exact uniqueFactorizationMonoid_of_exists_prime H hP
case mpr
R : Type u_1
inst✝¹ : CommSemiring R
inst✝ : IsDomain R
hP : Set.Nonempty {r | Prime r}
H : ∀ (I : Ideal R), I ≠ ⊥ → Ideal.IsPrime I → ∃ x ∈ I, Prime x
⊢ UniqueFactorizationMonoid R
no goals