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(g : global_env) (e : t) := e = of_global_env g. | Definition | common | From Coq Require Import ssreflect RelationClasses OrderedTypeAlt FMapAVL FMapFacts. From MetaCoq.Utils Require Import utils String2pos CanonicalTries. From MetaCoq.Common Require Import config uGraph Reflect BasicAst Kernames. From Equations Require Import Equations. Import String2pos. | common\theories\EnvMap.v | repr | 600 |
{cf:checker_flags} g d d' : fresh_global d.1 (d' :: g) -> fresh_global d'.1 g -> of_global_env (d :: d' :: g) = of_global_env (d' :: d :: g). Proof. intros hwf hwf'. cbn. f_equal. apply PTree.extensionality. intros i. unfold add. destruct (eq_dec i (pos_of_kername d'.1)). - subst. rewrite PTree.gss PTree.gso. intros eq. apply pos_of_kername_inj in eq. depelim hwf. cbn in H; congruence. now rewrite PTree.gss. - rewrite PTree.gso //. destruct (eq_dec i (pos_of_kername d.1)); [subst i|]. + rewrite !PTree.gss //. + rewrite !PTree.gso //. Qed. | Lemma | common | From Coq Require Import ssreflect RelationClasses OrderedTypeAlt FMapAVL FMapFacts. From MetaCoq.Utils Require Import utils String2pos CanonicalTries. From MetaCoq.Common Require Import config uGraph Reflect BasicAst Kernames. From Equations Require Import Equations. Import String2pos. | common\theories\EnvMap.v | of_global_env_comm | 601 |
g d d' : d.1 <> d'.1 -> add d.1 d.2 (add d'.1 d'.2 g) = add d'.1 d'.2 (add d.1 d.2 g). Proof. intros hwf. cbn. unfold add. apply PTree.extensionality=> i. destruct (eq_dec i (pos_of_kername d'.1)). - subst. rewrite PTree.gss PTree.gso. intros eq. apply pos_of_kername_inj in eq. congruence. now rewrite PTree.gss. - destruct (eq_dec i (pos_of_kername d.1)); [subst i|]. + rewrite !PTree.gss // PTree.gso // !PTree.gss //. + rewrite !PTree.gso //. Qed. | Lemma | common | From Coq Require Import ssreflect RelationClasses OrderedTypeAlt FMapAVL FMapFacts. From MetaCoq.Utils Require Import utils String2pos CanonicalTries. From MetaCoq.Common Require Import config uGraph Reflect BasicAst Kernames. From Equations Require Import Equations. Import String2pos. | common\theories\EnvMap.v | add_comm | 602 |
global_env -> Prop := | fresh_globals_empty : fresh_globals [] | fresh_globals_cons kn d g : fresh_globals g -> fresh_global kn g -> fresh_globals ((kn, d) :: g). | Inductive | common | From Coq Require Import ssreflect RelationClasses OrderedTypeAlt FMapAVL FMapFacts. From MetaCoq.Utils Require Import utils String2pos CanonicalTries. From MetaCoq.Common Require Import config uGraph Reflect BasicAst Kernames. From Equations Require Import Equations. Import String2pos. | common\theories\EnvMap.v | fresh_globals | 603 |
d g acc : fold_left (fun (genv : t) (decl : kername × global_decl) => add decl.1 decl.2 genv) (d :: g) acc = fold_left (fun (genv : t) (decl : kername × global_decl) => add decl.1 decl.2 genv) g (add d.1 d.2 acc). Proof. reflexivity. Qed. | Lemma | common | From Coq Require Import ssreflect RelationClasses OrderedTypeAlt FMapAVL FMapFacts. From MetaCoq.Utils Require Import utils String2pos CanonicalTries. From MetaCoq.Common Require Import config uGraph Reflect BasicAst Kernames. From Equations Require Import Equations. Import String2pos. | common\theories\EnvMap.v | fold_left_cons | 604 |
{cf:checker_flags} d g : fresh_globals (d :: g) -> of_global_env (d :: g) = add d.1 d.2 (of_global_env g). Proof. unfold of_global_env. generalize empty. induction g. - cbn; auto. - unfold fresh_global. intros acc hf. depelim hf. rewrite fold_left_cons. rewrite -IHg. constructor. now depelim hf. now depelim H. cbn. f_equal. rewrite (add_comm _ a (kn, d0)) //. cbn. now depelim H. Qed. | Lemma | common | From Coq Require Import ssreflect RelationClasses OrderedTypeAlt FMapAVL FMapFacts. From MetaCoq.Utils Require Import utils String2pos CanonicalTries. From MetaCoq.Common Require Import config uGraph Reflect BasicAst Kernames. From Equations Require Import Equations. Import String2pos. | common\theories\EnvMap.v | of_global_env_cons | 605 |
