∀ {X : ℕ → Type u_1} {mX : (n : ℕ) → MeasurableSpace (X n)} {a b : ℕ}
  {κ : (n : ℕ) → ProbabilityTheory.Kernel ((i : ↥(Finset.Iic n)) → X ↑i) (X (n + 1))} (hab : a ≤ b),
  ProbabilityTheory.Kernel.partialTraj κ a b =
    Nat.leRec ProbabilityTheory.Kernel.id
      (fun k x κ_k =>
        ((ProbabilityTheory.Kernel.id.prod ((κ k).map ⇑(MeasurableEquiv.piSingleton k))).comp κ_k).map
          (IicProdIoc k (k + 1)))
      hab