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