intuition.
subst.
rewrite eqb_refl in H.
discriminate.
case_eq (eqb a1 a2); intuition.
rewrite eqb_leibniz in H0.
intuition.
Qed.

Theorem eqbPair_symm :
forall (A B : Set)(eqda : EqDec A)(eqdb : EqDec B) (p1 p2 : (A * B)),
eqbPair _ _ p1 p2 = eqbPair _ _ p2 p1.