∀ {S : Type u_3} [inst : AddCommGroupWithOne S] (C : Type u_2) [inst_1 : CategoryTheory.Category.{u_1, u_2} C]
  [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] [inst_3 : CategoryTheory.HasShift C S] (m n : S)
  (X : CategoryTheory.DifferentialObject S C),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.DifferentialObject.shiftFunctor C (m + n)).obj X).d
      ((CategoryTheory.shiftFunctor C 1).map (CategoryTheory.shiftAdd X.obj m n).hom) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.shiftAdd X.obj m n).hom
      (((CategoryTheory.DifferentialObject.shiftFunctor C m).comp
              (CategoryTheory.DifferentialObject.shiftFunctor C n)).obj
          X).d