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 gcd2_rel_prime : forall a b s w : Z, (Zis_gcd a b 2) -> a = 4 * s -> b = 2 * w -> rel_prime s w.