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 Zodd_sum1 : forall a b : Z, Zodd a -> Zodd b -> Zeven (a + b).