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Proof step 12 from proof middle-coef-max_exp-le (previous step)

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

Rule argument

spec: int-pot inst: name: notneg-01 seq: ⊦ 0 < i ∧ 0 ≤ j → ¬ i ^ j ≤ 0 subst: [j, i] → [j0, i] flags: rewrite

Additional information

Used simplifier rules: lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%prime-not-neg-01: ⊦ j ≤ 0 → ¬ prime(j); from specification int-gcd%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: j0, i