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v s1 s2 : val v (Universe.sup s1 s2) = Nat.max (val v s1) (val v s2). Proof. eapply val_caract. cbn. split. - intros e' H. eapply LevelExprSet.union_spec in H. destruct H as [H|H]. + eapply val_In_le with (v:=v) in H. lia. + eapply val_In_le with (v:=v) in H. lia. - destruct (Nat.max_dec (val v s1) (val v s2)) as [H|H]; rewrite H; clear H. + destruct (val_In_max s1 v) as [e' [H1 H2]]. exists e'. split; tas. apply LevelExprSet.union_spec. now left. + destruct (val_In_max s2 v) as [e' [H1 H2]]. exists e'. split; tas. apply LevelExprSet.union_spec. now right. 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_sup | 1,100 |
(P : LevelExpr.t -> bool) u : LevelExprSet.for_all P u = forallb P (LevelExprSet.elements u). Proof. apply LevelExprSetFact.for_all_b; proper. 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 | for_all_elements | 1,101 |
u l : Universe.get_is_level u = Some l -> u = Universe.make' l. Proof. intro H. unfold Universe.get_is_level in *. destruct (LevelExprSet.elements u) as [|l0 L] eqn:Hu1; [discriminate |]. destruct l0, L; try discriminate. * destruct n; inversion H; subst. apply eq_univ''; apply Hu1. * destruct n; 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 | universe_get_is_level_correct | 1,102 |
x1 x2 : Universe.sup x1 x2 = Universe.sup x2 x1. Proof. apply eq_univ'; simpl. unfold LevelExprSet.Equal. intros H. 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 | sup0_comm | 1,103 |
v (l : Universe.t) : 0 <= val v l. Proof. rewrite val_fold_right. destruct (Universe.exprs l) as [e u']; clear l; cbn. induction (List.rev u'); simpl. - destruct e as [npl_expr]. destruct npl_expr as [t b]. cbn. assert (0 <= val v t) by apply Level.val_zero. destruct b;lia. - pose proof (LevelExpr.val_zero a v); 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_zero_exprs | 1,104 |
Set := Le (z : Z) | Eq. | 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 | t_ | 1,105 |
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 | t | 1,106 |
t -> t -> Prop := eq. | 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 | eq | 1,107 |
Equivalence eq := _. | 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 | eq_equiv | 1,108 |
Le 0. | 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 | Le0 | 1,109 |
Le 1. | 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 | Lt | 1,110 |
t -> t -> Prop := | LeLe n m : (n < m)%Z -> lt_ (Le n) (Le m) | LeEq n : lt_ (Le n) Eq. | 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 | lt_ | 1,111 |
lt_. Global Instance lt_strorder : StrictOrder lt. Proof. constructor. - intros []; intro X; inversion X. lia. - intros ? ? ? X Y; invs X; invs Y; constructor. lia. Qed. | 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 | lt | 1,112 |
(x y : t) : comparison := match x, y with | Le n, Le m => Z.compare n m | Le _, Eq => Datatypes.Lt | Eq, Eq => Datatypes.Eq | Eq, _ => Datatypes.Gt 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 | compare | 1,113 |
x y : CompareSpec (eq x y) (lt x y) (lt y x) (compare x y). Proof. destruct x, y; repeat constructor. simpl. destruct (Z.compare_spec z z0); simpl; constructor. subst; constructor. now constructor. now constructor. 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 | compare_spec | 1,114 |
x y : {eq x y} + {~ eq x y}. Proof. unfold eq. decide equality. apply Z.eq_dec. 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_dec | 1,115 |
Set := Level.t * ConstraintType.t * Level.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 | t | 1,116 |
t -> t -> Prop := eq. | 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 | eq | 1,117 |
Equivalence eq := _. | 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 | eq_equiv | 1,118 |
l1 ct l2 : t := (l1, ct, l2). | 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 | make | 1,119 |
t -> t -> Prop := | lt_Level2 l1 t l2 l2' : Level.lt l2 l2' -> lt_ (l1, t, l2) (l1, t, l2') | lt_Cstr l1 t t' l2 l2' : ConstraintType.lt t t' -> lt_ (l1, t, l2) (l1, t', l2') | lt_Level1 l1 l1' t t' l2 l2' : Level.lt l1 l1' -> lt_ (l1, t, l2) (l1', t', l2'). | 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 | lt_ | 1,120 |
lt_. | 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 | lt | 1,121 |
StrictOrder lt. Proof. constructor. - intros []; intro X; inversion X; subst; try (eapply Level.lt_strorder; eassumption). eapply ConstraintType.lt_strorder; eassumption. - intros ? ? ? X Y; invs X; invs Y; constructor; tea. etransitivity; eassumption. 2: etransitivity; eassumption. eapply ConstraintType.lt_strorder; 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 | lt_strorder | 1,122 |
Proper (eq ==> eq ==> iff) lt. Proof. intros ? ? X ? ? Y; invs X; invs Y. 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 | lt_compat | 1,123 |
