fact
stringlengths 2
32.6k
| type
stringclasses 10
values | library
stringclasses 5
values | imports
stringclasses 205
values | filename
stringclasses 216
values | symbolic_name
stringlengths 1
67
| index_level
int64 0
10.5k
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|---|---|---|---|---|---|---|
u Γ : context_assumptions (subst_instance u Γ) = context_assumptions Γ. Proof. apply context_assumptions_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
|
context_assumptions_subst_instance
| 300 |
s k Γ : context_assumptions (subst_context s k Γ) = context_assumptions Γ. Proof. apply context_assumptions_fold. 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_subst_context
| 301 |
n k Γ : context_assumptions (lift_context n k Γ) = context_assumptions Γ. Proof. apply context_assumptions_fold. 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_lift_context
| 302 |
(P : term -> term -> Type) : context_decl -> context_decl -> Type := | on_vass na t t' : P t t' -> All_decls P (vass na t) (vass na t') | on_vdef na b t b' t' : P b b' -> P t t' -> All_decls P (vdef na b t) (vdef na b' t').
|
Inductive
|
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
|
All_decls
| 303 |
(P : term -> term -> Type) : context_decl -> context_decl -> Type := | on_vass_alpha na na' t t' : eq_binder_annot na na' -> P t t' -> All_decls_alpha P (vass na t) (vass na' t') | on_vdef_alpha na na' b t b' t' : eq_binder_annot na na' -> P b b' -> P t t' -> All_decls_alpha P (vdef na b t) (vdef na' b' t').
|
Inductive
|
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
|
All_decls_alpha
| 304 |
(P Q : term -> term -> Type) d d' : All_decls P d d' -> (forall t t', P t t' -> Q t t') -> All_decls Q d d'. Proof. intros ond H; destruct ond; constructor; 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
|
All_decls_impl
| 305 |
(P Q : term -> term -> Type) d d' : All_decls_alpha P d d' -> (forall t t', P t t' -> Q t t') -> All_decls_alpha Q d d'. Proof. intros ond H; destruct ond; constructor; 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
|
All_decls_alpha_impl
| 306 |
(P : term -> term -> Type) d d' : All_decls P d d' -> All_decls_alpha P d d'. Proof. intros []; constructor; auto; 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
|
All_decls_to_alpha
| 307 |
(P : context -> context -> context_decl -> context_decl -> Type) Γ Γ' := All2_fold (All_over P Γ 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
|
All2_fold_over
| 308 |
(Σ Σ' : global_env) : reflectT (extends_decls_part Σ Σ') (extendsb_decls_part Σ Σ'). Proof. case: (@forallbP _ _ _ _ (fun _ => eqb_specT _ _)) => H; constructor. all: setoid_rewrite Forall_forall in H. { move => c. specialize (fun d => H (c, d)). cbn [fst] in *. specialize (fun pf : { d : _ | In (c, d) _ } => H (proj1_sig pf) (proj2_sig pf)). destruct (lookup_envs Σ c) eqn:H'. { eexists; rewrite app_nil_r; reflexivity. } rewrite <- H; clear H. { eexists; symmetry; apply firstn_skipn. } unfold lookup_envs in *. move: H'; elim: (declarations Σ); cbn [lookup_globals] => //= ??. case: eqb_specT => ?; subst. all: move => H H'; try destruct (H H'); rdest; eauto. } { intro H'; apply H; clear H; intros [c ?]; specialize (H' c). destruct H' as [decls H']. cbn [fst]. rewrite H' length_app Nat.add_sub skipn_all_app //. } 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 Environment Reflect. From Equations.Prop Require Import Classes EqDecInstances. Module EnvironmentReflect (T : Term) (Import E : EnvironmentSig T) (Import TDec : TermDecide T) (Import EDec : EnvironmentDecide T E).
|
common\theories\EnvironmentReflect.v
|
extends_decls_partT
| 309 |
(Σ Σ' : global_env) : reflectT (strictly_extends_decls_part Σ Σ') (strictly_extendsb_decls_part Σ Σ'). Proof. case: eqb_specT => H; constructor. { rewrite -H. eexists; symmetry; apply firstn_skipn. } { move => [Σ'' H']. move: H. rewrite H' length_app Nat.add_sub skipn_all_app //. } 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 Environment Reflect. From Equations.Prop Require Import Classes EqDecInstances. Module EnvironmentReflect (T : Term) (Import E : EnvironmentSig T) (Import TDec : TermDecide T) (Import EDec : EnvironmentDecide T E).
