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Proof step 3 from proof mod-by6 (previous step)

((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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
((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

Additional information

Used simplifier rules: succ: ⊦ (* m0) * m + m = (m0 + 1) * m; from specification nat-mult%two-02: ⊦ m + m = 2 * m; from specification nat-mult%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%succ: ⊦ m +1 = m + 1; from specification nat-basic2