proposition: Fact mul_poly0 : right_zero 0%:P mul_poly.
proof: Proof. move=> p; apply/polyP => i; rewrite coef_mul_poly_rev big_ord_recl subn0. by rewrite big1 => [|j _]; rewrite coefC !simp // coefC; case: ifP. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype bigop finset tuple) mathcomp(div ssralg countalg binomial)