theorem extracted_formal_statement_8.{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' : ∀ᵐ (ω : Ω) ∂μ, rexp (t * X ω) ≤ rexp (t * b)) (p : ∀ᵐ (ω : Ω) ∂μ, ↑‖rexp (t * X ω)‖₊ ≤ rexp (t * b))
  (p'' : ∫⁻ (ω : Ω), ↑‖rexp (t * X ω)‖₊ ∂μ ≤ ∫⁻ (x : Ω), ↑‖rexp (t * b)‖₊ ∂μ) :
  ↑‖rexp (t * b)‖₊ * μ Set.univ < ⊤ := sorry

State before:
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)
p : ∀ᵐ (ω : Ω) ∂μ, ↑‖rexp (t * X ω)‖₊ ≤ rexp (t * b)
p'' : ∫⁻ (ω : Ω), ↑‖rexp (t * X ω)‖₊ ∂μ ≤ ∫⁻ (x : Ω), ↑‖rexp (t * b)‖₊ ∂μ
⊢ ↑‖rexp (t * b)‖₊ * μ Set.univ < ⊤

Tactic: apply ENNReal.mul_lt_top ENNReal.coe_lt_top (IsFiniteMeasure.measure_univ_lt_top)

State after:

Relevant lemmas:
ENNReal.mul_lt_top : ∀ {a b : ℝ≥0∞}, a < ⊤ → b < ⊤ → a * b < ⊤
MeasureTheory.IsFiniteMeasure.measure_univ_lt_top : ∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : Measure α}
  [self : IsFiniteMeasure μ], μ Set.univ < ⊤
ENNReal.coe_lt_top : ∀ {r : ℝ≥0}, ↑r < ⊤