∀ (A : Type u_2) [inst : CategoryTheory.Category.{u_1, u_2} A] [inst_1 : CategoryTheory.Abelian A]
  (X : CategoryTheory.SimplicialObject A),
  CategoryTheory.CategoryStruct.comp (AlgebraicTopology.DoldKan.N₁.obj X).p
      (CategoryTheory.CategoryStruct.comp (AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex X)
        (((AlgebraicTopology.normalizedMooreComplex A).comp
                (CategoryTheory.Idempotents.toKaroubi (ChainComplex A ℕ))).obj
            X).p) =
    AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex X