∀ {A : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} A] [inst_1 : CategoryTheory.Abelian A]
  (X : CategoryTheory.SimplicialObject A) (n : ℕ),
  CategoryTheory.CategoryStruct.comp
      ((fun n =>
          (AlgebraicTopology.NormalizedMooreComplex.objX X n).factorThru (AlgebraicTopology.DoldKan.PInfty.f n) ⋯)
        (n + 1))
      (AlgebraicTopology.NormalizedMooreComplex.objD X n) =
    CategoryTheory.CategoryStruct.comp (AlgebraicTopology.AlternatingFaceMapComplex.objD X n)
      ((fun n =>
          (AlgebraicTopology.NormalizedMooreComplex.objX X n).factorThru (AlgebraicTopology.DoldKan.PInfty.f n) ⋯)
        n)