theorem extracted_formal_statement_65 (t : ℝ) : 0 ≤ |t| := sorry

State before:
case a0
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
⊢ 0 ≤ |t|

Tactic: exact abs_nonneg t

State after:

Relevant lemmas:
abs_nonneg : ∀ {α : Type u_1} [inst : Lattice α] [inst_1 : AddGroup α] [inst_2 : AddLeftMono α]
  [inst_3 : AddRightMono α] (a : α), 0 ≤ |a|