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Proof step 3 from proof mod-zero (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n))
Proof step 5:
n < m, 2 < m, prime(m), 2 ≤ n, ∃ n0. m = n0 * n ⊦ m = 2, n = 0

Rule argument

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

Additional information

Used terms: n, m