∀ {J : Type u_5} {K : Type u_2} [inst : CategoryTheory.Category.{u_6, u_5} J]
  [inst_1 : CategoryTheory.Category.{u_1, u_2} K] {C : Type u_4} [inst_2 : CategoryTheory.Category.{u_3, u_4} C]
  (F : CategoryTheory.Functor (J × K) C) [inst_3 : CategoryTheory.Limits.HasLimitsOfShape J C]
  [inst_4 : CategoryTheory.Limits.HasColimitsOfShape K C] (j : J) ⦃X Y : K⦄ (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp
      (((CategoryTheory.Functor.curry.obj ((CategoryTheory.Prod.swap K J).comp F)).comp CategoryTheory.Limits.lim).map
        f)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Limits.limit.π
          ((CategoryTheory.Functor.curry.obj ((CategoryTheory.Prod.swap K J).comp F)).obj Y) j)
        (CategoryTheory.Limits.colimit.ι ((CategoryTheory.Functor.curry.obj F).obj j) Y)) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Limits.limit.π
          ((CategoryTheory.Functor.curry.obj ((CategoryTheory.Prod.swap K J).comp F)).obj X) j)
        (CategoryTheory.Limits.colimit.ι ((CategoryTheory.Functor.curry.obj F).obj j) X))
      (((CategoryTheory.Functor.const K).obj
            (CategoryTheory.Limits.colimit.cocone ((CategoryTheory.Functor.curry.obj F).obj j)).1).map
        f)