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Proof step 15 from proof bertrand-estimate (previous step)

(2 * i) / 3 ≤ i, 0 ≤ 4 ^ i, 4 ^ (i - (2 * i) / 3) ≤ (2 * i) ^ sqrt(2 * i), 0 ≤ i, 0 < i, 1024 ≤ i, 4 ^ i ≤ 4 ^ ((2 * i) / 3) * (2 * i) ^ sqrt(2 * i), 0 < 4 ^ ((2 * i) / 3), 0 ≤ (2 * i) ^ sqrt(2 * i), 0 ≤ (2 * i) / 3 ⊦ i / 3 ≤ i - (2 * i) / 3

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
i < i / 3 + (2 * i) / 3, 0 ≤ (2 * i) / 3, 0 ≤ (2 * i) ^ sqrt(2 * i), 0 < 4 ^ ((2 * i) / 3), 4 ^ i ≤ 4 ^ ((2 * i) / 3) * (2 * i) ^ sqrt(2 * i), 1024 ≤ i, 0 < i, 0 ≤ i, 4 ^ (i - (2 * i) / 3) ≤ (2 * i) ^ sqrt(2 * i), 0 ≤ 4 ^ i, (2 * i) / 3 ≤ i, 0 < i / 3 + (2 * i) / 3, 1024 < i / 3 + (2 * i) / 3, 0 < i / 3 ⊦

Rule argument

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%ls-02: ⊦ i < i + j ↔ 0 < j; from specification int-basic2%numlslsdel-01: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j; from specification int-basic1%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs