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#[global, program] : ReflectEq LevelSet.Raw.t := {| eqb := levels_tree_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 | levels_tree_reflect | 700 |
x y := eqb (LevelSet.this x) (LevelSet.this y). | 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_LevelSet | 701 |
(x : t) (o o' : Ok x) : o = o'. Proof. unfold Ok in *. induction o. - now depelim o'. - depelim o'. f_equal; auto. clear -l0 l2. red in l0, l2. extensionality y. extensionality inl. apply lt_level_irrel. extensionality y. extensionality inl. apply lt_level_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 | ok_irrel | 702 |
#[global,program] : ReflectEq LevelSet.t := {| eqb := eqb_LevelSet |}. | 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_LevelSet | 703 |
(x y : t) := match x, y with | ConstraintSet.Raw.Leaf, ConstraintSet.Raw.Leaf => true | ConstraintSet.Raw.Node h l o r, ConstraintSet.Raw.Node h' l' o' r' => eqb h h' && cs_tree_eqb l l' && eqb o o' && cs_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 | cs_tree_eqb | 704 |
#[global,program] : ReflectEq ConstraintSet.Raw.t := {| eqb := cs_tree_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 | cs_tree_reflect | 705 |
x y := eqb (ConstraintSet.this x) (ConstraintSet.this y). | 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_ConstraintSet | 706 |
(x : t) (o o' : Ok x) : o = o'. Proof. unfold Ok in *. induction o. - now depelim o'. - depelim o'. f_equal; auto. clear -l0 l2. red in l0, l2. extensionality y. extensionality inl. apply constraint_lt_irrel. extensionality y. extensionality inl. apply constraint_lt_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 | ok_irrel | 707 |
#[global,program] : ReflectEq ConstraintSet.t := {| eqb := eqb_ConstraintSet |}. | 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_ConstraintSet | 708 |
x y := match x, y with | Monomorphic_ctx, Monomorphic_ctx => true | Polymorphic_ctx cx, Polymorphic_ctx cy => eqb cx cy | _, _ => 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_sorts_decl | 709 |
#[global,program] : ReflectEq universes_decl := {| eqb := eqb_sorts_decl |}. | 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_universes_decl | 710 |
x y := match x, y with | IntoSProp, IntoSProp | IntoPropSProp, IntoPropSProp | IntoSetPropSProp, IntoSetPropSProp | IntoAny, IntoAny => 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_allowed_eliminations | 711 |
#[global,program] : ReflectEq allowed_eliminations := {| eqb := eqb_allowed_eliminations |}. | 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_allowed_eliminations | 712 |
x y := match x, y with | Variance.Irrelevant, Variance.Irrelevant | Variance.Covariant, Variance.Covariant | Variance.Invariant, Variance.Invariant => 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_Variance | 713 |
#[global,program] : ReflectEq Variance.t := {| eqb := eqb_Variance |}. | 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_Variance | 714 |
forall {A B}, string -> (A -> B) -> A -> B := fun A B s f x => f x. | Definition | common | From Coq Require Import Program ssreflect ssrbool. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils. Import bytestring. | common\theories\Transform.v | time | 715 |
env term := env * term. | Definition | common | From Coq Require Import Program ssreflect ssrbool. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils. Import bytestring. | common\theories\Transform.v | program | 716 |
pre (transform : forall p : program, pre p -> program') (obseq : forall p : program, pre p -> program' -> value -> value' -> Prop) := forall p v (pr : pre p), eval p v -> let p' := transform p pr in exists v', eval' p' v' /\ obseq p pr p' v v'. | Definition | common | From Coq Require Import Program ssreflect ssrbool. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils. Import bytestring. | common\theories\Transform.v | preserves_eval | 717 |
