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φ leq_universe leq_refl u := @leq_sort_refl φ leq_universe leq_refl u. | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | leq_sort_refl' | 1,300 |
φ φ' pb t u : ConstraintSet.Subset φ φ' -> compare_sort φ pb t u -> compare_sort φ' pb t u. Proof using Type. intros Hctrs. destruct pb, t, u; cbnr; trivial. all: intros H; unfold_univ_rel; apply H. all: eapply satisfies_subset; eauto. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | cmp_sort_subset | 1,301 |
ctrs ctrs' t u : ConstraintSet.Subset ctrs ctrs' -> eq_sort ctrs t u -> eq_sort ctrs' t u. Proof using Type. apply cmp_sort_subset with (pb := Conv). Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | eq_sort_subset | 1,302 |
ctrs ctrs' t u : ConstraintSet.Subset ctrs ctrs' -> leq_sort ctrs t u -> leq_sort ctrs' t u. Proof using Type. apply cmp_sort_subset with (pb := Cumul). Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | leq_sort_subset | 1,303 |
Set := | IntoSProp | IntoPropSProp | IntoSetPropSProp | IntoAny. | Inductive | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | allowed_eliminations | 1,304 |
(allowed : allowed_eliminations) : concrete_sort -> bool := match allowed with | IntoSProp => Sort.is_sprop | IntoPropSProp => Sort.is_propositional | IntoSetPropSProp => is_propositional_or_set | IntoAny => fun _ => true end. | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | is_allowed_elimination_cuniv | 1,305 |
{cf} φ s := eq_sort φ s Sort.type0. | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | is_lSet | 1,306 |
{cf} φ allowed : Sort.t -> Prop := match allowed with | IntoSProp => Sort.is_sprop | IntoPropSProp => Sort.is_propositional | IntoSetPropSProp => fun s => Sort.is_propositional s \/ is_lSet φ s | IntoAny => fun s => true end. | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | is_allowed_elimination | 1,307 |
(a a' : allowed_eliminations) : bool := match a, a' with | IntoSProp, _ | IntoPropSProp, (IntoPropSProp | IntoSetPropSProp | IntoAny) | IntoSetPropSProp, (IntoSetPropSProp | IntoAny) | IntoAny, IntoAny => true | _, _ => false end. | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | allowed_eliminations_subset | 1,308 |
{cf} φ a a' s : allowed_eliminations_subset a a' -> is_allowed_elimination φ a s -> is_allowed_elimination φ a' s. Proof using Type. destruct a, a'; cbnr; trivial; destruct s; cbnr; trivial; intros H1 H2; try absurd; constructor; trivial. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | allowed_eliminations_subset_impl | 1,309 |
`{cf : checker_flags} Σ s1 s2 a : leq_sort Σ s1 s2 -> is_allowed_elimination Σ a s2 -> is_allowed_elimination Σ a s1. Proof. destruct a, s2 as [| |u2], s1 as [| |u1] => //=. 1: now left. intros Hle [H|]; right => //. unfold_univ_rel. cbn in H. lia. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | is_allowed_elimination_monotone | 1,310 |
φ ctrs : config.impl cf1 cf2 -> @valid_constraints cf1 φ ctrs -> @valid_constraints cf2 φ ctrs. Proof using Type. unfold valid_constraints, config.impl, is_true. do 2 destruct check_univs; trivial; cbn => //. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | valid_config_impl | 1,311 |
ctrs pb t u : config.impl cf1 cf2 -> @compare_universe cf1 ctrs pb t u -> @compare_universe cf2 ctrs pb t u. Proof using Type. unfold config.impl, compare_universe, leq_universe, eq_universe, leq_universe_n, is_true. destruct pb; do 2 destruct check_univs => //=. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | cmp_universe_config_impl | 1,312 |
ctrs t u : config.impl cf1 cf2 -> @eq_universe cf1 ctrs t u -> @eq_universe cf2 ctrs t u. Proof using Type. apply cmp_universe_config_impl with (pb := Conv). Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | eq_universe_config_impl | 1,313 |
