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_relp_odd : forall u v : Z, Zodd u -> Zodd v -> rel_prime u v -> (Zis_gcd (u - v) (u + v) 2).