{ name : string; pre : program -> Prop; transform : forall p : program, pre p -> program'; post : program' -> Prop; correctness : forall input (p : pre input), post (transform input p); obseq : forall p : program, pre p -> program' -> value -> value' -> Prop; preservation : preserves_eval pre transform obseq }. | Record | common | From Coq Require Import Program ssreflect ssrbool. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils. Import bytestring. | common\theories\Transform.v | t | 718 |
(x : t) (p : program) (pr : pre x p) : program' := time x.(name) (fun _ => x.(transform) p pr) tt. | Definition | common | From Coq Require Import Program ssreflect ssrbool. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils. Import bytestring. | common\theories\Transform.v | run | 719 |
env term eval eval' := t env env term term term term eval eval'. | Definition | common | From Coq Require Import Program ssreflect ssrbool. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils. Import bytestring. | common\theories\Transform.v | self_transform | 720 |
(b : bool) : Z := match b with | true => 1 | false => 0 end. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | Z_of_bool | 721 |
level (_ : string) | lvar (_ : nat). | Inductive | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | t_ | 722 |
t_. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | t | 723 |
t -> t -> Prop := fun x y => match x, y with | level _, lvar _ => True | level s, level s' => StringOT.lt s s' | lvar n, lvar n' => n < n' | lvar _, level _ => False end. Global Instance lt_strorder : StrictOrder lt. split. - intros [s|n] H; cbn in H. now eapply irreflexivity in H. lia. - intros [s1|n1] [s2|n2] [s3|n3]; cbn; intuition. eapply transitivity; eassumption. Qed. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | lt | 724 |
Transitive lt := _. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | lt_trans | 725 |
Proper (Logic.eq ==> Logic.eq ==> iff) lt. intros x y [] z t []; reflexivity. Qed. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | lt_compat | 726 |
t -> t -> comparison := fun x y => match x, y with | level _, lvar _ => Datatypes.Lt | level s, level s' => string_compare s s' | lvar n, lvar n' => Nat.compare n n' | lvar _, level _ => Datatypes.Gt end. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | compare | 727 |
forall x y : t, CompareSpec (x = y) (lt x y) (lt y x) (compare x y). intros [s|n] [s'|n']; cbn; try now constructor. - eapply CompareSpec_Proper. 2-4: reflexivity. 2: apply CompareSpec_string. split; congruence. - eapply CompareSpec_Proper. 2-4: reflexivity. 2: apply PeanoNat.Nat.compare_spec. split; congruence. Qed. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | compare_spec | 728 |
(x : t) : compare x x = Datatypes.Eq. Proof. destruct x => /= //. rewrite string_compare_eq //. now rewrite Nat.compare_refl. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | compare_refl | 729 |
forall x y : t, {x = y} + {x <> y}. intros [s|n] [s'|n']; try now constructor. destruct (Classes.eq_dec s s'); [left|right]; congruence. destruct (PeanoNat.Nat.eq_dec n n'); [left|right]; congruence. Defined. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | eq_dec | 730 |
forall x y : t, compare x y = Datatypes.Eq -> x = y. Proof. intros x y. destruct (compare_spec x y) => //. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | compare_eq | 731 |
forall x y : t, (compare y x) = CompOpp (compare x y). Proof. induction x; destruct y; simpl; auto. apply StringOT.compare_sym. apply PeanoNat.Nat.compare_antisym. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | compare_sym | 732 |
forall c (x y z : t), (x?=y)%var_level = c -> (y?=z)%var_level = c -> (x?=z)%var_level = c. Proof. intros c x y z. destruct (compare_spec x y) => <-; subst. destruct (compare_spec y z); auto. destruct (compare_spec y z); auto; try congruence. destruct (compare_spec x z); auto; try congruence. subst. exfalso. eapply irreflexivity. etransitivity; [exact H|exact H0]. exfalso. eapply irreflexivity. etransitivity; [exact H|]. eapply transitivity; [exact H0|exact H1]. destruct (compare_spec y z); auto; try congruence. destruct (compare_spec x z); auto; try congruence. subst. exfalso. eapply irreflexivity. etransitivity; [exact H|exact H0]. exfalso. eapply irreflexivity. etransitivity; [exact H|]. eapply transitivity; [exact H1|exact H0]. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | compare_trans | 733 |
(l : t) : Level.t := match l with | level s => Level.level s | lvar n => Level.lvar n end. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | to_noprop | 734 |
(l : t) : Level.t := to_noprop l. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | to_level | 735 |
| gc_le : VariableLevel.t -> Z -> VariableLevel.t -> t_ | gc_lt_set_level : nat -> string -> t_ | gc_le_set_var : nat -> nat -> t_ | gc_le_level_set : string -> nat -> t_ | gc_le_var_set : nat -> nat -> t_. | Inductive | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | t_ | 736 |
Set := t_. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | t | 737 |
t -> t -> Prop := Logic.eq. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | eq | 738 |
@eq_refl t. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | eq_refl | 739 |
@eq_sym t. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | eq_sym | 740 |
@eq_trans t. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | eq_trans | 741 |
RelationClasses.Equivalence eq := _. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | eq_equiv | 742 |
forall x y : t, {eq x y} + {~ eq x y}. unfold eq. decide equality. all: try apply VariableLevel.eq_dec. apply Z.eq_dec. all:apply Classes.eq_dec || apply Peano_dec.eq_nat_dec. Defined. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | eq_dec | 743 |
(x : t) (y : t) : comparison := match x, y with | gc_le u n v, gc_le u' n' v' => compare_cont (VariableLevel.compare u u') (compare_cont (Z.compare n n') (VariableLevel.compare v v')) | _, gc_le _ _ _ => Datatypes.Lt | gc_le _ _ _, _ => Gt | gc_lt_set_level n s, gc_lt_set_level n' s' => compare_cont (Nat.compare n n') (string_compare s s') | _, gc_lt_set_level _ _ => Datatypes.Lt | gc_lt_set_level _ _, _ => Gt | gc_le_set_var n s, gc_le_set_var n' s' => compare_cont (Nat.compare n n') (Nat.compare s s') | _, gc_le_set_var _ _ => Datatypes.Lt | gc_le_set_var _ _, _ => Datatypes.Gt | gc_le_level_set s n, gc_le_level_set s' n' => compare_cont (Nat.compare n n') (string_compare s s') | _, gc_le_level_set _ _ => Datatypes.Lt | gc_le_level_set _ _, _ => Datatypes.Gt | gc_le_var_set n k, gc_le_var_set n' k' => compare_cont (Nat.compare n n') (Nat.compare k k') end. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | compare | 744 |
(a b : t): compare b a = CompOpp (compare a b). Proof. revert b. destruct a, b; try easy; cbn; rewrite !compare_cont_CompOpp -?VariableLevel.compare_sym ?Zcompare_antisym -?PeanoNat.Nat.compare_antisym -?StringOT.compare_sym //. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | compare_sym | 745 |
forall c (x y z : nat), (x?=y)%nat = c -> (y?=z)%nat = c -> (x?=z)%nat = c. Proof. intros c x y z. destruct (Nat.compare_spec x y); subst => // <-; destruct (Nat.compare_spec y z); subst => //; destruct (Nat.compare_spec x z); subst => //; try lia. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | nat_compare_trans | 746 |
forall c (x y z : Z), (x?=y)%Z = c -> (y?=z)%Z = c -> (x?=z)%Z = c. Proof. intros c x y z. destruct (Z.compare_spec x y); subst => // <-; destruct (Z.compare_spec y z); subst => //; destruct (Z.compare_spec x z); subst => //; try lia. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | Z_compare_trans | 747 |
forall (x y : nat), (x?=y)%nat = Datatypes.Eq -> x = y. Proof. intros x y. destruct (Nat.compare_spec x y) => //. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | nat_compare_eq | 748 |
forall c (x y z : t), (x?=y) = c -> (y?=z) = c -> (x?=z) = c. Proof. intros c x y z. destruct x, y, z; cbn; try repeat apply compare_cont_trans; eauto using VariableLevel.compare_trans, VariableLevel.compare_eq; try congruence. all:eauto using StringOT.compare_trans, nat_compare_trans, nat_compare_eq. intros. eapply compare_cont_trans; tea; eauto using VariableLevel.compare_trans, VariableLevel.compare_eq, Z.compare_eq, Z_compare_trans. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | compare_trans | 749 |
