theorem extracted_formal_statement_25 (t : ℝ) : 0 < |t| + 1 := sorry

State before:
case ε_pos
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)
e' : ℝ → Ω → ℝ := fun t ω => rexp (t * X ω) * X ω
⊢ 0 < ?ε

Tactic: exact LE.le.trans_lt (abs_nonneg t) (lt_add_one |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|
lt_add_one : ∀ {α : Type u_1} [inst : One α] [inst_1 : AddZeroClass α] [inst_2 : PartialOrder α]
  [inst_3 : ZeroLEOneClass α] [inst_4 : NeZero 1] [inst_5 : AddLeftStrictMono α] (a : α), a < a + 1
LE.le.trans_lt : ∀ {α : Type u_1} [inst : Preorder α] {a b c : α}, a ≤ b → b < c → a < c