∀ {α : Type u_1} {β : Type u_2} [uniformSpace : UniformSpace α] [inst : UniformSpace β] {f : Filter β} (x : α)
  (motive : (∃ x_1, pure x ×ˢ f ≤ nhds x_1) → Prop) (x_1 : ∃ x_1, pure x ×ˢ f ≤ nhds x_1),
  (∀ (a : α) (b : β) (hab : pure x ×ˢ f ≤ nhds (a, b)), motive ⋯) → motive x_1