∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Preadditive C]
  {K L : CochainComplex C ℤ} (φ : K ⟶ L) {M : CochainComplex C ℤ} (α : M ⟶ K)
  (β : CochainComplex.HomComplex.Cochain M L (-1)),
  CochainComplex.HomComplex.δ (-1) 0 β +
        CochainComplex.HomComplex.Cochain.ofHom (CategoryTheory.CategoryStruct.comp α φ) =
      0 →
    CochainComplex.HomComplex.δ (-1) 0 β +
        (↑(CochainComplex.HomComplex.Cocycle.ofHom α)).comp (CochainComplex.HomComplex.Cochain.ofHom φ) ⋯ =
      0