∀ {X : Type u_1} {α : Type u_2} [inst : TopologicalSpace X] [BaireSpace X] {S : Set α} {f : α → Set X},
  (∀ s ∈ S, IsClosed (f s)) → S.Countable → ⋃ s ∈ S, f s = Set.univ → Dense (⋃ s ∈ S, interior (f s))