t -> t -> comparison := fun '(l1, t, l2) '(l1', t', l2') => compare_cont (Level.compare l1 l1') (compare_cont (ConstraintType.compare t t') (Level.compare l2 l2')). | 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 | compare | 1,124 |
x y : CompareSpec (eq x y) (lt x y) (lt y x) (compare x y). Proof. destruct x as [[l1 t] l2], y as [[l1' t'] l2']; cbn. destruct (Level.compare_spec l1 l1'); cbn; repeat constructor; tas. invs H. destruct (ConstraintType.compare_spec t t'); cbn; repeat constructor; tas. invs H. destruct (Level.compare_spec l2 l2'); cbn; repeat constructor; tas. invs H. 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 | compare_spec | 1,125 |
x y : {eq x y} + {~ eq x y}. Proof. unfold eq. decide equality; apply eq_dec. Defined. | 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_dec | 1,126 |
(x y : t) : eq x y -> x = y := id. | 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 | eq_leibniz | 1,127 |
levels (cstr : UnivConstraint.t) := let '(l1,_,l2) := cstr in LevelSet.In l1 levels /\ LevelSet.In l2 levels. | 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 | declared_cstr_levels | 1,128 |
levels (cstr : UnivConstraint.t) : bool := let '(l1,_,l2) := cstr in LevelSet.mem l1 levels && LevelSet.mem l2 levels. | 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_declared_cstr_levels | 1,129 |
s : ConstraintSet.union ConstraintSet.empty s =_cset s. Proof. intros x; rewrite ConstraintSet.union_spec. lsets. 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 | CS_union_empty | 1,130 |
f cst cst' : ConstraintSet.For_all f (ConstraintSet.union cst cst') -> ConstraintSet.For_all f cst. Proof. unfold CS.For_all. intros IH x inx. apply (IH x). now eapply CS.union_spec; left. 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 | CS_For_all_union | 1,131 |
P x s : CS.For_all P (CS.add x s) -> P x /\ CS.For_all P s. Proof. intros. split. * apply (H x), CS.add_spec; left => //. * intros y iny. apply (H y), CS.add_spec; right => //. 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 | CS_For_all_add | 1,132 |
P : Morphisms.Proper ((=_cset) ==> iff)%signature (ConstraintSet.For_all P). Proof. intros s s' eqs. unfold CS.For_all. split; intros IH x inxs; apply (IH x); now apply eqs. 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 | CS_For_all_proper | 1,133 |
Set := list Level.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 | t | 1,134 |
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 | empty | 1,135 |
(i : t) : bool := match i with | [] => 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 | is_empty | 1,136 |
(i j : t) := forallb2 Level.eqb i j. | 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 | eqb | 1,137 |
(f : Level.t -> Level.t -> bool) (i j : t) := forallb2 f i j. | 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 | equal_upto | 1,138 |
list name × (Instance.t × ConstraintSet.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 | t | 1,139 |
Instance.t -> ConstraintSet.t -> Instance.t × ConstraintSet.t := pair. | 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 | make' | 1,140 |
(ids : list name) (inst_ctrs : Instance.t × ConstraintSet.t) : t := (ids, inst_ctrs). | 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 | make | 1,141 |
t := ([], (Instance.empty, ConstraintSet.empty)). | 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 | empty | 1,142 |
t -> Instance.t := fun x => fst (snd x). | 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 | instance | 1,143 |
t -> ConstraintSet.t := fun x => snd (snd x). | 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 | constraints | 1,144 |
t -> list name * (Instance.t * ConstraintSet.t) := fun x => x. | 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 | dest | 1,145 |
list name × ConstraintSet.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 | t | 1,146 |
(ids : list name) (ctrs : ConstraintSet.t) : t := (ids, ctrs). | 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 | make | 1,147 |
(x : t) : UContext.t := let (u, cst) := x in (u, (mapi (fun i _ => Level.lvar i) u, cst)). | 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 | repr | 1,148 |
(uctx : t) : LevelSet.t := LevelSetProp.of_list (fst (snd (repr uctx))). | 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 | levels | 1,149 |
(au av : AUContext.t) : AUContext.t := let prefix := (split_prefix au.1 av.1).1.1 in let lvls := fold_left_i (fun s i _ => LevelSet.add (Level.lvar i) s) prefix LevelSet.empty in let filter := ConstraintSet.filter (is_declared_cstr_levels lvls) in make prefix (ConstraintSet.union (filter au.2) (filter av.2)). | 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 | inter | 1,150 |
