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Proof step 15 from proof middle-coef-max_exp-big-primes (previous step)

(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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ i ≠ j → (i ≤ j ↔ i ≤ j - 1)
Proof step 17:
¬ 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
Proof step 29:
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

Rule argument

spec: int-abs inst: name: le-rec seq: ⊦ i ≠ j → (i ≤ j ↔ i ≤ j - 1) subst: [j, i] → [2, i0] flags: rewrite

Additional information

Used terms: 2, i0