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 not_divide2 : forall a b : Z, 0 < a -> 0 < b -> b < a -> ~(a | b).