theorem extracted_formal_statement_37.{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) (τ : ℝ) (i : Fin n) (h1 : AEStronglyMeasurable (fun x => 1) μ)
  (h2 : AEStronglyMeasurable (fun ω => τ * X i ω) μ) (h3 : AEStronglyMeasurable (fun ω => X i ω ^ 2) μ)
  (h4 : AEStronglyMeasurable (fun ω => X i ω ^ 2 * (rexp τ - 1 - τ)) μ)
  (h5 : AEStronglyMeasurable ((fun x => 1) + ((fun ω => τ * X i ω) + fun ω => X i ω ^ 2 * (rexp τ - 1 - τ))) μ)
  (ω : Ω) :
  1 + τ * X i ω + X i ω ^ 2 * (rexp τ - 1 - τ) =
    ((fun ω => 1) + ((fun ω => τ * X i ω) + fun ω => X i ω ^ 2 * (rexp τ - 1 - τ))) ω := sorry

State before:
case h
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
h1 : AEStronglyMeasurable (fun x => 1) μ
h2 : AEStronglyMeasurable (fun ω => τ * X i ω) μ
h3 : AEStronglyMeasurable (fun ω => X i ω ^ 2) μ
h4 : AEStronglyMeasurable (fun ω => X i ω ^ 2 * (rexp τ - 1 - τ)) μ
h5 : AEStronglyMeasurable ((fun x => 1) + ((fun ω => τ * X i ω) + fun ω => X i ω ^ 2 * (rexp τ - 1 - τ))) μ
ω : Ω
⊢ 1 + τ * X i ω + X i ω ^ 2 * (rexp τ - 1 - τ) =
    ((fun ω => 1) + ((fun ω => τ * X i ω) + fun ω => X i ω ^ 2 * (rexp τ - 1 - τ))) ω

Tactic: simp only [Pi.add_apply, add_assoc]

State after:

Relevant lemmas:
add_assoc : ∀ {G : Type u_1} [inst : AddSemigroup G] (a b c : G), a + b + c = a + (b + c)
Pi.add_apply : ∀ {I : Type u} {f : I → Type v₁} (x y : (i : I) → f i) (i : I) [inst : (i : I) → Add (f i)],
  (x + y) i = x i + y i