theorem extracted_formal_statement_3.{u_2, u_1} {Ω : Type u_1} {ι : Type u_2} [inst : MeasurableSpace Ω] {μ : Measure Ω}
  [inst_1 : IsProbabilityMeasure μ] [inst_2 : Fintype ι]
  (h_original_goal : iIndepFun Function.eval (Measure.pi fun x => μ)) (s : Finset ι) {f : ι → Set (ι → Ω)}
  (_H : ∀ i ∈ s, MeasurableSet (f i)) :
  (Measure.pi fun x => μ) (⋂ i ∈ s, f i) = ∏ x ∈ s, (Measure.pi fun x => μ) (f x) := sorry

State before:
Ω : Type u_1
ι : Type u_2
inst✝³ : MeasurableSpace Ω
μ : Measure Ω
inst✝² : IsProbabilityMeasure μ
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
⊢ iIndepFun Function.eval (Measure.pi fun x => μ)

Tactic: simp only [iIndepFun, Kernel.iIndepFun, Kernel.iIndep, Kernel.iIndepSets, Set.mem_setOf_eq,
  Kernel.const_apply, ae_dirac_eq, Filter.eventually_pure]

State after:
[Ω : Type u_1
 ι : Type u_2
 inst✝³ : MeasurableSpace Ω
 μ : Measure Ω
 inst✝² : IsProbabilityMeasure μ
 inst✝¹ : Fintype ι
 inst✝ : DecidableEq ι
 ⊢ ∀ (s : Finset ι) {f : ι → Set (ι → Ω)},
     (∀ i ∈ s, MeasurableSet (f i)) → (Measure.pi fun x => μ) (⋂ i ∈ s, f i) = ∏ x ∈ s, (Measure.pi fun x => μ) (f x)]

Relevant lemmas:
Filter.eventually_pure : ∀ {α : Type u_1} {a : α} {p : α → Prop}, (∀ᶠ (x : α) in pure a, p x) ↔ p a
MeasureTheory.ae_dirac_eq : ∀ {α : Type u_1} [inst : MeasurableSpace α] [inst_3 : MeasurableSingletonClass α] (a : α),
  ae (Measure.dirac a) = pure a
Set.mem_setOf_eq : ∀ {α : Type u} {x : α} {p : α → Prop}, (x ∈ {y | p y}) = p x
ProbabilityTheory.Kernel.const_apply : ∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  (μβ : Measure β) (a : α), (Kernel.const α μβ) a = μβ