Definition distinct_parity (a b : Z) :=
(Zeven a) /\ (Zodd b) \/ (Zodd a) /\ (Zeven b).

Lemma relp_mult1 : forall a b c d k: Z, 0 <= a -> 0 <= b -> 0 < c -> 0 <= d ->
a = k * c -> b = k * d -> rel_prime a b -> k = 1.