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Proof step 35 from proof middle-coef-max_exp (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: intlist inst: name: sum-all-elems-le seq: ∀ i. i ∈ ints → i ≤ i0 ⊦ Σ ints ≤ i0 * n→i(# ints) subst: [ints, i0] → [countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0), 1] flags: []

Additional information

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