∀ {V : Type u_2} {W : Type u_11} [inst : CategoryTheory.Category.{u_1, u_2} V] {FV : V → V → Type u_3}
  {CV : V → Type u_4} [inst_1 : (X Y : V) → FunLike (FV X Y) (CV X) (CV Y)]
  [inst_2 : CategoryTheory.ConcreteCategory V FV] [inst_3 : CategoryTheory.HasForget₂ V TopCat]
  [inst_4 : CategoryTheory.Category.{u_10, u_11} W] {FW : W → W → Type u_12} {CW : W → Type u_13}
  [inst_5 : (X Y : W) → FunLike (FW X Y) (CW X) (CW Y)] [inst_6 : CategoryTheory.ConcreteCategory W FW]
  [inst_7 : CategoryTheory.HasForget₂ W TopCat] (G : Type u_5) [inst_8 : Monoid G] [inst_9 : TopologicalSpace G]
  {T : Type u_7} [inst_10 : CategoryTheory.Category.{u_6, u_7} T] {FT : T → T → Type u_8} {CT : T → Type u_9}
  [inst_11 : (X Y : T) → FunLike (FT X Y) (CT X) (CT Y)] [inst_12 : CategoryTheory.ConcreteCategory T FT]
  [inst_13 : CategoryTheory.HasForget₂ T TopCat] (F : CategoryTheory.Functor V W)
  (H : ∀ (X : ContAction V G), ((F.mapAction G).obj X.obj).IsContinuous) (F' : CategoryTheory.Functor W T)
  (H' : ∀ (X : ContAction W G), ((F'.mapAction G).obj X.obj).IsContinuous) {X Y : ContAction V G} (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.Functor.mapContAction G (F.comp F') ⋯).map f)
      ((fun x => CategoryTheory.Iso.refl ((CategoryTheory.Functor.mapContAction G (F.comp F') ⋯).obj x)) Y).hom =
    CategoryTheory.CategoryStruct.comp
      ((fun x => CategoryTheory.Iso.refl ((CategoryTheory.Functor.mapContAction G (F.comp F') ⋯).obj x)) X).hom
      (((CategoryTheory.Functor.mapContAction G F H).comp (CategoryTheory.Functor.mapContAction G F' H')).map f)