Fact mul_poly_key : unit.Definition mul_poly := locked_with mul_poly_key mul_poly_def.Fact mul_polyA : associative mul_poly.Fact mul_1poly : left_id 1%:P mul_poly.Fact mul_poly1 : right_id 1%:P mul_poly.Definition poly_ringMixin :=
  RingMixin mul_polyA mul_1poly mul_poly1 mul_polyDl mul_polyDr poly1_neq0.Canonical poly_ringType := Eval hnf in RingType {poly R} poly_ringMixin.Canonical polynomial_ringType :=
  Eval hnf in RingType (polynomial R) poly_ringMixin.

(* Specifications: *)
Lemma polyC1 : 1%:P = 1 :> {poly R}.
Lemma size_poly1 : size (1 : {poly R}) = 1%N.
Lemma lead_coef1 : lead_coef 1 = 1 :> R.