∀ {C : Type u_1} {D : Type u_2} {D' : Type u_3} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] [inst_2 : CategoryTheory.Category.{v_3, u_3} D']
  (W W_1 : CategoryTheory.MorphismProperty C) (e_W : W = W_1) (L : CategoryTheory.Functor C D)
  (L' : CategoryTheory.Functor C D') [inst_3 : L.IsLocalization W] [inst_4 : L'.IsLocalization W] {X : C},
  CategoryTheory.Localization.structuredArrowEquiv W L L' = CategoryTheory.Localization.structuredArrowEquiv W_1 L L'