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φ φ' pb t u : ConstraintSet.Subset φ φ' -> compare_universe φ pb t u -> compare_universe 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_universe_subset | 1,200 |
φ φ' t u : ConstraintSet.Subset φ φ' -> eq_universe φ t u -> eq_universe φ' t u. Proof using Type. apply cmp_universe_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_universe_subset | 1,201 |
φ φ' t u : ConstraintSet.Subset φ φ' -> leq_universe φ t u -> leq_universe φ' t u. Proof using Type. apply cmp_universe_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_universe_subset | 1,202 |
{univ} := sProp | sSProp | sType (_ : univ). | 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_ | 1,203 |
t_ Universe.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 | 1,204 |
Set := | fSProp | fProp | fType. | 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 | family | 1,205 |
{univ} `{ReflectEq univ} (u1 u2 : t_ univ) : bool := match u1, u2 with | sSProp, sSProp => true | sProp, sProp => true | sType e1, sType e2 => eqb e1 e2 | _, _ => 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 | eqb | 1,206 |
#[global, program] {univ} `{ReflectEq univ} : ReflectEq (t_ univ) := { eqb := eqb }. Next Obligation. destruct x, y; cbn; try constructor; auto; try congruence. destruct (eqb_spec u u0); constructor. now f_equal. congruence. 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 | reflect_eq_sort | 1,207 |
{univ} `{EqDec univ} : EqDec (t_ univ) := ltac:(intros s s'; decide equality). | 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 | eq_dec_sort | 1,208 |
{u u'} (f : u -> u') s := match s with | sType u => sType (f u) | sProp => sProp | sSProp => sSProp 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 | map | 1,209 |
{univ} {T} (P: univ -> T) (def: T) (s : t_ univ) := match s with | sProp | sSProp => def | sType l => P 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 | on_sort | 1,210 |
(s : t) : bool := match s with | sSProp | sProp => true | sType l => Universe.is_levels 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 | is_levels | 1,211 |
(s : t) : bool := match s with | sSProp | sProp => true | sType l => Universe.is_level 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 | is_level | 1,212 |
{univ} (s : t_ univ) : bool := match s with | sSProp => 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_sprop | 1,213 |
{univ} (s : t_ univ) : bool := match s with | sProp => 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_prop | 1,214 |
{univ} (s : t_ univ) : bool := match s with | sProp | sSProp => 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_propositional | 1,215 |
{univ} (s : t_ univ) : is_prop s -> is_propositional s. Proof. now 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 | is_prop_propositional | 1,216 |
{univ} (s : t_ univ) : is_sprop s -> is_propositional s. Proof. now 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 | is_sprop_propositional | 1,217 |
{univ} (s : t_ univ) : bool := match s with | sType _ => 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_type_sort | 1,218 |
t := sType (Universe.make LevelExpr.set). | 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 | type0 | 1,219 |
t := sType (Universe.make LevelExpr.type1). | 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 | type1 | 1,220 |
(l : PropLevel.t + Level.t) : t := match l with | inl PropLevel.lSProp => sSProp | inl PropLevel.lProp => sProp | inr l => sType (Universe.make' 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 | of_levels | 1,221 |
{univ} type1 univ_succ (s : t_ univ) : t_ univ := match s with | sSProp | sProp => sType type1 | sType l => sType (univ_succ 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 | super_ | 1,222 |
t -> t := super_ (Universe.make LevelExpr.type1) Universe.succ. | 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 | super | 1,223 |
super_ 1 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 | csuper | 1,224 |
{univ} univ_sup (s s' : t_ univ) : t_ univ := match s, s' with | sSProp, s' => s' | sProp, sSProp => sProp | sProp, s' => s' | sType u1, sType u2 => sType (univ_sup u1 u2) | sType _ as s, _ => s 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 | sup_ | 1,225 |
t -> t -> t := sup_ Universe.sup. | 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 | sup | 1,226 |
