∀ {J : Type u_1} {K : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} J]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} K] {C : Type u_3} [inst_2 : CategoryTheory.Category.{v_3, u_3} C]
  (F : CategoryTheory.Functor J (CategoryTheory.Functor K C)) [inst_3 : CategoryTheory.Limits.HasColimitsOfShape J C]
  [inst_4 : CategoryTheory.Limits.HasColimitsOfShape K C] (j : J) (k : K) {Z : C}
  (h : CategoryTheory.Limits.colimit (F.comp CategoryTheory.Limits.colim) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.colimit.ι (F.flip.obj k) j)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.colimit.ι (F.flip.comp CategoryTheory.Limits.colim) k)
        (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim F).hom h)) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.colimit.ι (F.obj j) k)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.colimit.ι (F.comp CategoryTheory.Limits.colim) j) h)