{cf} Σ : wf Σ -> fresh_globals Σ. Proof. induction 1; constructor; auto. Qed. | Lemma | common | From Coq Require Import ssreflect RelationClasses OrderedTypeAlt FMapAVL FMapFacts. From MetaCoq.Utils Require Import utils String2pos CanonicalTries. From MetaCoq.Common Require Import config uGraph Reflect BasicAst Kernames. From Equations Require Import Equations. Import String2pos. | common\theories\EnvMap.v | wf_fresh_globals | 606 |
k v g : lookup k (add k v g) = Some v. Proof. rewrite /lookup /add. rewrite PTree.gss //. Qed. | Lemma | common | From Coq Require Import ssreflect RelationClasses OrderedTypeAlt FMapAVL FMapFacts. From MetaCoq.Utils Require Import utils String2pos CanonicalTries. From MetaCoq.Common Require Import config uGraph Reflect BasicAst Kernames. From Equations Require Import Equations. Import String2pos. | common\theories\EnvMap.v | lookup_add | 607 |
k k' v g : k <> k' -> lookup k (add k' v g) = lookup k g. Proof. move=> eqk. rewrite /lookup /add. rewrite PTree.gso //. move/pos_of_kername_inj. congruence. Qed. | Lemma | common | From Coq Require Import ssreflect RelationClasses OrderedTypeAlt FMapAVL FMapFacts. From MetaCoq.Utils Require Import utils String2pos CanonicalTries. From MetaCoq.Common Require Import config uGraph Reflect BasicAst Kernames. From Equations Require Import Equations. Import String2pos. | common\theories\EnvMap.v | lookup_add_other | 608 |
d g : lookup_env (d :: g) d.1 = Some d.2. Proof. now rewrite /lookup_env eq_kername_refl. Qed. | Lemma | common | From Coq Require Import ssreflect RelationClasses OrderedTypeAlt FMapAVL FMapFacts. From MetaCoq.Utils Require Import utils String2pos CanonicalTries. From MetaCoq.Common Require Import config uGraph Reflect BasicAst Kernames. From Equations Require Import Equations. Import String2pos. | common\theories\EnvMap.v | lookup_env_head | 609 |
{cf : checker_flags} (g : global_env) (e : t) : wf g -> repr g e -> forall k, lookup k e = lookup_env g k. Proof. intros wf -> k. induction g in k, wf |- *; auto. change (eq_kername k a.1) with (eqb k a.1). destruct (eqb_spec k a.1). - subst. rewrite of_global_env_cons; [now apply wf_fresh_globals|]. now rewrite lookup_add lookup_env_head. - rewrite of_global_env_cons. now apply wf_fresh_globals. rewrite lookup_add_other //. destruct a; rewrite lookup_env_cons_fresh //. * cbn in n. congruence. * apply IHg. now depelim wf. Qed. | Lemma | common | From Coq Require Import ssreflect RelationClasses OrderedTypeAlt FMapAVL FMapFacts. From MetaCoq.Utils Require Import utils String2pos CanonicalTries. From MetaCoq.Common Require Import config uGraph Reflect BasicAst Kernames. From Equations Require Import Equations. Import String2pos. | common\theories\EnvMap.v | lookup_spec | 610 |
string_compare. | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | compare_ident | 611 |
string. | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | ident | 612 |
string. | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | qualid | 613 |
list ident. | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | dirpath | 614 |
Classes.EqDec dirpath := _. | Instance | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | dirpath_eqdec | 615 |
(dp : dirpath) : string := String.concat "." (List.rev dp). | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | string_of_dirpath | 616 |
| MPfile (dp : dirpath) | MPbound (dp : dirpath) (id : ident) (i : nat) | MPdot (mp : modpath) (id : ident). | Inductive | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | modpath | 617 |
(mp : modpath) : string := match mp with | MPfile dp => string_of_dirpath dp | MPbound dp id n => string_of_dirpath dp ^ "." ^ id ^ "." ^ string_of_nat n | MPdot mp id => string_of_modpath mp ^ "." ^ id end. | Fixpoint | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | string_of_modpath | 618 |
