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Proof step 9 from proof middle-coef-max_exp-le (previous step)

j0 < Σ countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0), 0 < i0, 0 < j0, 2 * j / i ^ j0 < (2 * j) / i ^ j0, 1 + 2 * j / i ^ j0 < (2 * j) / i ^ j0, 0 < j, 0 ≤ i0, i ^ i0 < i ^ (i0 + 1), i0 < Σ countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0), prime(i), 2 * j < i ^ (i0 + 1), i ^ i0 ≤ 2 * j, j0 ≤ i0, 1 < Σ countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0), 0 < Σ countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ 0 ≤ i ∧ 0 < j → ¬ 1 + 2 * i / j < (2 * i) / j
Proof step 11:
¬(0 ≤ j ∧ 0 < i ^ j0), j0 < Σ countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0), 0 < i0, 0 < j0, 2 * j / i ^ j0 < (2 * j) / i ^ j0, 1 + 2 * j / i ^ j0 < (2 * j) / i ^ j0, 0 < j, 0 ≤ i0, i ^ i0 < i ^ (i0 + 1), i0 < Σ countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0), prime(i), 2 * j < i ^ (i0 + 1), i ^ i0 ≤ 2 * j, j0 ≤ i0, 1 < Σ countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0), 0 < Σ countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0) ⊦

Rule argument

spec: int-div inst: name: div-mult-two-nls-01 seq: ⊦ 0 ≤ i ∧ 0 < j → ¬ 1 + 2 * i / j < (2 * i) / j subst: [j, i] → [i ^ j0, j] flags: rewrite

Additional information

Used terms: i ^ j0, j