proposition: Lemma mesymE k : 's_k = \sum_(h : {set 'I_n} | #|h| == k) 'X_[mesym1 h].
proof: Proof. apply/eq_bigr=> /= h _; rewrite mprodXE; congr 'X_[_]. apply/mnmP=> i; rewrite mnmE mnm_sumE big_mkcond /=. rewrite (bigD1 i) //= mnmE eqxx /= big1 ?addn0 // => j ne_ji. by case: (_ \in _); rewrite // mnmE (negbTE ne_ji). 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