∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → Set β},
  UpperHemicontinuous f →
    ∀ (x : α) (t : Set β), IsClosed t → (∃ᶠ (x' : α) in nhds x, (f x' ∩ t).Nonempty) → (f x ∩ t).Nonempty