∀ {R : Type u} [inst : CommRing R] {S : Type v} [inst_1 : CommRing S] (p : Ideal R) [inst_2 : IsDedekindDomain S]
  [inst_3 : Algebra R S] [p.IsMaximal]
  (P : ↥(UniqueFactorizationMonoid.factors (Ideal.map (algebraMap R S) p)).toFinset), (↑P).LiesOver p