proposition: Lemma mpolyME p q : p * q = \sum_(m <- msupp p @@ msupp q) (p@_m.1 * q@_m.2) *: 'X_[m.1 + m.2].
proof: Proof. apply/mpolyP=> m; rewrite {1}/GRing.mul /= mcoeff_MPoly. rewrite !raddf_sum; apply/eq_bigr=> i _ /=. by rewrite coeffU -mul_mpolyC mcoeffCM mcoeffX. 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