(x y : t) : x ?= y = Datatypes.Eq -> x = y. Proof. destruct x, y; cbn => //. destruct (VariableLevel.compare t0 t2) eqn:e => /= //. apply VariableLevel.compare_eq in e. subst. cbn. destruct (Z.compare z z0) eqn:e' => /= //. apply Z.compare_eq in e'; subst. intros H; apply VariableLevel.compare_eq in H; subst. reflexivity. destruct (Nat.compare_spec n n0) => /= //; subst. rewrite StringOT.compare_eq => -> //. destruct (Nat.compare_spec n n1) => /= //; subst. destruct (Nat.compare_spec n0 n2) => /= //; subst => //. destruct (Nat.compare_spec n n0) => /= //; subst. rewrite (StringOT.compare_eq) => -> //. destruct (Nat.compare_spec n n1) => /= //; subst. destruct (Nat.compare_spec n0 n2) => /= //; subst => //. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | compare_eq | 750 |
(x : t) : x ?= x = Datatypes.Eq. Proof. destruct x => /= //; rewrite ?VariableLevel.compare_refl /= ?Z.compare_refl /= ?Nat.compare_refl ?string_compare_eq //. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | compare_refl | 751 |
(x y : t) := (x ?= y = Datatypes.Lt). | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | lt | 752 |
(x y z : t) : lt x y -> lt y z -> lt x z. Proof. apply compare_trans. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | lt_trans | 753 |
(x y : t) : lt x y -> ~ eq x y. Proof. intros lt eq. red in eq. subst x. red in lt. rewrite compare_refl in lt => //. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | lt_not_eq | 754 |
StrictOrder lt. Proof. split. - intros x hlt. apply lt_not_eq in hlt. now apply hlt. - red. eapply lt_trans. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | lt_strorder | 755 |
Proper (eq ==> eq ==> iff) lt. Proof. intros x y ? ? ? ?. now rewrite H H0. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | lt_compat | 756 |
forall x y : t, CompSpec eq lt x y (compare x y). Proof. intros x y. destruct (x ?= y) eqn:e; constructor. - now eapply compare_eq in e. - now red. - red. rewrite compare_sym e //. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | compare_spec | 757 |
v (gc : GoodConstraint.t) : bool := match gc with | gc_le l z l' => (Z.of_nat (val v l) <=? Z.of_nat (val v l') - z)%Z | gc_lt_set_level k l => k <? Pos.to_nat (v.(valuation_mono) l) | gc_le_set_var k l => k <=? v.(valuation_poly) l | gc_le_level_set l k => Pos.to_nat (v.(valuation_mono) l) <=? k | gc_le_var_set l k => v.(valuation_poly) l <=? k end. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | satisfies | 758 |
x y : Prop := LevelSet.Equal x.1 y.1 /\ GoodConstraintSet.Equal x.2 y.2. Infix "=_gcs" := gcs_equal (at level 200). Notation "(=_gcs)" := gcs_equal (at level 0). Global Instance proper_pair_levels_gcs : Proper ((=_lset) ==> GoodConstraintSet.Equal ==> (=_gcs)) (@pair LevelSet.t GoodConstraintSet.t). Proof. intros l l' eq gcs gcs' eq'. split; cbn; auto. Qed. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gcs_equal | 759 |
x y := GoodConstraintSet.add y (GoodConstraintSet.singleton x). | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | GoodConstraintSet_pair | 760 |
x y z : GoodConstraintSet.In x (GoodConstraintSet_pair y z) -> x = y \/ x = z. Proof. intro H. apply GoodConstraintSetFact.add_iff in H. destruct H; [intuition|]. apply GoodConstraintSetFact.singleton_1 in H. intuition. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | GoodConstraintSet_pair_In | 761 |
x y z : GCS.In x (GoodConstraintSet_pair y z) <-> x = y \/ x = z. Proof. split; first apply: GoodConstraintSet_pair_In. move=> [->|->]; apply/GCS.add_spec; by [right; apply/GCS.singleton_spec| left]. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | GCS_pair_spec | 762 |
v : GoodConstraintSet.t -> bool := GoodConstraintSet.for_all (gc_satisfies0 v). | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_satisfies | 763 |
ctrs : Prop := exists v, gc_satisfies v ctrs. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_consistent | 764 |
v gc1 gc2 : (gc_satisfies0 v gc1 /\ gc_satisfies0 v gc2) <-> gc_satisfies v (GoodConstraintSet_pair gc1 gc2). Proof. unfold gc_satisfies, GoodConstraintSet_pair. rewrite [is_true (GoodConstraintSet.for_all _ _)]GoodConstraintSet.for_all_spec. split. - intros [sat1 sat2] x. rewrite GoodConstraintSet.add_spec. move=> [->|] //. rewrite GoodConstraintSet.singleton_spec => -> //. - intros ha. split; apply ha; rewrite GoodConstraintSet.add_spec; rewrite GoodConstraintSet.singleton_spec; auto. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_satisfies_pair | 765 |
