Qpower decomposition

@@ -304,7 +304,7 @@

Library Stdlib.QArith.Qpower

-

Compatibility of Qpower with relational operators

+

Compatibility of Qpower with relational operators

@@ -329,7 +329,7 @@

Library Stdlib.QArith.Qpower

-

Qpower and inject_Z

+

Qpower and inject_Z

@@ -341,7 +341,7 @@

Library Stdlib.QArith.Qpower

-

Square

+

Square

@@ -353,7 +353,7 @@

Library Stdlib.QArith.Qpower

-

Power of 2 positive upper bound

+

Power of 2 positive upper bound

diff --git a/master/stdlib/Stdlib.Reals.AltSeries.html b/master/stdlib/Stdlib.Reals.AltSeries.html index 01a0eb1fde..6023f18559 100644 --- a/master/stdlib/Stdlib.Reals.AltSeries.html +++ b/master/stdlib/Stdlib.Reals.AltSeries.html @@ -58,7 +58,7 @@

Library Stdlib.Reals.AltSeries

-

Formalization of alternated series

+

Formalization of alternated series

@@ -121,7 +121,7 @@

Library Stdlib.Reals.AltSeries

-

Convergence of alternated series

+

Convergence of alternated series

@@ -143,7 +143,7 @@

Library Stdlib.Reals.AltSeries

-

Application : construction of PI

+

Application : construction of PI

diff --git a/master/stdlib/Stdlib.Reals.Cauchy.ConstructiveCauchyReals.html b/master/stdlib/Stdlib.Reals.Cauchy.ConstructiveCauchyReals.html index 8ec643170f..3d0ce2df36 100644 --- a/master/stdlib/Stdlib.Reals.Cauchy.ConstructiveCauchyReals.html +++ b/master/stdlib/Stdlib.Reals.Cauchy.ConstructiveCauchyReals.html @@ -407,7 +407,7 @@

Library Stdlib.Reals.Cauchy.ConstructiveCauchyReals

-

Algebraic operations

+

Algebraic operations

diff --git a/master/stdlib/Stdlib.Reals.Cauchy.ConstructiveCauchyRealsMult.html b/master/stdlib/Stdlib.Reals.Cauchy.ConstructiveCauchyRealsMult.html index 344789e5b2..e5daa40606 100644 --- a/master/stdlib/Stdlib.Reals.Cauchy.ConstructiveCauchyRealsMult.html +++ b/master/stdlib/Stdlib.Reals.Cauchy.ConstructiveCauchyRealsMult.html @@ -297,7 +297,7 @@

Library Stdlib.Reals.Cauchy.ConstructiveCauchyRealsMult

-

Field

+

Field

diff --git a/master/stdlib/Stdlib.Reals.Cauchy.QExtra.html b/master/stdlib/Stdlib.Reals.Cauchy.QExtra.html index 9820227e9e..53daa904b1 100644 --- a/master/stdlib/Stdlib.Reals.Cauchy.QExtra.html +++ b/master/stdlib/Stdlib.Reals.Cauchy.QExtra.html @@ -55,7 +55,7 @@

Library Stdlib.Reals.Cauchy.QExtra

-

Power of 2 open and closed upper and lower bounds for q : Q

+

Power of 2 open and closed upper and lower bounds for q : Q

@@ -96,7 +96,7 @@

Library Stdlib.Reals.Cauchy.QExtra

-

Power of two closed upper bound q <= 2^z

+

Power of two closed upper bound q <= 2^z

@@ -125,7 +125,7 @@

Library Stdlib.Reals.Cauchy.QExtra

-

Power of two open upper bound q < 2^z and Qabs q < 2^z

+

Power of two open upper bound q < 2^z and Qabs q < 2^z

@@ -171,7 +171,7 @@

Library Stdlib.Reals.Cauchy.QExtra

-

Power of 2 open lower bounds for 2^z < q and 2^z < Qabs q

+

Power of 2 open lower bounds for 2^z < q and 2^z < Qabs q

@@ -202,7 +202,7 @@

Library Stdlib.Reals.Cauchy.QExtra

-

Existential formulations of power of 2 lower and upper bounds

+

Existential formulations of power of 2 lower and upper bounds

diff --git a/master/stdlib/Stdlib.Reals.ClassicalDedekindReals.html b/master/stdlib/Stdlib.Reals.ClassicalDedekindReals.html index 2c16c857e9..04f7f7655e 100644 --- a/master/stdlib/Stdlib.Reals.ClassicalDedekindReals.html +++ b/master/stdlib/Stdlib.Reals.ClassicalDedekindReals.html @@ -64,7 +64,7 @@

Library Stdlib.Reals.ClassicalDedekindReals

-

Q Auxiliary Lemmas

+

Q Auxiliary Lemmas

@@ -87,11 +87,11 @@

Library Stdlib.Reals.ClassicalDedekindReals

-

Dedekind cuts

+

Dedekind cuts

-

Definition

+

Definition

@@ -133,7 +133,7 @@

Library Stdlib.Reals.ClassicalDedekindReals

-

Properties

+

Properties

@@ -165,11 +165,11 @@

Library Stdlib.Reals.ClassicalDedekindReals

-

Classical Dedekind reals

+

Classical Dedekind reals

-

Definition

+

Definition

@@ -182,7 +182,7 @@

Library Stdlib.Reals.ClassicalDedekindReals

-

Induction principle

+

Induction principle

@@ -196,11 +196,11 @@

Library Stdlib.Reals.ClassicalDedekindReals

-

Conversion to and from constructive Cauchy real CReal

+

Conversion to and from constructive Cauchy real CReal

-

Conversion from CReal to DReal

+

Conversion from CReal to DReal

@@ -219,7 +219,7 @@

Library Stdlib.Reals.ClassicalDedekindReals

-

Conversion from DReal to CReal

+

Conversion from DReal to CReal

@@ -270,7 +270,7 @@

Library Stdlib.Reals.ClassicalDedekindReals

-

Order for DReal

+

Order for DReal

diff --git a/master/stdlib/Stdlib.Reals.RIneq.html b/master/stdlib/Stdlib.Reals.RIneq.html index ad9e1bd27f..2efca6a813 100644 --- a/master/stdlib/Stdlib.Reals.RIneq.html +++ b/master/stdlib/Stdlib.Reals.RIneq.html @@ -48,7 +48,7 @@

Library Stdlib.Reals.RIneq

-

Basic lemmas for the classical real numbers

+

Basic lemmas for the classical real numbers

@@ -136,7 +136,7 @@

Library Stdlib.Reals.RIneq

-

Relation between orders and equality

+

Relation between orders and equality

@@ -226,7 +226,7 @@

Library Stdlib.Reals.RIneq

-

Strong decidable equality

+

Strong decidable equality

@@ -238,11 +238,11 @@

Library Stdlib.Reals.RIneq

-

Relating <, >, <= and >=

+

Relating <, >, <= and >=

-

Relating strict and large orders

+

Relating strict and large orders

@@ -347,7 +347,7 @@

Library Stdlib.Reals.RIneq

-

Asymmetry

+

Asymmetry

@@ -368,7 +368,7 @@

Library Stdlib.Reals.RIneq

-

Antisymmetry

+

Antisymmetry

@@ -397,7 +397,7 @@

Library Stdlib.Reals.RIneq

-

Compatibility with equality

+

Compatibility with equality

@@ -414,7 +414,7 @@

Library Stdlib.Reals.RIneq

-

Transitivity

+

Transitivity

@@ -457,7 +457,7 @@

Library Stdlib.Reals.RIneq

-

(Classical) decidability with sumbool types

+

(Classical) decidability with sumbool types

@@ -508,7 +508,7 @@

Library Stdlib.Reals.RIneq

-

Same theorems with disjunctions instead of sumbools

+

Same theorems with disjunctions instead of sumbools

@@ -562,7 +562,7 @@

Library Stdlib.Reals.RIneq

-

Addition

+

Addition

@@ -636,7 +636,7 @@

Library Stdlib.Reals.RIneq

-

Opposite

+

Opposite

@@ -678,7 +678,7 @@

Library Stdlib.Reals.RIneq

-

Multiplication

+

Multiplication

@@ -794,7 +794,7 @@

Library Stdlib.Reals.RIneq

-

Opposite and multiplication

+

Opposite and multiplication

@@ -822,7 +822,7 @@

Library Stdlib.Reals.RIneq

-

Subtraction

+

Subtraction

@@ -934,7 +934,7 @@

Library Stdlib.Reals.RIneq

-

Inverse

+

Inverse

@@ -988,7 +988,7 @@

Library Stdlib.Reals.RIneq

-

Square function

+

Square function

@@ -1010,11 +1010,11 @@

Library Stdlib.Reals.RIneq

-

Order and addition

+

Order and addition

-

Compatibility

+

Compatibility

@@ -1115,7 +1115,7 @@

Library Stdlib.Reals.RIneq

-

Cancellation

+

Cancellation

@@ -1167,7 +1167,7 @@

Library Stdlib.Reals.RIneq

-

Comparison of addition with left operand

+

Comparison of addition with left operand

@@ -1188,7 +1188,7 @@

Library Stdlib.Reals.RIneq

-

Sign of addition

+

Sign of addition

@@ -1221,11 +1221,11 @@

Library Stdlib.Reals.RIneq

-

Order and opposite

+

Order and opposite

-

Contravariant compatibility

+

Contravariant compatibility

@@ -1301,7 +1301,7 @@

Library Stdlib.Reals.RIneq

-

Cancellation

+

Cancellation

@@ -1326,7 +1326,7 @@

Library Stdlib.Reals.RIneq

-

Sign of opposite

+

Sign of opposite

@@ -1341,14 +1341,14 @@

Library Stdlib.Reals.RIneq

-

Order and multiplication

+

Order and multiplication

Remark: Rmult_lt_compat_l is in Raxioms.v
-

Covariant compatibility

+

Covariant compatibility

@@ -1419,7 +1419,7 @@

Library Stdlib.Reals.RIneq

-

Contravariant compatibility

+

Contravariant compatibility

@@ -1444,7 +1444,7 @@

Library Stdlib.Reals.RIneq

-

Sign of multiplication

+

Sign of multiplication

@@ -1479,7 +1479,7 @@

Library Stdlib.Reals.RIneq

-

Order and square function

+

Order and square function

@@ -1500,7 +1500,7 @@

Library Stdlib.Reals.RIneq

-

Zero is less than one

+

Zero is less than one

@@ -1517,7 +1517,7 @@

Library Stdlib.Reals.RIneq

-

Sign of inverse

+

Sign of inverse

@@ -1536,7 +1536,7 @@

Library Stdlib.Reals.RIneq

-

Cancellation in inequalities of products

+

Cancellation in inequalities of products

@@ -1563,7 +1563,7 @@

Library Stdlib.Reals.RIneq

-

Order and inverse

+

Order and inverse

@@ -1594,7 +1594,7 @@

Library Stdlib.Reals.RIneq

-

Sign of inverse

+

Sign of inverse

@@ -1609,7 +1609,7 @@

Library Stdlib.Reals.RIneq

-

Order and subtraction

+

Order and subtraction

@@ -1653,7 +1653,7 @@

Library Stdlib.Reals.RIneq

-

Division

+

Division

@@ -1753,7 +1753,7 @@

Library Stdlib.Reals.RIneq

-

Sign of division

+

Sign of division

@@ -1778,7 +1778,7 @@

Library Stdlib.Reals.RIneq

-

Miscellaneous

+

Miscellaneous

@@ -1832,7 +1832,7 @@

Library Stdlib.Reals.RIneq

-

Injection from nat to R

+

Injection from nat to R

@@ -1931,7 +1931,7 @@

Library Stdlib.Reals.RIneq

-

Injection from positive to R

+

Injection from positive to R

@@ -2012,7 +2012,7 @@

Library Stdlib.Reals.RIneq

-

Injection from Z to R

+

Injection from Z to R

@@ -2154,7 +2154,7 @@

Library Stdlib.Reals.RIneq

-

Definitions of new types

+

Definitions of new types

@@ -2181,7 +2181,7 @@

Library Stdlib.Reals.RIneq

-

A few common instances

+

A few common instances

@@ -2197,7 +2197,7 @@

Library Stdlib.Reals.RIneq

-

Compatibility

+

Compatibility

diff --git a/master/stdlib/Stdlib.Reals.ROrderedType.html b/master/stdlib/Stdlib.Reals.ROrderedType.html index 794f60a999..8d5b12dad4 100644 --- a/master/stdlib/Stdlib.Reals.ROrderedType.html +++ b/master/stdlib/Stdlib.Reals.ROrderedType.html @@ -54,7 +54,7 @@

