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 gcd_rel_prime : forall x y d : Z, Zis_gcd x y d -> exists a : Z, exists b : Z, x = d * a /\ y = d * b /\ rel_prime a b.