diff options
Diffstat (limited to 'theories/Structures/EqualitiesFacts.v')
-rw-r--r-- | theories/Structures/EqualitiesFacts.v | 23 |
1 files changed, 5 insertions, 18 deletions
diff --git a/theories/Structures/EqualitiesFacts.v b/theories/Structures/EqualitiesFacts.v index d9b1d76f..c69885b4 100644 --- a/theories/Structures/EqualitiesFacts.v +++ b/theories/Structures/EqualitiesFacts.v @@ -8,21 +8,8 @@ Require Import Equalities Bool SetoidList RelationPairs. -(** In a BooleanEqualityType, [eqb] is compatible with [eq] *) - -Module BoolEqualityFacts (Import E : BooleanEqualityType). - -Instance eqb_compat : Proper (E.eq ==> E.eq ==> Logic.eq) eqb. -Proof. -intros x x' Exx' y y' Eyy'. -apply eq_true_iff_eq. -rewrite 2 eqb_eq, Exx', Eyy'; auto with *. -Qed. - -End BoolEqualityFacts. - - (** * Keys and datas used in FMap *) + Module KeyDecidableType(Import D:DecidableType). Section Elt. @@ -42,9 +29,9 @@ Module KeyDecidableType(Import D:DecidableType). (* eqk, eqke are equalities, ltk is a strict order *) - Global Instance eqk_equiv : Equivalence eqk. + Global Instance eqk_equiv : Equivalence eqk := _. - Global Instance eqke_equiv : Equivalence eqke. + Global Instance eqke_equiv : Equivalence eqke := _. (* Additionnal facts *) @@ -156,7 +143,7 @@ Module PairDecidableType(D1 D2:DecidableType) <: DecidableType. Definition eq := (D1.eq * D2.eq)%signature. - Instance eq_equiv : Equivalence eq. + Instance eq_equiv : Equivalence eq := _. Definition eq_dec : forall x y, { eq x y }+{ ~eq x y }. Proof. @@ -172,7 +159,7 @@ End PairDecidableType. Module PairUsualDecidableType(D1 D2:UsualDecidableType) <: UsualDecidableType. Definition t := (D1.t * D2.t)%type. Definition eq := @eq t. - Program Instance eq_equiv : Equivalence eq. + Instance eq_equiv : Equivalence eq := _. Definition eq_dec : forall x y, { eq x y }+{ ~eq x y }. Proof. intros (x1,x2) (y1,y2); |