∀ {D : Type u_3} [inst : CategoryTheory.Category.{u_2, u_3} D] {S' R : CategoryTheory.Functor Dᵒᵖ CommRingCat}
  (φ' : S' ⟶ R) {M' : PresheafOfModules (R.comp (CategoryTheory.forget₂ CommRingCat RingCat))} (d' : M'.Derivation' φ')
  {X Y : Dᵒᵖ} (f : X ⟶ Y) (b : ↑(R.obj X)),
  (CategoryTheory.ConcreteCategory.hom
        (CategoryTheory.CategoryStruct.comp
          ((PresheafOfModules.DifferentialsConstruction.relativeDifferentials' φ').map f)
          ((ModuleCat.restrictScalars
                (RingCat.Hom.hom ((R.comp (CategoryTheory.forget₂ CommRingCat RingCat)).map f))).map
            (d'.app Y).desc)))
      (CommRingCat.KaehlerDifferential.d b) =
    (CategoryTheory.ConcreteCategory.hom (CategoryTheory.CategoryStruct.comp (d'.app X).desc (M'.map f)))
      (CommRingCat.KaehlerDifferential.d b)