proposition: Lemma coefK p : \poly_(i < size p) p`_i = p.
proof: Proof. by apply/polyP=> i; rewrite coef_poly; case: ltnP => // /(nth_default 0)->. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype bigop finset tuple) mathcomp(div ssralg countalg binomial)