Datasets:

phanerozoic

/

Coq-MetaCoq

like 0

(Σ : global_env) (kn : kername) := lookup_globals Σ.(declarations) kn.

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

lookup_envs

(Σ Σ' : global_env) := [× Σ.(universes) ⊂_cs Σ'.(universes), extends_decls_part Σ Σ' & Retroknowledge.extends Σ.(retroknowledge) Σ'.(retroknowledge)].

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends

(Σ Σ' : global_env) := [× Σ.(universes) = Σ'.(universes), extends_decls_part Σ Σ' & Σ.(retroknowledge) = Σ'.(retroknowledge)].

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends_decls

(Σ Σ' : global_env) := [× Σ.(universes) ⊂_cs Σ'.(universes), strictly_extends_decls_part Σ Σ' & Retroknowledge.extends Σ.(retroknowledge) Σ'.(retroknowledge)].

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends_strictly_on_decls

(Σ Σ' : global_env) := [× Σ.(universes) = Σ'.(universes), strictly_extends_decls_part Σ Σ' & Σ.(retroknowledge) = Σ'.(retroknowledge)].

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

strictly_extends_decls

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

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

lookup_global_None

Σ kn : hd_error (lookup_globals Σ kn) = lookup_global Σ kn. Proof. move: Σ; elim => //= ?? <-. case: eqb_spec => //=. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

hd_error_lookup_globals

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

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

lookup_globals_nil

Σ : NoDup (List.map fst Σ) -> forall kn, List.length (lookup_globals Σ kn) = match lookup_global Σ kn with | Some _ => 1 | None => 0 end. 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

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

NoDup_length_lookup_globals

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

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

NoDup_lookup_globals_eq

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

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

lookup_globals_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

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

lookup_global_Some_if_In

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

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

lookup_global_Some_iff_In_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 => //=. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

lookup_global_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

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

lookup_env_extends_NoDup

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

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

lookup_globals_app

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

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

strictly_extends_decls_extends_part_globals

Σ Σ' : strictly_extends_decls_part Σ Σ' -> extends_decls_part Σ Σ'. Proof. apply strictly_extends_decls_extends_part_globals. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

strictly_extends_decls_extends_part

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

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

strictly_extends_decls_extends_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

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

strictly_extends_decls_extends_strictly_on_decls

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

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends_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

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends_strictly_on_decls_extends

CRelationClasses.subrelation strictly_extends_decls extends_decls := strictly_extends_decls_extends_decls.

Instance

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

strictly_extends_decls_extends_decls_subrel

CRelationClasses.subrelation strictly_extends_decls extends_strictly_on_decls := strictly_extends_decls_extends_strictly_on_decls.

Instance

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

strictly_extends_decls_extends_strictly_on_decls_subrel

CRelationClasses.subrelation extends_decls extends := extends_decls_extends.

Instance

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends_decls_extends_subrel

CRelationClasses.subrelation extends_strictly_on_decls extends := extends_strictly_on_decls_extends.

Instance

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends_strictly_on_decls_extends_subrel

CRelationClasses.subrelation strictly_extends_decls extends := fun _ => _.

Instance

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

strictly_extends_decls_extends_subrel

CRelationClasses.Reflexive strictly_extends_decls. Proof. red. intros x. split => //; try exists [] => //. Qed.

Instance

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

strictly_extends_decls_refl

CRelationClasses.Reflexive extends_decls. Proof. red. intros x. split => //; try exists [] => //. Qed.

Instance

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends_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

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends_strictly_on_decls_refl

CRelationClasses.Reflexive extends. Proof. red. intros x. split; [apply incl_cs_refl | try exists [] => // | apply Retroknowledge.extends_refl]. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends_refl

CRelationClasses.Reflexive extends. Proof. apply extends_refl. Qed.

