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Proof step 11 from proof gcdnex-prime (previous step)

n | m, n | m0 ⊦ n = 1, n = 0, m = 1, m0 = 1, prime(n), ∃ n. prime(n) ∧ n ≠ 0 ∧ n ≠ 1 ∧ n | m ∧ n | m0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ prime(n) ↔ 1 < n ∧ (∀ m. 2 ≤ m ∧ prime(m) ∧ m * m ≤ n → n % m ≠ 0)
Proof step 13:
n | m, n | m0 ⊦ n = 1, n = 0, m = 1, m0 = 1, 1 < n ∧ (∀ m. 2 ≤ m ∧ prime(m) ∧ m * m ≤ n → n % m ≠ 0), ∃ n. prime(n) ∧ n ≠ 0 ∧ n ≠ 1 ∧ n | m ∧ n | m0

Rule argument

spec: nat-prime inst: name: prime-prime seq: ⊦ prime(n) ↔ 1 < n ∧ (∀ m. 2 ≤ m ∧ prime(m) ∧ m * m ≤ n → n % m ≠ 0) subst: [n] → [n] flags: rewrite, current

Additional information

Used terms: n