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(check_leqb_sort_gen leqb_level_n). | 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 | check_leqb_sort | 900 |
(check_eqb_sort_gen leqb_level_n). | 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 | check_eqb_sort | 901 |
leqb_level_n_gen (leqb_correct : leqb_level_n_spec_gen leqb_level_n_gen) u : check_eqb_sort_gen leqb_level_n_gen u u. Proof using Type. unfold check_eqb_sort_gen; toProp; left. apply eqb_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 | check_eqb_sort_refl_gen | 902 |
check_eqb_sort_refl_gen _ leqb_level_n_spec. | 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 | check_eqb_sort_refl | 903 |
φ := leq_sort_n_ (fun n u u' => if check_univs then gc_leq0_universe_n n φ u u' else True) 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_sort | 904 |
φ := eq_sort_ (fun u u' => 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_sort | 905 |
leqb_level_n_gen (leqb_correct : leqb_level_n_spec_gen leqb_level_n_gen) (u1 u2 : Sort.t) (Hu1 : levels_declared_sort u1) (Hu2 : levels_declared_sort u2) : check_eqb_sort_gen leqb_level_n_gen u1 u2 <-> gc_eq_sort uctx.2 u1 u2. Proof. unfold check_eqb_sort_gen, gc_eq_sort. destruct u1, u2; cbnr; split; intuition auto. - now destruct prop_sub_type. - eapply check_eqb_universe_spec_gen; eauto; tas. unfold check_eqb_sort_gen, check_eqb_universe_gen in *; cbn in *. unfold check_leqb_universe_gen in *. destruct check_univs; cbnr. unfold eqb at 1, Sort.reflect_eq_sort, Sort.eqb in H. cbn in H. move/orP : H => /= [-> //|] /andP[] /orP[-> //|] H1 /orP[e | H2]. 1: apply NonEmptySetFacts.univ_expr_eqb_true_iff in e as ->. 1: toProp; left; now apply NonEmptySetFacts.univ_expr_eqb_true_iff. toProp; right; now toProp. - toProp; right. eapply check_eqb_universe_spec_gen in H; eauto; tas. unfold check_eqb_universe_gen in *; cbn in *. unfold check_leqb_universe_gen in *. destruct check_univs; [cbn in * | trivial]. move/orP : H => [H | /andP [H1 H2]]. + apply NonEmptySetFacts.univ_expr_eqb_true_iff in H as ->. toProp; toProp; left; now apply NonEmptySetFacts.univ_expr_eqb_true_iff. + toProp; toProp; right; assumption. 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 | check_eqb_sort_spec_gen | 906 |
check_eqb_sort_spec_gen _ leqb_level_n_spec. | 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 | check_eqb_sort_spec | 907 |
G uctx := on_Some (fun uctx => Equal_graph (make_graph uctx) G) (gc_of_uctx 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 | is_graph_of_uctx | 908 |
VSet.t × GoodConstraintSet.t. unfold is_graph_of_uctx, gc_of_uctx in HG. destruct (gc_of_constraints uctx.2) as [ctrs|]. exact (uctx.1, ctrs). contradiction HG. 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 | uctx' | 909 |
l : level_declared l -> gc_level_declared uctx' l. Proof using HG. clear. unfold uctx'. unfold is_graph_of_uctx, gc_of_uctx in HG. destruct (gc_of_constraints uctx.2); [|contradiction HG]. cbn; clear HG. unfold level_declared, gc_level_declared; cbn. destruct l; cbn; trivial; intro. 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 | level_gc_declared_declared | 910 |
e : expr_declared e -> gc_expr_declared uctx' e. Proof using HG level_declared. destruct e as [l b]; cbn; trivial. intro; now apply (level_gc_declared_declared l) in H. 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 | expr_gc_declared_declared | 911 |
(u : Universe.t) : levels_declared u -> gc_levels_declared uctx' u. Proof using HG expr_declared. unfold levels_declared, gc_levels_declared. intros HH e He; specialize (HH e He). now apply expr_gc_declared_declared. 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 | levels_gc_declared_declared | 912 |
leqb_level_n_gen (leqb_correct : leqb_level_n_spec_gen uctx' leqb_level_n_gen) lt e1 u (He1 : expr_declared e1) (Hu : levels_declared u) : leqb_expr_univ_n_gen leqb_level_n_gen ⎩ lt ⎭ e1 u <-> leq0_universe_n ⎩ lt ⎭ uctx.2 (Universe.make e1) u. Proof using HG' Huctx'. etransitivity. eapply (leqb_expr_univ_n_spec_gen G uctx' Huctx' HC' HG'); eauto; tas. - apply expr_gc_declared_declared; tas. - apply levels_gc_declared_declared; tas. - symmetry. etransitivity. apply gc_leq0_universe_n_iff. unfold uctx'; cbn; clear -HG. unfold is_graph_of_uctx, gc_of_uctx in *. destruct (gc_of_constraints uctx.2) as [ctrs|]. reflexivity. contradiction HG. 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 | leqb_univ_expr_n_spec_gen' | 913 |
leqb_univ_expr_n_spec_gen' _ (leqb_level_n_spec _ _ Huctx' HC' HG'). | 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 | leqb_univ_expr_n_spec' | 914 |
leqb_level_n_gen (leqb_correct : leqb_level_n_spec_gen uctx' leqb_level_n_gen) u1 u2 : levels_declared u1 -> levels_declared u2 -> check_leqb_universe_gen leqb_level_n_gen u1 u2 -> leq_universe uctx.2 u1 u2. Proof using HG' Huctx'. unfold check_leqb_universe_gen; intros Hu1 Hu2 H. unfold_univ_rel. cbn in H; toProp H; destruct H as [e | ]. { apply NonEmptySetFacts.univ_expr_eqb_true_iff in e. destruct e; lia. } eapply leqb_universe_n_spec0_gen in H; eauto. eapply gc_leq0_universe_iff; tea. unfold uctx' in *. unfold is_graph_of_uctx, gc_of_uctx in HG. destruct (gc_of_constraints uctx.2). cbn in *. exact H. exact I. Unshelve. all: try eapply levels_gc_declared_declared; eauto. 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 | check_leqb_universe_spec_gen' | 915 |
