∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
  {K L : CochainComplex C ℤ} {p q : ℤ} (f : K.X p ⟶ L.X q) (n m : ℤ),
  n + 1 = m →
    ∀ (p' q' : ℤ),
      p' + 1 = p →
        q + 1 = q' →
          CochainComplex.HomComplex.δ n m (CochainComplex.HomComplex.Cochain.single f n) =
            CochainComplex.HomComplex.Cochain.single (CategoryTheory.CategoryStruct.comp f (L.d q q')) m +
              m.negOnePow • CochainComplex.HomComplex.Cochain.single (CategoryTheory.CategoryStruct.comp (K.d p' p) f) m