{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {D : Type u'} →
      [inst_1 : CategoryTheory.Category.{v', u'} D] →
        (P : CategoryTheory.ObjectProperty D) →
          (F : CategoryTheory.Functor C D) → (hF : ∀ (X : C), P (F.obj X)) → (P.lift F hF).comp P.ι ≅ F