check_leqb_universe_spec_gen' _ (leqb_level_n_spec _ _ Huctx' HC' HG'). | 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 | check_leqb_universe_spec' | 916 |
leqb_level_n_gen (leqb_correct : leqb_level_n_spec_gen uctx' leqb_level_n_gen) u1 u2 : levels_declared u1 -> levels_declared u2 -> leq_universe uctx.2 u1 u2 -> check_leqb_universe_gen leqb_level_n_gen u1 u2. Proof using HG' Huctx'. intros decl1 decl2. apply levels_gc_declared_declared in decl1. apply levels_gc_declared_declared in decl2. rewrite gc_leq_universe_iff. unfold is_graph_of_uctx, gc_of_uctx in HG. unfold uctx' in *. destruct gc_of_constraints; [cbn in *|contradiction HG]. intros eq. apply <- check_leqb_universe_spec_gen; eauto. exact 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 | check_leqb_universe_complete_gen | 917 |
check_leqb_universe_complete_gen _ (leqb_level_n_spec _ _ Huctx' HC' HG'). | 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 | check_leqb_universe_complete | 918 |
leqb_level_n_gen (leqb_correct : leqb_level_n_spec_gen uctx' leqb_level_n_gen) u1 u2 : levels_declared u1 -> levels_declared u2 -> check_eqb_universe_gen leqb_level_n_gen u1 u2 -> eq_universe uctx.2 u1 u2. Proof using HG' Huctx'. unfold check_eqb_universe_gen; intros Hu1 Hu2 H. unfold_univ_rel. cbn in H; toProp H; destruct H as [e | ]. { apply NonEmptySetFacts.univ_expr_eqb_true_iff in e. destruct e; lia. } apply andb_prop in H. destruct H as [H1 H2]. unshelve eapply leqb_universe_n_spec0_gen in H1; eauto. unshelve eapply leqb_universe_n_spec0_gen in H2; eauto. unfold uctx' in *. unfold is_graph_of_uctx, gc_of_uctx in HG. apply <- eq0_leq0_universe; tea. split; eapply gc_leq0_universe_iff; (destruct (gc_of_constraints uctx.2); [cbn in *|contradiction HG]); tas. all: now eapply levels_gc_declared_declared. 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 | check_eqb_universe_spec_gen' | 919 |
check_eqb_universe_spec_gen' _ (leqb_level_n_spec _ _ Huctx' HC' HG'). | 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 | check_eqb_universe_spec' | 920 |
leqb_level_n_gen (leqb_correct : leqb_level_n_spec_gen uctx' leqb_level_n_gen) u1 u2 : levels_declared u1 -> levels_declared u2 -> eq_universe uctx.2 u1 u2 -> check_eqb_universe_gen leqb_level_n_gen u1 u2. Proof using HG' Huctx'. intros decl1 decl2. apply levels_gc_declared_declared in decl1. apply levels_gc_declared_declared in decl2. rewrite gc_eq_universe_iff. unfold is_graph_of_uctx, gc_of_uctx in HG. unfold uctx' in *. destruct gc_of_constraints; [cbn in *|contradiction HG]. intros eq. apply <- check_eqb_universe_spec_gen; eauto. exact 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 | check_eqb_universe_complete_gen | 921 |
check_eqb_universe_complete_gen _ (leqb_level_n_spec _ _ Huctx' HC' HG'). | 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 | check_eqb_universe_complete | 922 |
z l l' := leq0_universe_n z uctx.2 (Universe.make' l) (Universe.make' 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 | leq0_level_n | 923 |
(gc : GoodConstraint.t) := match gc with | GoodConstraint.gc_le l z l' => leq0_level_n z l l' | GoodConstraint.gc_lt_set_level k l => leq0_level_n (Z.of_nat (S k)) lzero (Level.level l) | GoodConstraint.gc_le_set_var k n => leq0_level_n (Z.of_nat k) lzero (Level.lvar n) | GoodConstraint.gc_le_level_set l k => leq0_level_n (- Z.of_nat k)%Z (Level.level l) lzero | GoodConstraint.gc_le_var_set n k => leq0_level_n (- Z.of_nat k)%Z (Level.lvar n) lzero 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 | valid_gc_constraint | 924 |
(gcs : GoodConstraintSet.t) := GoodConstraintSet.For_all valid_gc_constraint gcs. | 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 | valid_gc_constraints | 925 |
leqb_level_n_gen (leqb_correct : leqb_level_n_spec_gen uctx' leqb_level_n_gen) z l l' : level_declared l -> level_declared l' -> leq0_level_n z l l' -> leqb_level_n_gen z l l'. Proof using HG' Huctx'. intros decll decll'. unfold leq0_level_n. intros le; eapply gc_leq0_universe_n_iff in le. unfold is_graph_of_uctx, gc_of_uctx in HG. unfold uctx' in *. destruct gc_of_constraints; [cbn in *|contradiction HG]. now eapply leqb_correct. 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 | leq0_level_n_complete_gen | 926 |
leq0_level_n_complete_gen _ (leqb_level_n_spec _ _ Huctx' HC' HG'). | 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 | leq0_level_n_complete | 927 |
leqb_level_n_gen (leqb_correct : leqb_level_n_spec_gen uctx' leqb_level_n_gen) cstr : gc_levels_declared' uctx.1 cstr -> valid_gc_constraint cstr -> check_gc_constraint_gen leqb_level_n_gen cstr. Proof using HG' Huctx'. rewrite /check_gc_constraint_gen. destruct check_univs eqn:cu => //=. destruct cstr; cbn; intros hin; eapply leq0_level_n_complete_gen; intuition auto. all:apply Huctx. 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 | check_gc_constraint_complete_gen | 928 |
check_gc_constraint_complete_gen _ (leqb_level_n_spec _ _ Huctx' HC' HG'). | 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 | check_gc_constraint_complete | 929 |
