∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Preadditive C]
  (K : HomologicalComplex₂ C (ComplexShape.up ℤ) (ComplexShape.up ℤ)) (x : ℤ) [inst_2 : K.HasTotal (ComplexShape.up ℤ)]
  (n n' : ℤ) (h : n + x = n'),
  CategoryTheory.CategoryStruct.comp
      (K.totalDesc fun p q hpq =>
        CategoryTheory.CategoryStruct.comp
          (HomologicalComplex₂.XXIsoOfEq C (ComplexShape.up ℤ) (ComplexShape.up ℤ) K ⋯ ⋯).inv
          (((HomologicalComplex₂.shiftFunctor₁ C x).obj K).ιTotal (ComplexShape.up ℤ) (p - x) q n ⋯))
      (((HomologicalComplex₂.shiftFunctor₁ C x).obj K).totalDesc fun p q hpq =>
        K.ιTotal (ComplexShape.up ℤ) (p + x) q n' ⋯) =
    CategoryTheory.CategoryStruct.id ((K.total (ComplexShape.up ℤ)).X n')