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_parity : forall x y : Z, (rel_prime x y) -> (distinct_parity x y) \/ (both_odd x y).