∀ {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] [inst_2 : CategoryTheory.Preadditive C]
  {L : CategoryTheory.Functor C D} (W : CategoryTheory.MorphismProperty C) [inst_3 : L.IsLocalization W]
  [inst_4 : W.HasLeftCalculusOfFractions] {X Y Z : C} (f : L.obj X ⟶ L.obj Y) (g₁ g₂ : L.obj Y ⟶ L.obj Z) {Z_1 : D}
  (h : L.obj Z ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp f
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Localization.Preadditive.add' W g₁ g₂) h) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Localization.Preadditive.add' W (CategoryTheory.CategoryStruct.comp f g₁)
        (CategoryTheory.CategoryStruct.comp f g₂))
      h