|
common\theories\EnvironmentReflect.v
|
strictly_extends_decls_partT
| 310 |
(Σ Σ' : global_env) : bool := Σ.(universes) ⊂?_cs Σ'.(universes) && extendsb_decls_part Σ Σ' && Retroknowledge.extendsb 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 Environment Reflect. From Equations.Prop Require Import Classes EqDecInstances. Module EnvironmentReflect (T : Term) (Import E : EnvironmentSig T) (Import TDec : TermDecide T) (Import EDec : EnvironmentDecide T E).
|
common\theories\EnvironmentReflect.v
|
extendsb
| 311 |
(Σ Σ' : global_env) : bool := (Σ.(universes) == Σ'.(universes)) && extendsb_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 Environment Reflect. From Equations.Prop Require Import Classes EqDecInstances. Module EnvironmentReflect (T : Term) (Import E : EnvironmentSig T) (Import TDec : TermDecide T) (Import EDec : EnvironmentDecide T E).
|
common\theories\EnvironmentReflect.v
|
extends_declsb
| 312 |
(Σ Σ' : global_env) : bool := (Σ.(universes) ⊂?_cs Σ'.(universes)) && strictly_extendsb_decls_part Σ Σ' && Retroknowledge.extendsb 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 Environment Reflect. From Equations.Prop Require Import Classes EqDecInstances. Module EnvironmentReflect (T : Term) (Import E : EnvironmentSig T) (Import TDec : TermDecide T) (Import EDec : EnvironmentDecide T E).
|
common\theories\EnvironmentReflect.v
|
extends_strictly_on_declsb
| 313 |
(Σ Σ' : global_env) : bool := (Σ.(universes) == Σ'.(universes)) && strictly_extendsb_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 Environment Reflect. From Equations.Prop Require Import Classes EqDecInstances. Module EnvironmentReflect (T : Term) (Import E : EnvironmentSig T) (Import TDec : TermDecide T) (Import EDec : EnvironmentDecide T E).
|
common\theories\EnvironmentReflect.v
|
strictly_extends_declsb
| 314 |
Σ Σ' : reflectT (extends Σ Σ') (extendsb Σ Σ'). Proof. rewrite /extends/extendsb. case: extends_decls_partT; case: Retroknowledge.extendsT; case: ContextSet.subsetP; cbn; constructor; intuition. 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 Environment Reflect. From Equations.Prop Require Import Classes EqDecInstances. Module EnvironmentReflect (T : Term) (Import E : EnvironmentSig T) (Import TDec : TermDecide T) (Import EDec : EnvironmentDecide T E).
|
common\theories\EnvironmentReflect.v
|
extendsT
| 315 |
Σ Σ' : reflectT (extends_decls Σ Σ') (extends_declsb Σ Σ'). Proof. rewrite /extends_decls/extends_declsb. case: extends_decls_partT; case: eqb_specT; case: eqb_specT; cbn; constructor; intuition. 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 Environment Reflect. From Equations.Prop Require Import Classes EqDecInstances. Module EnvironmentReflect (T : Term) (Import E : EnvironmentSig T) (Import TDec : TermDecide T) (Import EDec : EnvironmentDecide T E).
|
common\theories\EnvironmentReflect.v
|
extends_declsT
| 316 |
Σ Σ' : reflectT (extends_strictly_on_decls Σ Σ') (extends_strictly_on_declsb Σ Σ'). Proof. rewrite /extends_strictly_on_decls/extends_strictly_on_declsb. case: strictly_extends_decls_partT; case: Retroknowledge.extendsT; case: ContextSet.subsetP; cbn; constructor; intuition. 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 Environment Reflect. From Equations.Prop Require Import Classes EqDecInstances. Module EnvironmentReflect (T : Term) (Import E : EnvironmentSig T) (Import TDec : TermDecide T) (Import EDec : EnvironmentDecide T E).
|
common\theories\EnvironmentReflect.v
|
extends_strictly_on_declsT
| 317 |
Σ Σ' : reflectT (strictly_extends_decls Σ Σ') (strictly_extends_declsb Σ Σ'). Proof. rewrite /strictly_extends_decls/strictly_extends_declsb. case: strictly_extends_decls_partT; case: eqb_specT; case: eqb_specT; cbn; constructor; intuition. 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 Environment Reflect. From Equations.Prop Require Import Classes EqDecInstances. Module EnvironmentReflect (T : Term) (Import E : EnvironmentSig T) (Import TDec : TermDecide T) (Import EDec : EnvironmentDecide T E).
|
common\theories\EnvironmentReflect.v
|
strictly_extends_declsT
| 318 |
Σ Σ' : extendsb Σ Σ' <~> extends Σ Σ'. Proof. case: extendsT; split; 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 Environment Reflect. From Equations.Prop Require Import Classes EqDecInstances. Module EnvironmentReflect (T : Term) (Import E : EnvironmentSig T) (Import TDec : TermDecide T) (Import EDec : EnvironmentDecide T E).
|
common\theories\EnvironmentReflect.v
|
extends_spec
| 319 |
Σ Σ' : extends_declsb Σ Σ' <~> extends_decls Σ Σ'. Proof. case: extends_declsT; split; 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 Environment Reflect. From Equations.Prop Require Import Classes EqDecInstances. Module EnvironmentReflect (T : Term) (Import E : EnvironmentSig T) (Import TDec : TermDecide T) (Import EDec : EnvironmentDecide T E).
|
common\theories\EnvironmentReflect.v
|
extends_decls_spec
| 320 |
Σ Σ' : extends_strictly_on_declsb Σ Σ' <~> extends_strictly_on_decls Σ Σ'. Proof. case: extends_strictly_on_declsT; split; 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 Environment Reflect. From Equations.Prop Require Import Classes EqDecInstances. Module EnvironmentReflect (T : Term) (Import E : EnvironmentSig T) (Import TDec : TermDecide T) (Import EDec : EnvironmentDecide T E).
|
common\theories\EnvironmentReflect.v
|
extends_strictly_on_decls_spec
| 321 |
Σ Σ' : strictly_extends_declsb Σ Σ' <~> strictly_extends_decls Σ Σ'. Proof. case: strictly_extends_declsT; split; 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 Environment Reflect. From Equations.Prop Require Import Classes EqDecInstances. Module EnvironmentReflect (T : Term) (Import E : EnvironmentSig T) (Import TDec : TermDecide T) (Import EDec : EnvironmentDecide T E).
|
common\theories\EnvironmentReflect.v
|
strictly_extends_decls_spec
| 322 |
(Σ Σ' : global_declarations) : bool := KernameSet.for_all (fun c => lookup_globals Σ c == lookup_globals Σ' c) (KernameSet.inter (declared_kername_set Σ) (declared_kername_set 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 Environment Reflect. From Equations.Prop Require Import Classes EqDecInstances. Module EnvironmentReflect (T : Term) (Import E : EnvironmentSig T) (Import TDec : TermDecide T) (Import EDec : EnvironmentDecide T E).
|
common\theories\EnvironmentReflect.v
|
compatible_globalsb
| 323 |
(Σ Σ' : global_env) : bool := Retroknowledge.compatible Σ.(retroknowledge) Σ'.(retroknowledge) && compatible_globalsb 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 Environment Reflect. From Equations.Prop Require Import Classes EqDecInstances. Module EnvironmentReflect (T : Term) (Import E : EnvironmentSig T) (Import TDec : TermDecide T) (Import EDec : EnvironmentDecide T E).
|
common\theories\EnvironmentReflect.v
|
compatibleb
| 324 |
Σ Σ' : reflect (compatible_globals Σ Σ') (compatible_globalsb Σ Σ'). Proof. rewrite /compatible_globals/compatible_globalsb. lazymatch goal with | [ |- context[KernameSet.for_all ?f ?s] ] => generalize (@KernameSet.for_all_spec s f _) end. rewrite /KernameSet.For_all. case: KernameSet.for_all; move => [H1 H2]; constructor. all: first [ specialize (H1 eq_refl); rename H1 into H | clear H1 ]. all: try pose proof (fun x => diff_false_true (H2 x)) as H; clear H2. all: move: H. all: setoid_rewrite KernameSet.inter_spec. all: setoid_rewrite declared_kername_set_spec. all: setoid_rewrite <- lookup_globals_nil. 1: move => H c; move: (H c); clear H. 2: move => H nH; apply H => c; move: (nH c); clear H nH. all: case: eqb_spec. all: intuition. 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 Environment Reflect. From Equations.Prop Require Import Classes EqDecInstances. Module EnvironmentReflect (T : Term) (Import E : EnvironmentSig T) (Import TDec : TermDecide T) (Import EDec : EnvironmentDecide T E).
|
common\theories\EnvironmentReflect.v
|
compatible_globalsP
| 325 |
Σ Σ' : compatible_globalsb Σ Σ' <-> compatible_globalsb Σ Σ'. Proof. case: compatible_globalsP; intuition. 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 Environment Reflect. From Equations.Prop Require Import Classes EqDecInstances. Module EnvironmentReflect (T : Term) (Import E : EnvironmentSig T) (Import TDec : TermDecide T) (Import EDec : EnvironmentDecide T E).
|
common\theories\EnvironmentReflect.v
|
compatible_globals_spec
| 326 |
Σ Σ' : reflect (compatible Σ Σ') (compatibleb Σ Σ'). Proof. rewrite /compatible/compatibleb. case: compatible_globalsP; destruct Retroknowledge.compatible; cbn; constructor; intuition. 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 Environment Reflect. From Equations.Prop Require Import Classes EqDecInstances. Module EnvironmentReflect (T : Term) (Import E : EnvironmentSig T) (Import TDec : TermDecide T) (Import EDec : EnvironmentDecide T E).
|
common\theories\EnvironmentReflect.v
|
compatibleP
| 327 |
Σ Σ' : compatibleb Σ Σ' <-> compatibleb Σ Σ'. Proof. case: compatibleP; intuition. 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 Environment Reflect. From Equations.Prop Require Import Classes EqDecInstances. Module EnvironmentReflect (T : Term) (Import E : EnvironmentSig T) (Import TDec : TermDecide T) (Import EDec : EnvironmentDecide T E).
|
common\theories\EnvironmentReflect.v
|
compatible_spec
| 328 |
(lookup : kername -> option global_decl) (id : kername) decl : Prop := lookup id = Some (ConstantDecl decl).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
declared_constant_gen
| 329 |
(Σ : global_env) id decl := In (id,ConstantDecl decl) (declarations Σ).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
declared_constant
| 330 |
(lookup : kername -> option global_decl) mind decl := lookup mind = Some (InductiveDecl decl).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
declared_minductive_gen
| 331 |
Σ mind decl := In (mind,InductiveDecl decl) (declarations Σ).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
declared_minductive
| 332 |
lookup ind mdecl decl := declared_minductive_gen lookup (inductive_mind ind) mdecl /\ List.nth_error mdecl.(ind_bodies) (inductive_ind ind) = Some decl.
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
declared_inductive_gen
| 333 |
Σ ind mdecl decl := declared_minductive Σ (inductive_mind ind) mdecl /\ List.nth_error mdecl.(ind_bodies) (inductive_ind ind) = Some decl.
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
declared_inductive
| 334 |
lookup cstr mdecl idecl cdecl : Prop := declared_inductive_gen lookup (fst cstr) mdecl idecl /\ List.nth_error idecl.(ind_ctors) (snd cstr) = Some cdecl.
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
declared_constructor_gen
| 335 |
Σ cstr mdecl idecl cdecl := declared_inductive Σ (fst cstr) mdecl idecl /\ List.nth_error idecl.(ind_ctors) (snd cstr) = Some cdecl.
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
declared_constructor
| 336 |
lookup (proj : projection) mdecl idecl cdecl pdecl : Prop := declared_constructor_gen lookup (proj.(proj_ind), 0) mdecl idecl cdecl /\ List.nth_error idecl.(ind_projs) proj.(proj_arg) = Some pdecl /\ mdecl.(ind_npars) = proj.(proj_npars).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
declared_projection_gen
| 337 |
Σ (proj : projection) mdecl idecl cdecl pdecl : Prop := declared_constructor Σ (proj.(proj_ind), 0) mdecl idecl cdecl /\ List.nth_error idecl.(ind_projs) proj.(proj_arg) = Some pdecl /\ mdecl.(ind_npars) = proj.(proj_npars).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
declared_projection
| 338 |
(lookup : kername -> option global_decl) kn := match lookup kn with | Some (ConstantDecl d) => Some d | _ => None end.
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lookup_constant_gen
| 339 |
Σ := lookup_constant_gen (lookup_env Σ).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lookup_constant
| 340 |
(lookup : kername -> option global_decl) mind := match lookup mind with | Some (InductiveDecl decl) => Some decl | _ => None end.
