proposition: Lemma take_polyD m p q : take_poly m (p + q) = take_poly m p + take_poly m q.
proof: Proof. by apply/polyP => i; rewrite !(coefD, coef_poly); case: leqP; rewrite ?add0r. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype bigop finset tuple) mathcomp(div ssralg countalg binomial)