leqb_level_n_gen (leqb_correct : leqb_level_n_spec_gen uctx' leqb_level_n_gen) cstrs : gcs_levels_declared uctx.1 cstrs -> valid_gc_constraints cstrs -> check_gc_constraints_gen leqb_level_n_gen cstrs. Proof using HG' Huctx'. rewrite /gcs_levels_declared /valid_gc_constraints /check_gc_constraints. intros hdecl hval. eapply GoodConstraintSetFact.for_all_iff. typeclasses eauto. intros cstr hcstr. specialize (hdecl cstr hcstr). specialize (hval cstr hcstr). eapply check_gc_constraint_complete_gen => //. 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 | check_gc_constraints_complete_gen | 930 |
check_gc_constraints_complete_gen _ (leqb_level_n_spec _ _ Huctx' HC' HG'). | 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 | check_gc_constraints_complete | 931 |
gc := forall v, satisfies v uctx.2 -> gc_satisfies v gc. | 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 | valid_gc_constraints_ext | 932 |
gc : valid_gc_constraints_ext gc -> valid_gc_constraints gc. Proof using Type. intros Hv v inv. unfold gc_satisfies in Hv. destruct v; cbn in *; red; intros v Hv'; specialize (Hv _ Hv'); eapply GoodConstraintSetFact.for_all_iff in Hv; try typeclasses eauto; specialize (Hv _ inv); cbn in Hv; cbn; rewrite ?val_level_of_variable_level //. now eapply Z.leb_le in Hv. eapply Nat.leb_le in Hv. lia. apply Nat.leb_le in Hv. lia. apply Nat.leb_le in Hv. lia. apply Nat.leb_le in Hv. 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 | valid_gc_constraints_aux | 933 |
cstrs gc : check_univs -> valid_constraints uctx.2 cstrs -> gc_of_constraints cstrs = Some gc -> valid_gc_constraints gc. Proof using Type. intros cu Hgc vgc. apply valid_gc_constraints_aux. intros v Hv. pose proof (gc_of_constraints_spec v cstrs). rewrite vgc /= in H. apply H. rewrite /valid_constraints cu in Hgc. apply Hgc. apply Hv. 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 | valid_valid_gc | 934 |
cstrs levels gc : global_uctx_invariants (levels, cstrs) -> gc_of_constraints cstrs = Some gc -> gcs_levels_declared levels gc. Proof using Type. intros Hlev hc. pose proof (gc_of_uctx_invariants (levels, cstrs) (levels, gc)). cbn in H. rewrite hc in H. specialize (H eq_refl). now apply H. 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_declared | 935 |
leqb_level_n_gen (leqb_correct : leqb_level_n_spec_gen uctx' leqb_level_n_gen) ctrs : global_uctx_invariants (uctx.1, ctrs) -> check_constraints_gen leqb_level_n_gen ctrs -> valid_constraints uctx.2 ctrs. Proof using HG' Huctx'. unfold check_constraints_gen, valid_constraints. case_eq (gc_of_constraints ctrs); [|try discriminate]. intros ctrs' Hctrs' Hdeclared HH. epose proof check_gc_constraints_spec_gen. destruct check_univs => //=. intros v Hv. apply gc_of_constraints_spec. apply gc_of_constraints_spec in Hv. rewrite Hctrs'; cbn. eapply H; eauto; clear -HG Hv Hdeclared Hctrs'; unfold is_graph_of_uctx, gc_of_uctx in HG; unfold uctx' in *; destruct (gc_of_constraints uctx.2) => //; cbn in *. eapply gc_of_constraints_declared; eauto. 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 | check_constraints_spec_gen | 936 |
check_constraints_spec_gen _ (leqb_level_n_spec _ _ Huctx' HC' HG'). | 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 | check_constraints_spec | 937 |
leqb_level_n_gen (leqb_correct : leqb_level_n_spec_gen uctx' leqb_level_n_gen) ctrs : check_univs -> global_uctx_invariants (uctx.1, ctrs) -> valid_constraints uctx.2 ctrs -> check_constraints_gen leqb_level_n_gen ctrs. Proof using HG' Huctx'. intros cu gu vc. unfold check_constraints_gen. case_eq (gc_of_constraints ctrs); [|try discriminate]. 2:{ destruct HC as [v Hv]. pose proof (gc_of_constraints_spec v ctrs). intros. rewrite /valid_constraints cu in vc. specialize (vc v Hv). rewrite H0 in H. intuition. } intros cstr gc. eapply check_gc_constraints_complete_gen; eauto. { eapply gc_of_constraints_declared. 2:tea. cbn. red in gu. unfold is_graph_of_uctx, gc_of_uctx in HG. unfold uctx' in *. destruct (gc_of_constraints uctx.2) => //; cbn in uctx', HG. } eapply valid_valid_gc; tea. 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 | check_constraints_complete_gen | 938 |
check_constraints_complete_gen _ (leqb_level_n_spec _ _ Huctx' HC' HG'). | 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 | check_constraints_complete | 939 |
(s : Sort.t) : levels_declared_sort s -> gc_levels_declared_sort uctx' s. Proof using HG levels_declared. destruct s; cbnr. apply levels_gc_declared_declared. 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 | levels_univ_gc_declared_declared | 940 |
leqb_level_n_gen (leqb_correct : leqb_level_n_spec_gen uctx' leqb_level_n_gen) s1 s2 : levels_declared_sort s1 -> levels_declared_sort s2 -> check_leqb_sort_gen leqb_level_n_gen s1 s2 -> leq_sort uctx.2 s1 s2. Proof using HG' Huctx'. intros Hu1 Hu2. move => /orP [H | H]. - apply eqb_true_iff in H as ->. reflexivity. - destruct s1, s2; cbn in *; trivial; try discriminate H. now eapply check_leqb_universe_spec_gen'. 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 | check_leqb_sort_spec_gen' | 941 |
