Arguments morphim_fixP {gT G f}.
Prenex Implicits aut.
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.

(* Specifications: *)
Lemma Aut_isom_subproof a :
{a' | a' \in Aut (f @* G) & a \in Aut G -> {in G, a' \o f =1 f \o a}}.