∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Preadditive C]
  (S : CategoryTheory.ShortComplex (CochainComplex C ℤ))
  (σ : (n : ℤ) → (S.map (HomologicalComplex.eval C (ComplexShape.up ℤ) n)).Splitting)
  [inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C] (p q : ℤ) (hpq : p + 1 = q),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.CategoryStruct.comp (S.g.f q)
          ((CochainComplex.mappingCone.inl (CochainComplex.homOfDegreewiseSplit S σ)).v q p ⋯) -
        CategoryTheory.CategoryStruct.comp (σ q).r
          (CategoryTheory.CategoryStruct.comp (HomologicalComplex.XIsoOfEq S.X₁ ⋯).hom
            ((CochainComplex.mappingCone.inr (CochainComplex.homOfDegreewiseSplit S σ)).f p)))
      (CategoryTheory.CategoryStruct.comp
          ((↑(CochainComplex.mappingCone.fst (CochainComplex.homOfDegreewiseSplit S σ))).v p q hpq) (σ q).s -
        CategoryTheory.CategoryStruct.comp
          ((CochainComplex.mappingCone.snd (CochainComplex.homOfDegreewiseSplit S σ)).v p p ⋯)
          ((CochainComplex.HomComplex.Cochain.ofHom S.f).v (p + 1) q ⋯)) =
    CategoryTheory.CategoryStruct.id (S.X₂.X q)