sup_ Nat.max. | 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 | csup | 1,227 |
{univ} univ_sup (domsort rangsort : t_ univ) : t_ univ := match rangsort with | sSProp | sProp => rangsort | _ => Sort.sup_ univ_sup domsort rangsort 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 | sort_of_product_ | 1,228 |
t -> t -> t := sort_of_product_ Universe.sup. | 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 | sort_of_product | 1,229 |
sort_of_product_ Nat.max. | 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 | csort_of_product | 1,230 |
(s : t) : option Level.t := match s with | sSProp => None | sProp => None | sType l => Universe.get_is_level 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 | get_is_level | 1,231 |
{univ} (s : t_ univ) := match s with | sSProp => fSProp | sProp => fProp | sType _ => fType 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 | to_family | 1,232 |
v s := match s with | sSProp => sSProp | sProp => sProp | sType u => sType (val v 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 | to_csort | 1,233 |
s v : to_family (to_csort v s) = to_family s. Proof. destruct s; cbnr. 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 | to_family_to_csort | 1,234 |
{univ type1 univ_succ} (s : t_ univ) : to_family (super_ type1 univ_succ s) = fType. Proof. now 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 | sType_super_ | 1,235 |
(s : t) : to_family (super s) = fType. Proof. apply sType_super_. 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 | sType_super | 1,236 |
{univ univ_lt} : t_ univ -> t_ univ -> Prop := | ltPropSProp : lt_ sProp sSProp | ltPropType s : lt_ sProp (sType s) | ltSPropType s : lt_ sSProp (sType s) | ltTypeType s1 s2 : univ_lt s1 s2 -> lt_ (sType s1) (sType s2). | 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_ | 1,237 |
lt_ Universe.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 | 1,238 |
lt_ Nat.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 | clt | 1,239 |
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 | 1,240 |
#[local] Definition eq : 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 | 1,241 |
#[local] Definition eq_equiv : 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 | 1,242 |
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 | 1,243 |
#[local] : StrictOrder lt. Proof. constructor. - intros [| |] X; inversion X. now eapply irreflexivity in H1. - intros [| |] [| |] [| |] X1 X2; inversion X1; inversion X2; constructor. subst. etransitivity; tea. 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 | lt_strorder | 1,244 |
Proper (eq ==> eq ==> iff) lt. Proof. intros x y e z t e'. hnf in * |- ; subst. reflexivity. 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_compat | 1,245 |
(x y : t) : comparison := match x, y with | sProp, sProp => Eq | sProp, _ => Lt | _, sProp => Gt | sSProp, sSProp => Eq | sSProp, _ => Lt | _, sSProp => Gt | sType x, sType y => LevelExprSet.compare x y 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 | 1,246 |
x y : CompareSpec (eq x y) (lt x y) (lt y x) (compare x y). Proof. cbv [compare eq]. destruct x, y. all: lazymatch goal with | [ |- context[LevelExprSet.compare ?x ?y] ] => destruct (LevelExprSet.compare_spec x y) | _ => idtac end. all: lazymatch goal with | [ H : LevelExprSet.eq (?f ?x) (?f ?y) |- _ ] => apply LevelExprSet.eq_leibniz in H; is_var x; is_var y; destruct x, y; cbn in H; subst | _ => idtac end. all: repeat constructor; try apply f_equal; try assumption. f_equal; apply Eqdep_dec.UIP_dec; decide equality. 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 | 1,247 |
(x y : t) : {x = y} + {x <> y}. Proof. repeat decide equality. apply Universe.eq_dec_univ0. Defined. | 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_dec | 1,248 |
v s1 s2 : Sort.to_csort v (Sort.sup s1 s2) = Sort.csup (Sort.to_csort v s1) (Sort.to_csort v s2). Proof. destruct s1 as [ | | u1]; destruct s2 as [ | | u2]; cbnr. f_equal. apply val_sup. 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_sort_sup | 1,249 |
s : Sort.is_prop s -> forall v, Sort.to_csort v s = Sort.sProp. 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 | is_prop_val | 1,250 |
s : Sort.is_sprop s -> forall v, Sort.to_csort v s = Sort.sSProp. 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 | is_sprop_val | 1,251 |
s v : Sort.to_csort v s = sProp <-> Sort.is_prop 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 | val_is_prop | 1,252 |
