theorem extracted_formal_statement_103.{u_1} {Ω : Type u_1} {m : MeasurableSpace Ω} {μ : Measure Ω}
  [inst : IsFiniteMeasure μ] (t : ℝ) (f : ℝ → ℝ) {X : Ω → ℝ} (hX : AEMeasurable X μ) (a : Ω)
  (h_original_goal :
    (fun ω => (rexp (t * X ω) / ∫ (x : Ω), (fun ω => rexp (t * X ω)) x ∂μ) * f (X ω)) a =
      (fun ω => rexp (t * X ω) * f (X ω) / ∫ (x : Ω), (fun ω => rexp (t * X ω)) x ∂μ) a) :
  (rexp (t * X a) / ∫ (x : Ω), rexp (t * X x) ∂μ) * f (X a) =
    rexp (t * X a) * f (X a) / ∫ (x : Ω), rexp (t * X x) ∂μ := sorry

State before:
Ω : Type u_1
m : MeasurableSpace Ω
μ : Measure Ω
inst✝ : IsFiniteMeasure μ
t : ℝ
f : ℝ → ℝ
X : Ω → ℝ
hX : AEMeasurable X μ
a : Ω
⊢ (fun ω => (rexp (t * X ω) / ∫ (x : Ω), (fun ω => rexp (t * X ω)) x ∂μ) * f (X ω)) a =
    (fun ω => rexp (t * X ω) * f (X ω) / ∫ (x : Ω), (fun ω => rexp (t * X ω)) x ∂μ) a

Tactic: simp only

State after:
[Ω : Type u_1
 m : MeasurableSpace Ω
 μ : Measure Ω
 inst✝ : IsFiniteMeasure μ
 t : ℝ
 f : ℝ → ℝ
 X : Ω → ℝ
 hX : AEMeasurable X μ
 a : Ω
 ⊢ (rexp (t * X a) / ∫ (x : Ω), rexp (t * X x) ∂μ) * f (X a) = rexp (t * X a) * f (X a) / ∫ (x : Ω), rexp (t * X x) ∂μ]

Relevant lemmas: