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Proof step 11 from proof middle-coef-max_exp (previous step)

i ^ i0 < i ^ max_exp(i, fac(2 * j) / (fac(2 * j - j) * fac(j))), 0 ≤ j, i ^ i0 ≤ 2 * j, 2 * j < i ^ (i0 + 1), i | fac(2 * j) / (fac(2 * j - j) * fac(j)), prime(i), 2 * j < i ^ max_exp(i, fac(2 * j) / (fac(2 * j - j) * fac(j))), 0 < j, 0 ≤ i0, i ^ i0 < i ^ (i0 + 1), i0 < max_exp(i, fac(2 * j) / (fac(2 * j - j) * fac(j))) ⊦ max_exp(i, fac(2 * j) / (fac(2 * j - j) * fac(j))) = 0

User applied rule insert lemma

And obtained the following new goals

Proof step 12:
⊦ i ≤ j ∧ 0 ≤ i → fac(j - i) * fac(i) | fac(j)
Proof step 13:
j ≤ 2 * j ∧ 0 ≤ j → fac(2 * j - j) * fac(j) | fac(2 * j), i ^ i0 < i ^ max_exp(i, fac(2 * j) / (fac(2 * j - j) * fac(j))), 0 ≤ j, i ^ i0 ≤ 2 * j, 2 * j < i ^ (i0 + 1), i | fac(2 * j) / (fac(2 * j - j) * fac(j)), prime(i), 2 * j < i ^ max_exp(i, fac(2 * j) / (fac(2 * j - j) * fac(j))), 0 < j, 0 ≤ i0, i ^ i0 < i ^ (i0 + 1), i0 < max_exp(i, fac(2 * j) / (fac(2 * j - j) * fac(j))) ⊦ max_exp(i, fac(2 * j) / (fac(2 * j - j) * fac(j))) = 0

Rule argument

spec: inst: name: fac-divides seq: ⊦ i ≤ j ∧ 0 ≤ i → fac(j - i) * fac(i) | fac(j) subst: [i, j] → [j, 2 * j] flags: current, []

Additional information

Used terms: j, 2 * j