s v : Sort.to_csort v s = sSProp <-> Sort.is_sprop 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 | val_is_sprop | 1,253 |
s : Sort.is_prop s = false -> Sort.is_sprop s = false -> forall v, ∑ n, Sort.to_csort v s = sType n. Proof. intros Hp Hsp v. destruct s => //. simpl. eexists; 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 | is_prop_and_is_sprop_val_false | 1,254 |
s v n : Sort.to_csort v s = sType n -> Sort.is_prop s = false. 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 | val_is_prop_false | 1,255 |
s l : Sort.get_is_level s = Some l -> s = sType (Universe.make' l). Proof. intro H; destruct s => //=. f_equal; now apply universe_get_is_level_correct. 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 | get_is_level_correct | 1,256 |
(s s' : sort) : eqb s s' <-> s = s'. Proof. split. apply /eqb_spec. eapply introP. apply /eqb_spec. 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 | eqb_true_iff | 1,257 |
x1 x2 : Sort.sup x1 x2 = Sort.sup x2 x1. Proof. destruct x1,x2;auto. cbn;apply f_equal;apply sup0_comm. 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_comm | 1,258 |
{univ} (s : Sort.t_ univ) : Sort.is_prop s = false -> Sort.is_sprop s = false -> ∑ s', s = sType s'. Proof. intros Hp Hsp. destruct s => //. now eexists. 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_not_prop_and_is_not_sprop | 1,259 |
x1 x2 : Sort.is_prop (Sort.sup x1 x2) -> Sort.is_prop x2 \/ Sort.is_sprop x2 . Proof. destruct x1,x2;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 | is_prop_sort_sup | 1,260 |
x1 x2 : Sort.is_prop (Sort.sup x1 x2) -> Sort.is_prop x1 \/ Sort.is_sprop x1 . Proof. destruct x1,x2;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 | is_prop_sort_sup' | 1,261 |
x1 x2 : Sort.is_sprop (Sort.sup x1 x2) -> Sort.is_sprop x2. Proof. destruct x1,x2;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 | is_prop_or_sprop_sort_sup | 1,262 |
x1 x2 : Sort.is_prop x1 && Sort.is_prop x2 -> Sort.is_prop (Sort.sup x1 x2). Proof. destruct x1,x2;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 | is_prop_sort_sup_prop | 1,263 |
x1 x2 : Sort.is_sprop x1 && Sort.is_sprop x2 -> Sort.is_sprop (Sort.sup x1 x2). Proof. destruct x1,x2;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 | is_prop_or_sprop_sort_sup_prop | 1,264 |
s s' : Sort.is_prop (Sort.sup s s') -> Sort.is_propositional s /\ Sort.is_propositional s'. Proof. destruct s, s'; 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 | is_prop_sup | 1,265 |
s s' : Sort.is_sprop (Sort.sup s s') <-> (Sort.is_sprop s /\ Sort.is_sprop s'). Proof. split; destruct s, s' => //=; 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 | is_sprop_sup_iff | 1,266 |
s1 s2 : Sort.is_type_sort s2 -> Sort.is_type_sort (Sort.sup s1 s2). Proof. destruct s2; try absurd; destruct s1; cbnr; intros; 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 | is_type_sup_r | 1,267 |
x2 x3 : Sort.is_prop (Sort.sort_of_product x2 x3) -> Sort.is_prop x3. Proof. unfold Sort.sort_of_product. destruct x3;cbn;auto. intros;simpl in *;destruct x2;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 | is_prop_sort_prod | 1,268 |
x2 x3 : Sort.is_sprop (Sort.sort_of_product x2 x3) -> Sort.is_sprop x3. Proof. unfold Sort.sort_of_product. destruct x3;cbn;auto. intros;simpl in *;destruct x2;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 | is_sprop_sort_prod | 1,269 |
{univ} (leq_universe_n : Z -> univ -> univ -> Prop) n s s' : Prop := match s, s' with | sProp, sProp | sSProp, sSProp => (n = 0)%Z | sType u, sType u' => leq_universe_n n u u' | sProp, sType u => prop_sub_type | _, _ => 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 | leq_sort_n_ | 1,270 |
n φ := leq_sort_n_ (fun n => leq_universe_n n φ) 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 | leq_sort_n | 1,271 |
leq_sort_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_sort | 1,272 |
leq_sort_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_sort | 1,273 |
{univ} (leqb_universe_n : bool -> univ -> univ -> bool) b s s' : bool := match s, s' with | sProp, sProp | sSProp, sSProp => negb b | sType u, sType u' => leqb_universe_n b u u' | sProp, sType u => prop_sub_type | _, _ => 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 | leqb_sort_n_ | 1,274 |
{univ} (eq_universe : univ -> univ -> Prop) s s' : Prop := match s, s' with | sProp, sProp | sSProp, sSProp => True | sType u, sType u' => eq_universe u u' | _, _ => 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 | eq_sort_ | 1,275 |
φ := eq_sort_ (eq_universe φ). | 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_sort | 1,276 |
{univ} (eqb_universe : univ -> univ -> bool) s s' : bool := match s, s' with | sProp, sProp | sSProp, sSProp => true | sType u, sType u' => eqb_universe u u' | _, _ => 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 | eqb_sort_ | 1,277 |
φ (pb : conv_pb) := match pb with | Conv => eq_sort φ | Cumul => leq_sort 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_sort | 1,278 |
(φ : ConstraintSet.t) s s' : leq_sort φ s s' <-> leq_sort_n 0 φ s s'. Proof using Type. intros. 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 | leq_sort_leq_sort_n | 1,279 |
φ pb u u' : compare_sort φ pb (sType u) (sType u') = compare_universe φ pb u u'. Proof. now destruct pb. 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_sort_type | 1,280 |
s : s <= sProp -> s = sProp. Proof using Type. 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 | sort_le_prop_inv | 1,281 |
s : s <= sSProp -> s = sSProp. Proof using Type. 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 | sort_le_sprop_inv | 1,282 |
s : sProp <= s -> (s = sProp \/ (prop_sub_type /\ exists n, s = sType n)). Proof using Type. destruct s => //= Hle. - now left. - right; split => //; now eexists. 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_prop_le_inv | 1,283 |
s : sSProp <= s -> s = sSProp. Proof using Type. 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 | sort_sprop_le_inv | 1,284 |
Irreflexive (leq_universe_n 1) -> Irreflexive lt_sort. Proof using Type. intros H []; unfold complement; cbnr. 1,2: lia. 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 | lt_sort_irrefl | 1,285 |
Sort.t_ nat. | 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 | concrete_sort | 1,286 |
Z -> concrete_sort -> concrete_sort -> Prop := leq_sort_n_ (fun n u u' => (Z.of_nat u <= Z.of_nat 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 | leq_csort_n | 1,287 |
leq_csort_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_csort | 1,288 |
leq_csort_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_csort | 1,289 |
s := match s with sSProp | sProp | sType 0 => 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_propositional_or_set | 1,290 |
s s' : Sort.csup s s' = Sort.csup s' s. Proof using Type. destruct s, s' => //=. f_equal; 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 | csort_sup_comm | 1,291 |
s s' : ~ Sort.is_propositional s -> ∑ n, Sort.csup s s' = sType n. Proof using Type. destruct s => //=. destruct s'; now eexists. 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 | csort_sup_not_uproplevel | 1,292 |
s s' v v' : (s <= s')%u -> (sType v <= sType v')%u -> (Sort.csup s (sType v) <= Sort.csup s' (sType v'))%u. Proof using Type. destruct s, s' => //=; intros Hle Hle'; 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 | csort_sup_mon | 1,293 |
u u' v v' : (u <= u')%u -> (v <= v')%u -> (Sort.csort_of_product u v <= Sort.csort_of_product u' v')%u. Proof using Type. intros Hle1 Hle2. destruct v, v'; cbn in Hle2 |- *; auto. - destruct u'; cbn; assumption. - apply csort_sup_mon; assumption. 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_csort_of_product_mon | 1,294 |
{univ} {univ_sup} {l u} : Sort.is_propositional u -> Sort.sort_of_product_ (univ := univ) univ_sup l u = u. Proof using Type. now destruct u. 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_csort_product | 1,295 |
φ u1 s2 : let s1 := sType u1 in leq_sort φ s1 (Sort.sup s1 s2). Proof using Type. destruct s2 as [| | u2]; cbnr. apply leq_universe_sup_l. 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_sup_l | 1,296 |
φ s1 u2 : let s2 := sType u2 in leq_sort φ s2 (Sort.sup s1 s2). Proof using Type. destruct s1 as [| | u1]; cbnr. apply leq_universe_sup_r. 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_sup_r | 1,297 |
φ (s1 s2 : Sort.t) : leq_sort φ s2 (Sort.sort_of_product s1 s2). Proof using Type. destruct s2 as [| | u2] => //. apply leq_sort_sup_r. 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 | 1,298 |
φ leq_universe eq_universe Hsub u u' := @eq_leq_sort φ leq_universe eq_universe Hsub 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_sort' | 1,299 |
Subsets and Splits