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Proof step 38 from proof coef-sub-mult (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: fac-zero-02: ⊦ fac(i) ≠ 0;