theorem extracted_formal_statement_9.{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)
  (t' : ℝ) : AEStronglyMeasurable (fun ω => rexp (t' * X ω) * X ω) μ := sorry

State before:
case hF_meas.hp
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
t' : ℝ
⊢ AEStronglyMeasurable (fun ω => rexp (t' * X ω) * X ω) μ

Tactic: rw [aestronglyMeasurable_iff_aemeasurable]
    apply AEMeasurable.mul _ hX
    exact Measurable.comp_aemeasurable' measurable_exp (hX.const_mul t')

State after:

Relevant lemmas:
Measurable.comp_aemeasurable' : ∀ {α : Type u_1} {β : Type u_2} {δ : Type u_4} {m : MeasurableSpace α}
  [inst : MeasurableSpace β] {μ : Measure α} [inst_1 : MeasurableSpace δ] {f : α → δ} {g : δ → β},
  Measurable g → AEMeasurable f μ → AEMeasurable (fun x => g (f x)) μ
AEMeasurable.mul : ∀ {M : Type u_2} {α : Type u_3} [inst : MeasurableSpace M] [inst_1 : Mul M] {m : MeasurableSpace α}
  {f g : α → M} {μ : Measure α} [inst_2 : MeasurableMul₂ M],
  AEMeasurable f μ → AEMeasurable g μ → AEMeasurable (fun a => f a * g a) μ
Real.measurable_exp : Measurable rexp
aestronglyMeasurable_iff_aemeasurable : ∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace β]
  {m₀ : MeasurableSpace α} {μ : Measure α} {f : α → β} [inst_1 : MeasurableSpace β]
  [inst_2 : TopologicalSpace.PseudoMetrizableSpace β] [inst_3 : BorelSpace β] [inst_4 : SecondCountableTopology β],
  AEStronglyMeasurable f μ ↔ AEMeasurable f μ