Instance

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends_refl

Σ : extends_decls_part_globals Σ Σ. Proof. now exists [] => //. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends_decls_part_globals_refl

Σ : extends_decls_part Σ Σ. Proof. apply extends_decls_part_globals_refl. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends_decls_part_refl

(Σ : global_declarations) : strictly_extends_decls_part_globals Σ Σ. Proof. now exists [] => //. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

strictly_extends_decls_part_globals_refl

Σ : strictly_extends_decls_part Σ Σ. Proof. apply strictly_extends_decls_part_globals_refl. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

strictly_extends_decls_part_refl

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

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends_decls_part_globals_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

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends_decls_part_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

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

strictly_extends_decls_part_globals_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

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

strictly_extends_decls_part_trans

CRelationClasses.Transitive strictly_extends_decls. Proof. extends_trans_t. Qed.

Instance

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

strictly_extends_decls_trans

CRelationClasses.Transitive extends_decls. Proof. extends_trans_t. Qed.

Instance

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends_decls_trans

CRelationClasses.Transitive extends_strictly_on_decls. Proof. extends_trans_t. Qed.

Instance

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends_strictly_on_decls_trans

CRelationClasses.Transitive extends. Proof. extends_trans_t. Qed.

Instance

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends_trans

(Σ : global_declarations) : KernameSet.t := List.fold_right KernameSet.add KernameSet.empty (List.map fst Σ).

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

declared_kername_set

(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

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

merge_globals

(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

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

merge_global_envs

(Σ Σ' : global_declarations) : Prop := forall c, lookup_globals Σ c <> [] -> lookup_globals Σ' c <> [] -> lookup_globals Σ c = lookup_globals Σ' c.

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

compatible_globals

(Σ Σ' : global_env) := Retroknowledge.compatible Σ.(retroknowledge) Σ'.(retroknowledge) /\ compatible_globals Σ.(declarations) Σ'.(declarations).

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

compatible

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

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

lookup_globals_filter

Σ Σ' : strictly_extends_decls_part_globals Σ (merge_globals Σ Σ'). Proof. now eexists. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

strictly_extends_decls_l_merge_globals

Σ Σ' : extends_decls_part_globals Σ (merge_globals Σ Σ'). Proof. rewrite /merge_globals. intro c. rewrite lookup_globals_app lookup_globals_filter. eexists; reflexivity. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends_l_merge_globals

Σ Σ' : extends_strictly_on_decls Σ (merge_global_envs Σ Σ'). Proof. rewrite /extends_strictly_on_decls/merge_global_envs/merge_globals; cbn. split; try first [ apply ContextSet.union_spec | apply Retroknowledge.extends_l_merge | apply strictly_extends_decls_l_merge_globals ]. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends_strictly_on_decls_l_merge

Σ Σ' : extends Σ (merge_global_envs Σ Σ'). Proof. exact _. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends_l_merge

forall Σ c, KernameSet.In c (declared_kername_set Σ) <-> List.In c (map fst Σ). Proof. elim => //=; try setoid_rewrite KernameSetFact.empty_iff => //=. move => [? ?] ? IH c //=. rewrite KernameSet.add_spec. intuition auto with *. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

declared_kername_set_spec

Σ c : KernameSet.mem c (declared_kername_set Σ) <-> List.In c (map fst Σ). Proof. setoid_rewrite <- KernameSetFact.mem_iff. apply declared_kername_set_spec. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

declared_kername_set_mem_iff

Σ Σ' : compatible_globals Σ Σ' -> extends_decls_part_globals Σ' (merge_globals Σ Σ'). Proof. rewrite /merge_globals. intro H2; cbn. cbv [compatible_globals] in *. intro c. specialize (H2 c). rewrite lookup_globals_app lookup_globals_filter. destruct (in_dec eq_dec c (map fst Σ')) as [H'|H']; [ exists nil | exists (lookup_globals Σ c) ]. 2: apply lookup_globals_nil in H'; rewrite H'; clear H'. 2: now destruct ?; cbn; rewrite app_nil_r. pose proof (lookup_globals_nil Σ c) as Hc. rewrite <- !lookup_globals_nil in H2. rewrite <- (declared_kername_set_mem_iff Σ) in *. destruct KernameSet.mem; cbn in *. { intuition auto. } { destruct Hc as [Hc _]. rewrite Hc ?app_nil_r //=. } Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends_r_merge_globals

Σ Σ' : compatible Σ Σ' -> extends Σ' (merge_global_envs Σ Σ'). Proof. rewrite /extends/compatible/merge_global_envs/lookup_envs. intros [H1 H2]. split; try first [ apply ContextSet.union_spec | now apply Retroknowledge.extends_r_merge | now apply extends_r_merge_globals ]. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

extends_r_merge

(Σ : global_env) (p : prim_tag) : option kername := match p with | primInt => Σ.(retroknowledge).(Retroknowledge.retro_int63) | primFloat => Σ.(retroknowledge).(Retroknowledge.retro_float64) | primString => Σ.(retroknowledge).(Retroknowledge.retro_string) | primArray => Σ.(retroknowledge).(Retroknowledge.retro_array) end.

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

primitive_constant

(dom codom : term) : term := tProd {| binder_name := nAnon; binder_relevance := Relevant |} dom (lift 1 0 codom).

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

tImpl

([nAnon], ConstraintSet.empty).

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

array_uctx

(p : prim_tag) (cdecl : constant_body) := match p with | primInt | primFloat | primString => [/\ cdecl.(cst_type) = tSort Sort.type0, cdecl.(cst_body) = None & cdecl.(cst_universes) = Monomorphic_ctx] | primArray => let s := sType (Universe.make' (Level.lvar 0)) in [/\ cdecl.(cst_type) = tImpl (tSort s) (tSort s), cdecl.(cst_body) = None & cdecl.(cst_universes) = Polymorphic_ctx array_uctx] end.

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

primitive_invariants

Type := global_env * universes_decl.

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

global_env_ext

global_env_ext -> global_env := fst.

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

fst_ctx

(Σ : global_env) : global_env_ext := (Σ, Monomorphic_ctx).

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

empty_ext

Type := global_env * term.

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

program

d t := match d.(decl_body) with | None => tLambda d.(decl_name) d.(decl_type) t | Some b => tLetIn d.(decl_name) b d.(decl_type) t end.

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

mkLambda_or_LetIn

(l : context) (t : term) := List.fold_left (fun acc d => mkLambda_or_LetIn d acc) l t.

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

it_mkLambda_or_LetIn

d t := match d.(decl_body) with | None => tProd d.(decl_name) d.(decl_type) t | Some b => tLetIn d.(decl_name) b d.(decl_type) t end.

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

mkProd_or_LetIn

(l : context) (t : term) := List.fold_left (fun acc d => mkProd_or_LetIn d acc) l t.

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

it_mkProd_or_LetIn

l l' t : it_mkProd_or_LetIn (l ++ l') t = it_mkProd_or_LetIn l' (it_mkProd_or_LetIn l t). Proof. induction l in l', t |- *; simpl; auto. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

it_mkProd_or_LetIn_app

(l : list term) (p : nat) (Γ0 : list context_decl) {struct Γ0} : list term := match Γ0 with | [] => l | {| decl_body := Some _ |} :: hyps => reln l (p + 1) hyps | {| decl_body := None |} :: hyps => reln (tRel p :: l) (p + 1) hyps end.

Fixpoint

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

reln

Γ k := reln [] k Γ.

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

to_extended_list_k

Γ := to_extended_list_k Γ 0.

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

to_extended_list

f ctx n acc : reln acc n (fold_context_k f ctx) = reln acc n ctx. Proof. induction ctx as [|[na [b|] ty] ctx] in n, acc |- *; simpl; auto; rewrite fold_context_k_snoc0 /=; apply IHctx. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

reln_fold

l p Γ : Forall (fun x => exists n, x = tRel n /\ p <= n /\ n < p + length Γ) l -> Forall (fun x => exists n, x = tRel n /\ p <= n /\ n < p + length Γ) (reln l p Γ). Proof. generalize (Nat.le_refl p). generalize p at 1 3 5. induction Γ in p, l |- *. simpl. auto. intros. destruct a. destruct decl_body. simpl. assert(p0 <= S p) by lia. specialize (IHΓ l (S p) p0 H1). rewrite <- Nat.add_succ_comm, Nat.add_1_r. simpl in *. rewrite <- Nat.add_succ_comm in H0. eauto. simpl in *. specialize (IHΓ (tRel p :: l) (S p) p0 ltac:(lia)). rewrite <- Nat.add_succ_comm, Nat.add_1_r. eapply IHΓ. simpl in *. rewrite <- Nat.add_succ_comm in H0. auto. simpl in *. constructor. exists p. intuition lia. auto. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

