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Proof step 25 from proof mod-by6 (previous step)

3 * n0 * n0 + (n0 * 2) * n0 * n0 + n0 = n * 6 ⊦ (9 * n0 * n0 + n0 * 13 + 2 * n0 * n0 * n0) % 6 = 0

User applied rule cut formula

And obtained the following new goals

Proof step 26:
3 * n0 * n0 + (n0 * 2) * n0 * n0 + n0 = n * 6, 9 * n0 * n0 + n0 * 13 + 2 * n0 * n0 * n0 = (3 * n0 * n0 + (n0 * 2) * n0 * n0 + n0) + 6 * (n0 * n0 + 2 * n0) ⊦ (9 * n0 * n0 + n0 * 13 + 2 * n0 * n0 * n0) % 6 = 0
Proof step 30:
3 * n0 * n0 + (n0 * 2) * n0 * n0 + n0 = n * 6 ⊦ (9 * n0 * n0 + n0 * 13 + 2 * n0 * n0 * n0) % 6 = 0, 9 * n0 * n0 + n0 * 13 + 2 * n0 * n0 * n0 = (3 * n0 * n0 + (n0 * 2) * n0 * n0 + n0) + 6 * (n0 * n0 + 2 * n0)

Rule argument

fma: 9 * n0 * n0 + n0 * 13 + 2 * n0 * n0 * n0 = (3 * n0 * n0 + (n0 * 2) * n0 * n0 + n0) + 6 * (n0 * n0 + 2 * n0)

Additional information

Used formulas: 9 * n0 * n0 + n0 * 13 + 2 * n0 * n0 * n0 = (3 * n0 * n0 + (n0 * 2) * n0 * n0 + n0) + 6 * (n0 * n0 + 2 * n0)