`{checker_flags} (uc : UnivConstraint.t) : option GoodConstraintSet.t := let empty := Some GoodConstraintSet.empty in let singleton := fun x => Some (GoodConstraintSet.singleton x) in let pair := fun x y => Some (GoodConstraintSet_pair x y) in match uc with | (Level.lzero, Le z, r) => match Z.compare z 0 with | Datatypes.Eq => empty | Datatypes.Lt => empty | Datatypes.Gt => match r with | Level.lzero => None | Level.level s => singleton (gc_lt_set_level (Z.to_nat (z - 1)) s) | Level.lvar n => singleton (gc_le_set_var (Z.to_nat z) n) end end | (Level.lzero, Eq, Level.lzero) => empty | (Level.lzero, Eq, Level.level _) => None | (Level.lzero, Eq, Level.lvar n) => singleton (gc_le_var_set n 0%nat) | (Level.level l, Le z, Level.lzero) => if (z <=? 0)%Z then singleton (gc_le_level_set l (Z.to_nat (Z.abs z))) else None | (Level.level l, Le z, Level.level l') => singleton (gc_le (level l) z (level l')) | (Level.level l, Le z, Level.lvar n) => singleton (gc_le (level l) z (lvar n)) | (Level.level _, Eq, Level.lzero) => None | (Level.level l, Eq, Level.level l') => pair (gc_le (level l) 0 (level l')) (gc_le (level l') 0 (level l)) | (Level.level l, Eq, Level.lvar n) => pair (gc_le (level l) 0 (lvar n)) (gc_le (lvar n) 0 (level l)) | (Level.lvar n, Le z, Level.lzero) => if (z <=? 0)%Z then singleton (gc_le_var_set n (Z.to_nat (Z.abs z))) else None | (Level.lvar n, Le z, Level.level l) => singleton (gc_le (lvar n) z (level l)) | (Level.lvar n, Le z, Level.lvar n') => singleton (gc_le (lvar n) z (lvar n')) | (Level.lvar n, Eq, Level.lzero) => singleton (gc_le_var_set n 0) | (Level.lvar n, Eq, Level.level l) => pair (gc_le (lvar n) 0%Z (level l)) (gc_le (level l) 0%Z (lvar n)) | (Level.lvar n, Eq, Level.lvar n') => pair (gc_le (lvar n) 0 (lvar n')) (gc_le (lvar n') 0 (lvar n)) end. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_of_constraint | 766 |
v c : gc_satisfies0 v c <-> gc_satisfies v (GoodConstraintSet.singleton c). Proof using Type. split. - intros H; unfold gc_satisfies. eapply GoodConstraintSet.for_all_spec; auto. proper. intros x xin. eapply GoodConstraintSet.singleton_spec in xin. now subst. - unfold gc_satisfies. intros gc. eapply GoodConstraintSet.for_all_spec in gc; auto. 2:proper. specialize (gc c). rewrite -> GoodConstraintSet.singleton_spec in gc. now apply gc. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_satisfies_singleton | 767 |
v uc : satisfies0 v uc <-> on_Some (gc_satisfies v) (gc_of_constraint uc). Proof using Type. split. - destruct 1; destruct l, l'; try constructor. all:unfold gc_of_constraint. all: cbn -[GoodConstraintSet_pair] in *. all: cbn -[GoodConstraintSet_pair]; try reflexivity. all: rewrite ?if_true_false; repeat toProp ; try lia. all: try solve [destruct (Z.compare_spec z 0); simpl; try constructor; lia]. destruct (Z.compare_spec z 0); simpl; try constructor; try lia. apply gc_satisfies_singleton. simpl. apply Nat.ltb_lt. lia. all:try (destruct (Z.compare_spec z 0); simpl; try constructor; try lia; apply gc_satisfies_singleton; simpl; try (apply Nat.ltb_lt||apply Nat.leb_le); lia). all:try (destruct (Z.leb_spec z 0); simpl; try constructor; try lia; apply gc_satisfies_singleton; simpl; apply Nat.leb_le; lia). all: try (apply gc_satisfies_pair; split; cbn; toProp; try lia). all: (apply gc_satisfies_singleton; cbn; toProp; lia). - destruct uc as [[[] []] []]; intro H; constructor. all: cbn -[GoodConstraintSet_pair] in *; try contradiction. all: rewrite -> ?if_true_false in *; cbn -[GoodConstraintSet_pair] in *; try contradiction; repeat toProp; try lia. all:try (destruct (Z.compare_spec z 0); simpl in H; auto; try lia; apply gc_satisfies_singleton in H; simpl in H; (apply Nat.ltb_lt in H || apply Nat.leb_le in H); try lia). all:try (destruct (Z.leb_spec z 0); simpl in H; auto; try lia; apply gc_satisfies_singleton in H; simpl in H; (apply Nat.ltb_lt in H || apply Nat.leb_le in H); try lia). all:(try apply gc_satisfies_singleton in H; cbn in H; try toProp H); try lia. all: apply gc_satisfies_pair in H; destruct H as [H1 H2]; cbn in *; repeat toProp; try lia. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_of_constraint_spec | 768 |
