∀ {C₁ : Type u_8} {C₂ : Type u_6} {C₃ : Type u_2} {C₄ : Type u_4} {C₁₂ : Type u_10}
  [inst : CategoryTheory.Category.{u_7, u_8} C₁] [inst_1 : CategoryTheory.Category.{u_5, u_6} C₂]
  [inst_2 : CategoryTheory.Category.{u_1, u_2} C₃] [inst_3 : CategoryTheory.Category.{u_3, u_4} C₄]
  [inst_4 : CategoryTheory.Category.{u_9, u_10} C₁₂] (F₁₂ : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ C₁₂))
  {G G' : CategoryTheory.Functor C₁₂ (CategoryTheory.Functor C₃ C₄)} (φ : G ⟶ G') (X₁ : C₁) (X₂ : C₂) ⦃X Y : C₃⦄
  (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp ((((CategoryTheory.bifunctorComp₁₂ F₁₂ G).obj X₁).obj X₂).map f)
      ((φ.app ((F₁₂.obj X₁).obj X₂)).app Y) =
    CategoryTheory.CategoryStruct.comp ((φ.app ((F₁₂.obj X₁).obj X₂)).app X)
      ((((CategoryTheory.bifunctorComp₁₂ F₁₂ G').obj X₁).obj X₂).map f)