∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α} {f : α → ℝ}
  (motive : {x | x ∈ s ∧ f x ≤ ⨍ (a : α) in s, f a ∂μ}.Nonempty → Prop)
  (x : {x | x ∈ s ∧ f x ≤ ⨍ (a : α) in s, f a ∂μ}.Nonempty),
  (∀ (x : α) (hx : x ∈ s) (h : f x ≤ ⨍ (a : α) in s, f a ∂μ), motive ⋯) → motive x