theorem extracted_formal_statement_13.{u} {Ω : Type u} [inst : MeasurableSpace Ω] {μ : Measure Ω}
  [inst_1 : IsProbabilityMeasure μ] {n : ℕ}
  (h_original_goal :
    (Measure.pi fun x => μ) = Measure.map (fun f x => Fin.snoc f.2 f.1 x) (μ.prod (Measure.pi fun x => μ)))
  (s : Fin (n + 1) → Set Ω) :
  (∀ (i : Fin (n + 1)), MeasurableSet (s i)) →
    (Measure.map (fun f x => Fin.snoc f.2 f.1 x) (μ.prod (Measure.pi fun x => μ))) (Set.univ.pi s) =
      ∏ i, μ (s i) := sorry

State before:
Ω : Type u
inst✝¹ : MeasurableSpace Ω
μ : Measure Ω
inst✝ : IsProbabilityMeasure μ
n : ℕ
⊢ (Measure.pi fun x => μ) = Measure.map (fun f x => Fin.snoc f.2 f.1 x) (μ.prod (Measure.pi fun x => μ))

Tactic: apply Measure.pi_eq

State after:
[case h
 Ω : Type u
 inst✝¹ : MeasurableSpace Ω
 μ : Measure Ω
 inst✝ : IsProbabilityMeasure μ
 n : ℕ
 ⊢ ∀ (s : Fin (n + 1) → Set Ω),
     (∀ (i : Fin (n + 1)), MeasurableSet (s i)) →
       (Measure.map (fun f x => Fin.snoc f.2 f.1 x) (μ.prod (Measure.pi fun x => μ))) (Set.univ.pi s) = ∏ i, μ (s i)]

Relevant lemmas:
MeasureTheory.Measure.pi_eq : ∀ {ι : Type u_1} {α : ι → Type u_3} [inst : Fintype ι]
  [inst_2 : (i : ι) → MeasurableSpace (α i)] {μ : (i : ι) → Measure (α i)} [inst_3 : ∀ (i : ι), SigmaFinite (μ i)]
  {μ' : Measure ((i : ι) → α i)},
  (∀ (s : (i : ι) → Set (α i)), (∀ (i : ι), MeasurableSet (s i)) → μ' (Set.univ.pi s) = ∏ i, (μ i) (s i)) →
    Measure.pi μ = μ'