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

Lemma not_rel_prime1 : forall x y : Z, ~ rel_prime x y -> exists d : Z, Zis_gcd x y d /\ d <> 1 /\ d <> -1.