modpath × ident. | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | kername | 619 |
(kn : kername) := string_of_modpath kn.1 ^ "." ^ kn.2. | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | string_of_kername | 620 |
modpath. | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | t | 621 |
@eq modpath. | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | eq | 622 |
RelationClasses.Equivalence eq := _. | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | eq_univ | 623 |
dp id k dp' id' k' := compare_cont (DirPathOT.compare dp dp') (compare_cont (IdentOT.compare id id') (Nat.compare k k')). | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | mpbound_compare | 624 |
mp mp' := match mp, mp' with | MPfile dp, MPfile dp' => DirPathOT.compare dp dp' | MPbound dp id k, MPbound dp' id' k' => mpbound_compare dp id k dp' id' k' | MPdot mp id, MPdot mp' id' => compare_cont (compare mp mp') (IdentOT.compare id id') | MPfile _, _ => Gt | _, MPfile _ => Lt | MPbound _ _ _, _ => Gt | _, MPbound _ _ _ => Lt end. | Fixpoint | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | compare | 625 |
forall x y, Nat.compare x y = CompOpp (Nat.compare y x). Proof. intros; apply PeanoNat.Nat.compare_antisym. Qed. | Lemma | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | nat_compare_sym | 626 |
x y : x ?= y = Eq -> x = y. Proof. induction x in y |- *; destruct y; simpl; auto; try congruence. intros c. eapply DirPathOT.compare_eq in c; now subst. unfold mpbound_compare. destruct (DirPathOT.compare dp dp0) eqn:eq => //. destruct (IdentOT.compare id id0) eqn:eq' => //. destruct (Nat.compare i i0) eqn:eq'' => //. apply DirPathOT.compare_eq in eq. apply string_compare_eq in eq'. apply PeanoNat.Nat.compare_eq in eq''. congruence. destruct (x ?= y) eqn:eq; try congruence. specialize (IHx _ eq). subst. now intros c; apply string_compare_eq in c; subst. all:simpl; discriminate. Qed. | Lemma | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | compare_eq | 627 |
forall x y, (y ?= x) = CompOpp (x ?= y). Proof. induction x; destruct y; simpl; auto. apply DirPathOT.compare_sym. unfold mpbound_compare. rewrite DirPathOT.compare_sym. rewrite IdentOT.compare_sym. destruct (DirPathOT.compare dp dp0); auto. simpl. destruct (IdentOT.compare id id0); simpl; auto. apply nat_compare_sym. rewrite IHx. destruct (x ?= y); simpl; auto. apply IdentOT.compare_sym. Qed. | Lemma | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | compare_sym | 628 |
forall c x y z, Nat.compare x y = c -> Nat.compare y z = c -> Nat.compare x z = c. Proof. intros c x y z. destruct (PeanoNat.Nat.compare_spec x y); subst; intros <-; destruct (PeanoNat.Nat.compare_spec y z); subst; try congruence; destruct (PeanoNat.Nat.compare_spec x z); subst; try congruence; lia. Qed. | Lemma | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | nat_compare_trans | 629 |
forall c x y z, (x?=y) = c -> (y?=z) = c -> (x?=z) = c. Proof. intros c x y z. revert c. induction x in y, z |- *; destruct y, z; intros c; simpl; auto; try congruence. apply DirPathOT.compare_trans. unfold mpbound_compare. eapply compare_cont_trans; eauto using DirPathOT.compare_trans, DirPathOT.compare_eq. intros c'. eapply compare_cont_trans; eauto using StringOT.compare_trans, StringOT.compare_eq, nat_compare_trans. intros x y. apply StringOT.compare_eq. destruct (x ?= y) eqn:eq. apply compare_eq in eq. subst. destruct (IdentOT.compare id id0) eqn:eq. apply string_compare_eq in eq; red in eq; subst. all:intros <-; auto. destruct (y ?= z) eqn:eq'; auto. apply compare_eq in eq'; subst. intros eq'. eapply IdentOT.compare_trans; eauto. cbn in *. destruct (y ?= z) eqn:eq'; auto. cbn. now apply IdentOT.compare_trans. destruct (y ?= z) eqn:eq'; auto; cbn; try congruence. apply compare_eq in eq'; subst. intros eq'. now rewrite eq. rewrite (IHx _ _ _ eq eq') //. destruct (y ?= z) eqn:eq'; cbn; auto; try congruence. apply compare_eq in eq'; subst. intros eq'. now rewrite eq. now rewrite (IHx _ _ _ eq eq'). Qed. | Lemma | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | compare_trans | 630 |
