theorem extracted_formal_statement_283.{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] [inst_2 : Nonempty ι]
  [inst_3 : Countable ι] {X : Ω → Z} (hf : ∀ (i : ι), Measurable (f i ∘ X)) {b : ℝ}
  (hf' : ∀ (i : ι) (z : Z), |f i z| ≤ b) (ω : (Fin n → Ω) × (Fin n → Ω)) (σ : Signs n) (i : ι) (k : Fin n) :
  |↑↑(σ k) * f i (X (ω.1 k))| = |f i (X (ω.1 k))| := sorry

State before:
case e_f.h.e_s.h.e_f.h
Ω : Type u
inst✝³ : MeasurableSpace Ω
Z : Type w
n : ℕ
ι : Type u_1
f : ι → Z → ℝ
μ : Measure Ω
inst✝² : IsProbabilityMeasure μ
inst✝¹ : Nonempty ι
inst✝ : Countable ι
X : Ω → Z
hf : ∀ (i : ι), Measurable (f i ∘ X)
b : ℝ
hf' : ∀ (i : ι) (z : Z), |f i z| ≤ b
ω : (Fin n → Ω) × (Fin n → Ω)
σ : Signs n
i : ι
k : Fin n
⊢ |↑↑(σ k) * f i (X (ω.1 k))| = |f i (X (ω.1 k))|

Tactic: simp only [Int.reduceNeg, abs_mul, Signs.apply_abs', one_mul]

State after:

Relevant lemmas:
Signs.apply_abs' : ∀ {n : ℕ} (σ : Signs n) (k : Fin n), |↑↑(σ k)| = 1
abs_mul : ∀ {α : Type u_1} [inst : LinearOrderedRing α] (a b : α), |a * b| = |a| * |b|
one_mul : ∀ {M : Type u} [inst : MulOneClass M] (a : M), 1 * a = a