proposition: Lemma group_set_iso2 : group_set isometries2.
proof: Proof. apply/group_setP; split => [|x y]; rewrite !inE ?eqxx //. do 2![case/orP; move/eqP->]; gsimpl; rewrite ?(eqxx, orbT) //. by rewrite -/sh -{1}sh_inv mulVg eqxx. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype tuple finfun bigop finset fingroup) mathcomp(action perm primitive_action)