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Proof step 13 from proof mod-by6 (previous step)

(3 * n0 * n0 + (n0 * 2) * n0 * n0 + n0) % 6 = 0 ⊦ (3 * n0 + 2 + (n0 * 5 + 4 * n0 * n0 + n0 * n0 * n0 + 2) * 2 + n0 * n0) % 6 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: nat-mult inst: name: dist seq: ⊦ m0 * (m + n) = m0 * m + m0 * n subst: [m0, n, m] → [2, 4 * n0 * n0 + n0 * n0 * n0 + 2, n0 * 5] 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%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: 2, 4 * n0 * n0 + n0 * n0 * n0 + 2, n0 * 5