∀ {C₁ : Type u_8} {C₂ : Type u_10} {C₃ : Type u_6} {C₄ : Type u_3} [inst : CategoryTheory.Category.{u_7, u_8} C₁]
  [inst_1 : CategoryTheory.Category.{u_9, u_10} C₂] [inst_2 : CategoryTheory.Category.{u_5, u_6} C₃]
  [inst_3 : CategoryTheory.Category.{u_2, u_3} C₄]
  (F : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ (CategoryTheory.Functor C₃ C₄))) {I₁ : Type u_11}
  {I₂ : Type u_12} {I₃ : Type u_4} {J : Type u_1} (p : I₁ × I₂ × I₃ → J) (X₁ : CategoryTheory.GradedObject I₁ C₁)
  [inst_4 :
    ∀ (X₂ : CategoryTheory.GradedObject I₂ C₂) (X₃ : CategoryTheory.GradedObject I₃ C₃),
      ((((CategoryTheory.GradedObject.mapTrifunctor F I₁ I₂ I₃).obj X₁).obj X₂).obj X₃).HasMap p]
  {X₂ Y₂ : CategoryTheory.GradedObject I₂ C₂} (φ : X₂ ⟶ Y₂) {X₃ Y₃ : CategoryTheory.GradedObject I₃ C₃} (ψ : X₃ ⟶ Y₃),
  CategoryTheory.CategoryStruct.comp
      ({ obj := fun X₃ => CategoryTheory.GradedObject.mapTrifunctorMapObj F p X₁ X₂ X₃,
            map := fun {x x_1} φ =>
              CategoryTheory.GradedObject.mapTrifunctorMapMap F p (CategoryTheory.CategoryStruct.id X₁)
                (CategoryTheory.CategoryStruct.id X₂) φ,
            map_id := ⋯, map_comp := ⋯ }.map
        ψ)
      (CategoryTheory.GradedObject.mapTrifunctorMapMap F p (CategoryTheory.CategoryStruct.id X₁) φ
        (CategoryTheory.CategoryStruct.id Y₃)) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.GradedObject.mapTrifunctorMapMap F p (CategoryTheory.CategoryStruct.id X₁) φ
        (CategoryTheory.CategoryStruct.id X₃))
      ({ obj := fun X₃ => CategoryTheory.GradedObject.mapTrifunctorMapObj F p X₁ Y₂ X₃,
            map := fun {x x_1} φ =>
              CategoryTheory.GradedObject.mapTrifunctorMapMap F p (CategoryTheory.CategoryStruct.id X₁)
                (CategoryTheory.CategoryStruct.id Y₂) φ,
            map_id := ⋯, map_comp := ⋯ }.map
        ψ)