∀ (J₁ : Type u_2) (J₂ : Type u_6) (C : Type u_4) [inst : CategoryTheory.Category.{u_1, u_2} J₁]
  [inst_1 : CategoryTheory.Category.{u_5, u_6} J₂] [inst_2 : CategoryTheory.Category.{u_3, u_4} C]
  [inst_3 : CategoryTheory.MonoidalCategory C] [inst_4 : CategoryTheory.BraidedCategory C]
  (x : CategoryTheory.Functor J₁ C) (x_1 : CategoryTheory.Functor J₂ C) (x_2 : J₂) {X Y : J₁} (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp
      ((((((CategoryTheory.Functor.postcompose₂.obj (CategoryTheory.flipFunctor J₁ J₂ C)).obj
                        (CategoryTheory.MonoidalCategory.externalProductBifunctorCurried J₁ J₂ C)).obj
                    x).obj
                x_1).obj
            x_2).map
        f)
      ((fun x_3 => β_ (x.obj x_3) (x_1.obj x_2)) Y).hom =
    CategoryTheory.CategoryStruct.comp ((fun x_3 => β_ (x.obj x_3) (x_1.obj x_2)) X).hom
      (((((CategoryTheory.MonoidalCategory.externalProductBifunctorCurried J₂ J₁ C).flip.obj x).obj x_1).obj x_2).map f)