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lookup_minductive_gen
| 341 |
Σ := lookup_minductive_gen (lookup_env Σ).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lookup_minductive
| 342 |
lookup ind := match lookup_minductive_gen lookup (inductive_mind ind) with | Some mdecl => match nth_error mdecl.(ind_bodies) (inductive_ind ind) with | Some idecl => Some (mdecl, idecl) | None => None end | None => None end.
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lookup_inductive_gen
| 343 |
Σ := lookup_inductive_gen (lookup_env Σ).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lookup_inductive
| 344 |
lookup ind k := match lookup_inductive_gen lookup ind with | Some (mdecl, idecl) => match nth_error idecl.(ind_ctors) k with | Some cdecl => Some (mdecl, idecl, cdecl) | None => None end | _ => None end.
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lookup_constructor_gen
| 345 |
Σ := lookup_constructor_gen (lookup_env Σ).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lookup_constructor
| 346 |
lookup p := match lookup_constructor_gen lookup p.(proj_ind) 0 with | Some (mdecl, idecl, cdecl) => match nth_error idecl.(ind_projs) p.(proj_arg) with | Some pdecl => Some (mdecl, idecl, cdecl, pdecl) | None => None end | _ => None end.
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lookup_projection_gen
| 347 |
Σ := lookup_projection_gen (lookup_env Σ).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lookup_projection
| 348 |
{lookup kn cdecl} : declared_constant_gen lookup kn cdecl -> lookup_constant_gen lookup kn = Some cdecl. Proof. unfold declared_constant_gen, lookup_constant_gen. now intros ->. Qed.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
declared_constant_lookup_gen
| 349 |
{lookup kn cdecl} : lookup_constant_gen lookup kn = Some cdecl -> declared_constant_gen lookup kn cdecl. Proof. unfold declared_constant_gen, lookup_constant_gen. destruct lookup as [[]|] => //. congruence. Qed.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lookup_constant_declared_gen
| 350 |
{lookup ind mdecl} : declared_minductive_gen lookup ind mdecl -> lookup_minductive_gen lookup ind = Some mdecl. Proof. rewrite /declared_minductive_gen /lookup_minductive_gen. now intros ->. Qed.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
declared_minductive_lookup_gen
| 351 |
{lookup ind mdecl} : lookup_minductive_gen lookup ind = Some mdecl -> declared_minductive_gen lookup ind mdecl. Proof. rewrite /declared_minductive_gen /lookup_minductive_gen. destruct lookup as [[]|] => //. congruence. Qed.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lookup_minductive_declared_gen
| 352 |
{lookup ind mdecl idecl} : declared_inductive_gen lookup ind mdecl idecl -> lookup_inductive_gen lookup ind = Some (mdecl, idecl). Proof. rewrite /declared_inductive_gen /lookup_inductive_gen. intros []. now rewrite (declared_minductive_lookup_gen H) H0. Qed.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
declared_inductive_lookup_gen
| 353 |
{lookup ind mdecl idecl} : lookup_inductive_gen lookup ind = Some (mdecl, idecl) -> declared_inductive_gen lookup ind mdecl idecl. Proof. rewrite /declared_inductive_gen /lookup_inductive_gen. destruct lookup_minductive_gen as [[]|] eqn:hl => //=. destruct nth_error eqn:hnth => //. intros [= <- <-]. split => //. apply (lookup_minductive_declared_gen hl). Qed.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lookup_inductive_declared_gen
| 354 |
{lookup id mdecl idecl cdecl} : declared_constructor_gen lookup id mdecl idecl cdecl -> lookup_constructor_gen lookup id.1 id.2 = Some (mdecl, idecl, cdecl). Proof. intros []. unfold lookup_constructor_gen. rewrite (declared_inductive_lookup_gen (lookup := lookup) H) /= H0 //. Qed.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
declared_constructor_lookup_gen
| 355 |
{lookup id mdecl idecl cdecl} : lookup_constructor_gen lookup id.1 id.2 = Some (mdecl, idecl, cdecl) -> declared_constructor_gen lookup id mdecl idecl cdecl. Proof. unfold lookup_constructor_gen. destruct lookup_inductive_gen as [[]|] eqn:hl => //=. destruct nth_error eqn:hnth => //. intros [= <- <-]. split => //. apply (lookup_inductive_declared_gen hl). congruence. Qed.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lookup_constructor_declared_gen
| 356 |
{lookup p mdecl idecl cdecl pdecl} : declared_projection_gen lookup p mdecl idecl cdecl pdecl -> lookup_projection_gen lookup p = Some (mdecl, idecl, cdecl, pdecl). Proof. intros [? []]. unfold lookup_projection_gen. rewrite (declared_constructor_lookup_gen (lookup := lookup) H) /= H0 //. Qed.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
declared_projection_lookup_gen
| 357 |
{lookup p mdecl idecl cdecl pdecl} : ind_npars mdecl = p.(proj_npars) -> lookup_projection_gen lookup p = Some (mdecl, idecl, cdecl, pdecl) -> declared_projection_gen lookup p mdecl idecl cdecl pdecl. Proof. intros hp. unfold lookup_projection_gen. destruct lookup_constructor_gen as [[[] ?]|] eqn:hl => //=. destruct nth_error eqn:hnth => //. intros [= <- <-]. subst c p0. split => //. apply (lookup_constructor_declared_gen (id:=(proj_ind p, 0)) hl). Qed.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lookup_projection_declared_gen
| 358 |
{A} (F : universes_decl -> A) d : A := match d with | ConstantDecl cb => F cb.(cst_universes) | InductiveDecl mb => F mb.(ind_universes) end.
