∀ {X : Type u_1} {𝓑 𝓧 : MeasurableSpace X} {π : ProbabilityTheory.Kernel X X} (motive : π.IsProper → Prop)
  (x : π.IsProper),
  (∀ (h : ∀ ⦃B : Set X⦄ (hB : MeasurableSet B) (x : X), (π.restrict ⋯) x = B.indicator (fun x => 1) x • π x),
      motive ⋯) →
    motive x