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Proof step 4 from proof mod-by6 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ m0 * (m + n) = m0 * m + m0 * n
Proof step 6:
(((n0 * 2) * n0 * n0 + (n0 * 2) * n0) + n0 * n0 + n0) % 6 = 0 ⊦ (3 * n0 + 2 + ((3 * n0 + 2 + n0 * n0) * n0 + 3 * n0 + 2 + n0 * n0) * 2 + n0 * n0) % 6 = 0

Rule argument

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

Additional information

Used simplifier rules: mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult Used terms: n0 * 2, n0, n0 * n0