LevelSet.t × ConstraintSet.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 | t | 1,151 |
t -> LevelSet.t := fst. | 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 | levels | 1,152 |
t -> ConstraintSet.t := snd. | 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 | constraints | 1,153 |
t := (LevelSet.empty, ConstraintSet.empty). | 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 | empty | 1,154 |
(uctx : t) := LevelSet.is_empty (fst uctx) && ConstraintSet.is_empty (snd uctx). | 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_empty | 1,155 |
(x y : t) : Prop := x.1 =_lset y.1 /\ x.2 =_cset y.2. | 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 | Equal | 1,156 |
(x y : t) : bool := x.1 ==_lset y.1 && x.2 ==_cset y.2. | 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 | equal | 1,157 |
(x y : t) : Prop := LevelSet.Subset (levels x) (levels y) /\ ConstraintSet.Subset (constraints x) (constraints y). | 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 | Subset | 1,158 |
(x y : t) : bool := LevelSet.subset (levels x) (levels y) && ConstraintSet.subset (constraints x) (constraints y). | 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 | subset | 1,159 |
(x y : t) : t := (LevelSet.inter (levels x) (levels y), ConstraintSet.inter (constraints x) (constraints y)). | 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 | inter | 1,160 |
(x y : t) : Subset (inter x y) x /\ Subset (inter x y) y /\ forall z, Subset z x -> Subset z y -> Subset z (inter x y). Proof. split; last split. 1,2: split=> ?; [move=> /LevelSet.inter_spec [//]|move=> /ConstraintSet.inter_spec [//]]. move=> ? [??] [??]; split=> ??; [apply/LevelSet.inter_spec|apply/ConstraintSet.inter_spec]; split; auto. Qed. | 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 | inter_spec | 1,161 |
(x y : t) : t := (LevelSet.union (levels x) (levels y), ConstraintSet.union (constraints x) (constraints y)). | 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 | union | 1,162 |
(x y : t) : Subset x (union x y) /\ Subset y (union x y) /\ forall z, Subset x z -> Subset y z -> Subset (union x y) z. Proof. split; last split. 1,2: split=> ??; [apply/LevelSet.union_spec|apply/ConstraintSet.union_spec ]; by constructor. move=> ? [??] [??]; split=> ?; [move=>/LevelSet.union_spec|move=>/ConstraintSet.union_spec]=>-[]; auto. Qed. | 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 | union_spec | 1,163 |
s s' : equal s s' <-> Equal s s'. Proof. rewrite /equal/Equal/is_true Bool.andb_true_iff LevelSet.equal_spec ConstraintSet.equal_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 | equal_spec | 1,164 |
s s' : subset s s' <-> Subset s s'. Proof. rewrite /subset/Subset/is_true Bool.andb_true_iff LevelSet.subset_spec ConstraintSet.subset_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 | subset_spec | 1,165 |
s s' : reflect (Subset s s') (subset s s'). Proof. generalize (subset_spec s s'). destruct subset; case; constructor; 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 | subsetP | 1,166 |
cs : cs ⊂_cs cs. Proof. split; [lsets|csets]. 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 | incl_cs_refl | 1,167 |
cs1 cs2 cs3 : cs1 ⊂_cs cs2 -> cs2 ⊂_cs cs3 -> cs1 ⊂_cs cs3. Proof. intros [? ?] [? ?]; split; [lsets|csets]. 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 | incl_cs_trans | 1,168 |
u : ContextSet.empty ⊂_cs u. Proof. red. split; cbn; [lsets|csets]. 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 | empty_contextset_subset | 1,169 |
| Irrelevant : t | Covariant : t | Invariant : 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 | t | 1,170 |
Type := | Monomorphic_ctx | Polymorphic_ctx (cst : AUContext.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_decl | 1,171 |
u := match u with | Monomorphic_ctx => LevelSet.empty | Polymorphic_ctx ctx => AUContext.levels ctx 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 | levels_of_udecl | 1,172 |
u := match u with | Monomorphic_ctx => ConstraintSet.empty | Polymorphic_ctx ctx => snd (snd (AUContext.repr ctx)) 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 | constraints_of_udecl | 1,173 |
(v : valuation) : UnivConstraint.t -> Prop := | satisfies0_Lt (l l' : Level.t) (z : Z) : (Z.of_nat (val v l) <= Z.of_nat (val v l') - z)%Z -> satisfies0 v (l, ConstraintType.Le z, l') | satisfies0_Eq (l l' : Level.t) : val v l = val v l' -> satisfies0 v (l, ConstraintType.Eq, l'). | 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 | satisfies0 | 1,174 |
v : ConstraintSet.t -> Prop := ConstraintSet.For_all (satisfies0 v). | 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 | satisfies | 1,175 |
