proposition: Lemma square_add_le : forall a b, 0<=a -> 0<=b -> (a+b)*(a+b) <= 2*(a*a + b*b).
proof: Proof. intros a b Ha Hb. rewrite !mul_add_distr_l, !mul_add_distr_r. nzsimpl'. rewrite <- !add_assoc. apply add_le_mono_l. rewrite !add_assoc. apply add_le_mono_r. apply crossmul_le_addsquare; order. Qed.
imports: NZAxioms NZAddOrder