∀ (A : Type u_2) [inst : CommRing A] (K : Type u_4) [inst_1 : CommRing K] [inst_2 : Algebra A K] [IsFractionRing A K],
  IsDedekindDomain A ↔
    IsDomain A ∧ IsNoetherianRing A ∧ Ring.DimensionLEOne A ∧ ∀ {x : K}, IsIntegral A x → ∃ y, (algebraMap A K) y = x