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Proof step 12 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(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 13:
⊦ i ≤ j → countFun(i, j, intfun) = intfun(i) ' + countFun(i + 1, j, intfun)
Proof step 14:
1 ≤ i0, (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(((2 * i) / j ^ 1 - 2 * i / j ^ 1)' + countFun(1 + 1, i0, λ i0. (2 * i) / j ^ i0 - 2 * i / j ^ i0)) = 0

Rule argument

spec: intlist inst: name: countFun-rec seq: ⊦ i ≤ j → countFun(i, j, intfun) = intfun(i) ' + countFun(i + 1, j, intfun) subst: [intfun, j, i] → [λ i0. (2 * i) / j ^ i0 - 2 * i / j ^ i0, i0, 1] flags: rewrite

Additional information

Used simplifier rules: leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: λ i0. (2 * i) / j ^ i0 - 2 * i / j ^ i0, i0, 1