statement stringlengths 1 15.6k | proof stringlengths 0 77.4k | type stringclasses 28
values | symbolic_name stringlengths 1 67 | library stringclasses 41
values | filename stringclasses 383
values | imports listlengths 0 71 | deps listlengths 0 64 | docstring stringlengths 0 6.76k | source_url stringclasses 1
value | commit stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|
subst_decl s k (d : context_decl) | := map_decl (subst s k) d. | Definition | subst_decl | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"context_decl",
"map_decl",
"subst"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
subst_context_length s n Γ : #|subst_context s n Γ| = #|Γ|. | Proof. now rewrite /subst_context; len. Qed. | Lemma | subst_context_length | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"len",
"subst_context"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
subst_context_nil s n : subst_context s n [] = []. | Proof. reflexivity. Qed. | Lemma | subst_context_nil | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"reflexivity",
"subst_context"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
subst_context_alt s k Γ :
subst_context s k Γ =
mapi (fun k' d => subst_decl s (Nat.pred #|Γ| - k' + k) d) Γ. | Proof.
unfold subst_context, fold_context_k. rewrite rev_mapi. rewrite List.rev_involutive.
apply mapi_ext. intros. f_equal. now rewrite List.length_rev.
Qed. | Lemma | subst_context_alt | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"apply",
"fold_context_k",
"length_rev",
"mapi",
"mapi_ext",
"rev_involutive",
"rev_mapi",
"subst_context",
"subst_decl",
"unfold"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
subst_context_snoc s k Γ d : subst_context s k (d :: Γ) = subst_context s k Γ ,, subst_decl s (#|Γ| + k) d. | Proof.
now rewrite /subst_context fold_context_k_snoc0.
Qed. | Lemma | subst_context_snoc | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"fold_context_k_snoc0",
"subst_context",
"subst_decl"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
subst_telescope s k (Γ : context) : context | :=
mapi (fun k' decl => map_decl (subst s (k' + k)) decl) Γ. | Definition | subst_telescope | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"context",
"map_decl",
"mapi",
"subst"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
subst_instance_decl : UnivSubst context_decl | := map_decl ∘ subst_instance. | Instance | subst_instance_decl | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"UnivSubst",
"context_decl",
"map_decl"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
subst_instance_context : UnivSubst context | := map_context ∘ subst_instance. | Instance | subst_instance_context | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"UnivSubst",
"context",
"map_context"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
subst_instance_length u (ctx : context)
: #|subst_instance u ctx| = #|ctx|. | Proof. unfold subst_instance, subst_instance_context, map_context. now rewrite length_map. Qed. | Lemma | subst_instance_length | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"context",
"map_context",
"subst_instance_context",
"unfold"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
set_binder_name (na : aname) (x : context_decl) : context_decl | :=
{| decl_name := na;
decl_body := decl_body x;
decl_type := decl_type x |}. | Definition | set_binder_name | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"aname",
"context_decl"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
context_assumptions (Γ : context) : nat | :=
match Γ with
| [] => 0
| d :: Γ =>
match d.(decl_body) with
| Some _ => context_assumptions Γ
| None => S (context_assumptions Γ)
end
end. | Fixpoint | context_assumptions | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"context"
] | Count the number of assumptions in a context (i.e. declarations that do not
contain a body). | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 |
is_assumption_context (Γ : context) | :=
match Γ with
| [] => true
| d :: Γ =>
match d.(decl_body) with
| Some _ => false
| None => is_assumption_context Γ
end
end. | Fixpoint | is_assumption_context | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"context"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
smash_context (Γ Γ' : context) : context | :=
match Γ' with
| {| decl_body := Some b |} :: Γ' => smash_context (subst_context [b] 0 Γ) Γ'
| {| decl_body := None |} as d :: Γ' => smash_context (Γ ++ [d]) Γ'
| [] => Γ
end. | Fixpoint | smash_context | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"context",
"subst_context"
] | Smashing a context produces an assumption context. | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 |
smash_context_length Γ Γ' : #|smash_context Γ Γ'| = #|Γ| + context_assumptions Γ'. | Proof.
induction Γ' as [|[na [body|] ty] tl] in Γ |- *; cbn; eauto.
- now rewrite IHtl subst_context_length.
- rewrite IHtl length_app. simpl. lia.
Qed. | Lemma | smash_context_length | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"context_assumptions",
"smash_context",
"subst_context_length",
"ty"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
smash_context_app Δ Γ Γ' :
smash_context Δ (Γ ++ Γ') = smash_context (smash_context Δ Γ) Γ'. | Proof.
revert Δ; induction Γ as [|[na [b|] ty]]; intros Δ; simpl; auto.
