∀ {R : Type u_1} [inst : Ring R] {s : Set R} {p : (x : R) → x ∈ Subring.closure s → Prop} {b : R}
  (motive : b ∈ {x | ∃ (hx : x ∈ Subring.closure s), p x hx} → Prop)
  (x : b ∈ {x | ∃ (hx : x ∈ Subring.closure s), p x hx}),
  (∀ (w : b ∈ Subring.closure s) (hpy : p b w), motive ⋯) → motive x