theorem extracted_formal_statement_23.{u} {Ω : Type u} [inst : MeasurableSpace Ω] {μ : Measure Ω}
  [inst_1 : IsProbabilityMeasure μ] {n : ℕ} (s : Fin (n + 1) → Set Ω) (hs : ∀ (i : Fin (n + 1)), MeasurableSet (s i))
  (this : (fun f x => Fin.snoc f.2 f.1 x) ⁻¹' Set.univ.pi s = s (Fin.last n) ×ˢ Set.univ.pi (s ∘ Fin.castSucc)) :
  (∏ i, μ ((s ∘ Fin.castSucc) i)) * μ (s (Fin.last n)) = (∏ i, (⇑μ ∘ s ∘ Fin.castSucc) i) * μ (s ↑n) := sorry

State before:
Ω : Type u
inst✝¹ : MeasurableSpace Ω
μ : Measure Ω
inst✝ : IsProbabilityMeasure μ
n : ℕ
s : Fin (n + 1) → Set Ω
hs : ∀ (i : Fin (n + 1)), MeasurableSet (s i)
this : (fun f x => Fin.snoc f.2 f.1 x) ⁻¹' Set.univ.pi s = s (Fin.last n) ×ˢ Set.univ.pi (s ∘ Fin.castSucc)
⊢ (∏ i, μ ((s ∘ Fin.castSucc) i)) * μ (s (Fin.last n)) = (∏ i, (⇑μ ∘ s ∘ Fin.castSucc) i) * μ (s ↑n)

Tactic: simp

State after:

Relevant lemmas: