∀ {β : Type u_1} [inst : AddCommGroup β] (b : β) (V : Type u_3) [inst_1 : CategoryTheory.Category.{u_2, u_3} V]
  [inst_2 : CategoryTheory.Limits.HasZeroMorphisms V] (X : HomologicalComplex V (ComplexShape.up' b)) (i j : β),
  (ComplexShape.up' b).Rel i j →
    CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.id (X.X i))
        ((((HomologicalComplex.homologicalComplexToDGO b V).comp (HomologicalComplex.dgoToHomologicalComplex b V)).obj
              X).d
          i j) =
      CategoryTheory.CategoryStruct.comp
        (((CategoryTheory.Functor.id (HomologicalComplex V (ComplexShape.up' b))).obj X).d i j)
        (CategoryTheory.CategoryStruct.id (X.X j))