∀ {X : Type u_2} {Y : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : C(X, Y)}
  {s : Set C(X, Y)},
  s ∈ nhds f ↔
    ∃ S,
      S.Finite ∧
        (∀ (K : Set X) (U : Set Y), (K, U) ∈ S → IsCompact K ∧ IsOpen U ∧ Set.MapsTo (⇑f) K U) ∧
          {g | ∀ (K : Set X) (U : Set Y), (K, U) ∈ S → Set.MapsTo (⇑g) K U} ⊆ s