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_divide1 : forall a b : Z, a <> 1 -> a <> -1 -> b <> 0 -> ~(a * b | b).