theorem extracted_formal_statement_236.{u_1, w, u} {Ω : Type u} [inst : MeasurableSpace Ω] {Z : Type w} {n : ℕ}
  {ι : Type u_1} {f : ι → Z → ℝ} {μ : Measure Ω} [inst_1 : IsProbabilityMeasure μ] {X : Ω → Z} [inst_2 : Nonempty ι]
  [inst_3 : Countable ι] (hf : ∀ (i : ι), Measurable (f i ∘ X)) {b : ℝ} (hf' : ∀ (i : ι) (z : Z), |f i z| ≤ b) (i : ι)
  (a : Fin n → Ω) (i_1 : Fin n) (hi_1 : i_1 ∈ Finset.univ) : -b ≤ f i (X (a i_1)) := sorry

State before:
Ω : Type u
inst✝¹ : MeasurableSpace Ω
Z : Type w
n : ℕ
ι : Type u_1
f : ι → Z → ℝ
μ : Measure Ω
inst✝ : IsProbabilityMeasure μ
X : Ω → Z
inst_2 : Nonempty ι
inst_3 : Countable ι
hf : ∀ (i : ι), Measurable (f i ∘ X)
b : ℝ
hf' : ∀ (i : ι) (z : Z), |f i z| ≤ b
ω' : Fin n → Ω
i : ι
a : Fin n → Ω
i_1 : Fin n
hi_1 : i_1 ∈ Finset.univ
⊢ -b ≤ f i (X (a i_1))

Tactic: exact neg_le_of_abs_le (hf' i (X (a i_1)))

State after:

Relevant lemmas:
neg_le_of_abs_le : ∀ {G : Type u_1} [inst : LinearOrderedAddCommGroup G] {a b : G}, |a| ≤ b → -b ≤ a