Classes.EqDec modpath := { eq_dec := modpath_eq_dec }. | Instance | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | modpath_EqDec | 631 |
kername. | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | t | 632 |
@eq kername. | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | eq | 633 |
RelationClasses.Equivalence eq. Proof. apply _. Qed. | Lemma | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | eq_equiv | 634 |
kn kn' := match kn, kn' with | (mp, id), (mp', id') => compare_cont (ModPathComp.compare mp mp') (IdentOT.compare id id') end. | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | compare | 635 |
forall x y, (y ?= x) = CompOpp (x ?= y). Proof. induction x; destruct y; simpl; auto. unfold compare_ident. rewrite ModPathComp.compare_sym IdentOT.compare_sym. destruct ModPathComp.compare, IdentOT.compare; auto. Qed. | Lemma | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | compare_sym | 636 |
forall c x y z, (x?=y) = c -> (y?=z) = c -> (x?=z) = c. Proof. intros c [] [] [] => /=. eapply compare_cont_trans; eauto using ModPathComp.compare_trans, ModPathComp.compare_eq, StringOT.compare_trans. Qed. | Lemma | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | compare_trans | 637 |
OT.lt. Global Instance lt_strorder : StrictOrder OT.lt. Proof. constructor. - intros x X. apply OT.lt_not_eq in X. apply X. apply OT.eq_refl. - intros x y z X1 X2. eapply OT.lt_trans; eauto. Qed. | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | lt | 638 |
Proper (eq ==> eq ==> iff) OT.lt. Proof. intros x x' H1 y y' H2. red in H1, H2. subst. reflexivity. Qed. | Lemma | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | lt_compat | 639 |
forall x y, CompareSpec (eq x y) (lt x y) (lt y x) (compare x y). Proof. induction x; destruct y. simpl. destruct (ModPathComp.compare a m) eqn:eq. destruct (IdentOT.compare b i) eqn:eq'. all:constructor. red. eapply ModPathComp.compare_eq in eq. eapply string_compare_eq in eq'. congruence. all:hnf; simpl; rewrite ?eq ?eq' //. rewrite ModPathComp.compare_sym eq /= IdentOT.compare_sym eq' //. now rewrite ModPathComp.compare_sym eq /=. Defined. | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | compare_spec | 640 |
x y : compare x y = Eq <-> x = y. Proof. split. - destruct (compare_spec x y); try congruence. - intros <-. destruct (compare_spec x x); auto. now apply irreflexivity in H. now apply irreflexivity in H. Qed. | Lemma | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | compare_eq | 641 |
kn kn' := match compare kn kn' with | Eq => true | _ => false end. | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | eqb | 642 |
#[global, program] : ReflectEq kername := { eqb := eqb }. Next Obligation. unfold eqb. destruct compare eqn:e; constructor. - now apply compare_eq in e. -intros e'; subst. now rewrite OT.eq_refl in e. -intros e'; subst. now rewrite OT.eq_refl in e. Defined. | Instance | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | reflect_kername | 643 |
forall (x y : t), { x = y } + { x <> y } := Classes.eq_dec. | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | eq_dec | 644 |
kn : eq_kername kn kn. Proof. eapply ReflectEq.eqb_refl. Qed. | Lemma | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | eq_kername_refl | 645 |
eq_kername. | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | eq_constant | 646 |
{A} kn f (l : list A) acc : KernameSet.In kn (fold_left (fun acc x => KernameSet.union (f x) acc) l acc) <-> (KernameSet.In kn acc \/ exists a, In a l /\ KernameSet.In kn (f a)). Proof. induction l in acc |- *; simpl. - split; auto. intros [H0|H0]; auto. now destruct H0. - rewrite IHl. rewrite KernameSet.union_spec. intuition auto. * right. now exists a; intuition auto. * destruct H0 as [a' [ina inkn]]. right. now exists a'; intuition auto. * destruct H0 as [a' [ina inkn]]. destruct ina as [<-|ina']; intuition auto. right. now exists a'. Qed. | Lemma | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | knset_in_fold_left | 647 |
Set := mkInd { inductive_mind : kername ; inductive_ind : nat }. | Record | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | inductive | 648 |
(i : inductive) := string_of_kername (inductive_mind i) ^ "," ^ string_of_nat (inductive_ind i). | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | string_of_inductive | 649 |
i i' := let 'mkInd i n := i in let 'mkInd i' n' := i' in eqb (i, n) (i', n'). | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | eq_inductive_def | 650 |
#[global, program] : ReflectEq inductive := { eqb := eq_inductive_def }. Next Obligation. destruct x as [m n], y as [m' n']; cbn -[eqb]. case: eqb_spec ; nodec. cbn. constructor. noconf p; reflexivity. Qed. | Instance | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | reflect_eq_inductive | 651 |
i : eq_inductive i i. Proof. apply ReflectEq.eqb_refl. Qed. | Lemma | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | eq_inductive_refl | 652 |
mkProjection { proj_ind : inductive; proj_npars : nat; proj_arg : nat }. | Record | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | projection | 653 |
(p p' : projection) := (p.(proj_ind), p.(proj_npars), p.(proj_arg)) == (p'.(proj_ind), p'.(proj_npars), p'.(proj_arg)). | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | eq_projection | 654 |
#[global, program] : ReflectEq projection := { eqb := eq_projection }. Next Obligation. unfold eq_projection. case: eqb_spec ; nodec. destruct x, y; cbn. now constructor. Qed. | Instance | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | reflect_eq_projection | 655 |
i : eq_projection i i. Proof. apply ReflectEq.eqb_refl. Qed. | Lemma | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | eq_projection_refl | 656 |
| VarRef : ident -> global_reference | ConstRef : kername -> global_reference | IndRef : inductive -> global_reference | ConstructRef : inductive -> nat -> global_reference. | Inductive | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | global_reference | 657 |
gr : string := match gr with | VarRef v => v | ConstRef s => string_of_kername s | IndRef (mkInd s n) => "Inductive " ^ string_of_kername s ^ " " ^ (string_of_nat n) | ConstructRef (mkInd s n) k => "Constructor " ^ string_of_kername s ^ " " ^ (string_of_nat n) ^ " " ^ (string_of_nat k) end. | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | string_of_gref | 658 |
(x y : global_reference) : bool := match x, y with | VarRef i, VarRef i' => eqb i i' | ConstRef c, ConstRef c' => eqb c c' | IndRef i, IndRef i' => eqb i i' | ConstructRef i k, ConstructRef i' k' => eqb i i' && eqb k k' | _, _ => false end. | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | gref_eqb | 659 |
#[global, program] : ReflectEq global_reference := {| eqb := gref_eqb |}. | Instance | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | grep_reflect_eq | 660 |
(gr gr' : global_reference) : {gr = gr'} + {~ gr = gr'} := Classes.eq_dec gr gr'. | Definition | common | From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From Coq Require Import ssreflect. From Equations Require Import Equations. | common\theories\Kernames.v | gref_eq_dec | 661 |
{A B} (f : A -> T B) (b : binder_annot A) : T (binder_annot B) := let '{| binder_name := binder_name; binder_relevance := binder_relevance |} := b in binder_name <- f binder_name;; ret {| binder_name := binder_name; binder_relevance := binder_relevance |}. | Definition | common | From MetaCoq.Utils Require Import utils monad_utils MCList. From MetaCoq.Common Require Import BasicAst. Import MCMonadNotation. | common\theories\MonadBasicAst.v | monad_map_binder_annot | 662 |
