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Proof step 47 from proof middle-coef-max_exp (previous step)

0 < Σ countFun(1, 0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0), 0 ≤ Σ countFun(1, 0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0), j < i, fac(j) * fac(j) | fac(2 * j), 0 ≤ j, 2 * j < i, i | fac(2 * j) / (fac(j) * fac(j)), prime(i), 2 * j < i ^ Σ countFun(1, 0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0), Σ countFun(1, 0, λ j0. 2 * j / i ^ j0) < Σ countFun(1, 0, λ j0. (2 * j) / i ^ j0), 1 < i, 0 < j, 0 < fac(2 * j), 0 < i, Σ countFun(1, 0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0) ≤ n→i(# countFun(1, 0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0)), 0 < fac(j) ⊦ Σ countFun(1, 0, λ j0. (2 * j) / i ^ j0) = Σ countFun(1, 0, λ j0. 2 * j / i ^ j0), countFun(1, 0, 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: intlist inst: name: countFun-base seq: ⊦ j < i → countFun(i, j, intfun) = [] subst: [intfun, j, i] → [λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0, 0, 1] flags: rewrite

Additional information

Used terms: λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0, 0, 1