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
on_udecl_decl
| 359 |
on_udecl_decl (fun x => x).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
universes_decl_of_decl
| 360 |
(univs : ContextSet.t) : LevelSet.t := LevelSet.union (ContextSet.levels univs) (LevelSet.singleton (Level.lzero)).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
global_levels
| 361 |
Σ : LevelSet.In Level.lzero (global_levels Σ). Proof. apply LevelSet.union_spec; right. now apply LevelSet.singleton_spec. Qed.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
global_levels_InSet
| 362 |
univs : LevelSet.mem Level.lzero (global_levels univs) = true. Proof. apply LevelSet.mem_spec, global_levels_InSet. Qed.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
global_levels_memSet
| 363 |
(Σ : global_env) : ConstraintSet.t := snd Σ.(universes).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
global_constraints
| 364 |
(Σ : global_env) : ContextSet.t := (global_levels Σ.(universes), global_constraints Σ).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
global_uctx
| 365 |
(Σ : global_env_ext) : LevelSet.t := LevelSet.union (levels_of_udecl (snd Σ)) (global_levels Σ.1.(universes)).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
global_ext_levels
| 366 |
(Σ : global_env_ext) : ConstraintSet.t := ConstraintSet.union (constraints_of_udecl (snd Σ)) (global_constraints Σ.1).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
global_ext_constraints
| 367 |
(Σ : global_env_ext) : ContextSet.t := (global_ext_levels Σ, global_ext_constraints Σ).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
global_ext_uctx
| 368 |
Σ : LevelSet.In Level.lzero (global_ext_levels Σ). Proof. apply LevelSet.union_spec; right. now apply global_levels_InSet. Qed.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
global_ext_levels_InSet
| 369 |
`{checker_flags} (lvs : LevelSet.t) (φ : ConstraintSet.t) uctx (u : Instance.t) := match uctx with | Monomorphic_ctx => List.length u = 0 | Polymorphic_ctx c => forallb (fun l => LevelSet.mem l lvs) u /\ List.length u = List.length c.1 /\ valid_constraints φ (subst_instance_cstrs u c.2) end.
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
consistent_instance
| 370 |
`{checker_flags} Σ := consistent_instance (global_ext_levels Σ) (global_ext_constraints Σ).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
consistent_instance_ext
| 371 |
{cf : checker_flags} {Σ : global_env_ext} {univs u} : consistent_instance_ext Σ univs u -> #|u| = #|abstract_instance univs|. Proof. unfold consistent_instance_ext, consistent_instance. destruct univs; simpl; auto. intros [_ [H _]]. destruct cst; simpl in *. now rewrite H; cbn; autorewrite with len. Qed.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
consistent_instance_length
| 372 |
Σ (u : Universe.t) : Prop := forall l, LevelExprSet.In l u -> LevelSet.In (LevelExpr.get_level l) (global_ext_levels Σ).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
wf_universe
| 373 |
Σ (s : sort) : Prop := Sort.on_sort (wf_universe Σ) True s.
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
wf_sort
| 374 |
Σ u : {wf_universe Σ u} + {~wf_universe Σ u}. Proof. cbv [wf_universe LevelExprSet.In LevelExprSet.this t_set]. destruct u as [[t _] _]. induction t as [|t ts [IHt|IHt]]; [ left | | right ]. { inversion 1. } { destruct (LevelSetProp.In_dec (LevelExpr.get_level t) (global_ext_levels Σ)) as [H|H]; [ left | right ]. { inversion 1; subst; auto. } { intro H'; apply H, H'; now constructor. } } { intro H; apply IHt; intros; apply H; now constructor. } Defined.
