∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  {X : CategoryTheory.SimplicialObject C} {Z : ChainComplex C ℕ}
  (h : AlgebraicTopology.AlternatingFaceMapComplex.obj X ⟶ Z),
  CategoryTheory.CategoryStruct.comp AlgebraicTopology.DoldKan.QInfty
      (CategoryTheory.CategoryStruct.comp AlgebraicTopology.DoldKan.QInfty h) =
    CategoryTheory.CategoryStruct.comp AlgebraicTopology.DoldKan.QInfty h