uc (S : option GoodConstraintSet.t) := S1 <- S ;; S2 <- gc_of_constraint uc ;; ret (GoodConstraintSet.union S1 S2). | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | add_gc_of_constraint | 769 |
(ctrs : ConstraintSet.t) : option GoodConstraintSet.t := ConstraintSet.fold add_gc_of_constraint ctrs (Some GoodConstraintSet.empty). | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_of_constraints | 770 |
v ctrs : satisfies v ctrs <-> on_Some (gc_satisfies v) (gc_of_constraints ctrs). Proof using Type. unfold gc_satisfies, satisfies, ConstraintSet.For_all, gc_of_constraints. set (S := GoodConstraintSet.empty). rewrite ConstraintSet.fold_spec. etransitivity. eapply iff_forall. intro; eapply imp_iff_compat_r. eapply ConstraintSetFact.elements_iff. set (l := ConstraintSet.elements ctrs). simpl. transitivity ((forall uc, InA Logic.eq uc l -> satisfies0 v uc) /\ (forall gc, GoodConstraintSet.In gc S -> gc_satisfies0 v gc)). { intuition. inversion H0. } clearbody S; revert S; induction l; intro S; cbn. - split. + intro. apply GoodConstraintSetFact.for_all_1. intros x y []; reflexivity. intro; apply H. + intros HS. split. intros ux H; inversion H. apply GoodConstraintSetFact.for_all_2. intros x y []; reflexivity. assumption. - split. + intros [H1 H2]. assert (HH : on_Some (gc_satisfies v) (gc_of_constraint a)). { apply gc_of_constraint_spec, H1. now constructor. } case_eq (gc_of_constraint a); [|intro e; rewrite e in HH; contradiction]. intros X HX; rewrite HX in HH; cbn in HH. apply IHl. split. * intros uc H0. apply H1. now apply InA_cons_tl. * intros gc H0. apply GoodConstraintSetFact.union_1 in H0. induction H0. intuition. apply GoodConstraintSetFact.for_all_2 in HH. apply HH. assumption. intros x y []; reflexivity. + intros HH. case_eq (gc_of_constraint a). * intros X HX; rewrite HX in HH; cbn in HH. destruct (proj2 (IHl _) HH) as [IH1 IH2]. clear IHl HH. split. intuition. apply InA_cons in H. induction H. subst. apply gc_of_constraint_spec. rewrite HX. cbn. apply GoodConstraintSetFact.for_all_1. intros x y []; reflexivity. intros gc Hgc. apply IH2. now apply GoodConstraintSetFact.union_3. firstorder. intros gc Hgc. apply IH2. now apply GoodConstraintSetFact.union_2. * intro HX; rewrite HX in HH. apply False_rect. revert HH; clear. induction l. inversion 1. assumption. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_of_constraints_spec | 771 |
ctrs : consistent ctrs <-> on_Some gc_consistent (gc_of_constraints ctrs). Proof using Type. split. - intros [v H]. apply gc_of_constraints_spec in H. destruct (gc_of_constraints ctrs); cbn in *. exists v. assumption. contradiction. - case_eq (gc_of_constraints ctrs); cbn; [|contradiction]. intros ctrs' e HC. destruct HC as [v Hv]. exists v. apply gc_of_constraints_spec. now rewrite e; cbn. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_consistent_iff | 772 |
n ctrs (u u' : Universe.t) := forall v, gc_satisfies v ctrs -> (Z.of_nat (val v u) <= Z.of_nat (val v u') - n)%Z. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_leq0_universe_n | 773 |
n ctrs (u u' : Universe.t) := if check_univs then gc_leq0_universe_n n ctrs u u' else True. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_leq_universe_n | 774 |
φ (u u' : Universe.t) := forall v, gc_satisfies v φ -> val v u = val v u'. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_eq0_universe | 775 |
φ (u u' : Universe.t) := if check_univs then gc_eq0_universe φ u u' else True. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_eq_universe | 776 |
gc_leq0_universe_n 0. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_leq0_universe | 777 |
gc_leq0_universe_n 1. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_lt0_universe | 778 |
gc_leq_universe_n 0. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_leq_universe | 779 |
gc_leq_universe_n 1. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_lt_universe | 780 |
