∀ {ι : Type u_1} {A : ι → Type u_2} [inst : (i : ι) → MeasurableSpace (A i)] (μ : (i : ι) → MeasureTheory.Measure (A i))
  [inst_1 : DecidableEq ι] {p : ℝ} [∀ (i : ι), MeasureTheory.SigmaFinite (μ i)],
  0 ≤ p →
    ∀ (s : Finset ι),
      ↑s.card * p ≤ 1 →
        ∀ i ∉ s,
          ∀ {f : ((i : ι) → A i) → ENNReal},
            Measurable f →
              MeasureTheory.GridLines.T μ p f (insert i s) ≤ MeasureTheory.GridLines.T μ p (∫⋯∫⁻_{i}, f ∂μ) s