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 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))).