∀ {C : Type u_4} [inst : CategoryTheory.Category.{u_3, u_4} C] {J : Type u_6}
  [inst_1 : CategoryTheory.Category.{u_5, u_6} J] {K : Type u_2} [inst_2 : CategoryTheory.Category.{u_1, u_2} K]
  [inst_3 : CategoryTheory.Limits.HasColimitsOfShape J C] (F : CategoryTheory.Functor K (CategoryTheory.Functor J C))
  {X Y : K} (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.Limits.colimit F.flip).map f)
      ((fun x =>
            CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation F.flip x ≪≫
              CategoryTheory.Limits.HasColimit.isoOfNatIso (CategoryTheory.flipCompEvaluation F x))
          Y).hom =
    CategoryTheory.CategoryStruct.comp
      ((fun x =>
            CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation F.flip x ≪≫
              CategoryTheory.Limits.HasColimit.isoOfNatIso (CategoryTheory.flipCompEvaluation F x))
          X).hom
      ((F.comp CategoryTheory.Limits.colim).map f)