∀ {X : ℕ → Type u_1} [inst : (n : ℕ) → MeasurableSpace (X n)]
  {κ : (n : ℕ) → ProbabilityTheory.Kernel ((i : ↥(Finset.Iic n)) → X ↑i) (X (n + 1))}
  [inst_1 : ∀ (n : ℕ), ProbabilityTheory.IsMarkovKernel (κ n)] (a : ℕ),
  ProbabilityTheory.Kernel.traj κ a =
    (ProbabilityTheory.Kernel.id.prod ((ProbabilityTheory.Kernel.traj κ a).map (Set.Ioi a).restrict)).map
      ⇑(MeasurableEquiv.IicProdIoi a)