Canonical prod_eqType := Eval hnf in EqType (T1 * T2) prod_eqMixin.

(* Specifications: *)
Lemma pair_eqE : pair_eq = eq_op :> rel _. Proof. by []. Qed.
Lemma xpair_eqE (x1 y1 : T1) (x2 y2 : T2) :
((x1, x2) == (y1, y2)) = ((x1 == y1) && (x2 == y2)).