∀ {α : Type u_2} {β : Type u_1} [inst : LinearOrder α] {f : β → α} {t : Set β}
  (motive : (∃ x ∈ t, IsMinOn f t x) → Prop) (x : ∃ x ∈ t, IsMinOn f t x),
  (∀ (x : β) (hxt : x ∈ t) (hfx : IsMinOn f t x), motive ⋯) → motive x