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Proof step 41 from proof middle-coef-max_exp-big-primes (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 42:
⊦ 2 ≤ j ∧ 2 < i → ¬ j ^ i / 3 < j

Rule argument

spec: int-pot inst: name: pot-div3-nls seq: ⊦ 2 ≤ j ∧ 2 < i → ¬ j ^ i / 3 < j subst: [i, j] → [i0, j] flags: rewrite

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%prime-small: ⊦ j < 2 → ¬ prime(j); from specification int-gcd Used terms: i0, j