∀ {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))} (a : ℕ),
  ProbabilityTheory.Kernel.partialTraj κ a a = ProbabilityTheory.Kernel.id