Notation "[ 'Aut' G ]" := (Aut_group G)
  (at level 0, format "[ 'Aut'  G ]") : Group_scope.Notation "H \char G" := (characteristic H G) : group_scope.Definition perm_in := perm perm_in_inj.

(* Specifications: *)
Lemma perm_in_on : perm_on A perm_in.