∀ {C₁ : Type u_8} {C₂ : Type u_6} {C₃ : Type u_4} {E : Type u_2} [inst : CategoryTheory.Category.{u_7, u_8} C₁]
  [inst_1 : CategoryTheory.Category.{u_5, u_6} C₂] [inst_2 : CategoryTheory.Category.{u_3, u_4} C₃]
  [inst_3 : CategoryTheory.Category.{u_1, u_2} E]
  (F : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ (CategoryTheory.Functor C₃ E))) (G : C₃) (H : C₂) (X : C₁),
  ((F.map (CategoryTheory.CategoryStruct.id X)).app H).app G =
    CategoryTheory.CategoryStruct.id (((F.obj X).obj H).obj G)