{A B} (tyf bodyf : A -> T B) (d : def A) := let '{| dname := dname; dtype := dtype; dbody := dbody; rarg := rarg |} := d in dtype <- tyf dtype;; dbody <- bodyf dbody;; ret {| dname := dname; dtype := dtype; dbody := dbody; rarg := rarg |}. | Definition | common | From MetaCoq.Utils Require Import utils monad_utils MCList. From MetaCoq.Common Require Import BasicAst. Import MCMonadNotation. | common\theories\MonadBasicAst.v | monad_map_def | 663 |
{univ T' T''} (f: T' -> T T'') (t : judgment_ univ T') := match t with | Judge tm ty u => ftm <- monad_option_map f tm;; fty <- f ty;; ret (Judge ftm fty u) end. | Definition | common | From MetaCoq.Utils Require Import utils monad_utils MCList. From MetaCoq.Common Require Import BasicAst. Import MCMonadNotation. | common\theories\MonadBasicAst.v | monad_typ_or_sort_map | 664 |
{term term'} (f : term -> T term') (d : context_decl term) : T (context_decl term') := let '{| decl_name := decl_name; decl_body := decl_body; decl_type := decl_type |} := d in decl_body <- monad_option_map f decl_body;; decl_type <- f decl_type;; ret {| decl_name := decl_name; decl_body := decl_body; decl_type := decl_type |}. | Definition | common | From MetaCoq.Utils Require Import utils monad_utils MCList. From MetaCoq.Common Require Import BasicAst. Import MCMonadNotation. | common\theories\MonadBasicAst.v | monad_map_decl | 665 |
{term term'} (f : term -> T term') (c : list (context_decl term)) := monad_map (monad_map_decl f) c. | Definition | common | From MetaCoq.Utils Require Import utils monad_utils MCList. From MetaCoq.Common Require Import BasicAst. Import MCMonadNotation. | common\theories\MonadBasicAst.v | monad_map_context | 666 |
(c : list (context_decl term)) : T (list (context_decl term')) := match c with | d :: Γ => d <- monad_map_decl (f #|Γ|) d;; Γ <- monad_mapi_context Γ;; ret (d :: Γ) | [] => ret [] end. | Fixpoint | common | From MetaCoq.Utils Require Import utils monad_utils MCList. From MetaCoq.Common Require Import BasicAst. Import MCMonadNotation. | common\theories\MonadBasicAst.v | monad_mapi_context | 667 |
(f : nat -> term -> T term') Γ := Γ <- monad_map_i (fun k' decl => monad_map_decl (f k') decl) (rev Γ);; ret (rev Γ). | Definition | common | From MetaCoq.Utils Require Import utils monad_utils MCList. From MetaCoq.Common Require Import BasicAst. Import MCMonadNotation. | common\theories\MonadBasicAst.v | monad_fold_context_k | 668 |
#[program,global] : ReflectEq Numbers.Cyclic.Int63.Uint63.int := { eqb := Numbers.Cyclic.Int63.Uint63.eqb }. Next Obligation. destruct (Uint63.eqb x y) eqn:eq; constructor. now apply (Numbers.Cyclic.Int63.Uint63.eqb_spec x y) in eq. now apply (Numbers.Cyclic.Int63.Uint63.eqb_false_spec x y) in eq. Qed. | Instance | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | reflect_prim_int | 669 |
ReflectEq PrimFloat.float := { eqb x y := eqb (ReflectEq := EqDec_ReflectEq SpecFloat.spec_float) (FloatOps.Prim2SF x) (FloatOps.Prim2SF y) }. Next Obligation. intros. cbn -[eqb]. destruct (eqb_spec (ReflectEq := EqDec_ReflectEq SpecFloat.spec_float) (FloatOps.Prim2SF x) (FloatOps.Prim2SF y)) as [H|H]; constructor. now apply FloatAxioms.Prim2SF_inj. intros e; apply H. rewrite e. reflexivity. Qed. | Instance | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | reflect_prim_float | 670 |
l1 l2 := match l1, l2 with | PropLevel.lProp, PropLevel.lProp => true | PropLevel.lSProp, PropLevel.lSProp => true | _, _ => false end. | Definition | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | eq_prop_level | 671 |
#[global, program] : ReflectEq PropLevel.t := { eqb := eq_prop_level }. Next Obligation. destruct x, y. all: unfold eq_prop_level. all: try solve [ constructor ; reflexivity ]. all: try solve [ constructor ; discriminate ]. Qed. | Instance | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | reflect_prop_level | 672 |
(l1 l2 : PropLevel.t + Level.t) := match l1, l2 with | inl l, inl l' => eqb l l' | inr l, inr l' => eqb l l' | _, _ => false end. | Definition | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | eq_levels | 673 |
#[global, program] : ReflectEq (PropLevel.t + Level.t) := { eqb := eq_levels }. Next Obligation. destruct x, y. cbn -[eqb]. destruct (eqb_spec t t0). subst. now constructor. all:try (constructor; cong). cbn -[eqb]. destruct (eqb_spec t t0). subst; now constructor. constructor; cong. Qed. | Instance | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | reflect_levels | 674 |
na nb := match na, nb with | nAnon, nAnon => true | nNamed a, nNamed b => eqb a b | _, _ => false end. | Definition | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | eq_name | 675 |
#[global, program] : ReflectEq name := { eqb := eq_name }. Next Obligation. intros x y. destruct x, y. - cbn. constructor. reflexivity. - cbn. constructor. discriminate. - cbn. constructor. discriminate. - unfold eq_name. destruct (eqb_spec i i0); nodec. constructor. f_equal. assumption. Qed. | Instance | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | reflect_name | 676 |
r r' := match r, r' with | Relevant, Relevant => true | Irrelevant, Irrelevant => true | _, _ => false end. | Definition | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | eq_relevance | 677 |
#[global, program] : ReflectEq relevance := { eqb := eq_relevance }. Next Obligation. intros x y. destruct x, y. - cbn. constructor. reflexivity. - cbn. constructor. discriminate. - cbn. constructor. discriminate. - simpl. now constructor. Qed. | Instance | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | reflect_relevance | 678 |
(na nb : binder_annot name) := eqb na.(binder_name) nb.(binder_name) && eqb na.(binder_relevance) nb.(binder_relevance). | Definition | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | eq_aname | 679 |
#[global, program] : ReflectEq aname := { eqb := eq_aname }. Next Obligation. intros x y. unfold eq_aname. destruct (eqb_spec x.(binder_name) y.(binder_name)); destruct (eqb_spec x.(binder_relevance) y.(binder_relevance)); constructor; destruct x, y; simpl in *; cong. Qed. | Instance | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | reflect_aname | 680 |
{A} `{ReflectEq A} (d1 d2 : def A) : bool := match d1, d2 with | mkdef n1 t1 b1 a1, mkdef n2 t2 b2 a2 => eqb n1 n2 && eqb t1 t2 && eqb b1 b2 && eqb a1 a2 end. | Definition | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | eq_def | 681 |
#[global, program] : forall {A} `{ReflectEq A}, ReflectEq (def A) := { eqb := eq_def }. Next Obligation. intros A RA. intros x y. destruct x as [n1 t1 b1 a1], y as [n2 t2 b2 a2]. unfold eq_def. destruct (eqb_spec n1 n2) ; nodec. destruct (eqb_spec t1 t2) ; nodec. destruct (eqb_spec b1 b2) ; nodec. destruct (eqb_spec a1 a2) ; nodec. cbn. constructor. subst. reflexivity. Qed. | Instance | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | reflect_def | 682 |
(c c' : cast_kind) : bool := match c, c' with | VmCast, VmCast | NativeCast, NativeCast | Cast, Cast => true | _, _ => false end. | Definition | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | eq_cast_kind | 683 |
#[global, program] : ReflectEq cast_kind := { eqb := eq_cast_kind }. Next Obligation. induction x, y. all: cbn. all: nodec. all: left. all: reflexivity. Qed. | Instance | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | reflect_cast_kind | 684 |
(ci ci' : BasicAst.case_info) := let (ci_ind, ci_npar, ci_relevance) := ci in let (ci_ind', ci_npar', ci_relevance') := ci' in eqb ci_ind ci_ind' && eqb ci_npar ci_npar' && eqb ci_relevance ci_relevance'. | Definition | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | eqb_case_info | 685 |
