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Proof step 10 from proof mod-by6 (previous step)

(3 * n0 * n0 + (n0 * 2) * n0 * n0 + n0) % 6 = 0 ⊦ (3 * n0 + 2 + (4 * n0 * n0 + n0 * (2 + n0 * n0) + 3 * n0 + 2) * 2 + n0 * n0) % 6 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ m0 * (m + n) = m0 * m + m0 * n
Proof step 12:
(3 * n0 * n0 + (n0 * 2) * n0 * n0 + n0) % 6 = 0 ⊦ (3 * n0 + 2 + (4 * n0 * n0 + (n0 * 2 + n0 * n0 * n0) + 3 * n0 + 2) * 2 + n0 * n0) % 6 = 0

Rule argument

spec: nat-mult inst: name: dist seq: ⊦ m0 * (m + n) = m0 * m + m0 * n subst: [n, m, m0] → [n0 * n0, 2, n0] flags: rewrite

Additional information

Used terms: n0 * n0, 2, n0