∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C] (q n : ℕ)
  {X Y : CategoryTheory.SimplicialObject C} (f : X ⟶ Y) {Z : C}
  (h : (AlgebraicTopology.AlternatingFaceMapComplex.obj Y).X n ⟶ Z),
  CategoryTheory.CategoryStruct.comp (f.app (Opposite.op (SimplexCategory.mk n)))
      (CategoryTheory.CategoryStruct.comp ((AlgebraicTopology.DoldKan.P q).f n) h) =
    CategoryTheory.CategoryStruct.comp ((AlgebraicTopology.DoldKan.P q).f n)
      (CategoryTheory.CategoryStruct.comp (f.app (Opposite.op (SimplexCategory.mk n))) h)