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Proof step 30 from proof pot-root-est (previous step)

2 * i = j * j + j0, j = sqrt(2 * i), 4 ^ (j / 6) < (j + 1) * (j + 1), 2 * i < (j + 1) * (j + 1), 0 < i, (2 * i) ^ j < ((j + 1) * (j + 1)) ^ j, 0 < j, 0 ≤ j, 0 ≤ j / 6, j / 6 * j ≤ (j ^ 2 / 2) / 3, j ^ 2 ≤ 2 * i, 0 ≤ i, 4 ^ (i / 3) ≤ (2 * i) ^ sqrt(2 * i), 1024 ≤ i, j0 ≤ 2 * j, 0 ≤ j0, j ^ 2 / 2 ≤ i, (j ^ 2 / 2) / 3 ≤ i / 3, (4 ^ (j / 6)) ^ j ≤ 4 ^ (i / 3), 0 ≤ 4 ^ (j / 6), 0 ≤ (j + 1) * (j + 1) ⊦ 36 ≤ j

User applied rule cut formula

And obtained the following new goals

Proof step 31:
2 * i = j * j + j0, j = sqrt(2 * i), 0 < j, (2 * i) ^ j < ((j + 1) * (j + 1)) ^ j, 0 < i, 2 * i < (j + 1) * (j + 1), 4 ^ (j / 6) < (j + 1) * (j + 1), 0 ≤ (j + 1) * (j + 1), 0 ≤ 4 ^ (j / 6), (4 ^ (j / 6)) ^ j ≤ 4 ^ (i / 3), (j ^ 2 / 2) / 3 ≤ i / 3, j ^ 2 / 2 ≤ i, 0 ≤ j0, j0 ≤ 2 * j, 1024 ≤ i, 4 ^ (i / 3) ≤ (2 * i) ^ sqrt(2 * i), 0 ≤ i, j ^ 2 ≤ 2 * i, j / 6 * j ≤ (j ^ 2 / 2) / 3, 0 ≤ j / 6, 0 ≤ j, 2 * 1024 ≤ 2 * i ⊦ 36 ≤ j

Rule argument

fma: 2 * 1024 ≤ 2 * i

Additional information

Used simplifier rules: ⊦ 0 < j ∧ 0 ≤ i → 0 ≤ i / j; (s)%j ≠ 0, j0 ≠ 0 ⊦ (i / (* j)) / (* j0) = i / (j * j0); (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ 0 ≤ i * i; (s)% ⊦ 0 < i ∧ 0 ≤ j → ((* j) ≤ (* i) * i0 ↔ (i + j - 1) / i ≤ i0); (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i ≤ j → ¬ j < i; (s) Used formulas: 2 * 1024 ≤ 2 * i