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Proof step 13 from proof coef-sub-mult (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
j ≤ i, 0 < i, 0 < j, fac(i - j) * fac(j) | fac(i), fac(i + 1 - j) * fac(j - 1) | fac(i), 0 ≤ j, 0 ≤ i ⊦ fac(i) / (fac(i - j) * fac(j)) * fac(j) * fac(i + 1 - j) = fac(i) * (i + 1 - 2 * j) + fac(i) / (fac(i + 1 - j) * fac(j - 1)) * fac(j) * fac(i + 1 - j)

Rule argument

Additional information

Used simplifier rules: sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs