proposition: Lemma coefMC c p i : (p * c%:P)`_i = p`_i * c.
proof: Proof. rewrite coefMr 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)