Library Stdlib.Reals.ROrderedType

-

DecidableType structure for real numbers

+

DecidableType structure for real numbers

@@ -89,7 +89,7 @@

Library Stdlib.Reals.ROrderedType

and a DecidableTypeOrig.
-

OrderedType structure for binary integers

+

OrderedType structure for binary integers

@@ -137,7 +137,7 @@

Library Stdlib.Reals.ROrderedType

and a OrderedType (and also as a DecidableType).
-

An order tactic for real numbers

+

An order tactic for real numbers

diff --git a/master/stdlib/Stdlib.Reals.R_Ifp.html b/master/stdlib/Stdlib.Reals.R_Ifp.html index 375f8f9ef9..d0a68b5850 100644 --- a/master/stdlib/Stdlib.Reals.R_Ifp.html +++ b/master/stdlib/Stdlib.Reals.R_Ifp.html @@ -61,7 +61,7 @@

Library Stdlib.Reals.R_Ifp

-

Fractional part

+

Fractional part

@@ -96,7 +96,7 @@

Library Stdlib.Reals.R_Ifp

-

Properties

+

Properties

diff --git a/master/stdlib/Stdlib.Reals.R_sqrt.html b/master/stdlib/Stdlib.Reals.R_sqrt.html index 5004233e34..afc0fee038 100644 --- a/master/stdlib/Stdlib.Reals.R_sqrt.html +++ b/master/stdlib/Stdlib.Reals.R_sqrt.html @@ -54,7 +54,7 @@

Library Stdlib.Reals.R_sqrt

-

Continuous extension of Rsqrt on R

+

Continuous extension of Rsqrt on R

@@ -195,7 +195,7 @@

Library Stdlib.Reals.R_sqrt

-

Resolution of a*X^2+b*X+c=0

+

Resolution of a*X^2+b*X+c=0

diff --git a/master/stdlib/Stdlib.Reals.Ranalysis1.html b/master/stdlib/Stdlib.Reals.Ranalysis1.html index 508385d158..a885729e0e 100644 --- a/master/stdlib/Stdlib.Reals.Ranalysis1.html +++ b/master/stdlib/Stdlib.Reals.Ranalysis1.html @@ -56,7 +56,7 @@

Library Stdlib.Reals.Ranalysis1

-

Basic operations on functions

+

Basic operations on functions

@@ -105,7 +105,7 @@

Library Stdlib.Reals.Ranalysis1

-

Variations of functions

+

Variations of functions

@@ -126,7 +126,7 @@

Library Stdlib.Reals.Ranalysis1

-

Definition of continuity as a limit

+

Definition of continuity as a limit

@@ -230,7 +230,7 @@

Library Stdlib.Reals.Ranalysis1

-

Derivative's definition using Landau's kernel

+

Derivative's definition using Landau's kernel

@@ -270,7 +270,7 @@

Library Stdlib.Reals.Ranalysis1

-

Class of differential functions

+

Class of differential functions

@@ -326,7 +326,7 @@

Library Stdlib.Reals.Ranalysis1

-

Equivalence of this definition with the one using limit concept

+

Equivalence of this definition with the one using limit concept

@@ -357,7 +357,7 @@

Library Stdlib.Reals.Ranalysis1

-

derivability -> continuity

+

derivability -> continuity

@@ -375,11 +375,11 @@

Library Stdlib.Reals.Ranalysis1

-

Main rules

+

Main rules

-

Rules for derivable_pt_lim (value of the derivative at a point)

+

Rules for derivable_pt_lim (value of the derivative at a point)

@@ -457,7 +457,7 @@

Library Stdlib.Reals.Ranalysis1

-

Rules for derivable_pt (derivability at a point)

+

Rules for derivable_pt (derivability at a point)

@@ -523,7 +523,7 @@

Library Stdlib.Reals.Ranalysis1

-

Rules for derivable (derivability on whole domain)

+

Rules for derivable (derivability on whole domain)

@@ -567,7 +567,7 @@

Library Stdlib.Reals.Ranalysis1

-

Rules for derive_pt (derivative function on whole domain)

+

Rules for derive_pt (derivative function on whole domain)

@@ -637,7 +637,7 @@

Library Stdlib.Reals.Ranalysis1

-

Definition and derivative of power function with natural number exponent

+

Definition and derivative of power function with natural number exponent

@@ -671,7 +671,7 @@

Library Stdlib.Reals.Ranalysis1

-

Irrelevance of derivability proof for derivative

+

Irrelevance of derivability proof for derivative

@@ -699,7 +699,7 @@

Library Stdlib.Reals.Ranalysis1

-

Local extremum's condition

+

Local extremum's condition

diff --git a/master/stdlib/Stdlib.Reals.Ranalysis5.html b/master/stdlib/Stdlib.Reals.Ranalysis5.html index b587fa9f2d..b0f80fbe26 100644 --- a/master/stdlib/Stdlib.Reals.Ranalysis5.html +++ b/master/stdlib/Stdlib.Reals.Ranalysis5.html @@ -62,7 +62,7 @@

Library Stdlib.Reals.Ranalysis5

-

Preliminaries lemmas

+

Preliminaries lemmas

@@ -138,11 +138,11 @@

Library Stdlib.Reals.Ranalysis5

-

The derivative of a reciprocal function

+

The derivative of a reciprocal function

-

Continuity of the reciprocal function

+

Continuity of the reciprocal function

@@ -170,7 +170,7 @@

Library Stdlib.Reals.Ranalysis5

-

Derivability of the reciprocal function

+

Derivability of the reciprocal function

@@ -244,7 +244,7 @@

Library Stdlib.Reals.Ranalysis5

-

Value of the derivative of the reciprocal function

+

Value of the derivative of the reciprocal function

@@ -320,7 +320,7 @@

Library Stdlib.Reals.Ranalysis5

-

Existence of the derivative of a function which is the limit of a sequence of functions

+

Existence of the derivative of a function which is the limit of a sequence of functions

diff --git a/master/stdlib/Stdlib.Reals.Ratan.html b/master/stdlib/Stdlib.Reals.Ratan.html index 87c6279217..a786394e2c 100644 --- a/master/stdlib/Stdlib.Reals.Ratan.html +++ b/master/stdlib/Stdlib.Reals.Ratan.html @@ -69,11 +69,11 @@

Library Stdlib.Reals.Ratan

-

Preliminaries

+

Preliminaries

-

Various generic lemmas which probably should go somewhere else

+

Various generic lemmas which probably should go somewhere else

@@ -121,11 +121,11 @@

Library Stdlib.Reals.Ratan

-

Properties of tangent

+

Properties of tangent

-

Derivative of tangent

+

Derivative of tangent

@@ -143,7 +143,7 @@

Library Stdlib.Reals.Ratan

-

Proof that tangent is a bijection

+

Proof that tangent is a bijection

@@ -193,11 +193,11 @@

Library Stdlib.Reals.Ratan

-

Definition of arctangent

+

Definition of arctangent

-

Definition of arctangent as the reciprocal function of tangent and proof of this status

+

Definition of arctangent as the reciprocal function of tangent and proof of this status

@@ -270,7 +270,7 @@

Library Stdlib.Reals.Ratan

-

Derivative of arctangent

+

Derivative of arctangent

@@ -287,7 +287,7 @@

Library Stdlib.Reals.Ratan

-

Definition of the arctangent function as the sum of the arctan power series

+

Definition of the arctangent function as the sum of the arctan power series

@@ -335,7 +335,7 @@

Library Stdlib.Reals.Ratan

-

Proof of the equivalence of the two definitions between -1 and 1

+

Proof of the equivalence of the two definitions between -1 and 1

@@ -474,7 +474,7 @@

Library Stdlib.Reals.Ratan

-

Relation between arctangent and sine and cosine

+

Relation between arctangent and sine and cosine

@@ -491,7 +491,7 @@

Library Stdlib.Reals.Ratan

-

Definition of arcsine based on arctangent

+

Definition of arcsine based on arctangent

@@ -509,7 +509,7 @@

Library Stdlib.Reals.Ratan

-

Relation between arcsin and arctangent

+

Relation between arcsin and arctangent

@@ -522,7 +522,7 @@

Library Stdlib.Reals.Ratan

-

arcsine of specific values

+

arcsine of specific values

@@ -544,7 +544,7 @@

Library Stdlib.Reals.Ratan

-

Bounds of arcsine

+

Bounds of arcsine

@@ -561,7 +561,7 @@

Library Stdlib.Reals.Ratan

-

arcsine is the left and right inverse of sine

+

arcsine is the left and right inverse of sine

@@ -578,7 +578,7 @@

Library Stdlib.Reals.Ratan

-

Relation between arcsin, cosine and tangent

+

Relation between arcsin, cosine and tangent

@@ -595,7 +595,7 @@

Library Stdlib.Reals.Ratan

-

Derivative of arcsine

+

Derivative of arcsine

@@ -612,7 +612,7 @@

Library Stdlib.Reals.Ratan

-

Definition of arccosine based on arctangent

+

Definition of arccosine based on arctangent

@@ -630,7 +630,7 @@

Library Stdlib.Reals.Ratan

-

Relation between arccosine, arcsine and arctangent

+

Relation between arccosine, arcsine and arctangent

@@ -651,7 +651,7 @@

Library Stdlib.Reals.Ratan

-

arccosine of specific values

+

arccosine of specific values

@@ -673,7 +673,7 @@

Library Stdlib.Reals.Ratan

-

Bounds of arccosine

+

Bounds of arccosine

@@ -690,7 +690,7 @@

Library Stdlib.Reals.Ratan

-

arccosine is the left and right inverse of cosine

+

arccosine is the left and right inverse of cosine

@@ -707,7 +707,7 @@

Library Stdlib.Reals.Ratan

-

Relation between arccosine, sine and tangent

+

Relation between arccosine, sine and tangent

@@ -724,7 +724,7 @@

Library Stdlib.Reals.Ratan

-

Derivative of arccosine

+

Derivative of arccosine

diff --git a/master/stdlib/Stdlib.Reals.Raxioms.html b/master/stdlib/Stdlib.Reals.Raxioms.html index 86f29bb626..ef84222c0d 100644 --- a/master/stdlib/Stdlib.Reals.Raxioms.html +++ b/master/stdlib/Stdlib.Reals.Raxioms.html @@ -69,11 +69,11 @@

Library Stdlib.Reals.Raxioms

-

Field operations

+

Field operations

-

Addition

+

Addition

@@ -141,7 +141,7 @@

Library Stdlib.Reals.Raxioms

-

Multiplication

+

Multiplication

@@ -176,7 +176,7 @@

Library Stdlib.Reals.Raxioms

-

Distributivity

+

Distributivity

@@ -192,11 +192,11 @@

Library Stdlib.Reals.Raxioms

-

Order

+

Order

-

Lower

+

Lower

@@ -222,7 +222,7 @@

Library Stdlib.Reals.Raxioms

-

Injection from N to R

+

Injection from N to R

@@ -241,7 +241,7 @@

Library Stdlib.Reals.Raxioms

-

R Archimedean

+

R Archimedean

@@ -269,7 +269,7 @@

Library Stdlib.Reals.Raxioms

-

R Complete

+

R Complete

diff --git a/master/stdlib/Stdlib.Reals.Rbasic_fun.html b/master/stdlib/Stdlib.Reals.Rbasic_fun.html index a2b6aff554..df0dbf9317 100644 --- a/master/stdlib/Stdlib.Reals.Rbasic_fun.html +++ b/master/stdlib/Stdlib.Reals.Rbasic_fun.html @@ -64,7 +64,7 @@

Library Stdlib.Reals.Rbasic_fun

-

Rmin

+

Rmin

@@ -130,7 +130,7 @@

Library Stdlib.Reals.Rbasic_fun

-

Rmax

+

Rmax

@@ -202,7 +202,7 @@

Library Stdlib.Reals.Rbasic_fun

-

Rabsolu

+

Rabsolu

diff --git a/master/stdlib/Stdlib.Reals.Rdefinitions.html b/master/stdlib/Stdlib.Reals.Rdefinitions.html index 8e5335951a..4921eae17a 100644 --- a/master/stdlib/Stdlib.Reals.Rdefinitions.html +++ b/master/stdlib/Stdlib.Reals.Rdefinitions.html @@ -178,7 +178,7 @@