Qed. | Lemma | smash_context_app | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"smash_context",
"ty"
] | Smashing a context Γ with Δ depending on it is the same as smashing Γ
and substituting all references to Γ in Δ by the expansions of let bindings. | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 |
extended_subst (Γ : context) (n : nat)
(* Δ, smash_context Γ, n |- extended_subst Γ n : Γ *) | :=
match Γ with
| nil => nil
| cons d vs =>
match decl_body d with
| Some b =>
(* Δ , vs |- b *)
let s := extended_subst vs n in
(* Δ , smash_context vs , n |- s : vs *)
let b' := lift (context_assumptions vs + n) #|s| b in
(* Δ, smash_context vs, n , vs |- b' *)
let b'... | Fixpoint | extended_subst | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"context",
"context_assumptions",
"lift",
"subst",
"tRel"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
extended_subst_length Γ n : #|extended_subst Γ n| = #|Γ|. | Proof.
induction Γ in n |- *; simpl; auto.
now destruct a as [? [?|] ?] => /=; simpl; rewrite IHΓ.
Qed. | Lemma | extended_subst_length | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"extended_subst"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
expand_lets_k Γ k t | :=
(subst (extended_subst Γ 0) k (lift (context_assumptions Γ) (k + #|Γ|) t)). | Definition | expand_lets_k | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"context_assumptions",
"extended_subst",
"lift",
"subst"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
expand_lets Γ t | := expand_lets_k Γ 0 t. | Definition | expand_lets | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"expand_lets_k"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
expand_lets_k_ctx Γ k Δ | :=
(subst_context (extended_subst Γ 0) k (lift_context (context_assumptions Γ) (k + #|Γ|) Δ)). | Definition | expand_lets_k_ctx | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"context_assumptions",
"extended_subst",
"lift_context",
"subst_context"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
expand_lets_ctx Γ Δ | := expand_lets_k_ctx Γ 0 Δ. | Definition | expand_lets_ctx | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"expand_lets_k_ctx"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
expand_lets_k_ctx_length Γ k Δ : #|expand_lets_k_ctx Γ k Δ| = #|Δ|. | Proof. now rewrite /expand_lets_k_ctx; len. Qed. | Lemma | expand_lets_k_ctx_length | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"expand_lets_k_ctx",
"len"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
expand_lets_ctx_length Γ Δ : #|expand_lets_ctx Γ Δ| = #|Δ|. | Proof. now rewrite /expand_lets_ctx; len. Qed. | Lemma | expand_lets_ctx_length | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"expand_lets_ctx",
"len"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
fix_context (m : mfixpoint term) : context | :=
List.rev (mapi (fun i d => vass d.(dname) (lift i 0 d.(dtype))) m). | Definition | fix_context | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"context",
"lift",
"mapi",
"mfixpoint",
"rev",
"term",
"vass"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
constructor_body | := {
(** Constructor name, without the module path. *)
cstr_name : ident;
(** Arguments of the constructor, which can depend on the inductives in the same block
and the parameters of the inductive : `ind_bodies ,,, ind_params |- cstr_args`. *)
cstr_args : context;
(** Indices of the construc... | Record | constructor_body | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"context",
"cstr_arity",
"ident",
"list",
"term"
] | Data associated to a single inductive constructor. | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 |
projection_body | := {
(** Projection name, without the module path. *)
proj_name : ident;
(** Relevance of the projection. *)
proj_relevance : relevance;
(** Type of the projection, wich can depend on the parameters of the inductive
and on the object we are projecting from : `ind_params ,,, x |- proj_type`. ... | Record | projection_body | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"ident",
"relevance",
"term"
] | Data associated to a primitive projection. | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 |
map_constructor_body npars arities f c | :=
{| cstr_name := c.(cstr_name);
cstr_args := fold_context_k (fun x => f (x + npars + arities)) c.(cstr_args);
cstr_indices := map (f (npars + arities + #|c.(cstr_args)|)) c.(cstr_indices);
(* Note only after positivity checking we can ensure that the indices do not mention the
ind... | Definition | map_constructor_body | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"cstr_arity",
"fold_context_k",
"map"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
map_projection_body npars f c | :=
{| proj_name := c.(proj_name);
proj_relevance := c.(proj_relevance);
proj_type := f (S npars) c.(proj_type)
|}. | Definition | map_projection_body | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [] | Here npars should be the `context_assumptions` of the parameters context. | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 |
one_inductive_body | := {
(** Name of the inductive, without the module path. *)
ind_name : ident;
(** Indices of the inductive, which can depend on the parameters :
`ind_params |- ind_indices`. *)
ind_indices : context;
(** Sort of the inductive. *)
ind_sort : Sort.t;
(** Full type of the inductive. Thi... | Record | one_inductive_body | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"allowed_eliminations",
"constructor_body",
"context",
"ident",
"list",
"projection_body",
"relevance",
"term"
] | Data associated to a single inductive in a mutual inductive block. | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 |
map_one_inductive_body npars arities f m | :=
match m with
| Build_one_inductive_body ind_name ind_indices ind_sort
ind_type ind_kelim ind_ctors ind_projs ind_relevance =>
Build_one_inductive_body
ind_name (fold_context_k (fun x => f (npars + x)) ind_indices) ind_sort
(f 0 ind_type) ind_kelim (map (map_constructo... | Definition | map_one_inductive_body | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"fold_context_k",
"map",
"map_constructor_body",
"map_projection_body"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
mutual_inductive_body | := {
(** Whether the block is inductive, coinductive or non-recursive (Records). *)
ind_finite : recursivity_kind;
(** Number of parameters (including non-uniform ones), _without_ counting let-in parameters.