(n: Z) ctrs u u' : leq0_universe_n n ctrs u u' <-> on_Some_or_None (fun ctrs => gc_leq0_universe_n n ctrs u u') (gc_of_constraints ctrs). Proof. split. - intro H. case_eq (gc_of_constraints ctrs). + intros ctrs' e. cbn. unfold_univ_rel0. apply H. apply gc_of_constraints_spec. rewrite e. assumption. + intro; exact I. - case_eq (gc_of_constraints ctrs); cbn. + intros ctrs' e H. unfold_univ_rel0. apply H. apply gc_of_constraints_spec in Hv. rewrite e in Hv; assumption. + intros e _. unfold_univ_rel0. apply gc_of_constraints_spec in Hv. rewrite e in Hv; contradiction. Defined. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_leq0_universe_n_iff | 781 |
ctrs u u': leq0_universe_n 0 ctrs u u' <-> on_Some_or_None (fun ctrs => gc_leq0_universe_n 0 ctrs u u') (gc_of_constraints ctrs). Proof using Type. apply gc_leq0_universe_n_iff. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_leq0_universe_iff | 782 |
ctrs u u' : eq0_universe ctrs u u' <-> on_Some_or_None (fun ctrs => gc_eq0_universe ctrs u u') (gc_of_constraints ctrs). Proof. split. - intro H. case_eq (gc_of_constraints ctrs). + intros ctrs' e. cbn. unfold_univ_rel0. apply H. apply gc_of_constraints_spec. rewrite e. assumption. + intro; exact I. - case_eq (gc_of_constraints ctrs); cbn. + intros ctrs' e H. unfold_univ_rel0. apply H. apply gc_of_constraints_spec in Hv. rewrite e in Hv; assumption. + intros e _. unfold_univ_rel0. apply gc_of_constraints_spec in Hv. rewrite e in Hv; contradiction. Defined. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_eq0_universe_iff | 783 |
n ctrs u u' : leq_universe_n n ctrs u u' <-> on_Some_or_None (fun ctrs => gc_leq_universe_n n ctrs u u') (gc_of_constraints ctrs). Proof using Type. unfold_univ_rel. apply gc_leq0_universe_n_iff. destruct (gc_of_constraints ctrs); reflexivity. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_leq_universe_n_iff | 784 |
ctrs u u' : leq_universe ctrs u u' <-> on_Some_or_None (fun ctrs => gc_leq_universe ctrs u u') (gc_of_constraints ctrs). Proof using Type. unfold_univ_rel. apply gc_leq0_universe_iff. destruct (gc_of_constraints ctrs); reflexivity. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_leq_universe_iff | 785 |
ctrs u u' : eq_universe ctrs u u' <-> on_Some_or_None (fun ctrs => gc_eq_universe ctrs u u') (gc_of_constraints ctrs). Proof using Type. unfold_univ_rel. apply gc_eq0_universe_iff. destruct (gc_of_constraints ctrs); reflexivity. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_eq_universe_iff | 786 |
t. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | universes_graph | 787 |
universes_graph := (VSet.singleton lzero, EdgeSet.empty, lzero). | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | init_graph | 788 |
invariants init_graph. Proof. repeat split; cbn in *. 1-2: inversion H. sets. apply VSet.singleton_spec in H. subst. exists (pathOf_refl _ _). simpl. sq. lia. Defined. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | init_graph_invariants | 789 |
Level.t -> LevelSet.t -> Prop := LevelSet.In. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | declared | 790 |
(uctx : ContextSet.t) := ConstraintSet.For_all (declared_cstr_levels uctx.1) uctx.2. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | uctx_invariants | 791 |
(uctx : ContextSet.t) := LevelSet.In Level.lzero uctx.1 /\ uctx_invariants uctx. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | global_uctx_invariants | 792 |
(uctx : VSet.t * GoodConstraintSet.t) := VSet.In lzero uctx.1 /\ GoodConstraintSet.For_all (fun gc => match gc with | GoodConstraint.gc_le l z l' => VSet.In (vtn l) uctx.1 /\ VSet.In (vtn l') uctx.1 | GoodConstraint.gc_lt_set_level _ n | GoodConstraint.gc_le_level_set n _ => VSet.In (Level.level n) uctx.1 | GoodConstraint.gc_le_var_set n _ | GoodConstraint.gc_le_set_var _ n => VSet.In (Level.lvar n) uctx.1 end) uctx.2. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | global_gc_uctx_invariants | 793 |
`{checker_flags} (uctx : ContextSet.t) : option (VSet.t * GoodConstraintSet.t) := ctrs <- gc_of_constraints uctx.2 ;; ret (uctx.1, ctrs). | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_of_uctx | 794 |
`{checker_flags} uctx gctx : gc_of_uctx uctx = Some gctx -> gc_of_constraints uctx.2 = Some gctx.2. Proof. rewrite/gc_of_uctx; case: (gc_of_constraints _)=> //= ? [=] <- //. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_of_uctx_of_constraints | 795 |