check_leqb_sort_spec_gen' _ (leqb_level_n_spec _ _ Huctx' HC' HG'). | 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 | check_leqb_sort_spec' | 942 |
leqb_level_n_gen (leqb_correct : leqb_level_n_spec_gen uctx' leqb_level_n_gen) s1 s2 : levels_declared_sort s1 -> levels_declared_sort s2 -> leq_sort uctx.2 s1 s2 -> check_leqb_sort_gen leqb_level_n_gen s1 s2. Proof using HG' Huctx'. move : s1 s2 => [| | u1] [| | u2] //. cbn. intros decl1 decl2 Hle. unfold check_leqb_sort_gen. toProp; right. apply check_leqb_universe_complete_gen => //. 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 | check_leqb_sort_complete_gen | 943 |
check_leqb_sort_complete_gen _ (leqb_level_n_spec _ _ Huctx' HC' HG'). | 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 | check_leqb_sort_complete | 944 |
leqb_level_n_gen (leqb_correct : leqb_level_n_spec_gen uctx' leqb_level_n_gen) s1 s2 : levels_declared_sort s1 -> levels_declared_sort s2 -> check_eqb_sort_gen leqb_level_n_gen s1 s2 -> eq_sort uctx.2 s1 s2. Proof using HG' Huctx'. move : s1 s2 => [| | u1] [| | u2] //; intros Hu1 Hu2. { move/andP => [H HH] //. } move/orP => [H | H]. - apply eqb_true_iff in H as ->. reflexivity. - eapply check_eqb_universe_spec_gen'; eauto. cbn in H. unfold check_eqb_universe_gen in *. move/andP: H => [/orP [/orP [-> | ->] | ->] /orP [/orP [He | HH] | ->]] //. all: try now rewrite orb_true_r. now rewrite He. apply NonEmptySetFacts.univ_expr_eqb_true_iff in HH as ->. toProp; left; toProp; right; now apply NonEmptySetFacts.univ_expr_eqb_true_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 | check_eqb_sort_spec_gen' | 945 |
check_eqb_sort_spec_gen' _ (leqb_level_n_spec _ _ Huctx' HC' HG'). | 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 | check_eqb_sort_spec' | 946 |
leqb_level_n_gen (leqb_correct : leqb_level_n_spec_gen uctx' leqb_level_n_gen) u1 u2 : levels_declared_sort u1 -> levels_declared_sort u2 -> eq_sort uctx.2 u1 u2 -> check_eqb_sort_gen leqb_level_n_gen u1 u2. Proof using HG' Huctx'. move : u1 u2 => [| | u1] [| | u2] //. cbn. intros decl1 decl2 Hle. eapply check_eqb_universe_complete_gen in Hle => //; eauto. unfold check_eqb_sort_gen, leqb_sort_gen, check_leqb_universe_gen; cbn. unfold check_eqb_universe_gen in Hle. move/orP: Hle => [/orP [-> | e] | /andP [H1 H2]] //=. now rewrite orb_true_r. apply eqb_eq in e as ->; rewrite eqb_refl //. toProp; right; toProp; toProp; right; 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 | check_eqb_sort_complete_gen | 947 |
check_eqb_sort_complete_gen _ (leqb_level_n_spec _ _ Huctx' HC' HG'). | 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 | check_eqb_sort_complete | 948 |
(uctx : VSet.t × GoodConstraintSet.t) (G : universes_graph) : universes_graph := let levels := VSet.union uctx.1 G.1.1 in let edges := add_level_edges uctx.1 G.1.2 in let edges := add_cstrs uctx.2 edges in (levels, edges, G.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 | add_uctx | 949 |
u : ContextSet.t := (levels_of_udecl u, constraints_of_udecl 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 | uctx_of_udecl | 950 |
s s' : GoodConstraintSet.Empty s' -> GoodConstraintSet.Equal (GoodConstraintSet.union s s') s. Proof. gcsets. 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_elements_union | 951 |
e x g : EdgeSet.In e (add_level_edges x g) <-> (exists c, option_edge_of_level c = Some e /\ VSet.In c x) \/ EdgeSet.In e g. Proof. rewrite /add_level_edges VSet.fold_spec. setoid_rewrite (VSetFact.elements_iff x). setoid_rewrite InA_In_eq. induction (VSet.elements x) in g |- *; simpl. intuition auto. now destruct H0 as [c [_ F]]. rewrite {}IHl. split. * intros [[c [eq inl]]|?]; firstorder auto. destruct a as [|s|n]; simpl in *; auto. rewrite -> EdgeSet.add_spec in H. intuition auto. subst e. left; exists (Level.level s); intuition auto. rewrite -> EdgeSet.add_spec in H. intuition auto. subst e. left; eexists; intuition eauto. reflexivity. * intros [[[|s|n] [[= <-] [->|inl]]]|?]; simpl; auto; rewrite -> ?EdgeSet.add_spec; simpl; intuition auto. left. exists (Level.level s); auto. left. exists (Level.lvar n); auto. destruct a; simpl; rewrite -> ?EdgeSet.add_spec; simpl; intuition 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 | add_level_edges_spec | 952 |
g ctrs1 ctrs2 : EdgeSet.Equal (add_cstrs (GoodConstraintSet.union ctrs1 ctrs2) g) (add_cstrs ctrs1 (add_cstrs ctrs2 g)). Proof. intros e. rewrite !add_cstrs_spec. setoid_rewrite GoodConstraintSet.union_spec. firstorder eauto. 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 | add_cstrs_union | 953 |
g l1 l2 : EdgeSet.Equal (add_level_edges (VSet.union l1 l2) g) (add_level_edges l1 (add_level_edges l2 g)). Proof. intros e. rewrite !add_level_edges_spec. setoid_rewrite VSet.union_spec. firstorder eauto. 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 | add_level_edges_union | 954 |
l c g : EdgeSet.Equal (add_level_edges l (add_cstrs c g)) (add_cstrs c (add_level_edges l g)). Proof. intros e. rewrite !add_level_edges_spec !add_cstrs_spec add_level_edges_spec. firstorder 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 | add_level_edges_add_cstrs_comm | 955 |
