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Proof step 59 from proof pot-root-est (previous step)

2 * i = j * j + j0, j = sqrt(2 * i), 0 < i, 0 ≤ i, 4 ^ (i / 3) ≤ (2 * i) ^ sqrt(2 * i), 1024 ≤ i, j0 ≤ 2 * j, 0 ≤ j, 0 ≤ j0 ⊦ 2 * i < (j + 1) * (j + 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 60:
⊦ (i + i0) * j = i * j + i0 * j
Proof step 61:
2 * i = j * j + j0, j = sqrt(2 * i), 0 < i, 0 ≤ j0, 0 ≤ j, j0 ≤ 2 * j, 1024 ≤ i, 4 ^ (i / 3) ≤ (2 * i) ^ sqrt(2 * i), 0 ≤ i ⊦ 2 * i < j * (j + 1) + 1 * (j + 1)

Rule argument

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

Additional information

Used terms: j + 1, 1, j