∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_3, u_2} C] ⦃X Y : ULift.{u_1, u_2} C⦄ (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.ULift.downFunctor.comp CategoryTheory.ULift.upFunctor).map f)
      (CategoryTheory.CategoryStruct.id
        ((CategoryTheory.ULift.downFunctor.comp CategoryTheory.ULift.upFunctor).obj Y)) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.CategoryStruct.id ((CategoryTheory.ULift.downFunctor.comp CategoryTheory.ULift.upFunctor).obj X))
      ((CategoryTheory.Functor.id (ULift.{u_1, u_2} C)).map f)