proposition: Lemma monic_mult : forall (p q : RX) m n, monic m p -> monic n q -> monic (m + n) (p[*]q).
proof: Proof. unfold monic in |- *. intros. elim H. clear H. intros. elim H0. clear H0. intros. split. astepl (nth_coeff m p[*]nth_coeff n q). Step_final ([1][*] ([1]:R)). apply degree_le_mult; auto. Qed.
imports: CoRN.algebra.CPoly_NthCoeff CoRN.algebra.CFields CoRN.tactics.Rational Lia