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 prop1 : forall m n : Z, rel_prime m n -> distinct_parity m n -> rel_prime (m + n) (n - m).