∀ {X : Type u_2} [inst : TopologicalSpace X] {s : Set X} {ι : Type u_4} {U : ι → TopologicalSpace.Opens X},
  TopologicalSpace.IsOpenCover U →
    (∀ (i : ι), Topology.IsLocallyConstructible (Subtype.val ⁻¹' s)) → Topology.IsLocallyConstructible s