∀ {C : Type u₁} [inst : CategoryTheory.Category.{u₂, u₁} C] (F : CategoryTheory.Functor C FintypeCat) (G : Type u_1)
  [inst_1 : Group G] [inst_2 : (X : C) → MulAction G (F.obj X).carrier]
  [inst_3 : CategoryTheory.PreGaloisCategory.IsNaturalSMul F G] [inst_4 : CategoryTheory.GaloisCategory C]
  [CategoryTheory.PreGaloisCategory.FiberFunctor F],
  Function.Surjective ⇑(CategoryTheory.PreGaloisCategory.toAut F G) →
    ∀ (X : C) [CategoryTheory.PreGaloisCategory.IsConnected X], MulAction.IsPretransitive G (F.obj X).carrier