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Proof step 9 from proof pot-root-est (previous step)

j ^ 2 ≤ 2 * i, (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 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
0 < i, 0 ≤ j ⊦ ¬ j / i ≤ i0 → ¬ j ≤ i * i0
Proof step 11:
¬(0 < 2 ∧ 0 ≤ j ^ 2 ∧ ¬ j ^ 2 / 2 ≤ i), j ^ 2 ≤ 2 * i, (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 ⊦

Rule argument

spec: int-div inst: name: div-mult-nle-est seq: 0 < i, 0 ≤ j ⊦ ¬ j / i ≤ i0 → ¬ j ≤ i * i0 subst: [i0, i, j] → [i, 2, j ^ 2] flags: rewrite

Additional information

Used terms: i, 2, j ^ 2