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).

Lemma autmE A a (AutAa : a \in Aut A) : autm AutAa = a.