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Proof step 15 from proof middle-coef-max_exp (previous step)

2 * j - j = 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))), fac(2 * j - j) * fac(j) | fac(2 * j) ⊦ max_exp(i, fac(2 * j) / (fac(2 * j - j) * fac(j))) = 0

User applied rule insert equation

And obtained the following new goals

Rule argument

pos: left 1 flags: discard

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