∀ {X : Type u_1} [inst : TopologicalSpace X] {ι : X → Sort u_3} {p : (a : X) → ι a → Prop} {s : (a : X) → ι a → Set X},
  (∀ (a : X), (nhds a).HasBasis (p a) (s a)) → (∀ (a : X) (i : ι a), p a i → IsClosed (s a i)) → RegularSpace X