∀ {β : Type u_3} [inst : AddCommGroup β] (b : β) (V : Type u_2) [inst_1 : CategoryTheory.Category.{u_1, u_2} V]
  [inst_2 : CategoryTheory.Limits.HasZeroMorphisms V]
  {X Y : CategoryTheory.DifferentialObject ℤ (CategoryTheory.GradedObjectWithShift b V)} (f : X ⟶ Y) (i j : β),
  (ComplexShape.up' b).Rel i j →
    CategoryTheory.CategoryStruct.comp (f.f i)
        ({ X := fun i => Y.obj i,
              d := fun i j => if h : i + b = j then CategoryTheory.CategoryStruct.comp (Y.d i) (Y.objEqToHom ⋯) else 0,
              shape := ⋯, d_comp_d' := ⋯ }.d
          i j) =
      CategoryTheory.CategoryStruct.comp
        ({ X := fun i => X.obj i,
              d := fun i j => if h : i + b = j then CategoryTheory.CategoryStruct.comp (X.d i) (X.objEqToHom ⋯) else 0,
              shape := ⋯, d_comp_d' := ⋯ }.d
          i j)
        (f.f j)