`{checker_flags} uctx gcstrs : gc_of_constraints uctx.2 = Some gcstrs -> gc_of_uctx uctx = Some (uctx.1, gcstrs). Proof. rewrite /gc_of_uctx=> -> //=. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_of_constraints_of_uctx | 796 |
`{cf:checker_flags} ctrs0 ctrs gc (HH : gc_of_constraints ctrs0 = Some ctrs) : GoodConstraintSet.In gc ctrs <-> ConstraintSet.Exists (fun e => on_Some (GoodConstraintSet.In gc) (gc_of_constraint e)) ctrs0. Proof. unfold gc_of_constraints in HH. rewrite ConstraintSet.fold_spec in HH. transitivity ((exists ctr, In ctr (ConstraintSet.elements ctrs0) /\ on_Some (GoodConstraintSet.In gc) (gc_of_constraint ctr)) \/ GoodConstraintSet.In gc GoodConstraintSet.empty). 2:{ split. - intros [[ctr [H1 H2]]|H]. exists ctr. split. apply ConstraintSetFact.elements_iff, InA_In_eq; tas. tas. now apply GoodConstraintSetFact.empty_iff in H. - intros [ctr H]. left. exists ctr. split. apply InA_In_eq, ConstraintSetFact.elements_1, H. apply H. } revert HH; generalize GoodConstraintSet.empty. induction (ConstraintSet.elements ctrs0). - cbn. intros X HH. apply some_inj in HH; subst. firstorder. - intros X HH. simpl in HH. unfold add_gc_of_constraint at 2 in HH. simpl in HH. case_eq (gc_of_constraint a). + intros Y HY. rewrite HY in HH. apply IHl in HH. etransitivity. exact HH. etransitivity. apply or_iff_compat_l. apply GoodConstraintSet.union_spec. split. * intros [[ctr H]|[H|H]]. left. exists ctr. intuition. intuition. left. exists a. intuition. rewrite HY; tas. * intros [[ctr [[H1|H1] H2]]|H]. subst a. right. right. rewrite HY in H2; tas. left. exists ctr. intuition. right. left; tas. + intro eq; rewrite eq in HH; simpl in HH. apply False_rect. clear -HH. induction l. * discriminate HH. * simpl in HH. apply IHl. apply HH. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_of_constraint_iff | 797 |
`{cf:checker_flags} uctx uctx' (H : gc_of_uctx uctx = Some uctx') : global_uctx_invariants uctx -> global_gc_uctx_invariants uctx'. Proof. intros [Hi0 Hi]. unfold gc_of_uctx in H. case_eq (gc_of_constraints uctx.2); [|intro eq; rewrite eq in H; discriminate]. intros ctrs eq; rewrite eq in H; apply some_inj in H. subst uctx'. split; simpl. - apply Hi0. - red in Hi. destruct uctx as [levels ctrs0]; cbn in *. intros gc Hgc. eapply gc_of_constraint_iff in Hgc; tea. destruct Hgc as [e [He HH]]. specialize (Hi e He); cbn in Hi. clear -Hi HH. destruct e as [[l ct] l']; simpl in Hi. destruct l, ct, l'; cbn in HH; destruct prop_sub_type; cbn in HH. change VSet.In with LevelSet.In. all:repeat match goal with | HH : context [ (?z ?= 0)%Z ] |- _ => destruct (Z.compare_spec z 0); simpl in HH; auto | HH : context [ (?z <=? 0)%Z ] |- _ => destruct (Z.leb_spec z 0); simpl in HH; auto | HH : False |- _ => contradiction HH | HH : GoodConstraintSet.In ?A GoodConstraintSet.empty |- _ => apply GoodConstraintSetFact.empty_iff in HH; contradiction HH | HH : GoodConstraintSet.In ?A (GoodConstraintSet.singleton ?B) |- _ => apply GoodConstraintSetFact.singleton_1 in HH; subst gc | HH : GoodConstraintSet.In ?A (GoodConstraintSet_pair ?B _) |- _ => apply GoodConstraintSet_pair_In in HH; destruct HH as [HH|HH]; subst gc end. all: try split; try apply Hi; try apply Hi. Qed. | Lemma | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | gc_of_uctx_invariants | 798 |
(l : VariableLevel.t) : EdgeSet.elt := match l with | VariableLevel.level l => (lzero, 1%Z, Level.level l) | VariableLevel.lvar n => (lzero, 0%Z, Level.lvar n) end. | Definition | common | Require Import ssreflect ssrbool OrderedTypeAlt MSetAVL MSetFacts MSetProperties MSetDecide Morphisms. From MetaCoq.Utils Require Import utils wGraph. From MetaCoq.Common Require Import config Universes. From Equations.Prop Require Import DepElim. From Equations Require Import Equations. Import ConstraintType. Import MCMonadNotation. Import VariableLevel GoodConstraint. Module Import wGraph := WeightedGraph Level LevelSet. Import NonEmptySetFacts. Import Nbar Datatypes. Require Import SetoidTactics. From MetaCoq.Utils Require Import MCUtils. | common\theories\uGraph.v | edge_of_level | 799 |
Subsets and Splits