∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Preadditive C]
  {X Y : CategoryTheory.SimplicialObject C} (f : X ⟶ Y) (n : ℕ),
  CategoryTheory.CategoryStruct.comp ((fun n => f.app (Opposite.op (SimplexCategory.mk n))) (n + 1))
      (AlgebraicTopology.AlternatingFaceMapComplex.objD Y n) =
    CategoryTheory.CategoryStruct.comp (AlgebraicTopology.AlternatingFaceMapComplex.objD X n)
      ((fun n => f.app (Opposite.op (SimplexCategory.mk n))) n)