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Proof step 21 from proof middle-coef-max_exp (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
fac(j) * fac(j) | fac(2 * j), 0 ≤ j, i ^ i0 ≤ 2 * j, 2 * j < i ^ (i0 + 1), i | fac(2 * j) / (fac(j) * fac(j)), prime(i), 2 * j < i ^ (max_exp(i, fac(2 * j)) - 2 * max_exp(i, fac(j))), 0 < j, 0 ≤ i0, i ^ i0 < i ^ (i0 + 1), 2 * max_exp(i, fac(j)) + i0 < max_exp(i, fac(2 * j)), 0 < fac(2 * j), i ^ i0 < i ^ (max_exp(i, fac(2 * j)) - 2 * max_exp(i, fac(j))), 0 < fac(j) ⊦ max_exp(i, fac(2 * j)) = 2 * max_exp(i, fac(j))

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-mult-two: ⊦ i + i = 2 * i; from specification int-mult