∀ {C : Type u_1} [inst : CategoryTheory.Category.{u_2, u_1} C] [inst_1 : CategoryTheory.Abelian C] (n a a' : ℤ),
  n + a = a' →
    ∀ (X : C) (i : ℤ),
      (((HomologicalComplex.single C (ComplexShape.up ℤ) a').comp
                  (CategoryTheory.shiftFunctor (CochainComplex C ℤ) n)).obj
              X).X
          i =
        ((HomologicalComplex.single C (ComplexShape.up ℤ) a).obj X).X i