proposition: Lemma coef_poly n E k : (\poly_(i < n) E i)`_k = (if k < n then E k else 0).
proof: Proof. rewrite unlock coef_Poly. have [lt_kn | le_nk] := ltnP k n; first by rewrite nth_mkseq. by rewrite nth_default // size_mkseq. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype bigop finset tuple) mathcomp(div ssralg countalg binomial)