∀ {X : Type u_1} {R : Type u_2} [inst : TopologicalSpace X] [inst_1 : Semiring R] [inst_2 : TopologicalSpace R]
  [inst_3 : IsTopologicalSemiring R] {I : Ideal C(X, R)} {x : X}, x ∈ ContinuousMap.setOfIdeal I ↔ ∃ f ∈ I, f x ≠ 0