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Proof step 12 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 * n0) + 3 * n0 + 2) * 2 + n0 * n0) % 6 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
(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

Rule argument

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%rdist: ⊦ m0 * (* m) + m0 * (* n) = m0 * (m + n); from specification nat-mult