ctrs t u : config.impl cf1 cf2 -> @leq_universe cf1 ctrs t u -> @leq_universe cf2 ctrs t u. Proof using Type. apply cmp_universe_config_impl with (pb := Cumul). Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | leq_universe_config_impl | 1,314 |
ctrs pb t u : config.impl cf1 cf2 -> @compare_sort cf1 ctrs pb t u -> @compare_sort cf2 ctrs pb t u. Proof using Type. unfold compare_sort, leq_sort, eq_sort, eq_sort_, leq_sort_n, leq_sort_n_, is_true. destruct pb, t, u => //=. - apply eq_universe_config_impl. - unfold config.impl. do 2 destruct check_univs, prop_sub_type; cbn => //=. - apply leq_universe_config_impl. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | cmp_sort_config_impl | 1,315 |
ctrs t u : config.impl cf1 cf2 -> @eq_sort cf1 ctrs t u -> @eq_sort cf2 ctrs t u. Proof using Type. apply cmp_sort_config_impl with (pb := Conv). Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | eq_sort_config_impl | 1,316 |
ctrs t u : config.impl cf1 cf2 -> @leq_sort cf1 ctrs t u -> @leq_sort cf2 ctrs t u. Proof using Type. apply cmp_sort_config_impl with (pb := Cumul). Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | leq_sort_config_impl | 1,317 |
φ a s : config.impl cf1 cf2 -> @is_allowed_elimination cf1 φ a s -> @is_allowed_elimination cf2 φ a s. Proof using Type. destruct a, s; cbnr; trivial. unfold eq_universe, config.impl, is_true. do 2 destruct check_univs; cbnr; auto => //. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | allowed_eliminations_config_impl | 1,318 |
{cf} ϕ s1 s1' s2 s2' : leq_sort ϕ s1 s1' -> leq_sort ϕ s2 s2' -> leq_sort ϕ (Sort.sort_of_product s1 s2) (Sort.sort_of_product s1' s2'). Proof. destruct s2 as [| | u2], s2' as [| | u2']; cbnr; try absurd; destruct s1 as [| | u1], s1' as [| | u1']; cbnr; try absurd; trivial. - intros _ H2; etransitivity; [apply H2 | apply leq_universe_sup_r]. - apply leq_universe_sup_mon. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | leq_sort_product_mon | 1,319 |
{cf} {ϕ l u} : Sort.is_propositional u -> leq_sort ϕ (Sort.sort_of_product l u) u. Proof. destruct u => //; reflexivity. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | impredicative_product | 1,320 |
s : Universe.sup s s = s. Proof using Type. apply eq_univ'; cbn. intro; rewrite !LevelExprSet.union_spec. intuition. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | univ_sup_idem | 1,321 |
s : Sort.sup s s = s. Proof using Type. destruct s; cbn; auto. apply f_equal. apply univ_sup_idem. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | sup_idem | 1,322 |
s : Sort.sort_of_product s s = s. Proof using Type. unfold Sort.sort_of_product; destruct s; try reflexivity. apply sup_idem. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | sort_of_product_idem | 1,323 |
s1 s2 s3 : Universe.sup s1 (Universe.sup s2 s3) = Universe.sup (Universe.sup s1 s2) s3. Proof using Type. apply eq_univ'; cbn. symmetry; apply LevelExprSetProp.union_assoc. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | univ_sup_assoc | 1,324 |
φ : Proper (eq_universe φ ==> eq_universe φ ==> eq_universe φ) Universe.sup. Proof using Type. intros u1 u1' H1 u2 u2' H2. unfold_univ_rel. rewrite !val_sup. lia. Qed. | Instance | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | proper_univ_sup_eq_univ | 1,325 |
φ : Proper (eq_sort φ ==> eq_sort φ ==> eq_sort φ) Sort.sup. Proof using Type. intros [| | u1] [| |u1'] H1 [| |u2] [| |u2'] H2; cbn in *; try absurd; auto. now apply proper_univ_sup_eq_univ. Qed. | Instance | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | proper_sort_sup_eq_sort | 1,326 |
u s : Sort.sort_of_product u (Sort.sort_of_product u s) = Sort.sort_of_product u s. Proof using Type. destruct u,s; cbnr. now rewrite univ_sup_assoc univ_sup_idem. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | sort_of_product_twice | 1,327 |
x y : LevelExpr.succ x = LevelExpr.succ y -> x = y. Proof using Type. unfold LevelExpr.succ. destruct x as [l n], y as [l' n']. simpl. congruence. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | succ_inj | 1,328 |
l x : LevelExprSet.In x (Universe.succ l) <-> exists x', LevelExprSet.In x' l /\ x = LevelExpr.succ x'. Proof using Type. rewrite map_spec. reflexivity. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | spec_map_succ | 1,329 |
v l : val v (LevelExpr.succ l) = val v l + 1. Proof using Type. destruct l as []; simpl. cbn. lia. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | val_succ | 1,330 |
v l : val v (Universe.succ l) = val v l + 1. Proof using Type. pose proof (spec_map_succ l). set (n := Universe.succ l) in *. destruct (val_In_max l v) as [max [inmax eqv]]. rewrite <-eqv. rewrite val_caract. split. intros. specialize (proj1 (H _) H0) as [x' [inx' eq]]. subst e. rewrite val_succ. eapply (val_In_le _ v) in inx'. rewrite <- eqv in inx'. simpl in *. unfold LevelExprSet.elt, LevelExpr.t in *. lia. exists (LevelExpr.succ max). split. apply H. exists max; split; auto. now rewrite val_succ. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | val_map_succ | 1,331 |
s s' : leq_sort ϕ s s' -> leq_sort ϕ (Sort.super s) (Sort.super s'). Proof using Type. destruct s as [| | u1], s' as [| | u1']; cbnr; try absurd; intros H; unfold_univ_rel; rewrite !val_map_succ; lia. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | leq_sort_super | 1,332 |
s1 s2 : prop_sub_type = false -> leq_sort ϕ s1 s2 -> Sort.is_prop s1 -> Sort.is_prop s2. Proof using Type. intros ps. destruct s1; cbn; [ | absurd | absurd]. rewrite ps. destruct s2; cbn; [ auto | absurd | absurd]. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | leq_sort_prop_no_prop_sub_type | 1,333 |
{s1 s2} : prop_sub_type = false -> leq_sort ϕ s1 s2 -> Sort.is_propositional s1 <-> Sort.is_propositional s2. Proof using Type. intros ps. destruct s1, s2; cbn; try absurd; intros H; split; trivial. now rewrite ps in H. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | leq_prop_is_propositonal | 1,334 |
Level.t := Level.level "__metacoq_fresh_level__". | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | fresh_level | 1,335 |
Universe.t := Universe.make' fresh_level. | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | fresh_universe | 1,336 |
UnivSubst Level.t := fun u l => match l with Level.lzero | Level.level _ => l | Level.lvar n => List.nth n u Level.lzero end. | Instance | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | subst_instance_level | 1,337 |
UnivSubst UnivConstraint.t := fun u c => (subst_instance_level u c.1.1, c.1.2, subst_instance_level u c.2). | Instance | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | subst_instance_cstr | 1,338 |
UnivSubst ConstraintSet.t := fun u ctrs => ConstraintSet.fold (fun c => ConstraintSet.add (subst_instance_cstr u c)) ctrs ConstraintSet.empty. | Instance | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | subst_instance_cstrs | 1,339 |
UnivSubst LevelExpr.t := fun u e => match e with | (Level.lzero, _) | (Level.level _, _) => e | (Level.lvar n, b) => match nth_error u n with | Some l => (l,b) | None => (Level.lzero, b) end end. | Instance | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | subst_instance_level_expr | 1,340 |
UnivSubst Universe.t := fun u => map (subst_instance_level_expr u). | Instance | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | subst_instance_universe | 1,341 |
UnivSubst Sort.t := fun u e => match e with | sProp | sSProp => e | sType u' => sType (subst_instance u u') end. | Instance | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | subst_instance_sort | 1,342 |
s u : Sort.to_family s@[u] = Sort.to_family s. Proof. destruct s => //. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | subst_instance_to_family | 1,343 |
UnivSubst Instance.t := fun u u' => List.map (subst_instance_level u) u'. | Instance | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | subst_instance_instance | 1,344 |
(l : Level.t) := match l with | Level.lvar n => (n <? k)%nat | _ => true end. | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | closedu_level | 1,345 |
(s : LevelExpr.t) := closedu_level (LevelExpr.get_level s). | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | closedu_level_expr | 1,346 |
(u : Universe.t) := LevelExprSet.for_all closedu_level_expr u. | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | closedu_universe | 1,347 |
(u : Sort.t) := match u with | sSProp | sProp => true | sType l => closedu_universe l end. | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | closedu_sort | 1,348 |
(u : Instance.t) := forallb closedu_level u. | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | closedu_instance | 1,349 |
u l : closedu_level 0 l -> subst_instance_level u l = l. Proof. destruct l; cbnr. discriminate. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | closedu_subst_instance_level | 1,350 |
u e : closedu_level_expr 0 e -> subst_instance_level_expr u e = e. Proof. intros. destruct e as [t b]. destruct t;cbnr. discriminate. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | closedu_subst_instance_level_expr | 1,351 |
u s : closedu_sort 0 s -> subst_instance_sort u s = s. Proof. intro H. destruct s as [| | t]; cbnr. apply f_equal. apply eq_univ'. destruct t as [ts H1]. unfold closedu_universe in *;cbn in *. intro e; split; intro He. - apply map_spec in He. destruct He as [e' [He' X]]. rewrite closedu_subst_instance_level_expr in X. apply LevelExprSet.for_all_spec in H; proper. exact (H _ He'). now subst. - apply map_spec. exists e; split; tas. symmetry; apply closedu_subst_instance_level_expr. apply LevelExprSet.for_all_spec in H; proper. now apply H. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | closedu_subst_instance_univ | 1,352 |
u t : closedu_instance 0 t -> subst_instance u t = t. Proof. intro H. apply forall_map_id_spec. apply Forall_forall; intros l Hl. apply closedu_subst_instance_level. eapply forallb_forall in H; eassumption. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | closedu_subst_instance | 1,353 |
l : closedu_level #|u| l -> closedu_level 0 (subst_instance_level u l). Proof using Hcl. destruct l; cbnr. unfold closedu_instance in Hcl. destruct (nth_in_or_default n u Level.lzero). - intros _. eapply forallb_forall in Hcl; tea. - rewrite e; reflexivity. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | subst_instance_level_closedu | 1,354 |
e : closedu_level_expr #|u| e -> closedu_level_expr 0 (subst_instance_level_expr u e). Proof using Hcl. destruct e as [l b]. destruct l;cbnr. case_eq (nth_error u n); cbnr. intros [] Hl X; cbnr. apply nth_error_In in Hl. eapply forallb_forall in Hcl; tea. discriminate. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | subst_instance_level_expr_closedu | 1,355 |
s : closedu_sort #|u| s -> closedu_sort 0 (subst_instance_sort u s). Proof using Hcl. intro H. destruct s as [| |t]; cbnr. destruct t as [l Hl]. apply LevelExprSet.for_all_spec; proper. intros e He. eapply map_spec in He. destruct He as [e' [He' X]]; subst. apply subst_instance_level_expr_closedu. apply LevelExprSet.for_all_spec in H; proper. now apply H. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | subst_instance_univ_closedu | 1,356 |
t : closedu_instance #|u| t -> closedu_instance 0 (subst_instance u t). Proof using Hcl. intro H. etransitivity. eapply forallb_map. eapply forallb_impl; tea. intros l Hl; cbn. apply subst_instance_level_closedu. Qed. | Lemma | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | subst_instance_closedu | 1,357 |
(l : Level.t) : string := match l with | Level.lzero => "Set" | Level.level s => s | Level.lvar n => "lvar" ^ string_of_nat n end. | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | string_of_level | 1,358 |
(e : LevelExpr.t) : string := let '(l, n) := e in string_of_level l ^ (if n is 0 then "" else "+" ^ string_of_nat n). | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | string_of_level_expr | 1,359 |
(u : Sort.t) := match u with | sSProp => "SProp" | sProp => "Prop" | sType l => "Type(" ^ string_of_list string_of_level_expr (LevelExprSet.elements l) ^ ")" end. | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | string_of_sort | 1,360 |
u := string_of_list string_of_level u. | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | string_of_universe_instance | 1,361 |
| Monomorphic_entry (ctx : ContextSet.t) | Polymorphic_entry (ctx : UContext.t). | Inductive | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | universes_entry | 1,362 |
(u : universes_decl) : universes_entry := match u with | Polymorphic_ctx ctx => Polymorphic_entry (Universes.AUContext.repr ctx) | Monomorphic_ctx => Monomorphic_entry ContextSet.empty end. | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | universes_entry_of_decl | 1,363 |
uctx := match uctx with | Monomorphic_ctx => Instance.empty | Polymorphic_ctx c => fst (snd (AUContext.repr c)) end. | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | polymorphic_instance | 1,364 |
decl := match decl with | Monomorphic_ctx => Instance.empty | Polymorphic_ctx auctx => UContext.instance (AUContext.repr auctx) end. | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | abstract_instance | 1,365 |
u := match u with | [] => "" | _ => "@{" ^ print_list string_of_level " " u ^ "}" end. | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | print_universe_instance | 1,366 |
t := print_list string_of_level " " (LevelSet.elements t). | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | print_lset | 1,367 |
d := match d with | ConstraintType.Le n => if (n =? 0)%Z then "<=" else if (n =? 1)%Z then "<" else if (n <? 0)%Z then "<=" ^ string_of_nat (Z.to_nat (Z.abs n)) ^ " + " else " + " ^ string_of_nat (Z.to_nat n) ^ " <= " | ConstraintType.Eq => "=" end. | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | print_constraint_type | 1,368 |
t := print_list (fun '(l1, d, l2) => string_of_level l1 ^ " " ^ print_constraint_type d ^ " " ^ string_of_level l2) " /\ " (ConstraintSet.elements t). | Definition | common | From Coq Require Import OrdersAlt MSetList MSetAVL MSetFacts MSetProperties MSetDecide FMapAVL. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils MCMSets MCFSets. From MetaCoq.Common Require Import BasicAst config. Require Import ssreflect. Import NonEmptySetFacts. | common\theories\Universes.v | print_constraint_set | 1,369 |
(cstr : ConstraintSet.t) : LevelSet.t := ConstraintSet.fold (fun '(l1, _, l2) acc => LevelSet.add l1 (LevelSet.add l2 acc)) cstr (LevelSet.singleton Level.lzero). | Definition | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | levels_of_cs | 1,370 |
cstr (lvls := levels_of_cs cstr) : uGraph.global_uctx_invariants (lvls, cstr). Proof. subst lvls; cbv [levels_of_cs]. cbv [uGraph.global_uctx_invariants uGraph.uctx_invariants ConstraintSet.For_all declared_cstr_levels]; cbn [fst snd ContextSet.levels ContextSet.constraints]. repeat first [ apply conj | progress intros | progress destruct ? | match goal with | [ |- ?x \/ ?y ] => first [ lazymatch x with context[LevelSet.In ?l (LevelSet.singleton ?l)] => idtac end; left | lazymatch y with context[LevelSet.In ?l (LevelSet.singleton ?l)] => idtac end; right ] | [ H : ConstraintSet.In ?l ?c |- ?x \/ ?y ] => first [ lazymatch x with context[LevelSet.In _ (ConstraintSet.fold _ c _)] => idtac end; left | lazymatch y with context[LevelSet.In _ (ConstraintSet.fold _ c _)] => idtac end; right ] end | rewrite !LevelSet.union_spec | progress rewrite <- ?ConstraintSet.elements_spec1, ?InA_In_eq in * | rewrite ConstraintSetProp.fold_spec_right ]. all: lazymatch goal with | [ |- LevelSet.In Level.lzero (List.fold_right ?f ?init ?ls) ] => first [ LevelSetDecide.fsetdec | cut (LevelSet.In Level.lzero init); [ generalize init; induction ls; intros; cbn in * | LevelSetDecide.fsetdec ] ] | [ H : List.In ?v ?ls |- LevelSet.In ?v' (List.fold_right ?f ?init (List.rev ?ls)) ] => rewrite List.in_rev in H; let ls' := fresh "ls" in set (ls' := List.rev ls); change (List.In v ls') in H; change (LevelSet.In v' (List.fold_right f init ls')); generalize init; induction ls'; cbn in * end. all: repeat first [ exfalso; assumption | progress destruct_head'_or | progress subst | progress intros | progress destruct ? | rewrite !LevelSetFact.add_iff | solve [ auto ] ]. Qed. | Lemma | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | levels_of_cs_spec | 1,371 |
