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Proof step 13 from proof middle-coef-max_exp (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
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))), fac(2 * j - j) * fac(j) | fac(2 * j) ⊦ max_exp(i, fac(2 * j) / (fac(2 * j - j) * fac(j))) = 0

Rule argument

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%le-same-01: ⊦ 0 < i → (i ≤ i * j ↔ 1 ≤ j); from specification int-mult