∀ {C₁ : Type u_1} {C₂ : Type u_2} {D₁ : Type u_4} {D₂ : Type u_5} [inst : CategoryTheory.Category.{v_1, u_1} C₁]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} C₂] [inst_2 : CategoryTheory.Category.{v_4, u_4} D₁]
  [inst_3 : CategoryTheory.Category.{v_5, u_5} D₂] (L₁ : CategoryTheory.Functor C₁ D₁)
  (W₁ : CategoryTheory.MorphismProperty C₁) [L₁.IsLocalization W₁] (L₂ : CategoryTheory.Functor C₂ D₂)
  (W₂ : CategoryTheory.MorphismProperty C₂) (E : C₁ ≌ C₂) (E' : D₁ ≌ D₂)
  [CategoryTheory.CatCommSq E.functor L₁ L₂ E'.functor],
  W₁ ≤ W₂.isoClosure.inverseImage E.functor → W₂.IsInvertedBy L₂ → L₂.IsLocalization W₂