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 distp_odd : forall p q : Z, (distinct_parity p q) -> both_odd (p + q) (q - p).