∀ {α : Type u_1} [inst : TopologicalSpace α] (x x_1 : Ultrafilter α)
  (motive : (∃ x_2, ↑x ≤ nhds x_2 ∧ ↑x_1 ≤ nhds x_2) → Prop) (x_2 : ∃ x_2, ↑x ≤ nhds x_2 ∧ ↑x_1 ≤ nhds x_2),
  (∀ (w : α) (hF : ↑x ≤ nhds w) (hG : ↑x_1 ≤ nhds w), motive ⋯) → motive x_2