{A : Type} (p : A -> bool) (l : list A) : match forallb p l with | true => forall x : A, In x l -> p x | false => exists x : A, In x l × p x = false end. Proof. induction l; cbn. - now intros. - destruct (forallb p l) eqn:heq. rewrite andb_true_r. destruct (p a) eqn:he. intros x []. subst; auto. now apply IHl. exists a; auto. rewrite andb_false_r. destruct IHl as [x [inx hx]]. exists x. intuition 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 | forallb_spec | 956 |
{A : Type} (p : A -> bool) (l l' : list A) : (forall x : A, In x l <-> In x l') -> forallb p l = forallb p l'. Proof. intros heq. generalize (forallb_spec p l). generalize (forallb_spec p l'). do 2 destruct forallb; intuition auto. destruct H0 as [x [hin hp]]. - specialize (H x (proj1 (heq x) hin)). red in H; congruence. - destruct H as [x [hin hp]]. specialize (H0 x (proj2 (heq _) hin)). congruence. 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 | forallb_in | 957 |
f f' l l' : (forall x, f x = f' x) -> LevelSet.Equal l l' -> LevelSet.for_all f l = LevelSet.for_all f' l'. Proof. intros Hf heq. rewrite !VSetFact.for_all_b. setoid_replace f with f'; auto. eapply forallb_in. intros x. red in heq. specialize (heq x). rewrite -!InA_In_eq. now rewrite -!LevelSetFact.elements_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 | levelset_for_all_eq | 958 |
n m v : Nbar.max n m = v -> (Nbar.le n m /\ v = m) \/ (Nbar.le m n /\ v = n). Proof. destruct n, m; cbn; firstorder. destruct (Z.max_spec_le z z0); firstorder; try lia. left. split; auto. congruence. right. split; auto. congruence. 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 | Nbar_max_spec | 959 |
n m : Nbar.le n m -> Nbar.max m n = m. Proof. destruct n, m; cbn; firstorder. f_equal. 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 | Nbar_max_spec' | 960 |
n m : Nbar.le n m -> Nbar.max n m = m. Proof. destruct n, m; cbn; firstorder. f_equal. 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 | Nbar_max_spec'' | 961 |
n m k : Nbar.le (Nbar.max n m) k -> Nbar.le n k /\ Nbar.le m k. Proof. intros hl. generalize (Nbar_max_spec n m _ eq_refl). intuition subst; try rewrite H1 in hl; auto. - now transitivity m. - now transitivity n. 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 | Nbar_max_le | 962 |
(l : list Nbar.t) acc n : fold_left Nbar.max l acc = n -> (n = acc /\ (forall x, In x l -> Nbar.le x n)) \/ (In n l /\ Nbar.le acc n /\ (forall x, In x l -> Nbar.le x n)). Proof. induction l in acc, n |- *. - cbn. intros ->; firstorder. - cbn. intros H. specialize (IHl _ _ H). destruct IHl. firstorder auto. symmetry in H0. apply Nbar_max_spec in H0. firstorder auto. right. firstorder auto. subst; auto. now rewrite H2. subst x n. rewrite H2. reflexivity. left. firstorder auto. subst x n. now rewrite H2. destruct H0. right. firstorder auto. now apply Nbar_max_le in H1. now apply Nbar_max_le in H1. 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 | fold_left_max_spec | 963 |
(l : list Nbar.t) acc n : (n = acc /\ (forall x, In x l -> Nbar.le x n)) \/ (In n l /\ Nbar.le acc n /\ (forall x, In x l -> Nbar.le x n)) -> fold_left Nbar.max l acc = n. Proof. induction l in acc, n |- *. - cbn. intuition. - cbn. intros H. apply IHl. intuition auto. subst acc. pose proof (H1 a). left. split. symmetry. eapply Nbar_max_spec'; auto. intuition auto. left. split; intuition auto. subst a. symmetry. now apply Nbar_max_spec''. right. intuition auto. specialize (H2 a). apply Nbar.max_lub; 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 | fold_left_max_spec' | 964 |
(l l' : list Nbar.t) : (forall x, In x l <-> In x l') -> fold_left Nbar.max l =1 fold_left Nbar.max l'. Proof. intros eql acc. generalize (fold_left_max_spec l acc _ eq_refl). generalize (fold_left_max_spec l' acc _ eq_refl). intuition auto. - now rewrite H H0. - rewrite H. apply fold_left_max_spec'. left; intuition auto. specialize (H2 x (proj1 (eql _) H3)). congruence. - rewrite H0. symmetry. apply fold_left_max_spec'. left; intuition auto. specialize (H4 x (proj2 (eql _) H2)). congruence. - apply fold_left_max_spec'. right. intuition auto. now apply eql. now apply H3, eql. 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 | fold_left_comm_ext | 965 |
f f' (l l' : list (Z × Level.t)) : f =1 f' -> (forall x, In x l <-> In x l') -> fold_left Nbar.max (map f l) =1 fold_left Nbar.max (map f' l'). Proof. intros eqf eqg. apply fold_left_comm_ext. intros. rewrite !in_map_iff. firstorder eauto. specialize (eqg x0). exists x0; intuition auto. now rewrite -eqf. exists x0. specialize (eqg x0). rewrite eqf; intuition 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 | fold_left_comm_ext2 | 966 |
{e e'} : Equal_graph e e' -> forall x, In x (EdgeSet.elements e.1.2) <-> In x (EdgeSet.elements e'.1.2). Proof. intros [vs [es ?]]. intros x. red in vs. now rewrite -!InA_In_eq -!EdgeSetFact.elements_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 | Equal_graph_edges | 967 |
x e e' v: Equal_graph e e' -> In x (succs e v) <-> In x (succs e' v). Proof. intros eq. unfold succs. rewrite !in_map_iff. setoid_rewrite filter_In. now setoid_rewrite (Equal_graph_edges 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 | succs_proper | 968 |
