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_rel_prime2 : forall x y d : Z, (d | x) -> (d | y) -> d <> 1 -> d <> -1 -> ~ rel_prime x y.