∀ {R : Type u_1} [inst : CommRing R] {S : Type u_2} [inst_1 : CommRing S] {I : Ideal S} [inst_2 : Algebra R S]
  [Nontrivial R] [IsDomain S] [Algebra.IsIntegral R S], Ideal.comap (algebraMap R S) I = ⊥ → I = ⊥