theorem extracted_formal_statement_12.{u_1} {Ω : Type u_1} {m : MeasurableSpace Ω} {μ : Measure Ω}
  [inst : IsFiniteMeasure μ] (a b : ℝ) {X : Ω → ℝ} (hX : AEMeasurable X μ) (h : ∀ᵐ (ω : Ω) ∂μ, X ω ∈ Set.Icc a b) :
  Integrable (fun x => X x ^ 2) μ := sorry

State before:
case bound_integrable.hg
Ω : Type u_1
m : MeasurableSpace Ω
μ : Measure Ω
inst✝ : IsFiniteMeasure μ
t a b : ℝ
X : Ω → ℝ
hX : AEMeasurable X μ
h : ∀ᵐ (ω : Ω) ∂μ, X ω ∈ Set.Icc a b
c : ℝ := ‖a‖ ⊔ ‖b‖
e : ℝ → Ω → ℝ := fun t ω => rexp (t * X ω) * X ω
e' : ℝ → Ω → ℝ := fun t ω => rexp (t * X ω) * X ω ^ 2
⊢ Integrable (fun x => X x ^ 2) μ

Tactic: rw [(by ext ω; ring : (fun ω ↦ X ω ^ 2) = (fun ω ↦ X ω * X ω))]
    apply MeasureTheory.Integrable.bdd_mul' (integrable_bounded a b hX h) (aestronglyMeasurable_iff_aemeasurable.mpr hX)
    ·
  filter_upwards [h] with x h
  exact (by simp; exact le_trans' (le_abs_self (max ‖a‖ ‖b‖)) (abs_le_max_abs_abs h.1 h.2) : ‖X x‖ ≤ |c|)

State after:

Relevant lemmas:
error