∀ {α : Type u_2} {m : MeasurableSpace α} (μ : MeasureTheory.Measure α) {β : Type u_1} [inst : CompleteLinearOrder β]
  (s : Set β) (f : α → β) (u v : β → β → Set α),
  (∀ (p q : β),
      MeasurableSet (u p q) ∧
        MeasurableSet (v p q) ∧
          {x | f x < p} ⊆ u p q ∧ {x | q < f x} ⊆ v p q ∧ (p ∈ s → q ∈ s → p < q → μ (u p q ∩ v p q) = 0)) →
    ∑' (p : { x // x ∈ s }) (q : { x // x ∈ s ∩ Set.Ioi ↑p }), μ (u ↑p ↑q ∩ v ↑p ↑q) =
      ∑' (p : { x // x ∈ s }) (x : { x // x ∈ s ∩ Set.Ioi ↑p }), 0