This should be equal to `context_assumptions ind_params`. *)
ind_npars : nat;
(** Co... | Record | mutual_inductive_body | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"context",
"list",
"one_inductive_body",
"recursivity_kind",
"universes_decl"
] | Data associated to a block of mutually inductive types. | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 |
constant_body | := {
(** Type of the constant. *)
cst_type : term;
(** Body of the constant. For axioms this is [None]. *)
cst_body : option term;
(** Whether the constant is universe monomorphic or polymorphic, and if polymorphic
information about its local universes. *)
cst_universes : universes_decl;... | Record | constant_body | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"relevance",
"term",
"universes_decl"
] | Data associated to a constant (definition, lemma or axiom). | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 |
map_constant_body f decl | :=
{| cst_type := f decl.(cst_type);
cst_body := option_map f decl.(cst_body);
cst_universes := decl.(cst_universes);
cst_relevance := decl.(cst_relevance) |}. | Definition | map_constant_body | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"option_map"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
map_cst_type f decl :
f (cst_type decl) = cst_type (map_constant_body f decl). | Proof. destruct decl; reflexivity. Qed. | Lemma | map_cst_type | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"map_constant_body",
"reflexivity"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
map_cst_body f decl :
option_map f (cst_body decl) = cst_body (map_constant_body f decl). | Proof. destruct decl; reflexivity. Qed. | Lemma | map_cst_body | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"map_constant_body",
"option_map",
"reflexivity"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
global_decl | :=
| ConstantDecl : constant_body -> global_decl
| InductiveDecl : mutual_inductive_body -> global_decl. | Inductive | global_decl | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"constant_body",
"mutual_inductive_body"
] | A global declaration is a definition, lemma, axiom or mutual inductive. | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 |
global_declarations | := list (kername * global_decl). | Definition | global_declarations | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"global_decl",
"kername",
"list"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
global_env | := mk_global_env
{ universes : ContextSet.t;
declarations : global_declarations;
retroknowledge : Retroknowledge.t }. | Record | global_env | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"declarations",
"global_declarations",
"universes"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
universes : global_env >-> ContextSet.t. | Coercion | universes | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"global_env"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | ||
empty_global_env | :=
{| universes := ContextSet.empty;
declarations := [];
retroknowledge := Retroknowledge.empty |}. | Definition | empty_global_env | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"declarations",
"empty",
"universes"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
add_global_decl Σ decl | :=
{| universes := Σ.(universes);
declarations := decl :: Σ.(declarations);
retroknowledge := Σ.(retroknowledge) |}. | Definition | add_global_decl | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"declarations",
"universes"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
eta_global_env Σ : Σ = {| universes := Σ.(universes); declarations := Σ.(declarations);
retroknowledge := Σ.(retroknowledge) |}. | Proof. now destruct Σ. Qed. | Lemma | eta_global_env | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"declarations",
"universes"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
set_declarations Σ decls | :=
{| universes := Σ.(universes);
declarations := decls;
retroknowledge := Σ.(retroknowledge) |}. | Definition | set_declarations | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"declarations",
"universes"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
lookup_global (Σ : global_declarations) (kn : kername) : option global_decl | :=
match Σ with
| nil => None
| d :: tl =>
if kn == d.1 then Some d.2
else lookup_global tl kn
end. | Fixpoint | lookup_global | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"global_decl",
"global_declarations",
"kername"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
lookup_env (Σ : global_env) (kn : kername) | := lookup_global Σ.(declarations) kn. | Definition | lookup_env | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"declarations",
"global_env",
"kername",
"lookup_global"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
lookup_globals (Σ : global_declarations) (kn : kername) : list global_decl | :=
match Σ with
| nil => nil
| d :: tl =>
let tl := lookup_globals tl kn in
if kn == d.1 then d.2 :: tl else tl
end. | Fixpoint | lookup_globals | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"global_decl",
"global_declarations",
"kername",
"list"
] | version for possibly duplicative environments | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 |
lookup_envs (Σ : global_env) (kn : kername) | := lookup_globals Σ.(declarations) kn. | Definition | lookup_envs | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"declarations",
"global_env",
"kername",
"lookup_globals"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
extends_decls_part_globals Σ Σ' | := (forall c, ∑ decls, lookup_globals Σ' c = decls ++ lookup_globals Σ c)
(only parsing). | Notation | extends_decls_part_globals | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"lookup_globals",
"Σ'"
] | We define four notions of environment extension. The two
configurable bits are: is universe and retroknowledge extension
strict ([Logic.eq]) or loose ([⊂_cs] / [Retroknowledge.extends]);
and is declaration extension strict (fully order-preserving,
i.e., new declarations are added only at the fr... | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 |
strictly_extends_decls_part_globals Σ Σ' | := (∑ Σ'', Σ' = Σ'' ++ Σ)
(only parsing). | Notation | strictly_extends_decls_part_globals | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
extends_decls_part Σ Σ' | := (forall c, ∑ decls, lookup_envs Σ' c = decls ++ lookup_envs Σ c)
(only parsing). | Notation | extends_decls_part | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"lookup_envs",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
strictly_extends_decls_part Σ Σ' | := (strictly_extends_decls_part_globals Σ.(declarations) Σ'.(declarations))
(only parsing). | Notation | strictly_extends_decls_part | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"declarations",
"strictly_extends_decls_part_globals",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
extends (Σ Σ' : global_env) | :=
[× Σ.(universes) ⊂_cs Σ'.(universes),
extends_decls_part Σ Σ' &
Retroknowledge.extends Σ.(retroknowledge) Σ'.(retroknowledge)]. | Definition | extends | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"extends_decls_part",
"global_env",
"universes",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
extends_decls (Σ Σ' : global_env) | :=
[× Σ.(universes) = Σ'.(universes),
extends_decls_part Σ Σ' &
Σ.(retroknowledge) = Σ'.(retroknowledge)]. | Definition | extends_decls | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"extends_decls_part",
"global_env",
"universes",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
extends_strictly_on_decls (Σ Σ' : global_env) | :=
[× Σ.(universes) ⊂_cs Σ'.(universes),
strictly_extends_decls_part Σ Σ' &
Retroknowledge.extends Σ.(retroknowledge) Σ'.(retroknowledge)]. | Definition | extends_strictly_on_decls | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"extends",
"global_env",
"strictly_extends_decls_part",
"universes",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
strictly_extends_decls (Σ Σ' : global_env) | :=
[× Σ.(universes) = Σ'.(universes),
strictly_extends_decls_part Σ Σ' &
Σ.(retroknowledge) = Σ'.(retroknowledge)]. | Definition | strictly_extends_decls | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"global_env",
"strictly_extends_decls_part",
"universes",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
lookup_global_None Σ kn : ~In kn (List.map fst Σ) <-> lookup_global Σ kn = None. | Proof.
move: Σ; elim => //=; try tauto.
move => ??; case: eqb_spec; intuition congruence.
Qed. | Lemma | lookup_global_None | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"case",
"eqb_spec",
"fst",
"lookup_global",
"map",
"tauto"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
hd_error_lookup_globals Σ kn : hd_error (lookup_globals Σ kn) = lookup_global Σ kn. | Proof.
move: Σ; elim => //= ?? <-.
case: eqb_spec => //=.
Qed. | Lemma | hd_error_lookup_globals | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"case",
"eqb_spec",
"lookup_global",
"lookup_globals"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
lookup_globals_nil Σ kn : ~In kn (List.map fst Σ) <-> lookup_globals Σ kn = nil. | Proof.
rewrite lookup_global_None-hd_error_lookup_globals.
case: lookup_globals => //.
Qed. | Lemma | lookup_globals_nil | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"case",
"fst",
"hd_error_lookup_globals",
"lookup_global_None",
"lookup_globals",
"map"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
NoDup_length_lookup_globals Σ
: NoDup (List.map fst Σ)
-> forall kn, List.length (lookup_globals Σ kn) = match lookup_global Σ kn with
| Some _ => 1
| None => 0
... | Proof.
move => H kn.
move: Σ H; elim => //=; try lia.
move => ?? H. inversion 1; subst.
move: (H ltac:(assumption)).
case: eqb_spec => //= ->.
rewrite (proj1 (@lookup_global_None _ _)) => //= -> //=.
Qed. | Lemma | NoDup_length_lookup_globals | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"case",
"eqb_spec",
"fst",
"length",
"lookup_global",
"lookup_global_None",
"lookup_globals",
"map",
"proj1",
"subst"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
NoDup_lookup_globals_eq Σ
: NoDup (List.map fst Σ)
-> forall kn, lookup_globals Σ kn = match lookup_global Σ kn with
| Some v => [v]
| None => []
end. | Proof.
move => H kn.
move: (NoDup_length_lookup_globals Σ H kn) (hd_error_lookup_globals Σ kn).
repeat destruct ?; subst.
all: case: lookup_globals; cbn; try congruence.
move => ? [|]; cbn; congruence.
Qed. | Lemma | NoDup_lookup_globals_eq | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"NoDup_length_lookup_globals",
"case",
"fst",
"hd_error_lookup_globals",
"lookup_global",
"lookup_globals",
"map",
"subst"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
lookup_globals_In Σ kn decl
: In (kn, decl) Σ <-> In decl (lookup_globals Σ kn). | Proof.
move: Σ; elim => //=; try tauto.
move => [??]?; case: eqb_spec => ? //=; subst => <-; cbn in *; firstorder (subst; auto).
all: (idtac + constructor); congruence.
Qed. | Lemma | lookup_globals_In | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"case",
"constructor",
"eqb_spec",
"lookup_globals",
"subst",
"tauto"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
lookup_global_Some_if_In Σ kn decl
: lookup_global Σ kn = Some decl -> In (kn, decl) Σ. | Proof.
move: Σ; elim => //=; try tauto.
move => [??]?; case: eqb_spec => ? IH; inversion 1; subst; try rewrite <- IH by assumption.
all: intuition try congruence; subst.
Qed. | Lemma | lookup_global_Some_if_In | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"IH",
"case",
"eqb_spec",
"lookup_global",
"subst",
"tauto"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
lookup_global_Some_iff_In_NoDup Σ kn decl (H : NoDup (List.map fst Σ))
: In (kn, decl) Σ <-> lookup_global Σ kn = Some decl. | Proof.
rewrite -hd_error_lookup_globals lookup_globals_In.
apply NoDup_length_lookup_globals with (kn:=kn) in H; move: H.
case: lookup_global; case: lookup_globals => [|?[]]; cbn.
all: try lia.
all: intuition congruence.
Qed. | Lemma | lookup_global_Some_iff_In_NoDup | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"NoDup_length_lookup_globals",
"apply",
"case",
"fst",
"hd_error_lookup_globals",
"lookup_global",
"lookup_globals",
"lookup_globals_In",
"map"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
lookup_global_extends_NoDup Σ Σ' k d :
NoDup (List.map fst Σ') ->
lookup_global Σ k = Some d ->
extends_decls_part_globals Σ Σ' -> lookup_global Σ' k = Some d. | Proof.
rewrite /= -!hd_error_lookup_globals => Hnd.
move: (@NoDup_length_lookup_globals _ Hnd k); clear Hnd.
rewrite -hd_error_lookup_globals.
move=> H Hd eq.
move: (eq k); clear eq.
case => ls eq.
move: eq Hd H => ->.
case: ls => //= ?.
case => //=.
case: lookup_globals => //=.
... | Lemma | lookup_global_extends_NoDup | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"NoDup_length_lookup_globals",
"case",
"eq",
"extends_decls_part_globals",
"fst",
"hd_error_lookup_globals",
"lookup_global",
"lookup_globals",
"map",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
lookup_env_extends_NoDup Σ Σ' k d :
NoDup (List.map fst Σ'.(declarations)) ->
lookup_env Σ k = Some d ->
extends Σ Σ' -> lookup_env Σ' k = Some d. | Proof.
move => Hnd Hd; case => *.
eapply lookup_global_extends_NoDup; tea.
