theorem extracted_formal_statement_2.{u_2, u_1} {ι : Type u_1} {Ω : ι → Type u_2} [inst : Fintype ι]
  [inst_1 : DecidableEq ι] [inst_2 : (i : ι) → MeasurableSpace (Ω i)] {μ : (i : ι) → Measure (Ω i)}
  [inst_3 : ∀ (i : ι), IsProbabilityMeasure (μ i)] (k : ι) (s : Set (Ω k)) (hs : MeasurableSet s) :
  (∏ i, if i = k then (μ k) s else 1) = (μ k) s := sorry

State before:
ι : Type u_1
Ω : ι → Type u_2
inst✝³ : Fintype ι
inst✝² : DecidableEq ι
inst✝¹ : (i : ι) → MeasurableSpace (Ω i)
μ : (i : ι) → Measure (Ω i)
inst✝ : ∀ (i : ι), IsProbabilityMeasure (μ i)
k : ι
s : Set (Ω k)
hs : MeasurableSet s
⊢ (∏ i, if i = k then (μ k) s else 1) = (μ k) s

Tactic: exact Fintype.prod_ite_eq' k fun j ↦ μ k s

State after:

Relevant lemmas:
Fintype.prod_ite_eq' : ∀ {ι : Type u_6} {α : Type u_8} [inst : Fintype ι] [inst_4 : CommMonoid α]
  [inst_5 : DecidableEq ι] (i : ι) (f : ι → α), (∏ j, if j = i then f j else 1) = f i