Library Stdlib.Reals.Rdefinitions

-

Injection from Z to R

+

Injection from Z to R

@@ -266,7 +266,7 @@

Library Stdlib.Reals.Rdefinitions

-

Number notation for constants

+

Number notation for constants

diff --git a/master/stdlib/Stdlib.Reals.Rfunctions.html b/master/stdlib/Stdlib.Reals.Rfunctions.html index e2270e7ffb..b9ad6130c0 100644 --- a/master/stdlib/Stdlib.Reals.Rfunctions.html +++ b/master/stdlib/Stdlib.Reals.Rfunctions.html @@ -74,7 +74,7 @@

Library Stdlib.Reals.Rfunctions

-

Lemmas about factorial

+

Lemmas about factorial

@@ -91,7 +91,7 @@

Library Stdlib.Reals.Rfunctions

-

Power

+

Power

@@ -230,7 +230,7 @@

Library Stdlib.Reals.Rfunctions

-

PowerRZ

+

PowerRZ

@@ -379,7 +379,7 @@

Library Stdlib.Reals.Rfunctions

-

Sum of n first naturals

+

Sum of n first naturals

@@ -403,7 +403,7 @@

Library Stdlib.Reals.Rfunctions

-

Sum

+

Sum

@@ -431,7 +431,7 @@

Library Stdlib.Reals.Rfunctions

-

Distance in R

+

Distance in R

@@ -477,7 +477,7 @@

Library Stdlib.Reals.Rfunctions

-

Infinite Sum

+

Infinite Sum

diff --git a/master/stdlib/Stdlib.Reals.Rgeom.html b/master/stdlib/Stdlib.Reals.Rgeom.html index c11a763960..f6cb787537 100644 --- a/master/stdlib/Stdlib.Reals.Rgeom.html +++ b/master/stdlib/Stdlib.Reals.Rgeom.html @@ -56,7 +56,7 @@

Library Stdlib.Reals.Rgeom

-

Distance

+

Distance

@@ -90,7 +90,7 @@

Library Stdlib.Reals.Rgeom

-

Translation

+

Translation

@@ -112,7 +112,7 @@

Library Stdlib.Reals.Rgeom

-

Rotation

+

Rotation

@@ -146,7 +146,7 @@

Library Stdlib.Reals.Rgeom

-

Similarity

+

Similarity

diff --git a/master/stdlib/Stdlib.Reals.RiemannInt_SF.html b/master/stdlib/Stdlib.Reals.RiemannInt_SF.html index 43db84bd35..6544e3fccc 100644 --- a/master/stdlib/Stdlib.Reals.RiemannInt_SF.html +++ b/master/stdlib/Stdlib.Reals.RiemannInt_SF.html @@ -62,7 +62,7 @@

Library Stdlib.Reals.RiemannInt_SF

-

Each bounded subset of N has a maximal element

+

Each bounded subset of N has a maximal element

@@ -84,7 +84,7 @@

Library Stdlib.Reals.RiemannInt_SF

-

Step functions

+

Step functions

@@ -124,7 +124,7 @@

Library Stdlib.Reals.RiemannInt_SF

-

Class of step functions

+

Class of step functions

@@ -156,7 +156,7 @@

Library Stdlib.Reals.RiemannInt_SF

-

Integral of step functions

+

Integral of step functions

@@ -170,7 +170,7 @@

Library Stdlib.Reals.RiemannInt_SF

-

Properties of step functions

+

Properties of step functions

diff --git a/master/stdlib/Stdlib.Reals.Rlimit.html b/master/stdlib/Stdlib.Reals.Rlimit.html index 8b97286ec2..3304e7f8ca 100644 --- a/master/stdlib/Stdlib.Reals.Rlimit.html +++ b/master/stdlib/Stdlib.Reals.Rlimit.html @@ -62,7 +62,7 @@

Library Stdlib.Reals.Rlimit

-

Calculus

+

Calculus

@@ -100,7 +100,7 @@

Library Stdlib.Reals.Rlimit

-

Metric space

+

Metric space

@@ -119,7 +119,7 @@

Library Stdlib.Reals.Rlimit

-

Limit in Metric space

+

Limit in Metric space

@@ -138,7 +138,7 @@

Library Stdlib.Reals.Rlimit

-

R is a metric space

+

R is a metric space

@@ -154,7 +154,7 @@

Library Stdlib.Reals.Rlimit

-

Limit 1 arg

+

Limit 1 arg

diff --git a/master/stdlib/Stdlib.Reals.Rlogic.html b/master/stdlib/Stdlib.Reals.Rlogic.html index cd0ebe8330..c0339b4090 100644 --- a/master/stdlib/Stdlib.Reals.Rlogic.html +++ b/master/stdlib/Stdlib.Reals.Rlogic.html @@ -77,7 +77,7 @@

Library Stdlib.Reals.Rlogic

-

Decidability of arithmetical statements

+

Decidability of arithmetical statements

@@ -103,7 +103,7 @@

Library Stdlib.Reals.Rlogic

-

Derivability of the Archimedean axiom

+

Derivability of the Archimedean axiom

@@ -123,7 +123,7 @@

Library Stdlib.Reals.Rlogic

-

Decidability of negated formulas

+

Decidability of negated formulas

diff --git a/master/stdlib/Stdlib.Reals.Rminmax.html b/master/stdlib/Stdlib.Reals.Rminmax.html index 5f6439e0f9..376235a0dc 100644 --- a/master/stdlib/Stdlib.Reals.Rminmax.html +++ b/master/stdlib/Stdlib.Reals.Rminmax.html @@ -54,7 +54,7 @@

Library Stdlib.Reals.Rminmax

-

Maximum and Minimum of two real numbers

+

Maximum and Minimum of two real numbers

@@ -111,7 +111,7 @@

Library Stdlib.Reals.Rminmax

-

Properties specific to the R domain

+

Properties specific to the R domain

diff --git a/master/stdlib/Stdlib.Reals.Rpower.html b/master/stdlib/Stdlib.Reals.Rpower.html index 33d8d34d7c..381e37c972 100644 --- a/master/stdlib/Stdlib.Reals.Rpower.html +++ b/master/stdlib/Stdlib.Reals.Rpower.html @@ -76,7 +76,7 @@

Library Stdlib.Reals.Rpower

-

Properties of Exp

+

Properties of Exp

@@ -129,7 +129,7 @@

Library Stdlib.Reals.Rpower

-

Properties of Ln

+

Properties of Ln

@@ -169,7 +169,7 @@

Library Stdlib.Reals.Rpower

-

Definition of Rpower

+

Definition of Rpower

@@ -181,7 +181,7 @@

Library Stdlib.Reals.Rpower

-

Properties of Rpower

+

Properties of Rpower

@@ -248,7 +248,7 @@

Library Stdlib.Reals.Rpower

-

Differentiability of Ln and Rpower

+

Differentiability of Ln and Rpower

diff --git a/master/stdlib/Stdlib.Reals.Rseries.html b/master/stdlib/Stdlib.Reals.Rseries.html index 4919253d93..30f1b161dd 100644 --- a/master/stdlib/Stdlib.Reals.Rseries.html +++ b/master/stdlib/Stdlib.Reals.Rseries.html @@ -57,7 +57,7 @@

Library Stdlib.Reals.Rseries

-

Definition of sequence and properties

+

Definition of sequence and properties

@@ -129,7 +129,7 @@

Library Stdlib.Reals.Rseries

-

Definition of Power Series and properties

+

Definition of Power Series and properties

diff --git a/master/stdlib/Stdlib.Reals.Rtopology.html b/master/stdlib/Stdlib.Reals.Rtopology.html index cba8258092..0e57809680 100644 --- a/master/stdlib/Stdlib.Reals.Rtopology.html +++ b/master/stdlib/Stdlib.Reals.Rtopology.html @@ -58,7 +58,7 @@

Library Stdlib.Reals.Rtopology

-

General definitions and propositions

+

General definitions and propositions

@@ -306,7 +306,7 @@

Library Stdlib.Reals.Rtopology

-

Proof of Bolzano-Weierstrass theorem

+

Proof of Bolzano-Weierstrass theorem

@@ -379,7 +379,7 @@

Library Stdlib.Reals.Rtopology

-

Proof of Heine's theorem

+

Proof of Heine's theorem

diff --git a/master/stdlib/Stdlib.Reals.Rtrigo1.html b/master/stdlib/Stdlib.Reals.Rtrigo1.html index bf275ac75d..82b7a1a014 100644 --- a/master/stdlib/Stdlib.Reals.Rtrigo1.html +++ b/master/stdlib/Stdlib.Reals.Rtrigo1.html @@ -165,7 +165,7 @@

Library Stdlib.Reals.Rtrigo1

-

Some properties of cos, sin and tan

+

Some properties of cos, sin and tan

@@ -259,7 +259,7 @@

Library Stdlib.Reals.Rtrigo1

-

Using series definitions of cos and sin

+

Using series definitions of cos and sin

@@ -293,7 +293,7 @@

Library Stdlib.Reals.Rtrigo1

-

Increasing and decreasing of cos and sin

+

Increasing and decreasing of cos and sin

diff --git a/master/stdlib/Stdlib.Reals.Rtrigo_def.html b/master/stdlib/Stdlib.Reals.Rtrigo_def.html index 2131237d60..0b080af517 100644 --- a/master/stdlib/Stdlib.Reals.Rtrigo_def.html +++ b/master/stdlib/Stdlib.Reals.Rtrigo_def.html @@ -54,7 +54,7 @@

Library Stdlib.Reals.Rtrigo_def

-

Definition of exponential

+

Definition of exponential

@@ -80,7 +80,7 @@

Library Stdlib.Reals.Rtrigo_def

-

Definition of hyperbolic functions

+

Definition of hyperbolic functions

@@ -154,7 +154,7 @@

Library Stdlib.Reals.Rtrigo_def

-

Properties

+

Properties

diff --git a/master/stdlib/Stdlib.Reals.Rtrigo_facts.html b/master/stdlib/Stdlib.Reals.Rtrigo_facts.html index 5a0a679c5b..7c88f49900 100644 --- a/master/stdlib/Stdlib.Reals.Rtrigo_facts.html +++ b/master/stdlib/Stdlib.Reals.Rtrigo_facts.html @@ -60,7 +60,7 @@

Library Stdlib.Reals.Rtrigo_facts

-

Bounds of expressions with trigonometric functions

+

Bounds of expressions with trigonometric functions

@@ -77,11 +77,11 @@

Library Stdlib.Reals.Rtrigo_facts

-

Express trigonometric functions with each other

+

Express trigonometric functions with each other

-

Express sin and cos with each other

+

Express sin and cos with each other

@@ -114,7 +114,7 @@

Library Stdlib.Reals.Rtrigo_facts

-

Express tan with sin and cos

+

Express tan with sin and cos

@@ -147,7 +147,7 @@

Library Stdlib.Reals.Rtrigo_facts

-

Express sin and cos with tan

+

Express sin and cos with tan

@@ -164,7 +164,7 @@

Library Stdlib.Reals.Rtrigo_facts

-

Additional shift lemmas for sin, cos, tan

+

Additional shift lemmas for sin, cos, tan

diff --git a/master/stdlib/Stdlib.Relations.Operators_Properties.html b/master/stdlib/Stdlib.Relations.Operators_Properties.html index eb89e6cab8..ef960451b0 100644 --- a/master/stdlib/Stdlib.Relations.Operators_Properties.html +++ b/master/stdlib/Stdlib.Relations.Operators_Properties.html @@ -48,8 +48,8 @@

Library Stdlib.Relations.Operators_Properties

-

Some properties of the operators on relations

-

Initial version by Bruno Barras

+

Some properties of the operators on relations

+

Initial version by Bruno Barras

@@ -184,12 +184,12 @@

Library Stdlib.Relations.Operators_Properties

-

Equivalences between the different definition of the reflexive,

+

Equivalences between the different definition of the reflexive,

symmetric, transitive closures
-

Contributed by P. Castéran

+

Contributed by P. Castéran

diff --git a/master/stdlib/Stdlib.Relations.Relation_Operators.html b/master/stdlib/Stdlib.Relations.Relation_Operators.html index df110c7bc5..8b3611bf54 100644 --- a/master/stdlib/Stdlib.Relations.Relation_Operators.html +++ b/master/stdlib/Stdlib.Relations.Relation_Operators.html @@ -48,14 +48,14 @@

Library Stdlib.Relations.Relation_Operators

-

Some operators on relations

-

Initial authors: Bruno Barras, Cristina Cornes

-

-

Some of the initial definitions were taken from :

-

Constructing Recursion Operators in Type Theory

-

L. Paulson JSC (1986) 2, 325-355

-

-

Further extensions by Pierre Castéran

+

Some operators on relations

+

Initial authors: Bruno Barras, Cristina Cornes

+

+

Some of the initial definitions were taken from :

+

Constructing Recursion Operators in Type Theory

+

L. Paulson JSC (1986) 2, 325-355

+

+

Further extensions by Pierre Castéran

@@ -67,7 +67,7 @@

Library Stdlib.Relations.Relation_Operators

-

Transitive closure

+

Transitive closure

@@ -123,7 +123,7 @@

Library Stdlib.Relations.Relation_Operators

-

Reflexive closure

+

Reflexive closure

@@ -153,7 +153,7 @@

Library Stdlib.Relations.Relation_Operators

-

Reflexive-transitive closure

+

Reflexive-transitive closure

@@ -213,7 +213,7 @@

Library Stdlib.Relations.Relation_Operators

-

Reflexive-symmetric-transitive closure

+

Reflexive-symmetric-transitive closure

@@ -275,7 +275,7 @@

Library Stdlib.Relations.Relation_Operators

-

Converse of a relation

+

Converse of a relation

@@ -293,7 +293,7 @@

Library Stdlib.Relations.Relation_Operators

-

Union of relations

+

Union of relations

@@ -311,7 +311,7 @@

Library Stdlib.Relations.Relation_Operators

-

Disjoint union of relations

+

Disjoint union of relations

@@ -335,7 +335,7 @@

Library Stdlib.Relations.Relation_Operators

-

Lexicographic order on dependent pairs

+

Lexicographic order on dependent pairs

@@ -368,7 +368,7 @@

Library Stdlib.Relations.Relation_Operators

-

Lexicographic order on pairs

+

Lexicographic order on pairs

@@ -403,7 +403,7 @@

Library Stdlib.Relations.Relation_Operators

-

Product of relations

+

Product of relations

@@ -429,7 +429,7 @@

Library Stdlib.Relations.Relation_Operators

-

Multiset of two relations

+

Multiset of two relations

diff --git a/master/stdlib/Stdlib.Sorting.CPermutation.html b/master/stdlib/Stdlib.Sorting.CPermutation.html index 3e06d08463..6344b7c19a 100644 --- a/master/stdlib/Stdlib.Sorting.CPermutation.html +++ b/master/stdlib/Stdlib.Sorting.CPermutation.html @@ -48,7 +48,7 @@

Library Stdlib.Sorting.CPermutation

-

Circular Shifts (aka Cyclic Permutations)

+

Circular Shifts (aka Cyclic Permutations)

diff --git a/master/stdlib/Stdlib.Sorting.Heap.html b/master/stdlib/Stdlib.Sorting.Heap.html index 887eb3394c..d6331a381f 100644 --- a/master/stdlib/Stdlib.Sorting.Heap.html +++ b/master/stdlib/Stdlib.Sorting.Heap.html @@ -73,11 +73,11 @@

Library Stdlib.Sorting.Heap

-

Trees and heap trees

+

Trees and heap trees

-

Definition of trees over an ordered set

+

Definition of trees over an ordered set

@@ -142,7 +142,7 @@

Library Stdlib.Sorting.Heap

-

The heap property

+

The heap property

@@ -194,7 +194,7 @@

Library Stdlib.Sorting.Heap

-

Merging two sorted lists

+

Merging two sorted lists

@@ -226,7 +226,7 @@

Library Stdlib.Sorting.Heap

-

From trees to multisets

+

From trees to multisets

@@ -262,11 +262,11 @@

Library Stdlib.Sorting.Heap

-

From lists to sorted lists

+

From lists to sorted lists

-

Specification of heap insertion

+

Specification of heap insertion

@@ -288,7 +288,7 @@

Library Stdlib.Sorting.Heap

-

Building a heap from a list

+

Building a heap from a list

@@ -308,7 +308,7 @@

Library Stdlib.Sorting.Heap

-

Building the sorted list

+

Building the sorted list

@@ -329,7 +329,7 @@

Library Stdlib.Sorting.Heap

-

Specification of treesort

+

Specification of treesort

diff --git a/master/stdlib/Stdlib.Sorting.PermutSetoid.html b/master/stdlib/Stdlib.Sorting.PermutSetoid.html index 649669fdb8..b703be35cb 100644 --- a/master/stdlib/Stdlib.Sorting.PermutSetoid.html +++ b/master/stdlib/Stdlib.Sorting.PermutSetoid.html @@ -88,7 +88,7 @@

Library Stdlib.Sorting.PermutSetoid

-

From lists to multisets

+

From lists to multisets

@@ -127,7 +127,7 @@

Library Stdlib.Sorting.PermutSetoid

-

permutation: definition and basic properties

+

permutation: definition and basic properties

@@ -201,7 +201,7 @@

Library Stdlib.Sorting.PermutSetoid

-

Some inversion results.

+

Some inversion results.

diff --git a/master/stdlib/Stdlib.Sorting.Permutation.html b/master/stdlib/Stdlib.Sorting.Permutation.html index 0c1e9da3a7..4beed87719 100644 --- a/master/stdlib/Stdlib.Sorting.Permutation.html +++ b/master/stdlib/Stdlib.Sorting.Permutation.html @@ -48,7 +48,7 @@

Library Stdlib.Sorting.Permutation

-

List permutations as a composition of adjacent transpositions

+

List permutations as a composition of adjacent transpositions

diff --git a/master/stdlib/Stdlib.Strings.Ascii.html b/master/stdlib/Stdlib.Strings.Ascii.html index 5e5cc5a51f..0ac436c561 100644 --- a/master/stdlib/Stdlib.Strings.Ascii.html +++ b/master/stdlib/Stdlib.Strings.Ascii.html @@ -61,7 +61,7 @@

Library Stdlib.Strings.Ascii

-

Definition of ascii characters

+

Definition of ascii characters

@@ -141,7 +141,7 @@

Library Stdlib.Strings.Ascii

-

Conversion between natural numbers modulo 256 and ascii characters

+

Conversion between natural numbers modulo 256 and ascii characters

@@ -283,7 +283,7 @@

Library Stdlib.Strings.Ascii

-

Concrete syntax

+

Concrete syntax

diff --git a/master/stdlib/Stdlib.Strings.PString.html b/master/stdlib/Stdlib.Strings.PString.html index 28bdab6aff..1fe37fdb9d 100644 --- a/master/stdlib/Stdlib.Strings.PString.html +++ b/master/stdlib/Stdlib.Strings.PString.html @@ -127,7 +127,7 @@

Library Stdlib.Strings.PString

-

Properties of string length

+

Properties of string length

@@ -168,7 +168,7 @@

Library Stdlib.Strings.PString

-

Properties of string get

+

Properties of string get

@@ -211,7 +211,7 @@

Library Stdlib.Strings.PString

-

Properties of string comparison

+

Properties of string comparison

@@ -292,7 +292,7 @@

Library Stdlib.Strings.PString

-

Properties of make

+

Properties of make

@@ -304,7 +304,7 @@

Library Stdlib.Strings.PString

-

Properties of cat

+

Properties of cat

@@ -326,7 +326,7 @@

Library Stdlib.Strings.PString

-

Properties of sub

+

Properties of sub

@@ -374,7 +374,7 @@

Library Stdlib.Strings.PString

-

Ordered type

+

Ordered type

diff --git a/master/stdlib/Stdlib.Strings.String.html b/master/stdlib/Stdlib.Strings.String.html index 7f73a1aeb3..6f57ecb685 100644 --- a/master/stdlib/Stdlib.Strings.String.html +++ b/master/stdlib/Stdlib.Strings.String.html @@ -64,7 +64,7 @@

Library Stdlib.Strings.String

-

Definition of strings

+

Definition of strings

@@ -135,7 +135,7 @@

Library Stdlib.Strings.String

-

Compare strings lexicographically

+

Compare strings lexicographically

@@ -185,7 +185,7 @@

Library Stdlib.Strings.String

-

Concatenation of strings

+

Concatenation of strings

@@ -276,7 +276,7 @@

Library Stdlib.Strings.String

-

Substrings

+

Substrings

@@ -325,7 +325,7 @@

Library Stdlib.Strings.String

-

Concatenating lists of strings

+

Concatenating lists of strings

@@ -346,7 +346,7 @@

Library Stdlib.Strings.String

-

Test functions

+

Test functions

@@ -498,7 +498,7 @@

Library Stdlib.Strings.String

-

Conversion to/from list ascii and list byte

+

Conversion to/from list ascii and list byte

@@ -541,7 +541,7 @@

Library Stdlib.Strings.String

-

Concrete syntax

+

Concrete syntax

diff --git a/master/stdlib/Stdlib.Structures.DecidableType.html b/master/stdlib/Stdlib.Structures.DecidableType.html index 7735998437..a4fb685fb1 100644 --- a/master/stdlib/Stdlib.Structures.DecidableType.html +++ b/master/stdlib/Stdlib.Structures.DecidableType.html @@ -59,7 +59,7 @@

Library Stdlib.Structures.DecidableType

FSets and FMap. Please use Structures/Equalities.v directly now.
-

Types with Equalities, and nothing more (for subtyping purpose)

+

Types with Equalities, and nothing more (for subtyping purpose)

@@ -71,7 +71,7 @@

Library Stdlib.Structures.DecidableType

-

Types with decidable Equalities (but no ordering)

+

Types with decidable Equalities (but no ordering)

@@ -83,7 +83,7 @@

Library Stdlib.Structures.DecidableType

-

Additional notions about keys and datas used in FMap

+

Additional notions about keys and datas used in FMap

diff --git a/master/stdlib/Stdlib.Structures.DecidableTypeEx.html b/master/stdlib/Stdlib.Structures.DecidableTypeEx.html index ad9fc139d4..cc1207a02a 100644 --- a/master/stdlib/Stdlib.Structures.DecidableTypeEx.html +++ b/master/stdlib/Stdlib.Structures.DecidableTypeEx.html @@ -56,7 +56,7 @@

Library Stdlib.Structures.DecidableTypeEx

FSets and FMap. Please use Structures/Equalities.v directly now.
-

Examples of Decidable Type structures.

+

Examples of Decidable Type structures.

diff --git a/master/stdlib/Stdlib.Structures.Equalities.html b/master/stdlib/Stdlib.Structures.Equalities.html index b5a2da82f5..9d73846add 100644 --- a/master/stdlib/Stdlib.Structures.Equalities.html +++ b/master/stdlib/Stdlib.Structures.Equalities.html @@ -68,7 +68,7 @@

Library Stdlib.Structures.Equalities

-

Structure with just a base type t

+

Structure with just a base type t

@@ -82,7 +82,7 @@

Library Stdlib.Structures.Equalities

-

Structure with an equality relation eq

+

Structure with an equality relation eq

@@ -108,7 +108,7 @@

Library Stdlib.Structures.Equalities

-

Specification of the equality via the Equivalence type class

+

Specification of the equality via the Equivalence type class

@@ -123,7 +123,7 @@

Library Stdlib.Structures.Equalities

-

Earlier specification of equality by three separate lemmas.

+

Earlier specification of equality by three separate lemmas.

@@ -143,7 +143,7 @@

Library Stdlib.Structures.Equalities

-

Types with decidable equality

+

Types with decidable equality

@@ -157,7 +157,7 @@

Library Stdlib.Structures.Equalities

-

Boolean Equality

+

Boolean Equality

@@ -252,7 +252,7 @@

Library Stdlib.Structures.Equalities

-

Compatibility wrapper from/to the old version of

+

Compatibility wrapper from/to the old version of

EqualityType and DecidableType
@@ -291,7 +291,7 @@

Library Stdlib.Structures.Equalities

-

Having eq_dec is equivalent to having eqb and its spec.

