Definition distinct_parity (a b : Z) :=
(Zeven a) /\ (Zodd b) \/ (Zodd a) /\ (Zeven b).

Lemma prop3 : forall m n : Z, rel_prime (m * m) (n * n) -> rel_prime m n.
Definition R_prime (x y : Z) := 1 < x /\ 1 < y /\ x < y.