∀ (X : Type u_2) (𝕜 : Type u_1) [inst : RCLike 𝕜] [inst_1 : TopologicalSpace X] (I : Ideal C(X, 𝕜))
  (s : TopologicalSpace.Opens X), ContinuousMap.setOfIdeal I ≤ ↑s ↔ I ≤ ContinuousMap.idealOfSet 𝕜 ↑s