proposition: Lemma map_Poly_id0 s : f 0 = 0 -> (Poly s)^f = Poly (map f s).
proof: Proof. move=> f0; apply/polyP=> j; rewrite coef_map_id0 ?coef_Poly //. have [/(nth_map 0 0)->// | le_s_j] := ltnP j (size s). by rewrite !nth_default ?size_map. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype bigop finset tuple) mathcomp(div ssralg countalg binomial)