∀ {X : Type u_2} [inst : TopologicalSpace X] {ι : Type u_4} {s : Finset ι} {hs : s.Nonempty} {t : ι → Set X},
  (∀ i ∈ s, Topology.IsLocallyConstructible (t i)) → Topology.IsLocallyConstructible (s.inf' hs t)