diff options
Diffstat (limited to 'theories/Structures/DecidableType.v')
| -rw-r--r-- | theories/Structures/DecidableType.v | 10 |
1 files changed, 8 insertions, 2 deletions
diff --git a/theories/Structures/DecidableType.v b/theories/Structures/DecidableType.v index 625f776bfa..5b0fb21ef8 100644 --- a/theories/Structures/DecidableType.v +++ b/theories/Structures/DecidableType.v @@ -96,6 +96,12 @@ Module KeyDecidableType(D:DecidableType). Hint Resolve eqk_trans eqke_trans eqk_refl eqke_refl. Hint Immediate eqk_sym eqke_sym. + Global Instance eqk_equiv : Equivalence eqk. + Proof. split; eauto. Qed. + + Global Instance eqke_equiv : Equivalence eqke. + Proof. split; eauto. Qed. + Lemma InA_eqke_eqk : forall x m, InA eqke x m -> InA eqk x m. Proof. @@ -105,7 +111,7 @@ Module KeyDecidableType(D:DecidableType). Lemma InA_eqk : forall p q m, eqk p q -> InA eqk p m -> InA eqk q m. Proof. - intros; apply InA_eqA with p; auto; apply eqk_trans; auto. + intros; apply InA_eqA with p; auto with *. Qed. Definition MapsTo (k:key)(e:elt):= InA eqke (k,e). @@ -128,7 +134,7 @@ Module KeyDecidableType(D:DecidableType). Lemma MapsTo_eq : forall l x y e, eq x y -> MapsTo x e l -> MapsTo y e l. Proof. - intros; unfold MapsTo in *; apply InA_eqA with (x,e); eauto. + intros; unfold MapsTo in *; apply InA_eqA with (x,e); eauto with *. Qed. Lemma In_eq : forall l x y, eq x y -> In x l -> In y l. |