theorem extracted_formal_statement_13.{u_1} {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_1 : ∀ᵐ (ω : Ω) ∂μ, X ω ∈ Set.Icc a b) :
  let c := ‖a‖ ⊔ ‖b‖;
  ∀ (ω : Ω), X ω ∈ Set.Icc a b → ‖rexp ((2 * |t| + 1) * |X ω|)‖ ≤ ‖rexp ((2 * |t| + 1) * c)‖ := sorry

State before:
case h
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
ω : Ω
h : X ω ∈ Set.Icc a b
⊢ ‖rexp ((2 * |t| + 1) * |X ω|)‖ ≤ ‖rexp ((2 * |t| + 1) * c)‖

Tactic: simp only [norm_eq_abs, abs_exp, exp_le_exp]
    rw [← (abs_eq_self.mpr (le_trans' (le_max_left |a| ‖b‖) (abs_nonneg a)) : |c| = c)]
    exact
  mul_le_mul_of_nonneg_left (le_trans' (le_abs_self (max ‖a‖ ‖b‖)) (abs_le_max_abs_abs h.1 h.2))
    (by linarith [abs_nonneg t] : 0 ≤ 2 * |t| + 1)

State after:

Relevant lemmas:
error