reln_list_lift_above

Γ k : Forall (fun x => exists n, x = tRel n /\ k <= n /\ n < k + length Γ) (to_extended_list_k Γ k). Proof. pose (reln_list_lift_above [] k Γ). unfold to_extended_list_k. forward f. constructor. apply f. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

to_extended_list_k_spec

Γ : Forall (fun x => exists n, x = tRel n /\ n < length Γ) (to_extended_list Γ). Proof. pose (reln_list_lift_above [] 0 Γ). unfold to_extended_list. forward f. constructor. eapply Forall_impl; eauto. intros. destruct H; eexists; intuition eauto. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

to_extended_list_lift_above

p (Γ : context) := match Γ with | [] => [] | {| decl_body := Some _ |} :: Γ => reln_alt (p + 1) Γ | {| decl_body := None |} :: Γ => tRel p :: reln_alt (p + 1) Γ end.

Fixpoint

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

reln_alt

l Γ k : reln l k Γ = List.rev (reln_alt k Γ) ++ l. Proof. induction Γ in l, k |- *; simpl; auto. destruct a as [na [body|] ty]; simpl. now rewrite IHΓ. now rewrite IHΓ -app_assoc. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

reln_alt_eq

d Γ k : to_extended_list_k (d :: Γ) k = match d.(decl_body) with | None => to_extended_list_k Γ (S k) ++ [tRel k] | Some b => to_extended_list_k Γ (S k) end. Proof. unfold to_extended_list_k. rewrite reln_alt_eq. simpl. destruct d as [na [body|] ty]. simpl. now rewrite reln_alt_eq Nat.add_1_r. simpl. rewrite reln_alt_eq. now rewrite <- app_assoc, !app_nil_r, Nat.add_1_r. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

to_extended_list_k_cons

(l : list one_inductive_body) := rev_map (fun ind => vass (mkBindAnn (nNamed ind.(ind_name)) (ind.(ind_relevance))) ind.(ind_type)) l.

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

arities_context

l : #|arities_context l| = #|l|. Proof. unfold arities_context. now rewrite length_rev_map. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

arities_context_length

f m := match m with | Build_mutual_inductive_body finite ind_npars ind_pars ind_bodies ind_universes ind_variance => let arities := arities_context ind_bodies in let pars := fold_context_k f ind_pars in Build_mutual_inductive_body finite ind_npars pars (map (map_one_inductive_body (context_assumptions pars) (length arities) f) ind_bodies) ind_universes ind_variance end.

Definition

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

map_mutual_inductive_body

f npars_ass arities oib : ind_type (map_one_inductive_body npars_ass arities f oib) = f 0 (ind_type oib). Proof. destruct oib. reflexivity. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

ind_type_map

f npars_ass arities oib : ind_ctors (map_one_inductive_body npars_ass arities f oib) = map (map_constructor_body npars_ass arities f) (ind_ctors oib). Proof. destruct oib; simpl; reflexivity. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

ind_ctors_map

f m : ind_params (map_mutual_inductive_body f m) = fold_context_k f (ind_params m). Proof. destruct m; simpl; reflexivity. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

ind_pars_map

f npars_ass arities oib : ind_projs (map_one_inductive_body npars_ass arities f oib) = map (map_projection_body npars_ass f) (ind_projs oib). Proof. destruct oib; simpl. reflexivity. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

ind_projs_map

ind npars k := match k with | 0 => [] | S k' => (tProj (mkProjection ind npars k') (tRel 0)) :: projs ind npars k' end.