Qed. | Lemma | lookup_env_extends_NoDup | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"case",
"declarations",
"extends",
"fst",
"lookup_env",
"lookup_global_extends_NoDup",
"map",
"tea",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
lookup_globals_app Σ Σ' kn :
lookup_globals (Σ ++ Σ') kn = lookup_globals Σ kn ++ lookup_globals Σ' kn. | Proof.
move: Σ.
elim => //= ??.
case: eqb_spec => //= -> -> //=.
Qed. | Lemma | lookup_globals_app | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"case",
"eqb_spec",
"lookup_globals",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
strictly_extends_decls_extends_part_globals Σ Σ'
: strictly_extends_decls_part_globals Σ Σ' -> extends_decls_part_globals Σ Σ'. | Proof.
case => //= ? -> c.
rewrite lookup_globals_app.
eexists; reflexivity.
Qed. | Lemma | strictly_extends_decls_extends_part_globals | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"case",
"extends_decls_part_globals",
"lookup_globals_app",
"reflexivity",
"strictly_extends_decls_part_globals",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
strictly_extends_decls_extends_part Σ Σ'
: strictly_extends_decls_part Σ Σ' -> extends_decls_part Σ Σ'. | Proof. apply strictly_extends_decls_extends_part_globals. Qed. | Lemma | strictly_extends_decls_extends_part | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"apply",
"extends_decls_part",
"strictly_extends_decls_extends_part_globals",
"strictly_extends_decls_part",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
strictly_extends_decls_extends_decls Σ Σ' : strictly_extends_decls Σ Σ' -> extends_decls Σ Σ'. | Proof.
destruct Σ, Σ'; case => //= -> ? ->.
rewrite /extends_decls; split; try reflexivity.
now apply strictly_extends_decls_extends_part.
Qed. | Instance | strictly_extends_decls_extends_decls | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"apply",
"case",
"extends_decls",
"reflexivity",
"split",
"strictly_extends_decls",
"strictly_extends_decls_extends_part",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
strictly_extends_decls_extends_strictly_on_decls Σ Σ' : strictly_extends_decls Σ Σ' -> extends_strictly_on_decls Σ Σ'. | Proof.
destruct Σ, Σ'; intros []. cbn in *; subst. split => //=.
split; [lsets|csets]. apply Retroknowledge.extends_refl.
Qed. | Instance | strictly_extends_decls_extends_strictly_on_decls | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"apply",
"csets",
"extends_refl",
"extends_strictly_on_decls",
"lsets",
"split",
"strictly_extends_decls",
"subst",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
extends_decls_extends Σ Σ' : extends_decls Σ Σ' -> extends Σ Σ'. | Proof.
destruct Σ, Σ'; intros []. cbn in *; subst. split => //=.
split; [lsets|csets]. apply Retroknowledge.extends_refl.
Qed. | Instance | extends_decls_extends | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"apply",
"csets",
"extends",
"extends_decls",
"extends_refl",
"lsets",
"split",
"subst",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
extends_strictly_on_decls_extends Σ Σ' : extends_strictly_on_decls Σ Σ' -> extends Σ Σ'. | Proof.
destruct Σ, Σ'; case => //= ? ? ?.
rewrite /extends; split => //=.
now apply strictly_extends_decls_extends_part.
Qed. | Instance | extends_strictly_on_decls_extends | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"apply",
"case",
"extends",
"extends_strictly_on_decls",
"split",
"strictly_extends_decls_extends_part",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
strictly_extends_decls_extends_decls_subrel : CRelationClasses.subrelation strictly_extends_decls extends_decls | := strictly_extends_decls_extends_decls. | Instance | strictly_extends_decls_extends_decls_subrel | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"extends_decls",
"strictly_extends_decls",
"strictly_extends_decls_extends_decls"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
strictly_extends_decls_extends_strictly_on_decls_subrel : CRelationClasses.subrelation strictly_extends_decls extends_strictly_on_decls | := strictly_extends_decls_extends_strictly_on_decls. | Instance | strictly_extends_decls_extends_strictly_on_decls_subrel | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"extends_strictly_on_decls",
"strictly_extends_decls",
"strictly_extends_decls_extends_strictly_on_decls"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
extends_decls_extends_subrel : CRelationClasses.subrelation extends_decls extends | := extends_decls_extends. | Instance | extends_decls_extends_subrel | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"extends",
"extends_decls",
"extends_decls_extends"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
extends_strictly_on_decls_extends_subrel : CRelationClasses.subrelation extends_strictly_on_decls extends | := extends_strictly_on_decls_extends. | Instance | extends_strictly_on_decls_extends_subrel | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"extends",
"extends_strictly_on_decls",
"extends_strictly_on_decls_extends"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
strictly_extends_decls_extends_subrel : CRelationClasses.subrelation strictly_extends_decls extends | := fun _ => _. | Instance | strictly_extends_decls_extends_subrel | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"extends",
"strictly_extends_decls"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
strictly_extends_decls_refl : CRelationClasses.Reflexive strictly_extends_decls. | Proof. red. intros x. split => //; try exists [] => //. Qed. | Instance | strictly_extends_decls_refl | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"Reflexive",
"red",
"split",
"strictly_extends_decls"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
extends_decls_refl : CRelationClasses.Reflexive extends_decls. | Proof. red. intros x. split => //; try exists [] => //. Qed. | Instance | extends_decls_refl | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"Reflexive",
"extends_decls",
"red",
"split"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
extends_strictly_on_decls_refl : CRelationClasses.Reflexive extends_strictly_on_decls. | Proof. red. intros x. split; [apply incl_cs_refl | try exists [] => // | apply Retroknowledge.extends_refl]. Qed. | Lemma | extends_strictly_on_decls_refl | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"Reflexive",
"apply",
"extends_refl",
"extends_strictly_on_decls",
"incl_cs_refl",
"red",
"split"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
extends_refl : CRelationClasses.Reflexive extends. | Proof. red. intros x. split; [apply incl_cs_refl | try exists [] => // | apply Retroknowledge.extends_refl]. Qed. | Lemma | extends_refl | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"Reflexive",
"apply",
"extends",
"incl_cs_refl",
"red",
"split"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
extends_decls_part_globals_refl Σ : extends_decls_part_globals Σ Σ. | Proof. now exists [] => //. Qed. | Lemma | extends_decls_part_globals_refl | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"extends_decls_part_globals"
] | easy prefers this to the local hypotheses, which is annoying
#[global] Instance extends_refl : CRelationClasses.Reflexive extends.
Proof. apply extends_refl. Qed. | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 |
extends_decls_part_refl Σ : extends_decls_part Σ Σ. | Proof. apply extends_decls_part_globals_refl. Qed. | Lemma | extends_decls_part_refl | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"apply",
"extends_decls_part",
"extends_decls_part_globals_refl"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
strictly_extends_decls_part_globals_refl (Σ : global_declarations)
: strictly_extends_decls_part_globals Σ Σ. | Proof. now exists [] => //. Qed. | Lemma | strictly_extends_decls_part_globals_refl | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"global_declarations",
"strictly_extends_decls_part_globals"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
strictly_extends_decls_part_refl Σ : strictly_extends_decls_part Σ Σ. | Proof. apply strictly_extends_decls_part_globals_refl. Qed. | Lemma | strictly_extends_decls_part_refl | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"apply",
"strictly_extends_decls_part",
"strictly_extends_decls_part_globals_refl"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
extends_decls_part_globals_trans Σ Σ' Σ''
: extends_decls_part_globals Σ Σ' -> extends_decls_part_globals Σ' Σ'' -> extends_decls_part_globals Σ Σ''. | Proof.
move => H1 H2 c; move: (H1 c) (H2 c) => [? ->] [? ->].
now eexists; rewrite app_assoc.
Qed. | Lemma | extends_decls_part_globals_trans | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"app_assoc",
"extends_decls_part_globals",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
extends_decls_part_trans Σ Σ' Σ''
: extends_decls_part Σ Σ' -> extends_decls_part Σ' Σ'' -> extends_decls_part Σ Σ''. | Proof. apply extends_decls_part_globals_trans. Qed. | Lemma | extends_decls_part_trans | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"apply",
"extends_decls_part",
"extends_decls_part_globals_trans",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
strictly_extends_decls_part_globals_trans (Σ Σ' Σ'' : global_declarations)
: strictly_extends_decls_part_globals Σ Σ' -> strictly_extends_decls_part_globals Σ' Σ'' -> strictly_extends_decls_part_globals Σ Σ''. | Proof.
move => [? ->] [? ->].
now eexists; rewrite app_assoc.
