(* step 6 *)
(* The set of Pythagorean triples *)

Lemma pytha_thm2 : forall a b c : Z, (pytha_set a b c) -> (is_pytha a b c).
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).