∀ {ι : Type u_1} {I : BoxIntegral.Box ι} {x : ι → ℝ} (motive : (∃ s, x ∈ I.splitCenterBox s) → Prop)
  (x_1 : ∃ s, x ∈ I.splitCenterBox s), (∀ (s : Set ι) (hs : x ∈ I.splitCenterBox s), motive ⋯) → motive x_1