+

Having eq_dec is equivalent to having eqb and its spec.

@@ -389,7 +389,7 @@

Library Stdlib.Structures.Equalities

-

UsualDecidableType

+

UsualDecidableType

diff --git a/master/stdlib/Stdlib.Structures.EqualitiesFacts.html b/master/stdlib/Stdlib.Structures.EqualitiesFacts.html index d9db4ae4e9..45cdbfe7eb 100644 --- a/master/stdlib/Stdlib.Structures.EqualitiesFacts.html +++ b/master/stdlib/Stdlib.Structures.EqualitiesFacts.html @@ -54,7 +54,7 @@

Library Stdlib.Structures.EqualitiesFacts

-

Keys and datas used in the future MMaps

+

Keys and datas used in the future MMaps

@@ -226,7 +226,7 @@

Library Stdlib.Structures.EqualitiesFacts

-

PairDecidableType

+

PairDecidableType

diff --git a/master/stdlib/Stdlib.Structures.GenericMinMax.html b/master/stdlib/Stdlib.Structures.GenericMinMax.html index 42fbb79451..6334b30dd7 100644 --- a/master/stdlib/Stdlib.Structures.GenericMinMax.html +++ b/master/stdlib/Stdlib.Structures.GenericMinMax.html @@ -51,11 +51,11 @@

Library Stdlib.Structures.GenericMinMax

-

A Generic construction of min and max

+

A Generic construction of min and max

-

First, an interface for types with max and/or min

+

First, an interface for types with max and/or min

@@ -81,7 +81,7 @@

Library Stdlib.Structures.GenericMinMax

-

Any OrderedTypeFull can be equipped by max and min

+

Any OrderedTypeFull can be equipped by max and min

based on the compare function.
@@ -122,7 +122,7 @@

Library Stdlib.Structures.GenericMinMax

-

Consequences of the minimalist interface: facts about max and min.

+

Consequences of the minimalist interface: facts about max and min.

@@ -200,7 +200,7 @@

Library Stdlib.Structures.GenericMinMax

-

Semi-lattice algebraic properties of max

+

Semi-lattice algebraic properties of max

@@ -227,7 +227,7 @@

Library Stdlib.Structures.GenericMinMax

-

Least-upper bound properties of max

+

Least-upper bound properties of max

@@ -386,7 +386,7 @@

Library Stdlib.Structures.GenericMinMax

-

Combined properties of min and max

+

Combined properties of min and max

@@ -468,7 +468,7 @@

Library Stdlib.Structures.GenericMinMax

-

Properties requiring a decidable order

+

Properties requiring a decidable order

@@ -548,7 +548,7 @@

Library Stdlib.Structures.GenericMinMax

-

When the equality is Leibniz, we can skip a few Proper precondition.

+

When the equality is Leibniz, we can skip a few Proper precondition.

diff --git a/master/stdlib/Stdlib.Structures.OrderedType.html b/master/stdlib/Stdlib.Structures.OrderedType.html index 09e7e9d7ab..dca0696b97 100644 --- a/master/stdlib/Stdlib.Structures.OrderedType.html +++ b/master/stdlib/Stdlib.Structures.OrderedType.html @@ -56,7 +56,7 @@

Library Stdlib.Structures.OrderedType

FSets and FMap. Please use Structures/Orders.v directly now.
-

Ordered types

+

Ordered types

@@ -137,7 +137,7 @@

Library Stdlib.Structures.OrderedType

-

Ordered types properties

+

Ordered types properties

diff --git a/master/stdlib/Stdlib.Structures.OrderedTypeAlt.html b/master/stdlib/Stdlib.Structures.OrderedTypeAlt.html index fdabfe49de..1aeee505c1 100644 --- a/master/stdlib/Stdlib.Structures.OrderedTypeAlt.html +++ b/master/stdlib/Stdlib.Structures.OrderedTypeAlt.html @@ -49,7 +49,7 @@

Library Stdlib.Structures.OrderedTypeAlt

-

An alternative (but equivalent) presentation for an Ordered Type

+

An alternative (but equivalent) presentation for an Ordered Type

inferface.
diff --git a/master/stdlib/Stdlib.Structures.OrderedTypeEx.html b/master/stdlib/Stdlib.Structures.OrderedTypeEx.html index fab127915d..487846685c 100644 --- a/master/stdlib/Stdlib.Structures.OrderedTypeEx.html +++ b/master/stdlib/Stdlib.Structures.OrderedTypeEx.html @@ -55,7 +55,7 @@

Library Stdlib.Structures.OrderedTypeEx

-

Examples of Ordered Type structures.

+

Examples of Ordered Type structures.

diff --git a/master/stdlib/Stdlib.Structures.Orders.html b/master/stdlib/Stdlib.Structures.Orders.html index 4e2111ff22..de5573660d 100644 --- a/master/stdlib/Stdlib.Structures.Orders.html +++ b/master/stdlib/Stdlib.Structures.Orders.html @@ -52,7 +52,7 @@

Library Stdlib.Structures.Orders

-

Ordered types

+

Ordered types

@@ -187,7 +187,7 @@

Library Stdlib.Structures.Orders

DecidableType.
-

Versions with eq being the usual Leibniz equality of Coq

+

Versions with eq being the usual Leibniz equality of Coq

@@ -219,7 +219,7 @@

Library Stdlib.Structures.Orders

-

Purely logical versions

+

Purely logical versions

@@ -242,7 +242,7 @@

Library Stdlib.Structures.Orders

-

Conversions

+

Conversions

@@ -303,7 +303,7 @@

Library Stdlib.Structures.Orders

-

Versions with boolean comparisons

+

Versions with boolean comparisons

@@ -405,7 +405,7 @@

Library Stdlib.Structures.Orders

-

From OrderedTypeFull to TotalTransitiveLeBool

+

From OrderedTypeFull to TotalTransitiveLeBool

@@ -436,7 +436,7 @@

Library Stdlib.Structures.Orders

-

From TotalTransitiveLeBool to OrderedTypeFull

+

From TotalTransitiveLeBool to OrderedTypeFull

diff --git a/master/stdlib/Stdlib.Structures.OrdersAlt.html b/master/stdlib/Stdlib.Structures.OrdersAlt.html index 00397291fe..d036cd2217 100644 --- a/master/stdlib/Stdlib.Structures.OrdersAlt.html +++ b/master/stdlib/Stdlib.Structures.OrdersAlt.html @@ -54,12 +54,12 @@

Library Stdlib.Structures.OrdersAlt

-

Some alternative (but equivalent) presentations for an Ordered Type

+

Some alternative (but equivalent) presentations for an Ordered Type

inferface.
-

The original interface

+

The original interface

@@ -71,7 +71,7 @@

Library Stdlib.Structures.OrdersAlt

-

An interface based on compare

+

An interface based on compare

@@ -101,7 +101,7 @@

Library Stdlib.Structures.OrdersAlt

-

From OrderedTypeOrig to OrderedType.

+

From OrderedTypeOrig to OrderedType.

@@ -140,7 +140,7 @@

Library Stdlib.Structures.OrdersAlt

-

From OrderedType to OrderedTypeOrig.

+

From OrderedType to OrderedTypeOrig.

@@ -169,7 +169,7 @@

Library Stdlib.Structures.OrdersAlt

-

From OrderedTypeAlt to OrderedType.

+

From OrderedTypeAlt to OrderedType.

diff --git a/master/stdlib/Stdlib.Structures.OrdersEx.html b/master/stdlib/Stdlib.Structures.OrdersEx.html index a582d867a8..14cd13f9f6 100644 --- a/master/stdlib/Stdlib.Structures.OrdersEx.html +++ b/master/stdlib/Stdlib.Structures.OrdersEx.html @@ -55,7 +55,7 @@

Library Stdlib.Structures.OrdersEx

-

Examples of Ordered Type structures.

+

Examples of Ordered Type structures.

diff --git a/master/stdlib/Stdlib.Structures.OrdersFacts.html b/master/stdlib/Stdlib.Structures.OrdersFacts.html index 166302d62c..0d3daf7e79 100644 --- a/master/stdlib/Stdlib.Structures.OrdersFacts.html +++ b/master/stdlib/Stdlib.Structures.OrdersFacts.html @@ -55,7 +55,7 @@

Library Stdlib.Structures.OrdersFacts

-

Properties of compare

+

Properties of compare

@@ -104,7 +104,7 @@

Library Stdlib.Structures.OrdersFacts

-

Properties of OrderedTypeFull

+

Properties of OrderedTypeFull

@@ -164,7 +164,7 @@

Library Stdlib.Structures.OrdersFacts

-

Properties of OrderedType

+

Properties of OrderedType

@@ -259,7 +259,7 @@

Library Stdlib.Structures.OrdersFacts

-

Tests of the order tactic

+

Tests of the order tactic

@@ -297,7 +297,7 @@

Library Stdlib.Structures.OrdersFacts

-

Reversed OrderedTypeFull.

+

Reversed OrderedTypeFull.

@@ -348,7 +348,7 @@

Library Stdlib.Structures.OrdersFacts

-

Order relations derived from a compare function.

+

Order relations derived from a compare function.

diff --git a/master/stdlib/Stdlib.Structures.OrdersLists.html b/master/stdlib/Stdlib.Structures.OrdersLists.html index 8c59b28a83..ed1fb5929f 100644 --- a/master/stdlib/Stdlib.Structures.OrdersLists.html +++ b/master/stdlib/Stdlib.Structures.OrdersLists.html @@ -54,7 +54,7 @@

Library Stdlib.Structures.OrdersLists

-

Specialization of results about lists modulo.

+

Specialization of results about lists modulo.

@@ -109,7 +109,7 @@

Library Stdlib.Structures.OrdersLists

-

Results about keys and data as manipulated in the future MMaps.

+

Results about keys and data as manipulated in the future MMaps.

diff --git a/master/stdlib/Stdlib.Structures.OrdersTac.html b/master/stdlib/Stdlib.Structures.OrdersTac.html index 02102250d6..54cd65a10c 100644 --- a/master/stdlib/Stdlib.Structures.OrdersTac.html +++ b/master/stdlib/Stdlib.Structures.OrdersTac.html @@ -52,7 +52,7 @@

Library Stdlib.Structures.OrdersTac

-

The order tactic

+

The order tactic

@@ -91,7 +91,7 @@

Library Stdlib.Structures.OrdersTac

-

The tactic requirements : a total order

+

The tactic requirements : a total order

@@ -127,7 +127,7 @@

Library Stdlib.Structures.OrdersTac

-

Properties that will be used by the order tactic

+

Properties that will be used by the order tactic

@@ -237,7 +237,7 @@

Library Stdlib.Structures.OrdersTac

-

MakeOrderTac : The functor providing the order tactic.

