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Proof step 34 from proof pot-root-est (previous step)

2 * i = j * j + j0, sqrt(2048) < 36, 0 < (j + 1) * (j + 1), 4 ^ (i / 3) < ((j + 1) * (j + 1)) ^ j, j ^ 2 < (j + 1) * (j + 1), j < 36, 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), (4 ^ (j / 6)) ^ j < ((j + 1) * (j + 1)) ^ j, (4 ^ (j / 6)) ^ j ≤ (2 * i) ^ j, j / 6 * j ≤ i / 3, sqrt(2048) ≤ j, 0 ≤ 4 ^ (j / 6), (4 ^ (j / 6)) ^ j ≤ 4 ^ (i / 3), j ^ 2 / 6 ≤ i / 3, j ^ 2 / 2 ≤ i, 0 ≤ j0, j0 ≤ 2 * j, 4 ^ (i / 3) ≤ (2 * i) ^ j, 0 ≤ i, j ^ 2 ≤ 2 * i, j / 6 * j ≤ j ^ 2 / 6, 0 ≤ j, 1024 ≤ i ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ i ^2 ≤ j → ¬ sqrt(j) < i
Proof step 36:
2 * i = j * j + j0, (4 ^ (j / 6)) ^ j < ((j + 1) * (j + 1)) ^ j, 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, j < 36, j ^ 2 < (j + 1) * (j + 1), 4 ^ (i / 3) < ((j + 1) * (j + 1)) ^ j, 0 < (j + 1) * (j + 1), sqrt(2048) < 36, 1024 ≤ i, 0 ≤ j, j / 6 * j ≤ j ^ 2 / 6, j ^ 2 ≤ 2 * i, 0 ≤ i, 4 ^ (i / 3) ≤ (2 * i) ^ j, j0 ≤ 2 * j, 0 ≤ j0, j ^ 2 / 2 ≤ i, j ^ 2 / 6 ≤ i / 3, (4 ^ (j / 6)) ^ j ≤ 4 ^ (i / 3), 0 ≤ 4 ^ (j / 6), sqrt(2048) ≤ j, j / 6 * j ≤ i / 3, (4 ^ (j / 6)) ^ j ≤ (2 * i) ^ j ⊦ 36 ^2 ≤ 2048

Rule argument

spec: int-square name: square-nls seq: ⊦ i ^2 ≤ j → ¬ sqrt(j) < i subst: [i, j] → [36, 2048] flags: <all paths>

Additional information

Used terms: 36, 2048