simp at this
case intro.intro.intro
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
hzero : 0 ∉ Submonoid.closure {r | Prime r}
h : Ideal.span {a} ∈ Kaplansky.set (Submonoid.closure {r | Prime r}).toSubsemigroup
T : Ideal R
hT : T ∈ Kaplansky.set (Submonoid.closure {r | Prime r}).toSubsemigroup
hT₂ : ∀ I ∈ Kaplansky.set (Submonoid.closure {r | Prime r}).toSubsemigroup, T ≤ I → I = T
hT₃ : T ≠ ⊥
x : R
hx : x ∈ {r | Prime r}
this : x ∈ ↑(Submonoid.closure {r | Prime r})
⊢ False
case intro.intro.intro
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
hzero : 0 ∉ Submonoid.closure {r | Prime r}
h : Ideal.span {a} ∈ Kaplansky.set (Submonoid.closure {r | Prime r}).toSubsemigroup
T : Ideal R
hT : T ∈ Kaplansky.set (Submonoid.closure {r | Prime r}).toSubsemigroup
hT₂ : ∀ I ∈ Kaplansky.set (Submonoid.closure {r | Prime r}).toSubsemigroup, T ≤ I → I = T
hT₃ : T ≠ ⊥
x : R
hx : x ∈ {r | Prime r}
this : x ∈ Submonoid.closure {r | Prime r}
⊢ False