proposition: Lemma mpolyXE (s : 'S_n) m : 'X_[m] = \prod_(i < n) 'X_(s i) ^+ m (s i).
proof: Proof. rewrite {1}[m](multinomUE s) -mprodXE. by apply/eq_bigr=> i _; rewrite mpolyXn. 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