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
wf_universe_dec
| 375 |
Σ s : {@wf_sort Σ s} + {~@wf_sort Σ s}. Proof. destruct s; try (left; exact I). apply wf_universe_dec. Defined.
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
wf_sort_dec
| 376 |
`{cf : checker_flags} {Σ ind mib oib} : declared_inductive Σ ind mib oib -> Alli (fun i => declared_constructor Σ (ind, i) mib oib) 0 (ind_ctors oib). Proof using. move=> inddecl. apply: forall_nth_error_Alli=> /= i x eq => //. Qed.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
declared_ind_declared_constructors
| 377 |
(P : context -> judgment -> Type) Γ d := P Γ (Typ d.(dtype)).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
on_def_type
| 378 |
(P : context -> judgment -> Type) types Γ d := P (Γ ,,, types) (TermTyp d.(dbody) (lift0 #|types| d.(dtype))).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
on_def_body
| 379 |
wf_term (j : judgment) := option_default wf_term (j_term j) (unit : Type) × wf_term (j_typ j).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lift_wf_term
| 380 |
wf_term wf_univ (j : judgment) := option_default wf_term (j_term j) unit × wf_term (j_typ j) × option_default wf_univ (j_univ j) unit.
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lift_wfu_term
| 381 |
wfb_term (j : judgment) := option_default wfb_term (j_term j) true && wfb_term (j_typ j).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lift_wfb_term
| 382 |
wfb_term wfb_univ (j : judgment) := option_default wfb_term (j_term j) true && wfb_term (j_typ j) && option_default wfb_univ (j_univ j) true.
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lift_wfbu_term
| 383 |
checking sorting : judgment -> Type := fun j => option_default (fun tm => checking tm (j_typ j)) (j_term j) (unit : Type) × ∑ s, sorting (j_typ j) s × option_default (fun u => (u = s : Type)) (j_univ j) unit.
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lift_sorting
| 384 |
typing := lift_sorting typing (typing_sort typing).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lift_typing0
| 385 |
(P Q : context -> _) := lift_typing1 (Prop_local_conj P Q).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lift_typing_conj
| 386 |
{P Q} {tm tm' : option term} {t t' : term} {u u'} : forall tu: lift_wf_term P (Judge tm t u), match tm', tm with None, _ => unit | Some tm', Some tm => P tm -> Q tm' | _, _ => False end -> (P t -> Q t') -> lift_wf_term Q (Judge tm' t' u'). Proof. intros (Htm & Hs) HPQc HPQs. split; auto. destruct tm, tm' => //=. now apply HPQc. Qed.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lift_wf_term_it_impl
| 387 |
P Q tm t u u' : forall f, lift_wf_term P (Judge tm t u) -> (forall t, P t -> Q (f t)) -> lift_wf_term Q (Judge (option_map f tm) (f t) u'). Proof. unfold lift_wf_term; cbn. intros f (Hb & Ht) HPQ. split; auto. destruct tm; cbn in *; auto. Defined.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lift_wf_term_f_impl
| 388 |
P Q j : lift_wf_term P j -> (forall t, P t -> Q t) -> lift_wf_term Q j. Proof. unfold lift_wf_term; cbn. intros (Hb & Ht) HPQ. split; auto. destruct j_term; cbn in *; auto. Defined.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lift_wf_term_impl
| 389 |
(P Q : term -> bool) tm t u : forall f fu, lift_wfbu_term P (P ∘ tSort) (Judge tm t u) -> (forall u, f (tSort u) = tSort (fu u)) -> (forall t, P t -> Q (f t)) -> lift_wfbu_term Q (Q ∘ tSort) (Judge (option_map f tm) (f t) (option_map fu u)). Proof. unfold lift_wfbu_term; cbn. intros. rtoProp. repeat split; auto. 1: destruct tm; cbn in *; auto. destruct u; rewrite //= -H0 //. auto. Defined.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lift_wfbu_term_f_impl
| 390 |
{Pc Ps tm ty u} : lift_sorting Pc Ps (Judge (Some tm) ty u) -> Pc tm ty. Proof. apply fst. Defined.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
unlift_TermTyp
| 391 |
{Pc Ps tm ty u} : lift_sorting Pc Ps (Judge tm ty (Some u)) -> Ps ty u := fun H => eq_rect_r _ H.2.π2.1 H.2.π2.2.
