intuition.
case_eq (eqb x y); intuition.
rewrite eqb_leibniz in H.
subst.
rewrite eqb_refl.
trivial.
case_eq (eqb y x); intuition.
rewrite eqb_leibniz in H0; subst.
rewrite eqb_refl in H.
discriminate.
Qed.

(* Specifications: *)
Theorem EqDec_dec : forall A,
EqDec A ->
forall (a b : A), {a = b} + {a <> b}.