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Proof step 24 from proof modby6-help (previous step)

⊦ (i + 1) * (i * 7 + 6 + i * 2 * i) = 12 * i + 6 * i * i + 6 + i * (i + 1) * (2 * i + 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ (i + i0) * j = i * j + i0 * j
Proof step 26:
⊦ i * (i * 7 + 6 + i * 2 * i) + 1 * (i * 7 + 6 + i * 2 * i) = 12 * i + 6 * i * i + 6 + i * (i + 1) * (2 * i + 1)

Rule argument

spec: int-mult name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [j, i0, i] → [i * 7 + 6 + i * 2 * i, 1, i] flags: <all paths>

Additional information

Used terms: i * 7 + 6 + i * 2 * i, 1, i