intro h
R : Type u_1
inst✝¹ : CommSemiring R
inst✝ : IsDomain R
a : R
ha : a ≠ 0
H : ∀ (I : Ideal R), I ≠ ⊥ → Ideal.IsPrime I → ∃ x ∈ I, Prime x
hP : Set.Nonempty {r | Prime r}
hzero : 0 ∉ Submonoid.closure {r | Prime r}
⊢ Ideal.span {a} ∉ Kaplansky.set (Submonoid.closure {r | Prime r}).toSubsemigroup
R : Type u_1
inst✝¹ : CommSemiring R
inst✝ : IsDomain R
a : R
ha : a ≠ 0
H : ∀ (I : Ideal R), I ≠ ⊥ → Ideal.IsPrime I → ∃ x ∈ I, Prime x
hP : Set.Nonempty {r | Prime r}
hzero : 0 ∉ Submonoid.closure {r | Prime r}
h : Ideal.span {a} ∈ Kaplansky.set (Submonoid.closure {r | Prime r}).toSubsemigroup
⊢ False