∀ {C₁ : Type u_7} {C₂ : Type u_8} {C₃ : Type u_2} {C₄ : Type u_5} {C₁₂ : Type u_4}
  [inst : CategoryTheory.Category.{u_9, u_7} C₁] [inst_1 : CategoryTheory.Category.{u_10, u_8} C₂]
  [inst_2 : CategoryTheory.Category.{u_6, u_2} C₃] [inst_3 : CategoryTheory.Category.{u_3, u_5} C₄]
  [inst_4 : CategoryTheory.Category.{u_1, u_4} C₁₂] (F₁₂ : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ C₁₂))
  (X : CategoryTheory.Functor C₁₂ (CategoryTheory.Functor C₃ C₄)),
  {
      app := fun X₁ =>
        {
          app := fun X₂ =>
            { app := fun X₃ => ((CategoryTheory.CategoryStruct.id X).app ((F₁₂.obj X₁).obj X₂)).app X₃,
              naturality := ⋯ },
          naturality := ⋯ },
      naturality := ⋯ } =
    CategoryTheory.CategoryStruct.id (CategoryTheory.bifunctorComp₁₂ F₁₂ X)