#[global, program] : ReflectEq case_info := {| eqb := eqb_case_info |}. | Instance | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | reflect_case_info | 686 |
{term : Type} (eqterm : term -> term -> bool) (x y : BasicAst.context_decl term) := let (na, b, ty) := x in let (na', b', ty') := y in eqb na na' && eq_option eqterm b b' && eqterm ty ty'. | Definition | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | eqb_context_decl | 687 |
#[global, program] {term} {Ht : ReflectEq term} : ReflectEq (BasicAst.context_decl term) := {| eqb := eqb_context_decl eqb |}. | Instance | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | eq_decl_reflect | 688 |
r r' := match r, r' with | Finite, Finite => true | CoFinite, CoFinite => true | BiFinite, BiFinite => true | _, _ => false end. | Definition | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | eqb_recursivity_kind | 689 |
ReflectEq recursivity_kind. | Instance | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | reflect_recursivity_kind | 690 |
x y := match x, y with | ConstraintType.Le n, ConstraintType.Le m => Z.eqb n m | ConstraintType.Eq, ConstraintType.Eq => true | _, _ => false end. | Definition | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | eqb_ConstraintType | 691 |
ReflectEq ConstraintType.t. | Instance | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | reflect_ConstraintType | 692 |
#[global, program] : ReflectEq Int.Z_as_Int.t := { eqb := Z.eqb }. Next Obligation. apply (reflect_reflectProp_2 Z.eqb_spec). Qed. | Instance | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | Z_as_int | 693 |
{s s'} {c} (H H' : string_compare s s' = c) : H = H'. Proof. apply uip. Qed. | Lemma | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | string_compare_irrel | 694 |
{x y : nat} (l l' : x <= y) : l = l'. Proof. induction l using le_ind_prop; depelim l'. - reflexivity. - lia. - lia. - f_equal. apply IHl. Qed. | Lemma | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | nat_le_irrel | 695 |
{x y : Level.t} (l l' : Level.lt_ x y) : l = l'. Proof. induction l using level_lt_ind_dep; depelim l'; auto. - now replace l with l0 by apply uip. - f_equal. apply nat_le_irrel. Qed. | Lemma | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | lt_level_irrel | 696 |
{x y} (l l' : ConstraintType.lt_ x y) : l = l'. Proof. induction l using constraint_type_lt_ind_dep; depelim l'; auto. f_equal. apply uip. Qed. | Lemma | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | constraint_type_lt_level_irrel | 697 |
(x y : UnivConstraint.t) (l l' : UnivConstraint.lt_ x y) : l = l'. Proof. revert l'. induction l using constraint_lt_ind_dep. - intros l'. depelim l'. now rewrite (lt_level_irrel l l4). now elim (irreflexivity (R:=ConstraintType.lt) l4). now elim (irreflexivity l4). - intros l'; depelim l'. now elim (irreflexivity (R:=ConstraintType.lt) l). now rewrite (constraint_type_lt_level_irrel l l4). now elim (irreflexivity l4). - intros l'; depelim l'. now elim (irreflexivity l). now elim (irreflexivity l). now rewrite (lt_level_irrel l l4). Qed. | Lemma | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | constraint_lt_irrel | 698 |
(x y : LevelSet.Raw.t) := match x, y with | LevelSet.Raw.Leaf, LevelSet.Raw.Leaf => true | LevelSet.Raw.Node h l o r, LevelSet.Raw.Node h' l' o' r' => eqb h h' && levels_tree_eqb l l' && eqb o o' && levels_tree_eqb r r' | _, _ => false end. | Fixpoint | common | From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Universes Kernames. Require Import ssreflect. From Equations Require Import Equations. Require Import RelationClasses. Import LevelSet.Raw. Import ConstraintSet.Raw. | common\theories\Reflect.v | levels_tree_eqb | 699 |
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