proposition: Lemma take_poly_id m p : size p <= m -> take_poly m p = p.
proof: Proof. move=> /leq_trans gep; apply/polyP => i; rewrite coef_poly if_nth//=. by case: ltnP => // /gep->. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype bigop finset tuple) mathcomp(div ssralg countalg binomial)