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Proof step 29 from proof middle-coef-max_exp-big-primes (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
1 < i, j ≤ 2 * i, 2 * i < j ^ 2, 0 < i, 2 < i, prime(j), j ≤ i, (2 * i) / 3 < j, j < j ^ 2, (2 * i) / 3 < 2 * i, (2 * i) / 3 < j ^ 2 ⊦ Σ countFun(2, 1, λ i0. (2 * i) / j ^ i0 - 2 * i / j ^ i0) + (2 * i) / j = 2 * i / j

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%one: ⊦ i ^ 1 = i; from specification int-pot%numlelsdel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j; from specification int-abs%lel: ⊦ i < i0 ∧ i = i1 → i1 < i0; (forward) from specification oelem[intlista]%bet: ⊦ 0 < i → (i ≤ 1 ↔ i = 1); from specification int-abs