∀ {ι : Type u_1} (n : ℕ) [inst : NeZero n] (s : Set (ι → ℝ)) (F : (ι → ℝ) → ℝ) [inst_1 : Fintype ι]
  {B : BoxIntegral.Box ι},
  BoxIntegral.hasIntegralVertices B →
    s ≤ ↑B →
      BoxIntegral.integralSum (s.indicator F) MeasureTheory.volume.toBoxAdditive.toSMul
          (BoxIntegral.unitPartition.prepartition n B) =
        (∑' (x : ↑(s ∩ (↑n)⁻¹ • ↑(Submodule.span ℤ (Set.range ⇑(Pi.basisFun ℝ ι))))), F ↑x) / ↑n ^ Fintype.card ι