∀ {ι : Type u_1} (W₁ : Type u_3) [inst : CategoryTheory.Category.{u_2, u_3} W₁]
  [inst_1 : CategoryTheory.Limits.HasZeroMorphisms W₁] (c : ComplexShape ι) (K : HomologicalComplex W₁ c) (i j : ι),
  c.Rel i j →
    CategoryTheory.CategoryStruct.comp
        ((fun x => CategoryTheory.Iso.refl ((((CategoryTheory.Functor.id W₁).mapHomologicalComplex c).obj K).X x))
            i).hom
        (((CategoryTheory.Functor.id (HomologicalComplex W₁ c)).obj K).d i j) =
      CategoryTheory.CategoryStruct.comp ((((CategoryTheory.Functor.id W₁).mapHomologicalComplex c).obj K).d i j)
        ((fun x => CategoryTheory.Iso.refl ((((CategoryTheory.Functor.id W₁).mapHomologicalComplex c).obj K).X x))
            j).hom