+

MakeOrderTac : The functor providing the order tactic.

diff --git a/master/stdlib/Stdlib.Vectors.VectorDef.html b/master/stdlib/Stdlib.Vectors.VectorDef.html index ae975fe15b..4e50f3dd24 100644 --- a/master/stdlib/Stdlib.Vectors.VectorDef.html +++ b/master/stdlib/Stdlib.Vectors.VectorDef.html @@ -436,7 +436,7 @@

Library Stdlib.Vectors.VectorDef

-

Here are special non dependent useful instantiation of induction schemes

+

Here are special non dependent useful instantiation of induction schemes

@@ -563,7 +563,7 @@

Library Stdlib.Vectors.VectorDef

-

vector <=> list functions

+

vector <=> list functions

diff --git a/master/stdlib/Stdlib.Vectors.VectorSpec.html b/master/stdlib/Stdlib.Vectors.VectorSpec.html index 92da33c3e5..ddf3f476e0 100644 --- a/master/stdlib/Stdlib.Vectors.VectorSpec.html +++ b/master/stdlib/Stdlib.Vectors.VectorSpec.html @@ -94,7 +94,7 @@

Library Stdlib.Vectors.VectorSpec

is true for the one that use lt
-

Properties of nth and nth_order

+

Properties of nth and nth_order

@@ -135,7 +135,7 @@

Library Stdlib.Vectors.VectorSpec

-

Properties of replace

+

Properties of replace

@@ -181,7 +181,7 @@

Library Stdlib.Vectors.VectorSpec

-

Properties of const

+

Properties of const

@@ -196,7 +196,7 @@

Library Stdlib.Vectors.VectorSpec

-

Properties of map

+

Properties of map

@@ -237,7 +237,7 @@

Library Stdlib.Vectors.VectorSpec

-

Properties of fold_left

+

Properties of fold_left

@@ -251,7 +251,7 @@

Library Stdlib.Vectors.VectorSpec

-

Properties of take

+

Properties of take

@@ -273,7 +273,7 @@

Library Stdlib.Vectors.VectorSpec

-

Properties of uncons and splitat

+

Properties of uncons and splitat

@@ -304,7 +304,7 @@

Library Stdlib.Vectors.VectorSpec

-

Properties of In

+

Properties of In

@@ -317,7 +317,7 @@

Library Stdlib.Vectors.VectorSpec

-

Properties of Forall and Forall2

+

Properties of Forall and Forall2

@@ -371,7 +371,7 @@

Library Stdlib.Vectors.VectorSpec

-

Properties of shiftin and shiftrepeat

+

Properties of shiftin and shiftrepeat

@@ -410,7 +410,7 @@

Library Stdlib.Vectors.VectorSpec

-

Properties of rev

+

Properties of rev

@@ -448,7 +448,7 @@

Library Stdlib.Vectors.VectorSpec

-

Properties of to_list

+

Properties of to_list

diff --git a/master/stdlib/Stdlib.ZArith.BinInt.html b/master/stdlib/Stdlib.ZArith.BinInt.html index f9802906d3..0897f507ca 100644 --- a/master/stdlib/Stdlib.ZArith.BinInt.html +++ b/master/stdlib/Stdlib.ZArith.BinInt.html @@ -54,7 +54,7 @@

Library Stdlib.ZArith.BinInt

-

Binary Integers

+

Binary Integers

@@ -89,7 +89,7 @@

Library Stdlib.ZArith.BinInt

-

Definitions of operations, now in a separate file

+

Definitions of operations, now in a separate file

@@ -121,7 +121,7 @@

Library Stdlib.ZArith.BinInt

-

Logic Predicates

+

Logic Predicates

@@ -159,7 +159,7 @@

Library Stdlib.ZArith.BinInt

-

Decidability of equality.

+

Decidability of equality.

@@ -171,7 +171,7 @@

Library Stdlib.ZArith.BinInt

-

Proofs of morphisms, obvious since eq is Leibniz

+

Proofs of morphisms, obvious since eq is Leibniz

@@ -196,7 +196,7 @@

Library Stdlib.ZArith.BinInt

-

Properties of pos_sub

+

Properties of pos_sub

@@ -267,7 +267,7 @@

Library Stdlib.ZArith.BinInt

-

Operations and constants

+

Operations and constants

@@ -285,7 +285,7 @@

Library Stdlib.ZArith.BinInt

-

Addition is commutative

+

Addition is commutative

@@ -297,7 +297,7 @@

Library Stdlib.ZArith.BinInt

-

Opposite distributes over addition

+

Opposite distributes over addition

@@ -309,7 +309,7 @@

Library Stdlib.ZArith.BinInt

-

Opposite is injective

+

Opposite is injective

@@ -321,7 +321,7 @@

Library Stdlib.ZArith.BinInt

-

Addition is associative

+

Addition is associative

@@ -343,7 +343,7 @@

Library Stdlib.ZArith.BinInt

-

Opposite is inverse for addition

+

Opposite is inverse for addition

@@ -355,7 +355,7 @@

Library Stdlib.ZArith.BinInt

-

Multiplication and Opposite

+

Multiplication and Opposite

@@ -367,7 +367,7 @@

Library Stdlib.ZArith.BinInt

-

Distributivity of multiplication over addition

+

Distributivity of multiplication over addition

@@ -386,11 +386,11 @@

Library Stdlib.ZArith.BinInt

-

Proofs of specifications

+

Proofs of specifications

-

Specification of constants

+

Specification of constants

@@ -405,7 +405,7 @@

Library Stdlib.ZArith.BinInt

-

Specification of addition

+

Specification of addition

@@ -420,7 +420,7 @@

Library Stdlib.ZArith.BinInt

-

Specification of opposite

+

Specification of opposite

@@ -435,7 +435,7 @@

Library Stdlib.ZArith.BinInt

-

Specification of successor and predecessor

+

Specification of successor and predecessor

@@ -453,7 +453,7 @@

Library Stdlib.ZArith.BinInt

-

Specification of subtraction

+

Specification of subtraction

@@ -468,7 +468,7 @@

Library Stdlib.ZArith.BinInt

-

Specification of multiplication

+

Specification of multiplication

@@ -483,7 +483,7 @@

Library Stdlib.ZArith.BinInt

-

Specification of comparisons and order

+

Specification of comparisons and order

@@ -575,7 +575,7 @@

Library Stdlib.ZArith.BinInt

-

Specification of minimum and maximum

+

Specification of minimum and maximum

@@ -596,7 +596,7 @@

Library Stdlib.ZArith.BinInt

-

Induction principles based on successor / predecessor

+

Induction principles based on successor / predecessor

@@ -637,7 +637,7 @@

Library Stdlib.ZArith.BinInt

-

Specification of absolute value

+

Specification of absolute value

@@ -652,7 +652,7 @@

Library Stdlib.ZArith.BinInt

-

Specification of sign

+

Specification of sign

@@ -670,7 +670,7 @@

Library Stdlib.ZArith.BinInt

-

Specification of power

+

Specification of power

@@ -699,7 +699,7 @@

Library Stdlib.ZArith.BinInt

-

Specification of square

+

Specification of square

@@ -711,7 +711,7 @@

Library Stdlib.ZArith.BinInt

-

Specification of square root

+

Specification of square root

@@ -734,7 +734,7 @@

Library Stdlib.ZArith.BinInt

-

Specification of logarithm

+

Specification of logarithm

@@ -763,7 +763,7 @@

Library Stdlib.ZArith.BinInt

-

Multiplication and Doubling

+

Multiplication and Doubling

@@ -781,7 +781,7 @@

Library Stdlib.ZArith.BinInt

-

Correctness proofs for Trunc division

+

Correctness proofs for Trunc division

@@ -813,7 +813,7 @@

Library Stdlib.ZArith.BinInt

-

Correctness proofs for Floor division

+

Correctness proofs for Floor division

@@ -846,7 +846,7 @@

Library Stdlib.ZArith.BinInt

-

Extra properties about divide

+

Extra properties about divide

@@ -864,7 +864,7 @@

Library Stdlib.ZArith.BinInt

-

Correctness proofs for gcd

+

Correctness proofs for gcd

@@ -905,7 +905,7 @@

Library Stdlib.ZArith.BinInt

-

Extra properties about testbit

+

Extra properties about testbit

@@ -930,7 +930,7 @@

Library Stdlib.ZArith.BinInt

-

Proofs of specifications for bitwise operations

+

Proofs of specifications for bitwise operations

@@ -1109,7 +1109,7 @@

Library Stdlib.ZArith.BinInt

-

Comparison and opposite

+

Comparison and opposite

@@ -1121,7 +1121,7 @@

Library Stdlib.ZArith.BinInt

-

Comparison and addition

+

Comparison and addition

@@ -1133,7 +1133,7 @@

Library Stdlib.ZArith.BinInt

-

testbit in terms of comparison.

+

testbit in terms of comparison.

diff --git a/master/stdlib/Stdlib.ZArith.BinIntDef.html b/master/stdlib/Stdlib.ZArith.BinIntDef.html index 2292bad6b6..6206dc05f5 100644 --- a/master/stdlib/Stdlib.ZArith.BinIntDef.html +++ b/master/stdlib/Stdlib.ZArith.BinIntDef.html @@ -61,7 +61,7 @@

Library Stdlib.ZArith.BinIntDef

-

Binary Integers, Definitions of Operations

+

Binary Integers, Definitions of Operations

@@ -82,7 +82,7 @@

Library Stdlib.ZArith.BinIntDef

-

Nicer names Z.pos and Z.neg for constructors

+

Nicer names Z.pos and Z.neg for constructors

@@ -95,7 +95,7 @@

Library Stdlib.ZArith.BinIntDef

-

Constants

+

Constants

@@ -109,7 +109,7 @@

Library Stdlib.ZArith.BinIntDef

-

Successor

+

Successor

@@ -121,7 +121,7 @@

Library Stdlib.ZArith.BinIntDef

-

Predecessor

+

Predecessor

@@ -133,7 +133,7 @@

Library Stdlib.ZArith.BinIntDef

-

Square

+

Square

@@ -150,7 +150,7 @@

Library Stdlib.ZArith.BinIntDef

-

Sign function

+

Sign function

@@ -201,7 +201,7 @@

Library Stdlib.ZArith.BinIntDef

-

Absolute value

+

Absolute value

@@ -218,7 +218,7 @@

Library Stdlib.ZArith.BinIntDef

-

Conversions

+

Conversions

@@ -333,7 +333,7 @@

Library Stdlib.ZArith.BinIntDef

-

Iteration of a function

+

Iteration of a function

@@ -358,7 +358,7 @@

Library Stdlib.ZArith.BinIntDef

-

Parity functions

+

Parity functions

@@ -376,7 +376,7 @@

Library Stdlib.ZArith.BinIntDef

-

Division by two

+

Division by two

@@ -403,7 +403,7 @@

Library Stdlib.ZArith.BinIntDef

NB: Z.quot2 used to be named Z.div2 in Coq <= 8.3
-

Base-2 logarithm

+

Base-2 logarithm

@@ -420,7 +420,7 @@

Library Stdlib.ZArith.BinIntDef

-

Square root

+

Square root

@@ -436,7 +436,7 @@

Library Stdlib.ZArith.BinIntDef

-

Greatest Common Divisor

+

Greatest Common Divisor

@@ -479,7 +479,7 @@

Library Stdlib.ZArith.BinIntDef

-

Bitwise functions

+

Bitwise functions

diff --git a/master/stdlib/Stdlib.ZArith.Int.html b/master/stdlib/Stdlib.ZArith.Int.html index 3512fb2db3..27335b2c60 100644 --- a/master/stdlib/Stdlib.ZArith.Int.html +++ b/master/stdlib/Stdlib.ZArith.Int.html @@ -48,7 +48,7 @@

Library Stdlib.ZArith.Int

-

An light axiomatization of integers (used in MSetAVL).

+

An light axiomatization of integers (used in MSetAVL).

@@ -73,7 +73,7 @@

Library Stdlib.ZArith.Int

-

A specification of integers

+

A specification of integers

@@ -209,7 +209,7 @@

Library Stdlib.ZArith.Int

-

Facts and tactics using Int

+

Facts and tactics using Int

@@ -563,7 +563,7 @@

Library Stdlib.ZArith.Int

-

An implementation of Int

+

An implementation of Int

diff --git a/master/stdlib/Stdlib.ZArith.ZArith_dec.html b/master/stdlib/Stdlib.ZArith.ZArith_dec.html index 556239edce..f0419e3525 100644 --- a/master/stdlib/Stdlib.ZArith.ZArith_dec.html +++ b/master/stdlib/Stdlib.ZArith.ZArith_dec.html @@ -73,7 +73,7 @@

Library Stdlib.ZArith.ZArith_dec

-

Decidability of order on binary integers

+

Decidability of order on binary integers

@@ -115,7 +115,7 @@

Library Stdlib.ZArith.ZArith_dec

-

Cotransitivity of order on binary integers

+

Cotransitivity of order on binary integers

diff --git a/master/stdlib/Stdlib.ZArith.Zabs.html b/master/stdlib/Stdlib.ZArith.Zabs.html index 7892a660a7..b76a6c11d6 100644 --- a/master/stdlib/Stdlib.ZArith.Zabs.html +++ b/master/stdlib/Stdlib.ZArith.Zabs.html @@ -73,7 +73,7 @@

Library Stdlib.ZArith.Zabs

-

Properties of absolute value

+

Properties of absolute value

@@ -91,7 +91,7 @@

Library Stdlib.ZArith.Zabs

-

Proving a property of the absolute value by cases

+

Proving a property of the absolute value by cases

@@ -116,7 +116,7 @@

Library Stdlib.ZArith.Zabs

-

Some results about the sign function.

+

Some results about the sign function.

diff --git a/master/stdlib/Stdlib.ZArith.Zbitwise.html b/master/stdlib/Stdlib.ZArith.Zbitwise.html index 3b5a62d0cd..ef09c88250 100644 --- a/master/stdlib/Stdlib.ZArith.Zbitwise.html +++ b/master/stdlib/Stdlib.ZArith.Zbitwise.html @@ -151,13 +151,13 @@

Library Stdlib.ZArith.Zbitwise

Explicit formulas for carry bits during addition. Conceptually, the theory -

here matches the bitblasting rules for integers. However, the vector of

+

here matches the bitblasting rules for integers. However, the vector of

-

carry bits is represented as a Z so it can be used in bitwise operations.

+

carry bits is represented as a Z so it can be used in bitwise operations.

-

The last three lemmas about addcarries are the main interface, but the

+

The last three lemmas about addcarries are the main interface, but the

-

generalization adccarries is provided as the same theory applies.

+

generalization adccarries is provided as the same theory applies.

diff --git a/master/stdlib/Stdlib.ZArith.Zbool.html b/master/stdlib/Stdlib.ZArith.Zbool.html index 7af2f43841..d85db90bb4 100644 --- a/master/stdlib/Stdlib.ZArith.Zbool.html +++ b/master/stdlib/Stdlib.ZArith.Zbool.html @@ -151,7 +151,7 @@

Library Stdlib.ZArith.Zbool

Properties of the deprecated Zeq_bool
-

Boolean operations from decidability of order

+

Boolean operations from decidability of order

The decidability of equality and order relations over type Z gives some boolean functions with the adequate specification.
@@ -183,7 +183,7 @@

Library Stdlib.ZArith.Zbool

-

Boolean comparisons of binary integers

+

Boolean comparisons of binary integers

diff --git a/master/stdlib/Stdlib.ZArith.Zcompare.html b/master/stdlib/Stdlib.ZArith.Zcompare.html index a5c21e1213..a3196231f9 100644 --- a/master/stdlib/Stdlib.ZArith.Zcompare.html +++ b/master/stdlib/Stdlib.ZArith.Zcompare.html @@ -67,7 +67,7 @@

Library Stdlib.ZArith.Zcompare

-

Comparison on integers

+

Comparison on integers

@@ -82,7 +82,7 @@

Library Stdlib.ZArith.Zcompare

-

Transitivity of comparison

+

Transitivity of comparison

@@ -99,7 +99,7 @@

Library Stdlib.ZArith.Zcompare

-

Comparison and opposite

+

Comparison and opposite

@@ -111,7 +111,7 @@

Library Stdlib.ZArith.Zcompare

-

Comparison first-order specification

+

Comparison first-order specification

@@ -123,7 +123,7 @@

Library Stdlib.ZArith.Zcompare

-

Comparison and addition

+

Comparison and addition

@@ -145,7 +145,7 @@

Library Stdlib.ZArith.Zcompare

-

Successor and comparison

+

Successor and comparison

@@ -157,7 +157,7 @@

Library Stdlib.ZArith.Zcompare

-

Multiplication and comparison

+

Multiplication and comparison

@@ -178,7 +178,7 @@

Library Stdlib.ZArith.Zcompare

-

Relating x ?= y to =, <=, <, >= or >

+

Relating x ?= y to =, <=, <, >= or >

diff --git a/master/stdlib/Stdlib.ZArith.Zdiv.html b/master/stdlib/Stdlib.ZArith.Zdiv.html index 045e4a27cd..5e48acaf68 100644 --- a/master/stdlib/Stdlib.ZArith.Zdiv.html +++ b/master/stdlib/Stdlib.ZArith.Zdiv.html @@ -48,7 +48,7 @@

Library Stdlib.ZArith.Zdiv

-

Euclidean Division

+

Euclidean Division

@@ -88,7 +88,7 @@

Library Stdlib.ZArith.Zdiv

-

Main division theorems

+

Main division theorems

@@ -237,7 +237,7 @@

Library Stdlib.ZArith.Zdiv

-

Basic values of divisions and modulo.

+

Basic values of divisions and modulo.

@@ -293,7 +293,7 @@

Library Stdlib.ZArith.Zdiv

-

Order results about Z.modulo and Z.div

+

Order results about Z.modulo and Z.div

@@ -451,7 +451,7 @@

Library Stdlib.ZArith.Zdiv

-

Relations between usual operations and Z.modulo and Z.div

+

Relations between usual operations and Z.modulo and Z.div

@@ -690,7 +690,7 @@

Library Stdlib.ZArith.Zdiv

-

Compatibility

+

Compatibility

@@ -726,7 +726,7 @@

Library Stdlib.ZArith.Zdiv

-

A direct way to compute Z.modulo

+

A direct way to compute Z.modulo

@@ -778,9 +778,9 @@

Library Stdlib.ZArith.Zdiv

Another convention is possible for division by negative numbers: -

quotient is always the biggest integer smaller than or equal to a/b

+

quotient is always the biggest integer smaller than or equal to a/b

-

remainder is hence always positive or null.

+

remainder is hence always positive or null.

diff --git a/master/stdlib/Stdlib.ZArith.Zeuclid.html b/master/stdlib/Stdlib.ZArith.Zeuclid.html index b0221ce559..9f2e661eea 100644 --- a/master/stdlib/Stdlib.ZArith.Zeuclid.html +++ b/master/stdlib/Stdlib.ZArith.Zeuclid.html @@ -62,7 +62,7 @@

Library Stdlib.ZArith.Zeuclid

-

Definitions of division for binary integers, Euclid convention.

+

Definitions of division for binary integers, Euclid convention.

diff --git a/master/stdlib/Stdlib.ZArith.Zeven.html b/master/stdlib/Stdlib.ZArith.Zeven.html index 4e40bf3214..0bc6d7af25 100644 --- a/master/stdlib/Stdlib.ZArith.Zeven.html +++ b/master/stdlib/Stdlib.ZArith.Zeven.html @@ -175,7 +175,7 @@

Library Stdlib.ZArith.Zeven

-

Definition of Z.quot2, Z.div2 and properties wrt Zeven

+

Definition of Z.quot2, Z.div2 and properties wrt Zeven

and Zodd
diff --git a/master/stdlib/Stdlib.ZArith.Zgcd_alt.html b/master/stdlib/Stdlib.ZArith.Zgcd_alt.html index f8f5c4e0cc..a9f1ce281b 100644 --- a/master/stdlib/Stdlib.ZArith.Zgcd_alt.html +++ b/master/stdlib/Stdlib.ZArith.Zgcd_alt.html @@ -48,7 +48,7 @@

Library Stdlib.ZArith.Zgcd_alt

-

Zgcd_alt : an alternate version of Z.gcd, based on Euclid's algorithm

+

Zgcd_alt : an alternate version of Z.gcd, based on Euclid's algorithm

diff --git a/master/stdlib/Stdlib.ZArith.Zhints.html b/master/stdlib/Stdlib.ZArith.Zhints.html index 3a8c0040b0..c945802113 100644 --- a/master/stdlib/Stdlib.ZArith.Zhints.html +++ b/master/stdlib/Stdlib.ZArith.Zhints.html @@ -101,7 +101,7 @@

Library Stdlib.ZArith.Zhints

-

Simplification lemmas

+

Simplification lemmas

@@ -115,7 +115,7 @@

Library Stdlib.ZArith.Zhints

  
-

Reversible simplification lemmas (no loss of information)

+

Reversible simplification lemmas (no loss of information)

Should clearly be declared as hints
@@ -170,7 +170,7 @@

Library Stdlib.ZArith.Zhints

  
-

Irreversible simplification lemmas

+

Irreversible simplification lemmas

Probably to be declared as hints, when no other simplification is possible
diff --git a/master/stdlib/Stdlib.ZArith.Znat.html b/master/stdlib/Stdlib.ZArith.Znat.html index be775329fd..fc892948d7 100644 --- a/master/stdlib/Stdlib.ZArith.Znat.html +++ b/master/stdlib/Stdlib.ZArith.Znat.html @@ -94,7 +94,7 @@

Library Stdlib.ZArith.Znat

-

Chains of conversions

+

Chains of conversions

@@ -147,7 +147,7 @@

Library Stdlib.ZArith.Znat

-

Conversions between Z and N

+

Conversions between Z and N

@@ -551,7 +551,7 @@

Library Stdlib.ZArith.Znat

-

Conversions between Z and nat

+

Conversions between Z and nat

diff --git a/master/stdlib/Stdlib.ZArith.Znumtheory.html b/master/stdlib/Stdlib.ZArith.Znumtheory.html index c94cbe8171..21077ebec5 100644 --- a/master/stdlib/Stdlib.ZArith.Znumtheory.html +++ b/master/stdlib/Stdlib.ZArith.Znumtheory.html @@ -244,7 +244,7 @@

Library Stdlib.ZArith.Znumtheory

-

Greatest common divisor (gcd).

+

Greatest common divisor (gcd).

@@ -306,7 +306,7 @@

Library Stdlib.ZArith.Znumtheory

-

Extended Euclid algorithm.

+

Extended Euclid algorithm.

@@ -394,7 +394,7 @@

Library Stdlib.ZArith.Znumtheory

-

Bezout's coefficients

+

Bezout's coefficients

@@ -430,7 +430,7 @@

Library Stdlib.ZArith.Znumtheory

-

Relative primality

+

Relative primality

@@ -524,7 +524,7 @@

Library Stdlib.ZArith.Znumtheory

-

Primality

+

Primality

diff --git a/master/stdlib/Stdlib.ZArith.Zorder.html b/master/stdlib/Stdlib.ZArith.Zorder.html index 621a9519b3..70589b32e5 100644 --- a/master/stdlib/Stdlib.ZArith.Zorder.html +++ b/master/stdlib/Stdlib.ZArith.Zorder.html @@ -70,7 +70,7 @@

Library Stdlib.ZArith.Zorder

Properties of the order relations on binary integers
-

Trichotomy

+

Trichotomy

@@ -85,7 +85,7 @@

Library Stdlib.ZArith.Zorder

-

Decidability of equality and order on Z

+

Decidability of equality and order on Z

@@ -111,7 +111,7 @@

Library Stdlib.ZArith.Zorder

-

Relating strict and large orders

+

Relating strict and large orders

@@ -151,7 +151,7 @@

Library Stdlib.ZArith.Zorder

-

Equivalence and order properties

+

Equivalence and order properties

@@ -275,11 +275,11 @@

Library Stdlib.ZArith.Zorder

-

Compatibility of order and operations on Z

+

Compatibility of order and operations on Z

-

Successor

+

Successor

@@ -457,7 +457,7 @@

Library Stdlib.ZArith.Zorder

-

Addition

+

Addition

Compatibility of addition wrt to order
@@ -527,7 +527,7 @@

Library Stdlib.ZArith.Zorder

-

Multiplication

+

Multiplication

Compatibility of multiplication by a positive wrt to order
@@ -655,7 +655,7 @@

Library Stdlib.ZArith.Zorder

-

Square

+

Square

Simplification of square wrt order
@@ -670,7 +670,7 @@

Library Stdlib.ZArith.Zorder

-

Equivalence between inequalities

+

Equivalence between inequalities

diff --git a/master/stdlib/Stdlib.ZArith.Zpow_def.html b/master/stdlib/Stdlib.ZArith.Zpow_def.html index e9b5e98a76..7ab77b6c48 100644 --- a/master/stdlib/Stdlib.ZArith.Zpow_def.html +++ b/master/stdlib/Stdlib.ZArith.Zpow_def.html @@ -52,7 +52,7 @@

Library Stdlib.ZArith.Zpow_def

-

Power functions over Z

+

Power functions over Z

diff --git a/master/stdlib/Stdlib.ZArith.Zpow_facts.html b/master/stdlib/Stdlib.ZArith.Zpow_facts.html index 448ac48a69..2035e552b1 100644 --- a/master/stdlib/Stdlib.ZArith.Zpow_facts.html +++ b/master/stdlib/Stdlib.ZArith.Zpow_facts.html @@ -131,7 +131,7 @@

Library Stdlib.ZArith.Zpow_facts

-

Z.pow and modulo

+

Z.pow and modulo

@@ -207,7 +207,7 @@

Library Stdlib.ZArith.Zpow_facts

-

Z.square: a direct definition of z^2

+

Z.square: a direct definition of z^2

diff --git a/master/stdlib/Stdlib.ZArith.Zpower.html b/master/stdlib/Stdlib.ZArith.Zpower.html index 7b5bc0d966..97b325f3f5 100644 --- a/master/stdlib/Stdlib.ZArith.Zpower.html +++ b/master/stdlib/Stdlib.ZArith.Zpower.html @@ -53,7 +53,7 @@

Library Stdlib.ZArith.Zpower

-

Power functions over Z

+

Power functions over Z

@@ -153,7 +153,7 @@

Library Stdlib.ZArith.Zpower

-

Powers of 2

+

Powers of 2

@@ -282,7 +282,7 @@

Library Stdlib.ZArith.Zpower

-

Division by a power of two.

