Section AutIsom.
Variables (gT rT : finGroupType) (G D : {group gT}) (f : {morphism D >-> rT}).
Hypotheses (injf : 'injm f) (sGD : G \subset D).
Let domG := subsetP sGD.
Definition Aut_isom a := s2val (Aut_isom_subproof a).

Lemma Aut_Aut_isom a : Aut_isom a \in Aut (f @* G).