End PolynomialComRing.
Canonical polynomial_countComRingType (R : countComRingType) :=
[countComRingType of polynomial R].
Canonical poly_countComRingType (R : countComRingType) :=
[countComRingType of {poly R}].
Section PolynomialIdomain.
(* Integral domain structure on poly *)
Variable R : idomainType.
Implicit Types (a b x y : R) (p q r m : {poly R}).

Lemma size_mul p q : p != 0 -> q != 0 -> size (p * q) = (size p + size q).-1.
Fact poly_idomainAxiom p q : p * q = 0 -> (p == 0) || (q == 0).