∀ {ι : Type u_1} {I : BoxIntegral.Box ι} {π₁ π₂ : BoxIntegral.Prepartition I}
  {πi₁ πi₂ : (J : BoxIntegral.Box ι) → BoxIntegral.Prepartition J},
  π₁ = π₂ → (∀ J ∈ π₁, πi₁ J = πi₂ J) → π₁.biUnion πi₁ = π₂.biUnion πi₂