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Proof step 7 from proof pot-root-est (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 8:
(2 * i) ^ j < ((j + 1) ^ 2) ^ j, 2 * i < (j + 1) ^ 2, 2 * i = j * j + j0 ∧ j0 ≤ 2 * j ∧ 0 ≤ j ∧ 0 ≤ j0 ∧ j = sqrt(2 * i), 4 ^ (i / 3) ≤ (2 * i) ^ sqrt(2 * i), 1024 ≤ i, 0 ≤ i, 0 < i ⊦
Proof step 46:
2 * i < (j + 1) ^ 2, 2 * i = j * j + j0 ∧ j0 ≤ 2 * j ∧ 0 ≤ j ∧ 0 ≤ j0 ∧ j = sqrt(2 * i), 4 ^ (i / 3) ≤ (2 * i) ^ sqrt(2 * i), 1024 ≤ i, 0 ≤ i, 0 < i ⊦ (2 * i) ^ j < ((j + 1) ^ 2) ^ j

Rule argument

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

Additional information

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