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Proof step 2 from proof bertrand-estimate (previous step)

4 ^ i ≤ 4 ^ ((2 * 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 3:
0 < i, 0 ≤ j ⊦ ¬ j / i ≤ i0 → ¬ j ≤ i * i0
Proof step 4:
¬(0 < 4 ^ ((2 * i) / 3) ∧ 0 ≤ 4 ^ i ∧ ¬ 4 ^ i / 4 ^ ((2 * i) / 3) ≤ (2 * i) ^ sqrt(2 * i)), 4 ^ i ≤ 4 ^ ((2 * 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] → [(2 * i) ^ sqrt(2 * i), 4 ^ ((2 * i) / 3), 4 ^ i] flags: rewrite

Additional information

Used terms: (2 * i) ^ sqrt(2 * i), 4 ^ ((2 * i) / 3), 4 ^ i