proposition: Lemma coeff_fgscale c D x : coeff x (c *:F D) = c * (coeff x D).
proof: Proof. rewrite -{2}[D]freeg_sumE /fgscale !raddf_sum /=. by rewrite mulr_sumr; apply/eq_bigr=> i _; rewrite !coeffU mulrA. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop order generic_quotient) mathcomp(ssralg ssrnum ssrint)