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Proof step 17 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, 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 18:
(2 * i) / 3 < j, j ≤ i, prime(j), 2 < i, 0 < i, 2 * i < j ^ 3, j ^ 2 ≤ 2 * i, j ^ 2 < j ^ 3 ⊦ (2 * i) / j + (2 * i) / j ^ 2 = 2 * i / j + 2 * i / j ^ 2

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%numlelsdel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j; from specification int-abs%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%sub-add-01: ⊦ i + (j - i0) = i + j - i0; from specification int-abs%sum-one: ⊦ Σ i ' = i; from specification intlist%countFun-one: ⊦ countFun(i, i, intfun) = intfun(i) '; from specification intlist