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 sqr_sum5 : forall a b: Z, a <> 0 -> b <> 0 -> distinct_parity a b -> a + b < a * a + b * b.