∀ {ι : Type u_1} {α : ι → Type u_2} (s₁ s₂ : Finset ι) (S₁ : Set ((i : ↥s₁) → α ↑i)) (S₂ : Set ((i : ↥s₂) → α ↑i))
  [inst : DecidableEq ι],
  MeasureTheory.cylinder s₁ S₁ ∩ MeasureTheory.cylinder s₂ S₂ =
    MeasureTheory.cylinder (s₁ ∪ s₂) (Finset.restrict₂ ⋯ ⁻¹' S₁ ∩ Finset.restrict₂ ⋯ ⁻¹' S₂)