∀ {X : ℕ → Type u_1} {mX : (n : ℕ) → MeasurableSpace (X n)}
  {κ : (n : ℕ) → ProbabilityTheory.Kernel ((i : ↥(Finset.Iic n)) → X ↑i) (X (n + 1))}
  [∀ (n : ℕ), ProbabilityTheory.IsSFiniteKernel (κ n)] (a b : ℕ),
  ProbabilityTheory.Kernel.partialTraj κ a b =
    (ProbabilityTheory.Kernel.id.prod ((ProbabilityTheory.Kernel.partialTraj κ a b).map (Finset.restrict₂ ⋯))).map
      (IicProdIoc a b)