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Proof step 1 from proof mod-by6 (conclusion)

⊦ (n * (n + 1) * (2 * n + 1)) % 6 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ ((n * n + n) * 2 * n + n * n + n) % 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%rsucc-02: ⊦ m * (n + 1) = m * n + m; from specification nat-mult