theorem extracted_formal_statement_2.{u_1} {Ω : Type u_1} {m : MeasurableSpace Ω} {μ : Measure Ω}
  [inst : IsFiniteMeasure μ] {X : Ω → ℝ} (t b : ℝ) (ht : t > 0) (hX : AEMeasurable X μ) (hb : ∀ᵐ (ω : Ω) ∂μ, X ω ≤ b)
  (b'_1 : ∀ᵐ (ω : Ω) ∂μ, rexp (t * X ω) ≤ rexp (t * b)) (ω : Ω) (b' : rexp (t * X ω) ≤ rexp (t * b)) :
  rexp (t * X ω) ≤ rexp (t * b) := sorry

State before:
case h
Ω : Type u_1
m : MeasurableSpace Ω
μ : Measure Ω
inst✝ : IsFiniteMeasure μ
X : Ω → ℝ
t b : ℝ
ht : t > 0
hX : AEMeasurable X μ
hb : ∀ᵐ (ω : Ω) ∂μ, X ω ≤ b
b'✝ : ∀ᵐ (ω : Ω) ∂μ, rexp (t * X ω) ≤ rexp (t * b)
ω : Ω
b' : rexp (t * X ω) ≤ rexp (t * b)
⊢ rexp (t * X ω) ≤ rexp (t * b)

Tactic: exact b'

State after:

Relevant lemmas: