∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {W : CategoryTheory.MorphismProperty C}
  [inst_1 : W.HasLeftCalculusOfFractions] {E : Type u_4} [inst_2 : CategoryTheory.Category.{u_3, u_4} E]
  (F : CategoryTheory.Functor C E) (hF : W.IsInvertedBy F)
  (X : CategoryTheory.MorphismProperty.LeftFraction.Localization W),
  CategoryTheory.MorphismProperty.LeftFraction.Localization.Hom.map (CategoryTheory.CategoryStruct.id X) F hF =
    CategoryTheory.CategoryStruct.id (F.obj X)