Variable (a : {perm gT}) (AutGa : a \in Aut G).
Notation f := (autm AutGa).
Notation fE := (autmE AutGa).

(* Specifications: *)
Lemma injm_autm : 'injm f.
Lemma Aut_closed x : x \in G -> a x \in G.
End Automorphism.