∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Abelian C]
  [inst_2 : CategoryTheory.EnoughInjectives C] {K : CochainComplex C ℤ},
  CochainComplex.HomComplex.δ 1 2
      (CochainComplex.HomComplex.Cochain.mk fun p q x =>
        CategoryTheory.CategoryStruct.comp (K.d p q) (CategoryTheory.Injective.ι (K.X q))) =
    0