theorem extracted_formal_statement_12.{u_1} {Ω : Type u_1} {m : MeasurableSpace Ω} {μ : Measure Ω}
  [inst : IsFiniteMeasure μ] {X : Ω → ℝ} {a b : ℝ} (hX : AEMeasurable X μ) (h : ∀ᵐ (ω : Ω) ∂μ, X ω ∈ Set.Icc a b) :
  Integrable (fun ω => rexp (0 * X ω)) μ := sorry

State before:
case inr.inl
Ω : Type u_1
m : MeasurableSpace Ω
μ : Measure Ω
inst✝ : IsFiniteMeasure μ
X : Ω → ℝ
t a b : ℝ
hX : AEMeasurable X μ
h : ∀ᵐ (ω : Ω) ∂μ, X ω ∈ Set.Icc a b
ht : t = 0
⊢ Integrable (fun ω => rexp (0 * X ω)) μ

Tactic: simp only [zero_mul, exp_zero, integrable_const]

State after:

Relevant lemmas:
Real.exp_zero : rexp 0 = 1
MeasureTheory.integrable_const : ∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : Measure α}
  [inst : NormedAddCommGroup β] [inst_1 : IsFiniteMeasure μ] (c : β), Integrable (fun x => c) μ
MulZeroClass.zero_mul : ∀ {M₀ : Type u} [self : MulZeroClass M₀] (a : M₀), 0 * a = 0