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Proof step 21 from proof coef-mult-rec (previous step)

¬(fac(j - 1) * fac(i - j) | fac(i - 1) ∧ fac(j - 1) * fac(i - j) ≠ 0), fac(i - j) * j * fac(j - 1) | fac(i), 0 < i, 0 < j, j ≤ i, 0 ≤ j, 0 ≤ i ⊦ i * fac(i - 1) / (fac(i - j) * fac(j - 1)) = fac(i) / (fac(i - j) * fac(j - 1))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
fac(i - j) * j * fac(j - 1) | fac(i), 0 < i, 0 < j, j ≤ i, 0 ≤ j, 0 ≤ i ⊦ i * fac(i - 1) / (fac(i - j) * fac(j - 1)) = fac(i) / (fac(i - j) * fac(j - 1)), fac(j - 1) * fac(i - j) | fac(i - 1)

Rule argument

Additional information

Used simplifier rules: 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