proposition: Lemma coefCM c p i : (c%:P * p)`_i = c * p`_i.
proof: Proof. rewrite coefM big_ord_recl subn0. by rewrite big1 => [|j _]; rewrite coefC !simp. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype bigop finset tuple) mathcomp(div ssralg countalg binomial)