Step
*
of Lemma
prime_ideals_in_int_ring
∀i:ℕ+. (ℤ-rng-Prime(i)
⇐⇒ prime(i))
BY
{ (RepUR ``rprime ring_divs int_ring`` 0 THEN Auto) }
1
1. i : ℕ+@i
2. ¬(∃c:ℤ. ((c * i) = 1 ∈ ℤ))@i
3. ∀v,w:ℤ. ((∃c:ℤ. ((c * i) = (v * w) ∈ ℤ))
⇒ ((∃c:ℤ. ((c * i) = v ∈ ℤ)) ∨ (∃c:ℤ. ((c * i) = w ∈ ℤ))))@i
⊢ prime(i)
2
1. i : ℕ+@i
2. prime(i)@i
⊢ ¬(∃c:ℤ. ((c * i) = 1 ∈ ℤ))
3
1. i : ℕ+@i
2. prime(i)@i
3. v : ℤ@i
4. w : ℤ@i
5. ∃c:ℤ. ((c * i) = (v * w) ∈ ℤ)@i
⊢ (∃c:ℤ. ((c * i) = v ∈ ℤ)) ∨ (∃c:ℤ. ((c * i) = w ∈ ℤ))
Latex:
Latex:
\mforall{}i:\mBbbN{}\msupplus{}. (\mBbbZ{}-rng-Prime(i) \mLeftarrow{}{}\mRightarrow{} prime(i))
By
Latex:
(RepUR ``rprime ring\_divs int\_ring`` 0 THEN Auto)
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