f f' e e' x : f =1 f' -> Equal_graph e e' -> fold_left Nbar.max (map f (succs e x)) =1 fold_left Nbar.max (map f' (succs e' x)). Proof. intros eqf eqg. apply fold_left_comm_ext2; auto. intros. now apply succs_proper. 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 | fold_left_comm_ext3 | 969 |
Morphisms.Proper ((=_g) ==> Logic.eq ==> Logic.eq ==> Logic.eq)%signature lsp. Proof. intros e e' He x ? <- y ? <-. unfold lsp, lsp0. pose proof (proj1 He). change (wGraph.V e) with e.1.1. change (wGraph.V e') with e'.1.1. replace (LevelSet.cardinal e'.1.1) with (LevelSet.cardinal e.1.1). 2:{ now rewrite H. } revert H. generalize e.1.1, e'.1.1. intros t0 t1. induction (LevelSet.cardinal t0) in t0, t1, e, e', He, x, y |- *. cbn; auto. cbn. intros eqt. replace (LevelSet.mem x t0) with (LevelSet.mem x t1). 2:{ now rewrite eqt. } destruct LevelSet.mem; auto. apply fold_left_comm_ext3; auto. intros [n0 y0]. f_equal. apply (IHn e e' He). intros elt. rewrite !LevelSet.remove_spec. intuition auto. now apply eqt. now apply eqt. Qed. | Instance | 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 | lsp_proper | 970 |
Morphisms.Proper ((=_g) ==> Logic.eq)%signature is_acyclic. Proof. intros e e' eq. unfold is_acyclic. eapply levelset_for_all_eq; tea. cbn. intros x. now setoid_rewrite eq. apply eq. Qed. | Instance | 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 | is_acyclic_proper | 971 |
levels1 levels2 ctrs1 ctrs2 : Equal_graph (add_uctx (levels1, ctrs1) (make_graph (levels2, ctrs2))) (make_graph (VSet.union levels1 levels2, GoodConstraintSet.union ctrs1 ctrs2)). Proof. rewrite /make_graph /= /add_uctx /=. unfold Equal_graph. split => //. split => //. now rewrite add_cstrs_union /= add_level_edges_add_cstrs_comm add_level_edges_union. 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 | add_uctx_make_graph | 972 |
uctx G : subgraph G (add_uctx uctx G). Proof. constructor. - apply: VSetProp.union_subset_2. - move=> x hx. apply/add_cstrs_spec; right. apply/add_level_edges_spec; by right. - 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 | add_uctx_subgraph | 973 |
G uctx : wGraph.acyclic_no_loop (add_uctx uctx G) -> wGraph.acyclic_no_loop G. Proof. apply: wGraph.subgraph_acyclic ; apply: add_uctx_subgraph. 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 | acyclic_no_loop_add_uctx | 974 |
(x y : option GoodConstraintSet.t) := match x, y with | Some x, Some y => GoodConstraintSet.eq x y | None, None => True | _, _ => False 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_result_eq | 975 |
{cf:checker_flags} gc t : match add_gc_of_constraint gc (Some t) with | Some t' => exists gcs, gc_of_constraint gc = Some gcs /\ GCS.Equal t' (GCS.union t gcs) | None => gc_of_constraint gc = None end. Proof. unfold add_gc_of_constraint. simpl. destruct gc_of_constraint; simpl; auto. eexists; split; eauto. 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 | add_gc_of_constraint_spec | 976 |
{cf:checker_flags} l : fold_left (fun a e => add_gc_of_constraint e a) l None = None. Proof. induction l; simpl; 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 | fold_left_add_gc_None | 977 |
{cf:checker_flags} l t t': fold_left (fun a e => add_gc_of_constraint e a) l (Some t) = Some t' -> GCS.Subset t t'. Proof. induction l in t |- *; simpl; auto. intros [= ->]. reflexivity. pose proof (add_gc_of_constraint_spec a t). destruct add_gc_of_constraint; simpl. intros. specialize (IHl _ H0). destruct H as [gcs [gca eq]]. rewrite -> eq in IHl. gcsets. now rewrite fold_left_add_gc_None. 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 | fold_left_add_gc_Some_subset | 978 |
{cf:checker_flags} s : gc_of_constraints_view s (gc_of_constraints s). Proof. unfold gc_of_constraints. rewrite ConstraintSet.fold_spec. destruct fold_left eqn:eq. - constructor. + intros. setoid_rewrite ConstraintSetFact.elements_iff. setoid_rewrite InA_In_eq. transitivity ((exists (c : UnivConstraint.t) (gcs : GoodConstraintSet.t), gc_of_constraint c = Some gcs /\ In c (ConstraintSet.elements s) /\ GoodConstraintSet.In gc gcs) \/ GCS.In gc GCS.empty). 2:gcsets. revert eq. generalize (GCS.empty). induction (ConstraintSet.elements s) in t0 |- *; simpl in *. intros ? [= ->]. firstorder auto. intros t' Ht'. pose proof (add_gc_of_constraint_spec a t'). destruct add_gc_of_constraint eqn:addgc. destruct H as [gcs [gceq cseq]]. specialize (IHl _ _ Ht'). rewrite {}IHl. rewrite cseq GCS.union_spec. split. * intros [[c [gcs' [gceq' [incl ingcgcs']]]]|[]]; auto. left. exists c, gcs'; intuition auto. left. exists a, gcs; intuition auto. * intros [[c [gcs' [gceq' [[->|incl] ingcgcs']]]]|?]; auto. ++ rewrite gceq in gceq'. noconf gceq'. auto. ++ left. exists c, gcs'. intuition auto. * rewrite fold_left_add_gc_None in Ht'. discriminate. + intros c. setoid_rewrite ConstraintSetFact.elements_iff; setoid_rewrite InA_In_eq at 1. revert eq. generalize (GCS.empty). induction (ConstraintSet.elements s) in t0 |- *; simpl in *. intros ? [= ->]. firstorder auto. intros t' Ht'. pose proof (add_gc_of_constraint_spec a t'). destruct add_gc_of_constraint eqn:addgc. destruct H as [gcs [gceq cseq]]. specialize (IHl _ _ Ht'). intros [->|incl]. eexists; split; eauto. intros gc gcin. apply fold_left_add_gc_Some_subset in Ht'. rewrite -> cseq in Ht'. gcsets. now specialize (IHl incl). now rewrite fold_left_add_gc_None in Ht'. - constructor. setoid_rewrite ConstraintSetFact.elements_iff; setoid_rewrite InA_In_eq at 1. revert eq. generalize GCS.empty. induction (ConstraintSet.elements s); simpl in * => //. intros t' eq. pose proof (add_gc_of_constraint_spec a t'). destruct add_gc_of_constraint eqn:addgc. destruct H as [gcs [gceq cseq]]. specialize (IHl _ eq). destruct IHl as [c [incl gcn]]. exists c; intuition auto. exists a; intuition 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_of_constraintsP | 979 |
