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 divide_2 : forall z : Z, 0 <= z -> z <> 0 -> z <> 1 -> (z | 2) -> z = 2.