proposition: Lemma mesymnnE : 's_n = \prod_(i < n) 'X_i.
proof: Proof. rewrite mesymE (bigD1 setT) ?cardsT ?card_ord //=. rewrite [X in _+X]big1 ?addr0; last first. move=> i /andP []; rewrite eqEcard => /eqP ->. by rewrite subsetT cardsT card_ord leqnn. by rewrite mprodXE mesym1_setT. 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