proposition: Lemma multinomUE n (s : 'S_n) (m : 'X_{1..n}) : m = (\sum_i U_(s i) *+ m (s i))%MM.
proof: Proof. rewrite (reindex s^-1)%g //=; last first. by exists s=> i _; rewrite (permK, permKV). by rewrite [LHS]multinomUE_id; apply/eq_bigr => i _; rewrite permKV. 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