Fixpoint

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

projs

ind npars k : #|projs ind npars k| = k. Proof. induction k; simpl; auto. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

projs_length

Γ f : context_assumptions (fold_context_k f Γ) = context_assumptions Γ. Proof. rewrite fold_context_k_alt. unfold mapi. generalize 0 (Nat.pred #|Γ|). induction Γ as [|[na [body|] ty] tl]; cbn; intros; eauto. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

context_assumptions_fold

(f : nat -> term -> term): forall (Γ' Γ'' : context) (v : nat), v < length Γ' -> forall nth, nth_error Γ' v = Some nth -> nth_error (fold_context_k f Γ') v = Some (map_decl (f (length Γ' - S v)) nth). Proof. induction Γ'; intros. - easy. - simpl. destruct v; rewrite fold_context_k_snoc0. + simpl. repeat f_equal; try lia. simpl in *. congruence. + simpl. apply IHΓ'; simpl in *; (lia || congruence). Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

nth_error_fold_context_k

forall (Γ' : context) (v : nat) (f : nat -> term -> term), nth_error (fold_context_k f Γ') v = option_map (map_decl (f (length Γ' - S v))) (nth_error Γ' v). Proof. induction Γ'; intros. - simpl. unfold fold_context_k; simpl. now rewrite nth_error_nil. - simpl. destruct v; rewrite fold_context_k_snoc0. + simpl. repeat f_equal; try lia. + simpl. apply IHΓ'; simpl in *; (lia || congruence). Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

nth_error_fold_context_k_eq

{Γ Γ' v Γ''} (f : nat -> term -> term) : length Γ' <= v -> nth_error (Γ' ++ Γ) v = nth_error (fold_context_k f Γ' ++ Γ'' ++ Γ) (length Γ'' + v). Proof. intros Hv. rewrite -> !nth_error_app_ge, ?fold_context_k_length. f_equal. lia. rewrite fold_context_k_length. lia. rewrite fold_context_k_length. lia. auto. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

nth_error_ge

{Γ Γ' Γ'' v} (f : nat -> term -> term) : v < length Γ' -> nth_error (fold_context_k f Γ' ++ Γ'' ++ Γ) v = option_map (map_decl (f (length Γ' - S v))) (nth_error (Γ' ++ Γ) v). Proof. simpl. intros Hv. rewrite -> !nth_error_app_lt. rewrite nth_error_fold_context_k_eq. do 2 f_equal. lia. now rewrite fold_context_k_length. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

nth_error_lt

Γ : context_assumptions Γ <= #|Γ|. Proof. induction Γ; simpl; auto. destruct a as [? [?|] ?]; simpl; auto. lia. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

context_assumptions_length_bound

f Γ : context_assumptions (map_context f Γ) = context_assumptions Γ. Proof. induction Γ as [|[? [?|] ?] ?]; simpl; auto. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

context_assumptions_map

Γ Δ : context_assumptions (Γ ++ Δ) = context_assumptions Γ + context_assumptions Δ. Proof. induction Γ as [|[? [] ?] ?]; simpl; auto. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

context_assumptions_app

Γ : context_assumptions (List.rev Γ) = context_assumptions Γ. Proof using Type. induction Γ; simpl; auto. rewrite context_assumptions_app IHΓ /=. destruct (decl_body a); simpl; lia. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

context_assumptions_rev

f Γ : context_assumptions (mapi (fun i => map_decl (f i)) Γ) = context_assumptions Γ. Proof. rewrite /mapi; generalize 0. induction Γ; simpl; intros; eauto. destruct a as [? [b|] ?]; simpl; auto. Qed.

Lemma

common

From Coq Require Import ssreflect ssrbool ssrfun Morphisms Setoid. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Primitive Universes. From Equations.Prop Require Import Classes EqDecInstances. Module Type TermDecide (Import T : Term). Module TermDecideReflectInstances (Import T : Term) (Import TDec : TermDecide T). Import T. Module Type EnvironmentDecide (T : Term) (Import E : EnvironmentSig T). Module EnvironmentDecideReflectInstances (T : Term) (Import E : EnvironmentSig T) (Import EDec : EnvironmentDecide T E). Import T E.

common\theories\Environment.v

context_assumptions_mapi