+

Division by a power of two.

diff --git a/master/stdlib/Stdlib.ZArith.Zquot.html b/master/stdlib/Stdlib.ZArith.Zquot.html index 886d16aa3b..ba1a3aec86 100644 --- a/master/stdlib/Stdlib.ZArith.Zquot.html +++ b/master/stdlib/Stdlib.ZArith.Zquot.html @@ -153,7 +153,7 @@

Library Stdlib.ZArith.Zquot

-

Division and Opposite

+

Division and Opposite

@@ -232,7 +232,7 @@

Library Stdlib.ZArith.Zquot

-

Unicity results

+

Unicity results

@@ -265,7 +265,7 @@

Library Stdlib.ZArith.Zquot

-

Order results about Zrem and Zquot

+

Order results about Zrem and Zquot

@@ -363,7 +363,7 @@

Library Stdlib.ZArith.Zquot

-

Relations between usual operations and Z.modulo and Z.div

+

Relations between usual operations and Z.modulo and Z.div

@@ -527,7 +527,7 @@

Library Stdlib.ZArith.Zquot

-

Interaction with "historic" Zdiv

+

Interaction with "historic" Zdiv

diff --git a/master/stdlib/Stdlib.ZArith.auxiliary.html b/master/stdlib/Stdlib.ZArith.auxiliary.html index b34b76708b..cbffc51fbd 100644 --- a/master/stdlib/Stdlib.ZArith.auxiliary.html +++ b/master/stdlib/Stdlib.ZArith.auxiliary.html @@ -67,7 +67,7 @@

Library Stdlib.ZArith.auxiliary

-

Moving terms from one side to the other of an inequality

+

Moving terms from one side to the other of an inequality

diff --git a/master/stdlib/Stdlib.btauto.Algebra.html b/master/stdlib/Stdlib.btauto.Algebra.html index 6258555dcb..a610ff67de 100644 --- a/master/stdlib/Stdlib.btauto.Algebra.html +++ b/master/stdlib/Stdlib.btauto.Algebra.html @@ -143,7 +143,7 @@

Library Stdlib.btauto.Algebra

-

Global, inductive definitions.

+

Global, inductive definitions.

@@ -216,7 +216,7 @@

Library Stdlib.btauto.Algebra

-

The core reflexive part.

+

The core reflexive part.

diff --git a/master/stdlib/Stdlib.extraction.ExtrHaskellNatInt.html b/master/stdlib/Stdlib.extraction.ExtrHaskellNatInt.html index ab42558404..128ddfbc14 100644 --- a/master/stdlib/Stdlib.extraction.ExtrHaskellNatInt.html +++ b/master/stdlib/Stdlib.extraction.ExtrHaskellNatInt.html @@ -61,11 +61,11 @@

Library Stdlib.extraction.ExtrHaskellNatInt

-

Disclaimer: trying to obtain efficient certified programs

+

Disclaimer: trying to obtain efficient certified programs

-

by extracting nat into Int is definitively *not* a good idea.

+

by extracting nat into Int is definitively *not* a good idea.

-

See comments in ExtrOcamlNatInt.v.

+

See comments in ExtrOcamlNatInt.v.

diff --git a/master/stdlib/Stdlib.extraction.ExtrHaskellNatInteger.html b/master/stdlib/Stdlib.extraction.ExtrHaskellNatInteger.html index 27d4301cee..282fb6f60f 100644 --- a/master/stdlib/Stdlib.extraction.ExtrHaskellNatInteger.html +++ b/master/stdlib/Stdlib.extraction.ExtrHaskellNatInteger.html @@ -61,11 +61,11 @@

Library Stdlib.extraction.ExtrHaskellNatInteger

-

Disclaimer: trying to obtain efficient certified programs

+

Disclaimer: trying to obtain efficient certified programs

-

by extracting nat into Integer isn't necessarily a good idea.

+

by extracting nat into Integer isn't necessarily a good idea.

-

See comments in ExtrOcamlNatInt.v.

+

See comments in ExtrOcamlNatInt.v.

diff --git a/master/stdlib/Stdlib.extraction.ExtrHaskellNatNum.html b/master/stdlib/Stdlib.extraction.ExtrHaskellNatNum.html index 16919627ec..cbe1e33eec 100644 --- a/master/stdlib/Stdlib.extraction.ExtrHaskellNatNum.html +++ b/master/stdlib/Stdlib.extraction.ExtrHaskellNatNum.html @@ -46,15 +46,15 @@

Library Stdlib.extraction.ExtrHaskellNatNum

-

Efficient (but uncertified) extraction of usual nat functions

+

Efficient (but uncertified) extraction of usual nat functions

-

into equivalent versions in Haskell's Prelude that are defined

+

into equivalent versions in Haskell's Prelude that are defined

-

for any Num typeclass instances. Useful in combination with

+

for any Num typeclass instances. Useful in combination with

-

Extract Inductive nat that maps nat onto a Haskell type that

+

Extract Inductive nat that maps nat onto a Haskell type that

-

implements Num.

+

implements Num.

diff --git a/master/stdlib/Stdlib.extraction.ExtrHaskellString.html b/master/stdlib/Stdlib.extraction.ExtrHaskellString.html index a93c08a757..a03fcc1971 100644 --- a/master/stdlib/Stdlib.extraction.ExtrHaskellString.html +++ b/master/stdlib/Stdlib.extraction.ExtrHaskellString.html @@ -46,7 +46,7 @@

Library Stdlib.extraction.ExtrHaskellString

-

Special handling of ascii and strings for extraction to Haskell.

+

Special handling of ascii and strings for extraction to Haskell.

@@ -67,16 +67,16 @@

Library Stdlib.extraction.ExtrHaskellString

-

At the moment, Coq's extraction has no way to add extra import

+

At the moment, Coq's extraction has no way to add extra import

-

statements to the extracted Haskell code. You will have to

+

statements to the extracted Haskell code. You will have to

-

manually add:

+

manually add:

* -

import qualified Data.Bits

+

import qualified Data.Bits

-

import qualified Data.Char

+

import qualified Data.Char

diff --git a/master/stdlib/Stdlib.extraction.ExtrHaskellZInt.html b/master/stdlib/Stdlib.extraction.ExtrHaskellZInt.html index 9488da3154..30e6430ea9 100644 --- a/master/stdlib/Stdlib.extraction.ExtrHaskellZInt.html +++ b/master/stdlib/Stdlib.extraction.ExtrHaskellZInt.html @@ -61,11 +61,11 @@

Library Stdlib.extraction.ExtrHaskellZInt

-

Disclaimer: trying to obtain efficient certified programs

+

Disclaimer: trying to obtain efficient certified programs

-

by extracting Z into Int is definitively *not* a good idea.

+

by extracting Z into Int is definitively *not* a good idea.

-

See comments in ExtrOcamlNatInt.v.

+

See comments in ExtrOcamlNatInt.v.

diff --git a/master/stdlib/Stdlib.extraction.ExtrHaskellZNum.html b/master/stdlib/Stdlib.extraction.ExtrHaskellZNum.html index cc005038ab..094b6c1860 100644 --- a/master/stdlib/Stdlib.extraction.ExtrHaskellZNum.html +++ b/master/stdlib/Stdlib.extraction.ExtrHaskellZNum.html @@ -46,15 +46,15 @@

Library Stdlib.extraction.ExtrHaskellZNum

-

Efficient (but uncertified) extraction of usual Z functions

+

Efficient (but uncertified) extraction of usual Z functions

-

into equivalent versions in Haskell's Prelude that are defined

+

into equivalent versions in Haskell's Prelude that are defined

-

for any Num typeclass instances. Useful in combination with

+

for any Num typeclass instances. Useful in combination with

-

Extract Inductive Z that maps Z onto a Haskell type that

+

Extract Inductive Z that maps Z onto a Haskell type that

-

implements Num.

+

implements Num.

diff --git a/master/stdlib/Stdlib.omega.PreOmega.html b/master/stdlib/Stdlib.omega.PreOmega.html index 193a336295..04ac777300 100644 --- a/master/stdlib/Stdlib.omega.PreOmega.html +++ b/master/stdlib/Stdlib.omega.PreOmega.html @@ -54,7 +54,7 @@

Library Stdlib.omega.PreOmega

-

Z.div_mod_to_equations, Z.quot_rem_to_equations, Z.to_euclidean_division_equations:

+

Z.div_mod_to_equations, Z.quot_rem_to_equations, Z.to_euclidean_division_equations:

the tactics for preprocessing Z.div and Z.modulo, Z.quot and Z.rem
diff --git a/master/stdlib/index_global_B.html b/master/stdlib/index_global_B.html index facb5cc1eb..7610282c78 100644 --- a/master/stdlib/index_global_B.html +++ b/master/stdlib/index_global_B.html @@ -952,8 +952,8 @@ BVeq [definition, in Stdlib.Bool.Bvector]
BVor [definition, in Stdlib.Bool.Bvector]
BVxor [definition, in Stdlib.Bool.Bvector]
-Byte [library]
Byte [library]
+Byte [library]
ByteNotations [module, in Stdlib.Strings.Byte]
_ =? _ (byte_scope) [notation, in Stdlib.Strings.Byte]
byte_of_ascii_via_nat [lemma, in Stdlib.Strings.Ascii]
diff --git a/master/stdlib/index_global_T.html b/master/stdlib/index_global_T.html index 318575ec98..0c2cfba09a 100644 --- a/master/stdlib/index_global_T.html +++ b/master/stdlib/index_global_T.html @@ -527,8 +527,8 @@ t [abbreviation, in Stdlib.micromega.VarMap]
t [inductive, in Stdlib.micromega.VarMap]
t [inductive, in Stdlib.Vectors.Fin]
-Tactics [library]
Tactics [library]
+Tactics [library]
Tadd [definition, in Stdlib.rtauto.Bintree]
tail [abbreviation, in Stdlib.Lists.List]
tail [definition, in Stdlib.micromega.Env]
@@ -576,8 +576,8 @@ tan_PI [lemma, in Stdlib.Reals.Rtrigo_calc]
target [projection, in Stdlib.micromega.ZifyClasses]
target_prop [projection, in Stdlib.micromega.ZifyClasses]
-Tauto [library]
Tauto [library]
+Tauto [library]
tauto_checker_sound [lemma, in Stdlib.micromega.Tauto]
tauto_checker [definition, in Stdlib.micromega.Tauto]
TBOp [projection, in Stdlib.micromega.ZifyClasses]
diff --git a/master/stdlib/index_global_W.html b/master/stdlib/index_global_W.html index 015ea39209..5da261edc6 100644 --- a/master/stdlib/index_global_W.html +++ b/master/stdlib/index_global_W.html @@ -928,8 +928,8 @@ WEqProperties_fun.Add [definition, in Stdlib.FSets.FSetEqProperties]
WEqProperties_fun.MP [module, in Stdlib.FSets.FSetEqProperties]
WEqProperties_fun [module, in Stdlib.FSets.FSetEqProperties]
-Wf [library]
Wf [library]
+Wf [library]
WFacts [module, in Stdlib.MSets.MSetFacts]
WFacts [module, in Stdlib.FSets.FMapFacts]
WFacts [module, in Stdlib.FSets.FSetFacts]
diff --git a/master/stdlib/index_library_B.html b/master/stdlib/index_library_B.html index ec247f1a79..d0fde6a76b 100644 --- a/master/stdlib/index_library_B.html +++ b/master/stdlib/index_library_B.html @@ -543,8 +543,8 @@ Bool_nat
Btauto
Bvector
-Byte
Byte
+Byte