ctrs : {@consistent ctrs} + {~@consistent ctrs}. Proof. pose proof (@uGraph.is_consistent_spec config.default_checker_flags (levels_of_cs ctrs, ctrs) (levels_of_cs_spec ctrs)) as H. destruct uGraph.is_consistent; [ left; apply H | right; intro H'; apply H in H' ]; auto. Defined. | Definition | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | consistent_dec | 1,372 |
(cs1 cs2 : ConstraintSet.t) : LevelSet.t := LevelSet.union (levels_of_cs cs1) (levels_of_cs cs2). | Definition | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | levels_of_cs2 | 1,373 |
cs1 cs2 (lvls := levels_of_cs2 cs1 cs2) : uGraph.global_uctx_invariants (lvls, cs1) /\ uGraph.global_uctx_invariants (lvls, cs2). Proof. split; apply global_uctx_invariants_union_or; constructor; apply levels_of_cs_spec. Qed. | Lemma | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | levels_of_cs2_spec | 1,374 |
(cs : ContextSet.t) (cstr : ConstraintSet.t) : LevelSet.t := LevelSet.union (ContextSet.levels cs) (levels_of_cs2 cstr (ContextSet.constraints cs)). | Definition | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | levels_of_cscs | 1,375 |
cs cstr (lvls := levels_of_cscs cs cstr) : uGraph.global_uctx_invariants (lvls, ContextSet.constraints cs) /\ uGraph.global_uctx_invariants (lvls, cstr). Proof. generalize (levels_of_cs2_spec cstr (ContextSet.constraints cs)). split; apply global_uctx_invariants_union_or; constructor; apply levels_of_cs2_spec. Qed. | Lemma | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | levels_of_cscs_spec | 1,376 |
(u : Universe.t) : VSet.t := LevelExprSet.fold (fun gc acc => match LevelExpr.get_noprop gc with | Some l => VSet.add l acc | None => acc end) u VSet.empty. | Definition | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | levels_of_universe | 1,377 |
u cstr (lvls := levels_of_universe u) : gc_levels_declared (lvls, cstr) u. Proof. subst lvls; cbv [levels_of_universe gc_levels_declared gc_expr_declared on_Some_or_None LevelExpr.get_noprop]; cbn [fst snd]. cbv [LevelExprSet.For_all]; cbn [fst snd]. repeat first [ apply conj | progress intros | progress destruct ? | exact I | progress rewrite <- ?LevelExprSet.elements_spec1, ?InA_In_eq in * | rewrite LevelExprSetProp.fold_spec_right ]. all: lazymatch goal with | [ H : List.In ?v ?ls |- VSet.In ?v' (List.fold_right ?f ?init (List.rev ?ls)) ] => rewrite List.in_rev in H; let ls' := fresh "ls" in set (ls' := List.rev ls); change (List.In v ls') in H; change (VSet.In v' (List.fold_right f init ls')); generalize init; induction ls'; cbn in * end. all: repeat first [ exfalso; assumption | progress destruct_head'_or | progress subst | progress intros | progress destruct ? | rewrite !VSetFact.add_iff | solve [ auto ] ]. Qed. | Lemma | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | levels_of_universe_spec | 1,378 |
(shared_levels : LevelSet.t) (shared_prefix : Byte.byte) (prefix : Byte.byte) (x : string) : string := (String.String (if LevelSet.mem (Level.level x) shared_levels then shared_prefix else prefix) x). | Definition | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | uniquify_level_level | 1,379 |
(x : string) : string := match x with | String.EmptyString => String.EmptyString | String.String _ x => x end. | Definition | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | ununiquify_level_level | 1,380 |
