proposition: Lemma mpolyC_eq0 c : (c%:MP == 0 :> {mpoly R[n]}) = (c == 0).
proof: Proof. rewrite eqE /=; apply/idP/eqP=> [/freeg_eqP/(_ 0%MM)|->//]. by rewrite !coeffU eqxx !mulr1. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq path) mathcomp(choice fintype tuple finfun bigop finset binomial) mathcomp(order fingroup perm ssralg zmodp poly ssrint) mathcomp(matrix vector) mathcomp(bigenough) ssrcomplements freeg