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Proof step 19 from proof coef-sub-mult (previous step)

fac(i + 1 - j) * fac(j - 1) | fac(i) ∧ fac(i + 1 - j) * fac(j - 1) ≠ 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(i + 1 - j)) / (fac(i + 1 - j) * fac(j - 1))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: fac-zero-02: ⊦ fac(i) ≠ 0;%fac-not-zero: ⊦ fac(i) * fac(j) ≠ 0;%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%div-mult-01: j ≠ 0, i0 ≠ 0 ⊦ (i * i0) / (j * i0) = i / j; from specification int-div