Lemma for_mba_pytha2: forall m n u v a b : Z, u * u = m * m + n * n -> v * v = n * n - m * m -> u - v = 2 * (b * b) -> u + v = 4 * (a * a) -> b * b * (b * b) + 2 * (a * a) * (2 * (a * a)) = n * n.