theorem extracted_formal_statement_233.{w, v, u} {Z : Type w} {ι : Type v} {f : ι → Z → ℝ} {Ω : Type u}
  [inst : MeasurableSpace Ω] {X : Ω → Z} {μ : Measure Ω} [inst_1 : IsProbabilityMeasure μ] {n : ℕ}
  [inst_2 : Countable ι] [inst_3 : Nonempty ι] (h𝓕 : ∀ (I : ι), Measurable (f I ∘ X)) {b : ℝ}
  (h𝓕' : ∀ (I : ι) (z : Z), |f I z| ≤ b) (s : Fin 2) (I : ι) (h : (↑s == 0) = true)
  (h_original_goal : Measurable ((if (↑(s, I).1 == 0) = true then f (s, I).2 else -f (s, I).2) ∘ X)) :
  Measurable (f (s, I).2 ∘ X) := sorry

State before:
Z : Type w
ι : Type v
f : ι → Z → ℝ
Ω : Type u
inst✝³ : MeasurableSpace Ω
X : Ω → Z
μ : Measure Ω
inst✝² : IsProbabilityMeasure μ
n : ℕ
inst✝¹ : Countable ι
inst✝ : Nonempty ι
h𝓕 : ∀ (I : ι), Measurable (f I ∘ X)
b : ℝ
h𝓕' : ∀ (I : ι) (z : Z), |f I z| ≤ b
f' : Fin 2 × ι → Z → ℝ := fun i => if (↑i.1 == 0) = true then f i.2 else -f i.2
s : Fin 2
I : ι
h : (↑s == 0) = true
⊢ Measurable ((if (↑(s, I).1 == 0) = true then f (s, I).2 else -f (s, I).2) ∘ X)

Tactic: rw [if_pos h]

State after:
[Z : Type w
 ι : Type v
 f : ι → Z → ℝ
 Ω : Type u
 inst✝³ : MeasurableSpace Ω
 X : Ω → Z
 μ : Measure Ω
 inst✝² : IsProbabilityMeasure μ
 n : ℕ
 inst✝¹ : Countable ι
 inst✝ : Nonempty ι
 h𝓕 : ∀ (I : ι), Measurable (f I ∘ X)
 b : ℝ
 h𝓕' : ∀ (I : ι) (z : Z), |f I z| ≤ b
 f' : Fin 2 × ι → Z → ℝ := fun i => if (↑i.1 == 0) = true then f i.2 else -f i.2
 s : Fin 2
 I : ι
 h : (↑s == 0) = true
 ⊢ Measurable (f (s, I).2 ∘ X)]

Relevant lemmas:
if_pos : ∀ {c : Prop} {h : Decidable c}, c → ∀ {α : Sort u} {t e : α}, (if c then t else e) = t