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Proof step 9 from proof middle-coef-max_exp-big-primes (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
i0 ≤ 2, 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, i0 < i ⊦ Σ countFun(1, i0, λ i0. (2 * i) / j ^ i0 - 2 * i / j ^ i0) = 0

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs