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Proof step 30 from proof middle-coef-max_exp-big-primes (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ j < i → countFun(i, j, intfun) = []
Proof step 32:
1 < 2, 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 [] + (2 * i) / j = 2 * i / j

Rule argument

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

Additional information

Used terms: λ i0. (2 * i) / j ^ i0 - 2 * i / j ^ i0, 1, 2