∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {W : CategoryTheory.MorphismProperty C}
  [inst_1 : W.HasLeftCalculusOfFractions] {X Y : C} (s : X ⟶ Y) (hs : W s),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.MorphismProperty.LeftFraction.Localization.Q W).map s)
      (CategoryTheory.MorphismProperty.LeftFraction.Localization.Qinv s hs) =
    CategoryTheory.CategoryStruct.id ((CategoryTheory.MorphismProperty.LeftFraction.Localization.Q W).obj X)