∀ {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} {β : ι → Type u_8}
  {m : (i : ι) → MeasurableSpace (β i)} {f : (i : ι) → Ω → β i},
  ProbabilityTheory.Kernel.iIndepFun f κ μ →
    (∀ (i : ι), AEMeasurable (f i) (μ.bind ⇑κ)) →
      ∀ (i j k l : ι),
        i ≠ k →
          i ≠ l →
            j ≠ k → j ≠ l → ProbabilityTheory.Kernel.IndepFun (fun a => (f i a, f j a)) (fun a => (f k a, f l a)) κ μ