∀ {α : Type u_1} {Ω : Type u_2} {ι : Type u_3} {_mα : MeasurableSpace α} {_mΩ : MeasurableSpace Ω}
  {κ : ProbabilityTheory.Kernel α Ω} {μ : MeasureTheory.Measure α} {s : ι → Set (Set Ω)} {S T : Set ι},
  ProbabilityTheory.Kernel.iIndepSets s κ μ →
    Disjoint S T → ProbabilityTheory.Kernel.IndepSets (piiUnionInter s S) (piiUnionInter s T) κ μ