proposition: Lemma inj_msym (s : 'S_n) : injective (msym s).
proof: Proof. move=> p q; move/(congr1 (msym s^-1)%g). by rewrite -!msymMm mulgV !msym1m. 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