Section Automorphism.
Variable gT : finGroupType.
Implicit Type A : {set gT}.
Implicit Types a b : {perm gT}.
Definition Aut A := [set a | perm_on A a & morphic A a].
(* The morphism that is represented by a given element of Aut A. *)
Definition autm A a (AutAa : a \in Aut A) := morphm (Aut_morphic AutAa).
Canonical Aut_group := group Aut_group_set.
Variable (a : {perm gT}) (AutGa : a \in Aut G).
Notation f := (autm AutGa).
Notation fE := (autmE AutGa).

Lemma Aut_closed x : x \in G -> a x \in G.