∀ {R : Type u_1} {S : Type u_2} [inst : CommSemiring R] [inst_1 : CommSemiring S] (f : R →+* S)
  (Z : Set (PrimeSpectrum S)),
  IsClosed Z → (StableUnderSpecialization (PrimeSpectrum.comap f '' Z) ↔ IsClosed (PrimeSpectrum.comap f '' Z))