proposition: Lemma flip_odd : forall (p : RX) n, Nat.Odd n -> monic n p -> monic n (flip p).
proof: Proof. unfold monic in |- *. unfold degree_le in |- *. intros. elim H0. clear H0. intros. split. astepl ( [--] ( [--][1][^]n) [*]nth_coeff n p). astepl ( [--][--] ([1][^]n) [*]nth_coeff n p). astepl ([1][^]n[*]nth_coeff n p). astepl ([1][*]nth_coeff n p). Step_final ([1][*] ([1]:R)). intros. astepl ( [--] ( [--][1][^]m) [*]nth_coeff m p). Step_final ( [--] ( [--][1][^]m) [*] ([0]:R)). Qed.
imports: CoRN.reals.IVT