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Proof step 7 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 ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 8:
2 * i = j * j + j0, j = sqrt(2 * i), 0 < i, 2 * i < (j + 1) ^ 2, 0 ≤ j0, 0 ≤ j, j0 ≤ 2 * j, 1024 ≤ i, 4 ^ (i / 3) ≤ (2 * i) ^ sqrt(2 * i), 0 ≤ i ⊦
Proof step 57:
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

Rule argument

fma: 2 * i < (j + 1) ^ 2

Additional information

Used formulas: 2 * i < (j + 1) ^ 2