v φ1 φ2 : satisfies v (CS.union φ1 φ2) <-> (satisfies v φ1 /\ satisfies v φ2). Proof using Type. unfold satisfies. split. - intros H; split; intros c Hc; apply H; now apply CS.union_spec. - intros [H1 H2] c Hc; apply CS.union_spec in Hc; destruct Hc; 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 | satisfies_union | 1,176 |
φ φ' val : ConstraintSet.Subset φ φ' -> satisfies val φ' -> satisfies val φ. Proof using Type. intros sub sat ? isin. apply sat, sub; 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 | satisfies_subset | 1,177 |
ctrs := exists v, satisfies v ctrs. | 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 | consistent | 1,178 |
cs cstr := forall v, satisfies v (ContextSet.constraints cs) -> exists v', satisfies v' cstr /\ LevelSet.For_all (fun l => val v l = val v' l) (ContextSet.levels cs). | 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 | consistent_extension_on | 1,179 |
Σ : consistent_extension_on Σ CS.empty. Proof using Type. move=> v hv; exists v; split; [move=> ? /CS.empty_spec[]| move=> ??//]. 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 | consistent_extension_on_empty | 1,180 |
X cstrs (wfX : forall c, CS.In c X.2 -> LS.In c.1.1 X.1 /\ LS.In c.2 X.1) : consistent_extension_on X cstrs <-> consistent_extension_on X (CS.union cstrs X.2). Proof using Type. split. 2: move=> h v /h [v' [/satisfies_union [??] eqv']]; exists v'; split=> //. move=> hext v /[dup] vsat /hext [v' [v'sat v'eq]]. exists v'; split=> //. apply/satisfies_union; split=> //. move=> c hc. destruct (wfX c hc). destruct (vsat c hc); constructor; rewrite -!v'eq //. 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 | consistent_extension_on_union | 1,181 |
n φ (u u' : Universe.t) := forall v, satisfies v φ -> (Z.of_nat (val v u) <= Z.of_nat (val v u') - n)%Z. | 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 | leq0_universe_n | 1,182 |
{cf} n φ (u u' : Universe.t) := if check_univs then leq0_universe_n n φ u u' else True. | 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_universe_n | 1,183 |
{cf} := leq_universe_n 1. | 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 | lt_universe | 1,184 |
{cf} := leq_universe_n 0. | 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_universe | 1,185 |
φ (u u' : Universe.t) := forall v, satisfies v φ -> val v u = val v 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 | eq0_universe | 1,186 |
{cf} φ (u u' : Universe.t) := if check_univs then eq0_universe φ u u' else True. | 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 | eq_universe | 1,187 |
φ ctrs := forall v, satisfies v φ -> satisfies v ctrs. | 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 | valid_constraints0 | 1,188 |
{cf} φ ctrs := if check_univs then valid_constraints0 φ ctrs else True. | 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 | valid_constraints | 1,189 |
{cf} φ (pb : conv_pb) := match pb with | Conv => eq_universe φ | Cumul => leq_universe φ 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 | compare_universe | 1,190 |
φ φ' ctrs : ConstraintSet.Subset φ φ' -> valid_constraints φ ctrs -> valid_constraints φ' ctrs. Proof using Type. unfold_univ_rel. intros Hφ H v Hv. apply H. intros ctr Hc. apply Hv. now apply Hφ. 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_subset | 1,191 |
(x y z : Z) : (x <= y - z <-> x + z <= y)%Z. Proof using Type. split; 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 | switch_minus | 1,192 |
φ u u' : eq0_universe φ u u' <-> leq0_universe_n 0 φ u u' /\ leq0_universe_n 0 φ u' u. Proof using Type. split. - intros H. split; unfold_univ_rel0; lia. - intros [H1 H2]. unfold_univ_rel0; 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 | eq0_leq0_universe | 1,193 |
φ u u' : eq_universe φ u u' <-> leq_universe φ u u' /\ leq_universe φ u' u. Proof using Type. unfold_univ_rel => //. apply eq0_leq0_universe. 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_leq_universe | 1,194 |
φ u1 u2 : leq_universe φ u1 (Universe.sup u1 u2). Proof using Type. unfold_univ_rel. rewrite val_sup; 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_universe_sup_l | 1,195 |
φ u1 u2 : leq_universe φ u2 (Universe.sup u1 u2). Proof using Type. unfold_univ_rel. rewrite val_sup; 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_universe_sup_r | 1,196 |
φ u1 u1' u2 u2' : leq_universe φ u1 u1' -> leq_universe φ u2 u2' -> leq_universe φ (Universe.sup u1 u2) (Universe.sup u1' u2'). Proof using Type. intros H1 H2; unfold_univ_rel. rewrite !val_sup. 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_universe_sup_mon | 1,197 |
φ u u' := @eq_leq_universe φ u 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 | eq_leq_universe' | 1,198 |
φ u := @leq_universe_refl φ 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_universe_refl' | 1,199 |
Subsets and Splits