{ι : Type u_3} →
  {M : Type u_4} →
    [inst : AddCommMonoid M] →
      {I : WithTop (BoxIntegral.Box ι)} →
        {motive : BoxIntegral.BoxAdditiveMap ι M I → Sort u} →
          (t : BoxIntegral.BoxAdditiveMap ι M I) →
            ((toFun : BoxIntegral.Box ι → M) →
                (sum_partition_boxes' :
                    ∀ (J : BoxIntegral.Box ι),
                      ↑J ≤ I → ∀ (π : BoxIntegral.Prepartition J), π.IsPartition → ∑ Ji ∈ π.boxes, toFun Ji = toFun J) →
                  motive { toFun := toFun, sum_partition_boxes' := sum_partition_boxes' }) →
              motive t