∀ {C : Type u_6} [inst : CategoryTheory.Category.{u_5, u_6} C] {D : Type u_4}
  [inst_1 : CategoryTheory.Category.{u_3, u_4} D] {F : CategoryTheory.Functor C D} [inst_2 : F.Final] {E : Type u_2}
  [inst_3 : CategoryTheory.Category.{u_1, u_2} E] {G : CategoryTheory.Functor D E}
  (c : CategoryTheory.Limits.Cocone (F.comp G)) (X Y : D) (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp (G.map f)
      (CategoryTheory.CategoryStruct.comp (G.map (CategoryTheory.Functor.Final.homToLift F Y))
        (c.ι.app (CategoryTheory.Functor.Final.lift F Y))) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.CategoryStruct.comp (G.map (CategoryTheory.Functor.Final.homToLift F X))
        (c.ι.app (CategoryTheory.Functor.Final.lift F X)))
      (((CategoryTheory.Functor.const D).obj c.pt).map f)