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Proof step 16 from proof pot-root-est (previous step)

4 ^ (j * j / 6) ≤ 4 ^ (i / 3), j * j / 6 ≤ (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) ^ 2) ^ j, 2 * i < (j + 1) ^ 2, 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

Rule argument

fma: 4 ^ (j * j / 6) < ((j + 1) ^ 2) ^ j

Additional information

Used simplifier rules: div-div-num: j ≠ 0, j0 ≠ 0 ⊦ (i / (* j)) / (* j0) = i / (j * j0); from specification int-div%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used formulas: 4 ^ (j * j / 6) < ((j + 1) ^ 2) ^ j