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Proof step 11 from proof coef-rec-add-01 (previous step)

0 ≤ j, 0 ≤ i, 0 < j, j ≤ i, j < i, 1 < i, 0 < i ⊦ fac(i) / (fac(i - j) * fac(j)) = fac(i - 1) / (fac(i - j) * fac(j - 1)) + fac(i - 1) / (fac(i - 1 + j) * fac(j))

User applied rule cut formula

And obtained the following new goals

Proof step 12:
fac(i - 1) / (fac(i - j) * fac(j - 1)) = (j * fac(i - 1)) / (fac(i - j) * fac(j)), 0 ≤ j, 0 ≤ i, 0 < j, j ≤ i, j < i, 1 < i, 0 < i ⊦ fac(i) / (fac(i - j) * fac(j)) = fac(i - 1) / (fac(i - j) * fac(j - 1)) + fac(i - 1) / (fac(i - 1 + j) * fac(j))
Proof step 35:
0 ≤ j, 0 ≤ i, 0 < j, j ≤ i, j < i, 1 < i, 0 < i ⊦ fac(i - 1) / (fac(i - j) * fac(j - 1)) = (j * fac(i - 1)) / (fac(i - j) * fac(j)), fac(i) / (fac(i - j) * fac(j)) = fac(i - 1) / (fac(i - j) * fac(j - 1)) + fac(i - 1) / (fac(i - 1 + j) * fac(j))

Rule argument

fma: fac(i - 1) / (fac(i - j) * fac(j - 1)) = (j * fac(i - 1)) / (fac(i - j) * fac(j))

Additional information

Used formulas: fac(i - 1) / (fac(i - j) * fac(j - 1)) = (j * fac(i - 1)) / (fac(i - j) * fac(j))