{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    {D₁ : Type u_4} →
      {D₂ : Type u_5} →
        [inst_1 : CategoryTheory.Category.{v_4, u_4} D₁] →
          [inst_2 : CategoryTheory.Category.{v_5, u_5} D₂] →
            (L₁ : CategoryTheory.Functor C D₁) →
              (L₂ : CategoryTheory.Functor C D₂) →
                (W' : CategoryTheory.MorphismProperty C) →
                  [inst_3 : L₁.IsLocalization W'] →
                    [inst_4 : L₂.IsLocalization W'] → L₁.comp (CategoryTheory.Localization.uniq L₁ L₂ W').functor ≅ L₂