∀ {A : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} A] [inst_1 : CategoryTheory.Abelian A]
  {X Y : CategoryTheory.SimplicialObject A} (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp (AlgebraicTopology.AlternatingFaceMapComplex.map f)
      (AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex Y) =
    CategoryTheory.CategoryStruct.comp (AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex X)
      (AlgebraicTopology.NormalizedMooreComplex.map f)