proposition: Lemma perm_mxV (s : 'S_n) : perm_mx s^-1 = (perm_mx s)^-1.
proof: Proof. rewrite -[_^-1]mul1r; apply: (canRL (mulmxK (unitmx_perm s))). by rewrite -perm_mxM mulVg perm_mx1. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype finfun bigop finset fingroup perm order) mathcomp(div prime binomial ssralg countalg finalg zmodp)