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

Lemma Zodd_mult : forall u v : Z,
Zodd u -> Zodd v ->
(exists s : Z,
(exists w : Z, (u - v = 4 * s /\ u + v = 2 * w) \/
(u - v = 2 * w /\ u + v = 4 * s))).