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Proof step 28 from proof pot-root-est (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 29:
2 * 1024 ≤ 2 * i, ¬ 36 ≤ j, 0 ≤ 4 ^ (j / 6) ∧ 0 ≤ (j + 1) * (j + 1) ∧ 0 < j, 0 ≤ j / 6 ∧ 0 ≤ j, 4 ^ (j / 6) < (j + 1) * (j + 1), (4 ^ (j / 6)) ^ j ≤ 4 ^ (i / 3), j / 6 * j ≤ (j ^ 2 / 2) / 3, (j ^ 2 / 2) / 3 ≤ i / 3, 0 ≤ j0, j = sqrt(2 * i), 0 ≤ j, j0 ≤ 2 * j, 2 * i = j * j + j0, j ^ 2 ≤ 2 * i, (2 * i) ^ j < ((j + 1) * (j + 1)) ^ j, 2 * i < (j + 1) * (j + 1), 4 ^ (i / 3) ≤ (2 * i) ^ sqrt(2 * i), 1024 ≤ i, 0 ≤ i, 0 < i ⊦ sqrt(2 * 1024) ≤ sqrt(2 * i), ¬ j ^ 2 / 2 ≤ i

Rule argument

fma: sqrt(2 * 1024) ≤ sqrt(2 * i)

Additional information

Used simplifier rules: square-nls: ⊦ i ^ 2 ≤ j → ¬ sqrt(j) < i;%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%nummult-le-02: ⊦ 0 < i ∧ 0 ≤ j → ((* j) ≤ (* i) * i0 ↔ (i + j - 1) / i ≤ i0); from specification int-div%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%numleledel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j; from specification int-abs%square-gez: ⊦ 0 ≤ i * i; from specification int-mult%zero-03: ⊦ 0 < i ∧ 0 < j → 0 ≤ i / j; from specification int-div%div-div-num: j ≠ 0, j0 ≠ 0 ⊦ (i / (* j)) / (* j0) = i / (j * j0); from specification int-div%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs Used formulas: sqrt(2 * 1024) ≤ sqrt(2 * i)