proposition: Lemma lreg_size c p : GRing.lreg c -> size (c *: p) = size p.
proof: Proof. move=> reg_c; have [-> | nz_p] := eqVneq p 0; first by rewrite scaler0. rewrite -mul_polyC size_proper_mul; first by rewrite size_polyC lreg_neq0. by rewrite lead_coefC mulrI_eq0 ?lead_coef_eq0. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype bigop finset tuple) mathcomp(div ssralg countalg binomial)