∀ {α : Type u_1} [inst : TopologicalSpace α] {s : Set α} (motive : (∃ u, IsOpen u ∧ s =ᶠ[residual α] u) → Prop)
  (x : ∃ u, IsOpen u ∧ s =ᶠ[residual α] u),
  (∀ (w : Set α) (uo : IsOpen w) (ueq : s =ᶠ[residual α] w), motive ⋯) → motive x