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Proof step 22 from proof mod-by6 (previous step)

(3 * n0 * n0 + (n0 * 2) * n0 * n0 + n0) % 6 = 0 ⊦ (9 * n0 * n0 + n0 * 13 + 2 * n0 * n0 * n0) % 6 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n))
Proof step 24:
6 ≠ 0, ∃ n1. 3 * n0 * n0 + (n0 * 2) * n0 * n0 + n0 = n1 * 6 ⊦ (9 * n0 * n0 + n0 * 13 + 2 * n0 * n0 * n0) % 6 = 0

Rule argument

spec: inst: name: modex seq: ⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n)) subst: [n, m] → [6, 3 * n0 * n0 + (n0 * 2) * n0 * n0 + n0] flags: rewrite, current

Additional information

Used terms: 6, 3 * n0 * n0 + (n0 * 2) * n0 * n0 + n0