-- File: FoML/FoML/Rademacher.lean
Theorem statement:
theorem extracted_formal_statement_161.{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] [inst_2 : Countable ι] {X : Ω → Z}
  (hf : ∀ (i : ι), Measurable (f i ∘ X)) {b : ℝ} (hb : 0 ≤ b) (hf' : ∀ (i : ι) (z : Z), |f i z| ≤ b) (ω : Fin n → Ω × Ω)
  (σ : Signs n) (a : σ ∈ Finset.univ) :
  BddAbove (Set.range fun i => ∑ k, |↑↑(σ k) * (f i (X (ω k).1) - f i (X (ω k).2))|) := sorry

Tactic state before:
case h.B
Ω : Type u
inst✝² : MeasurableSpace Ω
Z : Type w
n : ℕ
ι : Type u_1
f : ι → Z → ℝ
μ : Measure Ω
inst✝¹ : IsProbabilityMeasure μ
inst✝ : Countable ι
X : Ω → Z
hf : ∀ (i : ι), Measurable (f i ∘ X)
b : ℝ
hb : 0 ≤ b
hf' : ∀ (i : ι) (z : Z), |f i z| ≤ b
ω : Fin n → Ω × Ω
ω₁ : Fin n → Ω := fun k => (ω k).1
ω₂ : Fin n → Ω := fun k => (ω k).2
σ : Signs n
a✝ : σ ∈ Finset.univ
⊢ BddAbove (Set.range fun i => ∑ k, |↑↑(σ k) * (f i (X (ω k).1) - f i (X (ω k).2))|)

Tactic: apply bdd_above_aux30 X hf' ω σ

Tactic state after:

Premises used:
bdd_above_aux30 : ∀ {Ω : Type u} {Z : Type w} {n : ℕ} {ι : Type u_1} {f : ι → Z → ℝ} [inst : Countable ι] (X : Ω → Z)
  {b : ℝ},
  (∀ (i : ι) (z : Z), |f i z| ≤ b) →
    ∀ (ω : Fin n → Ω × Ω) (σ : Signs n),
      BddAbove (Set.range fun i => ∑ k, |↑↑(σ k) * (f i (X (ω k).1) - f i (X (ω k).2))|)