Canonical coefp_additive i :=
  Additive ((fun p => (coefB p)^~ i) : additive (coefp i)).Canonical polyC_additive := Additive polyC_sub.

(* Specifications: *)
Lemma size_opp p : size (- p) = size p.
Lemma lead_coef_opp p : lead_coef (- p) = - lead_coef p.
Lemma size_add p q : size (p + q) <= maxn (size p) (size q).
Lemma size_addl p q : size p > size q -> size (p + q) = size p.
Lemma lead_coefDl p q : size p > size q -> lead_coef (p + q) = lead_coef p.
Lemma lead_coefDr p q : size q > size p -> lead_coef (p + q) = lead_coef q.