Qed. | Lemma | strictly_extends_decls_part_globals_trans | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"app_assoc",
"global_declarations",
"strictly_extends_decls_part_globals",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
strictly_extends_decls_part_trans Σ Σ' Σ''
: strictly_extends_decls_part Σ Σ' -> strictly_extends_decls_part Σ' Σ'' -> strictly_extends_decls_part Σ Σ''. | Proof. apply strictly_extends_decls_part_globals_trans. Qed. | Lemma | strictly_extends_decls_part_trans | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"apply",
"strictly_extends_decls_part",
"strictly_extends_decls_part_globals_trans",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
extends_trans_t | :=
intros [?] [?] [?] [?] [?]; red; cbn in *; split;
try solve [ etransitivity; eassumption
| eapply incl_cs_trans; eassumption
| eapply strictly_extends_decls_part_globals_trans; eassumption
| eapply extends_decls_part_globals_trans; eassumption ]. | Ltac | extends_trans_t | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"extends_decls_part_globals_trans",
"incl_cs_trans",
"red",
"split",
"strictly_extends_decls_part_globals_trans"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
strictly_extends_decls_trans : CRelationClasses.Transitive strictly_extends_decls. | Proof. extends_trans_t. Qed. | Instance | strictly_extends_decls_trans | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"Transitive",
"extends_trans_t",
"strictly_extends_decls"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
extends_decls_trans : CRelationClasses.Transitive extends_decls. | Proof. extends_trans_t. Qed. | Instance | extends_decls_trans | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"Transitive",
"extends_decls",
"extends_trans_t"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
extends_strictly_on_decls_trans : CRelationClasses.Transitive extends_strictly_on_decls. | Proof. extends_trans_t. Qed. | Instance | extends_strictly_on_decls_trans | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"Transitive",
"extends_strictly_on_decls",
"extends_trans_t"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
extends_trans : CRelationClasses.Transitive extends. | Proof. extends_trans_t. Qed. | Instance | extends_trans | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"Transitive",
"extends",
"extends_trans_t"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
declared_kername_set (Σ : global_declarations) : KernameSet.t | := List.fold_right KernameSet.add KernameSet.empty (List.map fst Σ). | Definition | declared_kername_set | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"add",
"empty",
"fst",
"global_declarations",
"map"
] | Merge two lists of global_declarations, assuming that any globals sharing a name are identical | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 |
merge_globals (Σ Σ' : global_declarations) : global_declarations | := let known_kns := declared_kername_set Σ in
List.filter (fun '(kn, _) => negb (KernameSet.mem kn known_kns)) Σ' ++ Σ. | Definition | merge_globals | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"declared_kername_set",
"global_declarations",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
merge_global_envs (Σ Σ' : global_env) : global_env | := {| universes := ContextSet.union Σ.(universes) Σ'.(universes)
; declarations := merge_globals Σ.(declarations) Σ'.(declarations)
; retroknowledge := Retroknowledge.merge Σ.(retroknowledge) Σ'.(retroknowledge) |}. | Definition | merge_global_envs | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"declarations",
"global_env",
"merge",
"merge_globals",
"union",
"universes",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
compatible_globals (Σ Σ' : global_declarations) : Prop | := forall c, lookup_globals Σ c <> [] -> lookup_globals Σ' c <> [] -> lookup_globals Σ c = lookup_globals Σ' c. | Definition | compatible_globals | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"global_declarations",
"lookup_globals",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
compatible (Σ Σ' : global_env) | := Retroknowledge.compatible Σ.(retroknowledge) Σ'.(retroknowledge)
/\ compatible_globals Σ.(declarations) Σ'.(declarations). | Definition | compatible | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"compatible_globals",
"declarations",
"global_env",
"Σ'"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 | |
lookup_globals_filter p Σ c
: lookup_globals (filter (fun '(kn, _) => p kn) Σ) c = if p c then lookup_globals Σ c else []. | Proof.
induction Σ as [|?? IH]; cbn; rdest; cbn; try now repeat destruct ?.
case: eqb_spec => ?; repeat destruct ?; subst => //=.
all: rewrite ?eqb_refl.
all: try case: eqb_spec => ?; subst.
all: rewrite IH //=.
all: try congruence.
Qed. | Lemma | lookup_globals_filter | common.theories | common/theories/Environment.v | [
"Stdlib",
"ssreflect",
"ssrbool",
"ssrfun",
"Morphisms",
"Setoid",
"MetaRocq.Utils",
"utils",
"MetaRocq.Common",
"BasicAst",
"Primitive",
"Universes",
"Equations.Prop",
"Classes",
"EqDecInstances",
"hints",
"Retroknowledge",
"T",
"E"
] | [
"IH",
"case",
"eqb_refl",
"eqb_spec",
"lookup_globals",
"rdest",
"subst"
] | https://github.com/MetaCoq/metacoq | 971b2cc5c8bdc011068f67fa272245d8e5b54209 |
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