-- File: FoML/FoML/Bennett.lean
Theorem statement:
theorem extracted_formal_statement_42.{u_1} {Ω : Type u_1} [inst : MeasurableSpace Ω] (μ : Measure Ω)
  [inst_1 : IsProbabilityMeasure μ] {n : ℕ} {X : Fin n → Ω → ℝ} (hXm : ∀ (i : Fin n), Measurable (X i))
  (hX_bdd : ∀ (i : Fin n), ∀ᵐ (ω : Ω) ∂μ, |X i ω| ≤ 1) (i : Fin n) (h_const : Integrable (fun x => 1) μ)
  (h_bound : ∀ᵐ (ω : Ω) ∂μ, ‖X i ω‖ ≤ 1) (h_original_goal : HasFiniteIntegral (fun ω => X i ω) μ) :
  ∀ᵐ (a : Ω) ∂μ, ‖X i a‖ ≤ 1 := sorry

Tactic state before:
case right
Ω : Type u_1
inst : MeasurableSpace Ω
μ : Measure Ω
inst_1 : IsProbabilityMeasure μ
n : ℕ
X : Fin n → Ω → ℝ
hXm : ∀ (i : Fin n), Measurable (X i)
hX_bdd : ∀ (i : Fin n), ∀ᵐ (ω : Ω) ∂μ, |X i ω| ≤ 1
τ : ℝ
i : Fin n
h_const : Integrable (fun x => 1) μ
h_bound : ∀ᵐ (ω : Ω) ∂μ, ‖X i ω‖ ≤ 1
⊢ HasFiniteIntegral (fun ω => X i ω) μ

Tactic: apply hasFiniteIntegral_of_bounded (C := 1)

Tactic state after:
[case right
 Ω : Type u_1
 inst : MeasurableSpace Ω
 μ : Measure Ω
 inst_1 : IsProbabilityMeasure μ
 n : ℕ
 X : Fin n → Ω → ℝ
 hXm : ∀ (i : Fin n), Measurable (X i)
 hX_bdd : ∀ (i : Fin n), ∀ᵐ (ω : Ω) ∂μ, |X i ω| ≤ 1
 τ : ℝ
 i : Fin n
 h_const : Integrable (fun x => 1) μ
 h_bound : ∀ᵐ (ω : Ω) ∂μ, ‖X i ω‖ ≤ 1
 ⊢ ∀ᵐ (a : Ω) ∂μ, ‖X i a‖ ≤ 1]

Premises used:
MeasureTheory.hasFiniteIntegral_of_bounded : ∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : Measure α}
  [inst : NormedAddCommGroup β] [inst_2 : IsFiniteMeasure μ] {f : α → β} {C : ℝ},
  (∀ᵐ (a : α) ∂μ, ‖f a‖ ≤ C) → HasFiniteIntegral f μ