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Proof step 41 from proof coef-sub-mult (previous step)

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) + j) * fac(i - j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
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) = (j + i + 1 - 2 * j) * fac(i - j)

Rule argument

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%sub-add-01: ⊦ i + (j - i0) = i + j - i0; from specification int-abs