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 relp_neq : forall m n : Z, m <> 1 -> m <> -1 -> rel_prime m n -> m <> n.