proposition: Fact add_poly0 : left_id 0%:P add_poly.
proof: Proof. by move=> p; apply/polyP=> i; rewrite coef_add_poly coefC if_same add0r. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype bigop finset tuple) mathcomp(div ssralg countalg binomial)