theorem extracted_formal_statement_203.{u_1, w, u} {Ω : Type u} [inst : MeasurableSpace Ω] {Z : Type w} {n : ℕ}
  {ι : Type u_1} {f : ι → Z → ℝ} {μ : Measure Ω} [inst_1 : IsProbabilityMeasure μ] {X : Ω → Z} [inst_2 : Nonempty ι]
  [inst_3 : Countable ι] (hf : ∀ (i : ι), Measurable (f i ∘ X)) {b : ℝ} (hf' : ∀ (i : ι) (z : Z), |f i z| ≤ b) :
  Measurable fun a => ⨆ i, |∫ (x : Fin n → Ω), ∑ k, (f i (X (a k)) - f i (X (x k))) ∂Measure.pi fun x => μ| := sorry

State before:
case left.hf
Ω : Type u
inst✝¹ : MeasurableSpace Ω
Z : Type w
n : ℕ
ι : Type u_1
f : ι → Z → ℝ
μ : Measure Ω
inst✝ : IsProbabilityMeasure μ
X : Ω → Z
inst_2 : Nonempty ι
inst_3 : Countable ι
hf : ∀ (i : ι), Measurable (f i ∘ X)
b : ℝ
hf' : ∀ (i : ι) (z : Z), |f i z| ≤ b
⊢ Measurable fun a => ⨆ i, |∫ (x : Fin n → Ω), ∑ k, (f i (X (a k)) - f i (X (x k))) ∂Measure.pi fun x => μ|

Tactic: apply measurable_aux10 hf

State after:

Relevant lemmas:
measurable_aux10 : ∀ {Ω : Type u} [inst : MeasurableSpace Ω] {Z : Type w} {n : ℕ} {ι : Type u_1} {f : ι → Z → ℝ}
  {μ : Measure Ω} [inst_4 : IsProbabilityMeasure μ] {X : Ω → Z} [inst_3 : Countable ι],
  (∀ (i : ι), Measurable (f i ∘ X)) →
    Measurable fun ω => ⨆ i, |∫ (x : Fin n → Ω), ∑ k, (f i (X (ω k)) - f i (X (x k))) ∂Measure.pi fun x => μ|