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Proof step 57 from proof pot-root-est (previous step)

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 + 1) ^ 2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 58:
⊦ i ^ 2 = i * i
Proof step 59:
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)

Rule argument

spec: <toplevel> name: pot-square-04 seq: ⊦ i ^ 2 = i * i subst: [i] → [j + 1] flags: <all paths>

Additional information

Used terms: j + 1