(shared_levels : LevelSet.t) (total_sets : nat) (offset : nat) (x : nat) : nat := x * S total_sets + (if LevelSet.mem (Level.lvar x) shared_levels then O else S offset). | Definition | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | uniquify_level_var | 1,381 |
(total_sets : nat) (x : nat) : nat := Z.to_nat (Z.of_nat x / Z.of_nat (S total_sets)). | Definition | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | ununiquify_level_var | 1,382 |
(shared_levels : LevelSet.t) (shared_prefix : Byte.byte) (total_sets : nat) (prefix : Byte.byte) (offset : nat) (lvl : Level.t) : Level.t := match lvl with | Level.lzero => Level.lzero | Level.level x => Level.level (uniquify_level_level shared_levels shared_prefix prefix x) | Level.lvar x => Level.lvar (uniquify_level_var shared_levels total_sets offset x) end. | Definition | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | uniquify_level | 1,383 |
(total_sets : nat) (lvl : Level.t) : Level.t := match lvl with | Level.lzero => Level.lzero | Level.level x => Level.level (ununiquify_level_level x) | Level.lvar x => Level.lvar (ununiquify_level_var total_sets x) end. | Definition | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | ununiquify_level | 1,384 |
(shared_levels : LevelSet.t) (shared_prefix : Byte.byte) (total_sets : nat) (prefix : Byte.byte) (offset : nat) (c : ConstraintSet.elt) : ConstraintSet.elt := let '((l1, c), l2) := c in let u := uniquify_level shared_levels shared_prefix total_sets prefix offset in ((u l1, c), u l2). | Definition | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | uniquify_constraint | 1,385 |
(total_sets : nat) (c : ConstraintSet.elt) : ConstraintSet.elt := let '((l1, c), l2) := c in let u := ununiquify_level total_sets in ((u l1, c), u l2). | Definition | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | ununiquify_constraint | 1,386 |
(shared_levels : LevelSet.t) (shared_prefix : Byte.byte) (total_sets : nat) (prefix : Byte.byte) (offset : nat) (v : valuation) : valuation := {| valuation_mono s := v.(valuation_mono) (uniquify_level_level shared_levels shared_prefix prefix s) ; valuation_poly n := v.(valuation_poly) (uniquify_level_var shared_levels total_sets offset n) |}. | Definition | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | uniquify_valuation | 1,387 |
(total_sets : nat) (v : valuation) : valuation := {| valuation_mono s := v.(valuation_mono) (ununiquify_level_level s) ; valuation_poly n := v.(valuation_poly) (ununiquify_level_var total_sets n) |}. | Definition | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | ununiquify_valuation | 1,388 |
lvls (side:bool) lvl := uniquify_level lvls "b"%byte 2 (if side then "l" else "r")%byte (if side then 0 else 1) lvl. | Definition | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | uniquify_level_for | 1,389 |
lvls (side:bool) c := uniquify_constraint lvls "b"%byte 2 (if side then "l" else "r")%byte (if side then 0 else 1) c. | Definition | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | uniquify_constraint_for | 1,390 |
lvls (side:bool) v := uniquify_valuation lvls "b"%byte 2 (if side then "l" else "r")%byte (if side then 0 else 1) v. | Definition | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | uniquify_valuation_for | 1,391 |
ContextSet.t * ConstraintSet.t -> ContextSet.t * ConstraintSet.t := fun '(cs, cstr) => let '(lvls, cs) := (ContextSet.levels cs, ContextSet.constraints cs) in let '(cs_all_lvls, cstr_all_lvls) := (levels_of_cs cs, levels_of_cs cstr) in ((LevelSet.fold (fun l => LevelSet.add (uniquify_level_for lvls true l)) cs_all_lvls (LevelSet.fold (fun l => LevelSet.add (uniquify_level_for lvls true l)) lvls (LevelSet.singleton Level.lzero)), ConstraintSet.fold (fun c => ConstraintSet.add (uniquify_constraint_for lvls true c)) cs ConstraintSet.empty), ConstraintSet.fold (fun c => ConstraintSet.add (uniquify_constraint_for lvls false c)) cstr ConstraintSet.empty). | Definition | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | declare_and_uniquify_levels | 1,392 |
