∀ {C₁ : Type u_4} {C₂ : Type u_2} [inst : CategoryTheory.Category.{u_3, u_4} C₁]
  [inst_1 : CategoryTheory.Category.{u_1, u_2} C₂] {W₁ : CategoryTheory.MorphismProperty C₁}
  {W₂ : CategoryTheory.MorphismProperty C₂} (Φ : CategoryTheory.LocalizerMorphism W₁ W₂) {D : Type u_6}
  [inst_2 : CategoryTheory.Category.{u_5, u_6} D] (L : CategoryTheory.Functor C₂ D) [inst_3 : L.IsLocalization W₂]
  {X₂ : C₂} {X₃ : D} (y : L.obj X₂ ⟶ X₃) {R R' : Φ.RightResolution X₂} (φ : R ⟶ R'),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.CostructuredArrow.mk
            (CategoryTheory.StructuredArrow.homMk
              (CategoryTheory.CategoryStruct.comp (CategoryTheory.Localization.isoOfHom L W₂ R.w ⋯).inv y) ⋯)).left.hom
      (Φ.functor.map φ.f) =
    (CategoryTheory.CostructuredArrow.mk
          (CategoryTheory.StructuredArrow.homMk
            (CategoryTheory.CategoryStruct.comp (CategoryTheory.Localization.isoOfHom L W₂ R'.w ⋯).inv y) ⋯)).left.hom