{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {ι : Type u_2} →
        {c : ComplexShape ι} →
          (K : HomologicalComplex C c) →
            [inst_2 : DecidableRel c.Rel] →
              [inst_3 : ∀ (i : ι), CategoryTheory.Limits.HasBinaryBiproduct (K.X i) (K.X i)] →
                [inst_4 :
                    HomologicalComplex.HasHomotopyCofiber
                      (CategoryTheory.Limits.biprod.lift (CategoryTheory.CategoryStruct.id K)
                        (-CategoryTheory.CategoryStruct.id K))] →
                  (∀ (j : ι), ∃ i, c.Rel i j) →
                    Homotopy (HomologicalComplex.cylinder.ι₀ K) (HomologicalComplex.cylinder.ι₁ K)