∀ {α : Type u_1} {Ω : Type u_2} {ι : Type u_3} {_mα : MeasurableSpace α} {s : ι → Set (Set Ω)} {s' : Set (Set Ω)}
  {_mΩ : MeasurableSpace Ω} {κ : ProbabilityTheory.Kernel α Ω} {μ : MeasureTheory.Measure α} {u : Set ι},
  (∃ n ∈ u, ProbabilityTheory.Kernel.IndepSets (s n) s' κ μ) → ProbabilityTheory.Kernel.IndepSets (⋂ n ∈ u, s n) s' κ μ