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Proof step 38 from proof middle-coef-max_exp (previous step)

i1 ∈ countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0), 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), 1 < i1, 0 < i1 ⊦ Σ countFun(1, i0, λ j0. (2 * j) / i ^ j0) = Σ countFun(1, i0, λ j0. 2 * j / i ^ j0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: intlist inst: name: countFun-in seq: ⊦ i0 ∈ countFun(i, j, intfun) ↔ (∃ j0. i ≤ j0 ∧ j0 ≤ j ∧ intfun(j0) = i0) subst: [intfun, j, i, i0] → [λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0, i0, 1, i1] flags: rewrite

Additional information

Used terms: λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0, i0, 1, i1