proposition: Lemma nth_coeff_S : forall m p c, in_coeff (nth_coeff m p) p -> in_coeff (nth_coeff (S m) (c[+X*]p)) (c[+X*]p).
proof: Proof. simpl in |- *; auto. Qed.
imports: CoRN.algebra.CPolynomials Coq.Classes.Morphisms CoRN.algebra.CRings