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Proof step 2 from proof mod-by6 (previous step)

⊦ ((n * n + n) * 2 * n + n * n + n) % 6 = 0

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 3:
((n0 * n0 + n0) * 2 * n0 + n0 * n0 + n0) % 6 = 0 ⊦ ((n0 +1 * n0 +1 + n0 +1) * 2 * n0 +1 + n0 +1 * n0 +1 + n0 +1) % 6 = 0

Rule argument

term: n

Additional information

Used simplifier rules: nat freely generated by 0, +1;;%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