proposition: Lemma take_polyZ k m p : take_poly m (k *: p) = k *: take_poly m p.
proof: Proof. apply/polyP => i; rewrite !(coefZ, coef_take_poly); case: leqP => //. by rewrite mulr0. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype bigop finset tuple) mathcomp(div ssralg countalg binomial)