∀ {R : Type u_2} {S : Type u_1} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {x : S} {I : Ideal R}
  (z : S), conductor R x ⊔ Ideal.map (algebraMap R S) I = ⊤ → z ∈ conductor R x ⊔ Ideal.map (algebraMap R S) I