proposition: Lemma Aut_isomM : {in Aut G &, {morph Aut_isom: x y / x * y}}.
proof: Proof. move=> a b AutGa AutGb. apply: (eq_Aut (Aut_Aut_isom _)); rewrite ?groupM ?Aut_Aut_isom // => fx. case/morphimP=> x Dx Gx ->{fx}. by rewrite permM !Aut_isomE ?groupM /= ?permM ?Aut_closed. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat fintype) mathcomp(finset fingroup perm morphism)