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Proof step 39 from proof middle-coef-max_exp-big-primes (previous step)

0 < i0, 2 < i0, j ^ i0 ≤ 2 * i, 2 * i < j ^ (i0 + 1), 0 < i, 2 < i, prime(j), j ≤ i, (2 * i) / 3 < j, 0 ≤ i0, j ^ i0 < j ^ (i0 + 1) ⊦ Σ countFun(1, i0, λ i0. (2 * i) / j ^ i0 - 2 * i / j ^ i0) = 0

User applied rule cut formula

And obtained the following new goals

Proof step 40:
j ^ i0 / 3 ≤ (2 * i) / 3, 0 < i0, 2 < i0, j ^ i0 ≤ 2 * i, 2 * i < j ^ (i0 + 1), 0 < i, 2 < i, prime(j), j ≤ i, (2 * i) / 3 < j, 0 ≤ i0, j ^ i0 < j ^ (i0 + 1) ⊦ Σ countFun(1, i0, λ i0. (2 * i) / j ^ i0 - 2 * i / j ^ i0) = 0

Rule argument

fma: j ^ i0 / 3 ≤ (2 * i) / 3

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%lsfc-01: 0 < i0 ⊦ i / i0 < j / i0 → i < j; (forward) from specification int-div%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs Used formulas: j ^ i0 / 3 ≤ (2 * i) / 3