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
unlift_TypUniv
| 392 |
{c s tm ty u} (w : lift_sorting c s (Judge tm ty u)) : lift_sorting c s (Judge tm ty (Some w.2.π1)) := (w.1, existT _ w.2.π1 (w.2.π2.1, eq_refl)).
|
Definition
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lift_sorting_extract
| 393 |
{Pc Ps tm ty u} : lift_sorting Pc Ps (Judge tm ty u) -> lift_sorting Pc Ps (TermoptTyp tm ty). Proof. intros (? & ? & ? & ?). repeat (eexists; tea). Qed.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lift_sorting_forget_univ
| 394 |
{Pc Ps tm ty u} : lift_sorting Pc Ps (Judge tm ty u) -> lift_sorting Pc Ps (Judge None ty u). Proof. intros (? & ? & ? & ?). repeat (eexists; tea). Qed.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lift_sorting_forget_body
| 395 |
{Pc Qc Ps Qs} {tm tm' : option term} {t t' : term} : forall tu: lift_sorting Pc Ps (TermoptTyp tm t), let s := tu.2.π1 in match tm', tm with None, _ => unit | Some tm', Some tm => Pc tm t -> Qc tm' t' | _, _ => False end -> (Ps t s -> ∑ s', Qs t' s') -> lift_sorting Qc Qs (TermoptTyp tm' t'). Proof. intros (? & ? & Hs & e) s HPQc HPQs. split. - destruct tm, tm' => //=. now apply HPQc. - specialize (HPQs Hs) as (s' & H). eexists. split; eassumption. Qed.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lift_sorting_ex_it_impl_gen
| 396 |
{Pc Qc Ps Qs} {tm tm' : option term} {t t' : term} {u} : forall tu: lift_sorting Pc Ps (Judge tm t u), let s := tu.2.π1 in match tm', tm with None, _ => unit | Some tm', Some tm => Pc tm t -> Qc tm' t' | _, _ => False end -> (Ps t s -> Qs t' s) -> lift_sorting Qc Qs (Judge tm' t' u). Proof. intros (? & ? & Hs & e) s HPQc HPQs. split. - destruct tm, tm' => //=. now apply HPQc. - eexists. split; [now apply HPQs|]. destruct u => //. Qed.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lift_sorting_it_impl_gen
| 397 |
{Pc Qc Ps Qs} {tm : option term} {t : term} {u} : forall f fu, forall tu: lift_sorting Pc Ps (Judge tm t u), let s := tu.2.π1 in option_default (fun tm => Pc tm t -> Qc (f tm) (f t)) tm unit -> (Ps t s -> Qs (f t) (fu s)) -> lift_sorting Qc Qs (Judge (option_map f tm) (f t) (option_map fu u)). Proof. intros ?? (? & ? & Hs & e) s HPQc HPQs. split. - destruct tm => //=. now apply HPQc. - eexists. split; [now apply HPQs|]. destruct u => //. cbn. f_equal => //. Qed.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lift_sorting_fu_it_impl
| 398 |
{Pc Qc Ps Qs} {j : judgment} : forall f, forall tu: lift_sorting Pc Ps j, let s := tu.2.π1 in option_default (fun tm => Pc tm (j_typ j) -> Qc (f tm) (f (j_typ j))) (j_term j) unit -> (Ps (j_typ j) s -> Qs (f (j_typ j)) s) -> lift_sorting Qc Qs (judgment_map f j). Proof. intro f. replace (judgment_map f j) with (Judge (option_map f (j_term j)) (f (j_typ j)) (option_map id (j_univ j))). 2: unfold judgment_map; destruct j_univ => //. apply lift_sorting_fu_it_impl with (fu := id). Qed.
|
Lemma
|
common
|
From Coq Require Import ssreflect ssrbool. From Coq Require CMorphisms CRelationClasses. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config BasicAst Universes Environment Primitive. From Equations Require Import Equations. Import T E. Import T E TU. Import T E TU ET. Import T E TU ET C L. Import T E TU ET. Import T E TU ET CT CS. Import T E L TU ET CT GM CS Ty.
|
common\theories\EnvironmentTyping.v
|
lift_sorting_f_it_impl
| 399 |
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