{cf:checker_flags} S S' : gc_result_eq (gc_of_constraints (ConstraintSet.union S S')) (S1 <- gc_of_constraints S ;; S2 <- gc_of_constraints S' ;; ret (GoodConstraintSet.union S1 S2)). Proof. case: (gc_of_constraintsP S) => [GS HS HS0|[c [incs gcn]]]; simpl. case: (gc_of_constraintsP S') => [GS' HS' HS'0|GS']; simpl. case: (gc_of_constraintsP (ConstraintSet.union S S')) => [GSS' HSS' HSS'0|[c [inc gcn]]]. simpl. - intros gc. rewrite HSS' GCS.union_spec HS HS'. setoid_rewrite ConstraintSet.union_spec. split. intros [c [gcs ?]]. intuition auto. left; firstorder auto. right; firstorder auto. intros [[c [gcs ?]]|[c [gcs ?]]]; exists c, gcs; intuition auto. - cbn. apply ConstraintSet.union_spec in inc. destruct inc. specialize (HS0 _ H). rewrite gcn in HS0. now destruct HS0. specialize (HS'0 _ H). rewrite gcn in HS'0. now destruct HS'0. - destruct GS' as [c [inc gcn]]. case: (gc_of_constraintsP (ConstraintSet.union S S')) => [GSS' HSS' HSS'0|[c' [inc' gcn']]]. cbn. specialize (HSS'0 c). rewrite -> ConstraintSet.union_spec in HSS'0. specialize (HSS'0 (or_intror inc)) as [gcs [eq _]]. now congruence. split. - case: (gc_of_constraintsP (ConstraintSet.union S S')) => [GSS' HSS' HSS'0|[c' [inc' gcn']]]. cbn. specialize (HSS'0 c). rewrite -> ConstraintSet.union_spec in HSS'0. specialize (HSS'0 (or_introl incs)) as [gcs [eq _]]. now congruence. split. 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_union | 980 |
`{checker_flags} uctx1 uctx2 gc1 gc2 : gc_of_uctx uctx1 = Some gc1 -> gc_of_uctx uctx2 = Some gc2 -> ∑ gc, gc_of_uctx (ContextSet.union uctx1 uctx2) = Some (LevelSet.union gc1.1 gc2.1, gc ) /\ GCS.eq gc (GCS.union gc1.2 gc2.2). Proof. unfold gc_of_uctx. pose proof (H' := gc_of_constraints_union uctx1.2 uctx2.2). move=> eq1 eq2; move: eq1 eq2 H'. case: (gc_of_constraints _) => //?. case: (gc_of_constraints _) => //?. case: (gc_of_constraints _) => //=? [=] <- [=] <- /=. eexists; split; [reflexivity| eassumption]. 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_union | 981 |
levels : Morphisms.Proper (wGraph.EdgeSet.Equal ==> wGraph.EdgeSet.Equal)%signature (add_level_edges levels). Proof. intros e e' he. rewrite /add_level_edges. rewrite !VSet.fold_spec. induction (VSet.elements levels) in e, e', he |- *; cbn; auto. apply IHl. destruct variable_of_level => //. now rewrite he. Qed. | Instance | 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 | proper_add_level_edges | 982 |
cstrs : Morphisms.Proper ((=_g) ==> Equal_graph)%signature (add_uctx cstrs). Proof. intros g g' eq. rewrite /add_uctx; cbn. split. cbn. now rewrite (proj1 eq). cbn. split => //. rewrite /add_level_edges. now rewrite (proj1 (proj2 eq)). apply eq. Qed. | Instance | 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 | proper_add_uctx | 983 |
{cf : checker_flags} : Proper ((=_cset) ==> R_opt GoodConstraintSet.Equal) gc_of_constraints. Proof. intros c c' eqc; cbn. destruct (gc_of_constraintsP c); destruct (gc_of_constraintsP c'); cbn. - intros cs; rewrite i i0. firstorder eauto. - destruct e0 as [cs [incs gcn]]. apply eqc in incs. destruct (e cs incs) as [? []]. congruence. - destruct e as [cs [incs gcn]]. apply eqc in incs. destruct (e0 cs incs) as [? []]. congruence. - exact I. Qed. | Instance | 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_proper | 984 |
Morphisms.Proper ((=_lset) ==> wGraph.EdgeSet.Equal ==> wGraph.EdgeSet.Equal)%signature add_level_edges. Proof. intros l l' hl e e' <-. intros x; rewrite !add_level_edges_spec. firstorder eauto. Qed. | Instance | 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 | proper_add_level_edges' | 985 |
Proper ((=_gcs) ==> (=_g)) make_graph. Proof. intros [v c] [v' c'] [eqv eqc]; cbn. unfold make_graph; cbn in *. split; cbn; auto. split; cbn; try reflexivity. now rewrite eqc eqv. Qed. | Instance | 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 | make_graph_proper | 986 |
{cf : checker_flags} G : Proper ((=_cs) ==> iff) (is_graph_of_uctx G). Proof. intros [l c] [l' c'] [eql eqc]; cbn. unfold is_graph_of_uctx; cbn. cbn in *. pose proof (gc_of_constraints_proper _ _ eqc). destruct (gc_of_constraints c); cbn in *; destruct (gc_of_constraints c'); cbn. now setoid_replace (l, t0) with (l', t1) using relation gcs_equal. elim H. elim H. intuition. Qed. | Instance | 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 | is_graph_of_uctx_proper | 987 |
