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Proof step 22 from proof coef-sub-mult (previous step)

¬(fac(i - j) | fac(i) * fac(i + 1 - j) ∧ fac(i - j) ≠ 0), 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 + 1 - j)) / fac(i - j) = fac(i) * (i + 1 - 2 * j) + (fac(i) * fac(j)) / fac(j - 1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
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 + 1 - j)) / fac(i - j) = fac(i) * (i + 1 - 2 * j) + (fac(i) * fac(j)) / fac(j - 1), fac(i - j) | fac(i) * fac(i + 1 - j)

Rule argument

Additional information

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