∀ {ι : Type u_1} {I J : BoxIntegral.Box ι} {boxes : Finset (WithBot (BoxIntegral.Box ι))} {h₁ : ∀ J ∈ boxes, J ≤ ↑I}
  {h₂ : (↑boxes).Pairwise Disjoint}, (J ∈ BoxIntegral.Prepartition.ofWithBot boxes h₁ h₂) = (↑J ∈ boxes)