(* A specific case *)

Definition pytha_set_even (a b c : Z) :=
  exists p : Z, exists q : Z, exists m : Z,
    a = m * (q * q - p * p) /\ b = 2 * m * (p * q) /\
    c = m * (p * p + q * q) /\ m >= 0 /\ (cond_pq p q).

Lemma pytha_thm3 : forall a b c : Z, is_pytha a b c -> Zodd a -> pytha_set_even a b c.