proposition: Lemma addm0 : left_id zero fgadd.
proof: Proof. elim/quotW=> [[D redD]]; unlock fgadd; rewrite !(reprfg0, piE). apply/eqmodP/freegequivP=> /= k. by rewrite precoeff_reduce precoeff_repr. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop order generic_quotient) mathcomp(ssralg ssrnum ssrint)