∀ {X : Type u_1} [inst : TopologicalSpace X] {U : X → Set X} (motive : (∃ t, ⋃ x ∈ t, interior (U x) = Set.univ) → Prop)
  (x : ∃ t, ⋃ x ∈ t, interior (U x) = Set.univ),
  (∀ (t : Finset X) (ht : ⋃ x ∈ t, interior (U x) = Set.univ), motive ⋯) → motive x