∀ {R : Type u_1} [inst : CommRing R] {S : Type u_2} [inst_1 : CommRing S] {f : R →+* S},
  f.SurjectiveOnStalks →
    ∀ (P : Ideal R) [inst_2 : P.IsPrime] (Q : Ideal S) [inst_3 : Q.IsPrime] (e : P = Ideal.comap f Q),
      Function.Surjective ⇑(Localization.localRingHom P Q f e)