ContextSet.t * ConstraintSet.t -> ContextSet.t * ConstraintSet.t := fun '(cs, cstr) => let cscstr := declare_and_uniquify_levels (cs, cstr) in let '(cs, cstr) := (cscstr.1, cscstr.2) in (cs, ConstraintSet.union cstr (ContextSet.constraints cs)). | Definition | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | declare_and_uniquify_and_combine_levels | 1,393 |
(shared_prefix prefixl prefixr : Byte.byte) (total_sets : nat := 2) (vd vl vr : valuation) : valuation := let __ := reflectEq_Z in {| valuation_mono s := match s with | ""%bs => vd.(valuation_mono) s | String.String p _ => if p == shared_prefix then vd.(valuation_mono) s else if p == prefixl then vl.(valuation_mono) s else if p == prefixr then vr.(valuation_mono) s else vd.(valuation_mono) s end ; valuation_poly n := let r := (Z.of_nat n mod 3)%Z in if r == 0%Z then vd.(valuation_poly) n else if r == 1%Z then vl.(valuation_poly) n else if r == 2%Z then vr.(valuation_poly) n else vd.(valuation_poly) n |}. | Definition | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | combine_valuations | 1,394 |
c cs1 cs2 f : ConstraintSet.In c (ConstraintSet.fold (fun c => ConstraintSet.add (f c)) cs1 cs2) <-> (ConstraintSet.Exists (fun c' => c = f c') cs1 \/ ConstraintSet.In c cs2). Proof. cbv [ConstraintSet.Exists]; rewrite ConstraintSetProp.fold_spec_right. setoid_rewrite (ConstraintSetFact.elements_iff cs1). setoid_rewrite InA_In_eq. setoid_rewrite (@List.in_rev _ (ConstraintSet.elements cs1)). induction (List.rev (ConstraintSet.elements cs1)) as [|x xs IH]; cbn [List.In List.fold_right]; [ now firstorder idtac | ]. rewrite ConstraintSet.add_spec. repeat first [ progress destruct_head'_ex | progress destruct_head'_and | progress destruct_head'_or | progress subst | progress intuition eauto ]. Qed. | Lemma | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | ConstraintSet_In_fold_add | 1,395 |
c cs1 cs2 f : LevelSet.In c (LevelSet.fold (fun c => LevelSet.add (f c)) cs1 cs2) <-> (LevelSet.Exists (fun c' => c = f c') cs1 \/ LevelSet.In c cs2). Proof. cbv [LevelSet.Exists]; rewrite LevelSetProp.fold_spec_right. setoid_rewrite (LevelSetFact.elements_iff cs1). setoid_rewrite InA_In_eq. setoid_rewrite (@List.in_rev _ (LevelSet.elements cs1)). induction (List.rev (LevelSet.elements cs1)) as [|x xs IH]; cbn [List.In List.fold_right]; [ now firstorder idtac | ]. rewrite LevelSet.add_spec. repeat first [ progress destruct_head'_ex | progress destruct_head'_and | progress destruct_head'_or | progress subst | progress intuition eauto ]. Qed. | Lemma | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | LevelSet_In_fold_add | 1,396 |
lvls n offset v (Hn : offset < n) : ununiquify_level_var n (uniquify_level_var lvls n offset v) = v. Proof. cbv [uniquify_level_var ununiquify_level_var]. destruct ?; f_equal. all: Z.to_euclidean_division_equations; nia. Qed. | Lemma | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | ununiquify_level_var__uniquify_level_var | 1,397 |
lvls sp p v : ununiquify_level_level (uniquify_level_level lvls sp p v) = v. Proof. reflexivity. Qed. | Lemma | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | ununiquify_level_level__uniquify_level_level | 1,398 |
lvls n offset sp p v (Hn : offset < n) : ununiquify_level n (uniquify_level lvls sp n p offset v) = v. Proof. destruct v; try reflexivity. cbv [ununiquify_level uniquify_level]. f_equal; now apply ununiquify_level_var__uniquify_level_var. Qed. | Lemma | common | From Coq Require Import PArith NArith ZArith Lia. From MetaCoq.Utils Require Import MCList MCOption MCUtils. From MetaCoq.Common Require Import uGraph. From MetaCoq.Common Require Import Universes. Import wGraph. | common\theories\UniversesDec.v | ununiquify_level__uniquify_level | 1,399 |
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