{C : Type u₁} →
  {inst : CategoryTheory.Category.{v₁, u₁} C} →
    {D : Type u₂} →
      {inst_1 : CategoryTheory.Category.{v₂, u₂} D} →
        {J : Type w} →
          {inst_2 : CategoryTheory.Category.{w', w} J} →
            {K : CategoryTheory.Functor J C} →
              {F : CategoryTheory.Functor C D} →
                {c : CategoryTheory.Limits.Cocone (K.comp F)} →
                  {P : Sort u} →
                    {liftedCocone : CategoryTheory.Limits.Cocone K} →
                      {validLift : F.mapCocone liftedCocone ≅ c} →
                        {liftedCocone' : CategoryTheory.Limits.Cocone K} →
                          {validLift' : F.mapCocone liftedCocone' ≅ c} →
                            { liftedCocone := liftedCocone, validLift := validLift } =
                                { liftedCocone := liftedCocone', validLift := validLift' } →
                              (liftedCocone ≍ liftedCocone' → validLift ≍ validLift' → P) → P