∀ {α : Type u_1} {γ : Type u_2} {mα : MeasurableSpace α} {mγ : MeasurableSpace γ} {κ η : ProbabilityTheory.Kernel α γ}
  [hαγ : MeasurableSpace.CountableOrCountablyGenerated α γ] [ProbabilityTheory.IsFiniteKernel κ]
  [inst : ProbabilityTheory.IsFiniteKernel η] {a : α} {s : Set γ},
  s ⊆ κ.mutuallySingularSetSlice η a → ((η.withDensity (κ.rnDeriv η)) a) s = 0