∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] (L : CategoryTheory.Functor C D)
  (W : CategoryTheory.MorphismProperty C) {E : Type u_3} [inst_2 : CategoryTheory.Category.{v_3, u_3} E]
  [inst_3 : L.IsLocalization W] (F₁ F₂ : CategoryTheory.Functor C E) (F₁' F₂' : CategoryTheory.Functor D E)
  [h₁ : CategoryTheory.Localization.Lifting L W F₁ F₁'] [h₂ : CategoryTheory.Localization.Lifting L W F₂ F₂']
  (e e_1 : F₁ ≅ F₂),
  e = e_1 →
    CategoryTheory.Localization.liftNatIso L W F₁ F₂ F₁' F₂' e =
      CategoryTheory.Localization.liftNatIso L W F₁ F₂ F₁' F₂' e_1