theorem extracted_formal_statement_3 : 0 ≤ 2⁻¹ := sorry

State before:
case a0
Ω : Type u
inst✝¹ : MeasurableSpace Ω
μ : autoParam (Measure Ω) _auto✝
inst✝ : IsProbabilityMeasure μ
t a b : ℝ
X : Ω → ℝ
ht : 0 ≤ t
hX : AEMeasurable X μ
h : ∀ᵐ (ω : Ω) ∂μ, X ω ∈ Set.Icc a b
h0 : ∫ (x : Ω), X x ∂μ = 0
w : ¬t = 0
f : ℝ → ℝ := fun t => cgf X μ t
hf : f 0 = 0
f' : ℝ → ℝ := fun t => ∫ (x : Ω), X x ∂Measure.tilted μ fun ω => t * X ω
hf' : f' 0 = 0
f'' : ℝ → ℝ := fun t => Var[X; Measure.tilted μ fun ω => t * X ω]
c : ℝ
left✝ : 0 < c ∧ c < t
cq' : f t = f'' c * t ^ 2 / 2
⊢ 0 ≤ 2⁻¹

Tactic: simp only [inv_nonneg, Nat.ofNat_nonneg]

State after:

Relevant lemmas:
inv_nonneg : ∀ {G₀ : Type u_2} [inst : GroupWithZero G₀] [inst_1 : PartialOrder G₀] [inst_2 : ZeroLEOneClass G₀]
  [inst_3 : PosMulReflectLT G₀] {a : G₀}, 0 ≤ a⁻¹ ↔ 0 ≤ a
Nat.ofNat_nonneg : ∀ {α : Type u_3} [inst : OrderedSemiring α] (n : ℕ) [inst_1 : n.AtLeastTwo], 0 ≤ OfNat.ofNat n