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Diffstat (limited to 'theories/Structures/Equalities.v')
| -rw-r--r-- | theories/Structures/Equalities.v | 13 |
1 files changed, 13 insertions, 0 deletions
diff --git a/theories/Structures/Equalities.v b/theories/Structures/Equalities.v index 14d34f1eb..8e72bd611 100644 --- a/theories/Structures/Equalities.v +++ b/theories/Structures/Equalities.v @@ -7,6 +7,7 @@ (***********************************************************************) Require Export RelationClasses. +Require Import Bool Morphisms Setoid. Set Implicit Arguments. Unset Strict Implicit. @@ -165,6 +166,18 @@ Module Dec2Bool (E:DecidableType) <: BooleanDecidableType Module Bool2Dec (E:BooleanEqualityType) <: BooleanDecidableType := E <+ HasEqBool2Dec. +(** 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. +now rewrite 2 eqb_eq, Exx', Eyy'. +Qed. + +End BoolEqualityFacts. (** * UsualDecidableType |