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Proof step 2 from proof mod-zero (previous step)

m % n = 0, n < m, 2 ≤ n, prime(m), 2 < m ⊦ m = 2, m = 0, n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n))
Proof step 4:
n ≠ 0, ∃ n0. m = n0 * n, n < m, 2 ≤ n, prime(m), 2 < m ⊦ m = 2, m = 0, n = 0

Rule argument

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

Additional information

Used terms: n, m