{α : Type u_1} →
  {β : Type u_2} →
    {mα : MeasurableSpace α} →
      {mβ : MeasurableSpace β} →
        {κ : ProbabilityTheory.Kernel α β} →
          {motive : ProbabilityTheory.IsFiniteKernel κ → Sort u} →
            ((exists_univ_le : ∃ C < ⊤, ∀ (a : α), (κ a) Set.univ ≤ C) → motive ⋯) →
              (t : ProbabilityTheory.IsFiniteKernel κ) → motive t