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Proof step 14 from proof gcdnex-prime (previous step)

n % m1 = 0, n | m, n | m0, 2 ≤ m1, prime(m1), m1 * m1 ≤ n ⊦ n = 1, n = 0, m = 1, m0 = 1, m1 = 0, ∃ 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 15:
⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n))
Proof step 16:
m1 ≠ 0, ∃ n0. n = n0 * m1, n | m, n | m0, 2 ≤ m1, prime(m1), m1 * m1 ≤ n ⊦ n = 1, n = 0, m = 1, m0 = 1, m1 = 0, ∃ n. prime(n) ∧ n ≠ 0 ∧ n ≠ 1 ∧ n | m ∧ n | m0

Rule argument

spec: nat-div inst: name: modex seq: ⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n)) subst: [n, m] → [m1, n] flags: rewrite

Additional information

Used terms: m1, n