Proper ((=_g) ==> (=_g) ==> iff) subgraph. Proof. unshelve apply: proper_sym_impl_iff_2. move=> g1 g1' [eqv1 [eqe1 eqs1]] g2 g2' [eqv2 [eqe2 eqs2]]. move=> [*]; constructor. + by rewrite <- eqv1, <- eqv2. + by rewrite <- eqe1, <- eqe2. + by rewrite <- eqs1, <- eqs2. Qed. | Instance | 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 | subgraph_proper | 988 |
Proper ((=_g) ==> (=_g) ==> iff) full_subgraph. Proof. unshelve apply: proper_sym_impl_iff_2. move=> g1 g1' eq1 g2 g2' eq2. move=> [?] lsp_dom; constructor=> *; rewrite -eq1 -eq2 //. apply lsp_dom; rewrite /wGraph.V (proj1 eq1) //. Qed. | Instance | 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 | full_subgraph_proper | 989 |
uctx1 uctx2 : add_uctx uctx2 (make_graph uctx1) =_g make_graph (VSet.union uctx2.1 uctx1.1, GCS.union uctx2.2 uctx1.2). Proof. destruct uctx1, uctx2; apply: add_uctx_make_graph. 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 | add_uctx_make_graph2 | 990 |
`{checker_flags} udecl uctx : gc_of_uctx udecl = Some uctx -> ContextSet.levels udecl = uctx.1. 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_levels | 991 |
gctx1 gctx2 := (LS.union gctx1.1 gctx2.1, GCS.union gctx1.2 gctx2.2). | 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 | gctx_union | 992 |
`{cf : checker_flags} [uctx gph] : is_graph_of_uctx gph uctx -> global_uctx_invariants uctx -> wGraph.invariants gph. Proof. move=> /on_SomeP [? [Huctx <-]] H0. pose proof (gc_of_uctx_invariants _ _ Huctx H0). apply: make_graph_invariants. 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 | global_uctx_graph_invariants | 993 |
`{checker_flags} [uctx G v] : is_graph_of_uctx G uctx -> global_uctx_invariants uctx -> correct_labelling G (labelling_of_valuation v) <-> satisfies v uctx.2. Proof. move=> /on_SomeP [gctx [eqSome <-]] inv. rewrite -make_graph_spec gc_of_constraints_spec (gc_of_uctx_of_constraints _ _ eqSome) //. 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 | correct_labelling_of_valuation_satisfies_iff | 994 |
`{cf:checker_flags} G uctx : is_graph_of_uctx G uctx -> forall x, VSet.In x (wGraph.V G) <-> LS.In x uctx.1. Proof. move=> /on_SomeP [gctx [eqSome HG]] ?. rewrite /wGraph.V -(proj1 HG) /= -(gc_of_uctx_levels _ _ eqSome) //. 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 | is_graph_of_uctx_levels | 995 |
`{checker_flags} [uctx G l] : is_graph_of_uctx G uctx -> global_uctx_invariants uctx -> correct_labelling G l -> forall x, VSet.In x uctx.1 -> val (valuation_of_labelling l) x = l x. Proof. move=> /on_SomeP [gctx [eqSome HG]] inv hl x hx. apply: val_valuation_of_labelling. 1: symmetry; eassumption. 2: done. red; rewrite -(gc_of_uctx_levels _ _ eqSome) //. 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 | val_valuation_of_labelling2 | 996 |
`{checker_flags} [uctx G l] : is_graph_of_uctx G uctx -> global_uctx_invariants uctx -> correct_labelling G l -> satisfies (valuation_of_labelling l) uctx.2. Proof. move=> /on_SomeP [gctx [eqSome <-]] inv. rewrite gc_of_constraints_spec (gc_of_uctx_of_constraints _ _ eqSome) /=. apply: make_graph_spec'; by apply: gc_of_uctx_invariants. 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 | correct_valuation_of_labelling_satisfies | 997 |
`{cf: checker_flags} [uctx G uctx' G'] `{wGraph.invariants G, wGraph.invariants G', wGraph.acyclic_no_loop G'} : wGraph.subgraph G G' -> global_uctx_invariants uctx -> global_uctx_invariants uctx' -> is_graph_of_uctx G uctx -> is_graph_of_uctx G' uctx' -> consistent_extension_on uctx uctx'.2 <-> wGraph.IsFullSubgraph.is_full_extension G G'. Proof. move=> sub Huctx Huctx' HG HG'. rewrite IsFullSubgraph.is_full_extension_spec //; split. - move=> hext; split=> //. pose proof (wGraph.subgraph_acyclic _ _ sub _). apply: labelling_ext_lsp. move=> l1 /[dup] hl1 /(correct_valuation_of_labelling_satisfies HG). move=> /hext[v' [+ v'val]]. move=> /(correct_labelling_of_valuation_satisfies_iff HG'). exists (labelling_of_valuation v'); split=> //. move=> z /[dup] hz /(is_graph_of_uctx_levels _ _ HG) ?. rewrite -(val_valuation_of_labelling2 HG) // v'val //. - move=> fsub v /(correct_labelling_of_valuation_satisfies_iff HG) hl. pose (l := labelling_of_valuation v). pose (Gl := relabel_on G G' l). pose (l' := to_label ∘ (lsp Gl (wGraph.s Gl))). pose proof (hl' := extends_correct_labelling _ _ l hl fsub _). exists (valuation_of_labelling l'); split. + apply: (correct_valuation_of_labelling_satisfies HG')=> //. + move=> ? /[dup] ? /(is_graph_of_uctx_levels _ _ HG) ?. rewrite (val_valuation_of_labelling2 HG') //. * apply/(is_graph_of_uctx_levels _ _ HG'). by apply: (vertices_sub _ _ sub). * rewrite /l' extends_labelling //. 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 | consistent_ext_on_full_ext0 | 998 |
`{cf: checker_flags} [uctx G uctx' G'] : is_graph_of_uctx G uctx -> is_graph_of_uctx G' uctx' -> global_uctx_invariants uctx -> global_uctx_invariants uctx' -> wGraph.is_acyclic G' -> wGraph.subgraph G G' -> consistent_extension_on uctx uctx'.2 <-> wGraph.IsFullSubgraph.is_full_extension G G'. Proof. move=> HG HG' /[dup] ? /(global_uctx_graph_invariants HG) ?. move=> /[dup] ? /(global_uctx_graph_invariants HG') ? /wGraph.is_acyclic_spec ??. by apply: consistent_ext_on_full_ext0. 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 | consistent_ext_on_full_ext | 999 |
Subsets and Splits