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Proof step 6 from proof mod-by6 (previous step)

(i0 * (i0 + 1) * (2 * i0 + 1)) % 6 = 0, 0 ≤ i0 ⊦ ((i0 + 1) * (2 + i0) * (2 * (i0 + 1) + 1)) % 6 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ (i + 1) * (2 + i) * (2 * (i + 1) + 1) = 6 * (i + 1) * (i + 1) + i * (i + 1) * (2 * i + 1)
Proof step 8:
(i0 * (i0 + 1) * (2 * i0 + 1)) % 6 = 0, 0 ≤ i0 ⊦ (6 * (i0 + 1) * (i0 + 1) + i0 * (i0 + 1) * (2 * i0 + 1)) % 6 = 0

Rule argument

spec: inst: name: modby6-help seq: ⊦ (i + 1) * (2 + i) * (2 * (i + 1) + 1) = 6 * (i + 1) * (i + 1) + i * (i + 1) * (2 * i + 1) subst: [i] → [i0] flags: rewrite, current

Additional information

Used terms: i0