proposition: Lemma group_set_iso : group_set isometries.
proof: Proof. apply/group_setP; split; first by rewrite inE eqxx /=. by move=> x y hx hy; apply/is_isoP => ci; rewrite !permM !isometries_iso. 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)