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Proof step 15 from proof coef-rec-add-01 (previous step)

fac(i - 1) / (fac(i - 1 + j) * fac(j)) = ((i - j) * fac(i - 1)) / (fac(i - j) * fac(j)), 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)) = (j * fac(i - 1)) / (fac(i - j) * fac(j)) + ((i - j) * fac(i - 1)) / (fac(i - j) * fac(j))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: div-add1-pospos seq: ⊦ i % j = 0 ∧ 0 ≤ i ∧ 0 ≤ i0 ∧ 0 < j → (i + i0) / j = i / j + i0 / j subst: [i0, j, i] → [(i - j) * fac(i - 1), fac(i - j) * fac(j), j * fac(i - 1)] flags: rewrite

Additional information

Used terms: (i - j) * fac(i - 1), fac(i - j) * fac(j), j * fac(i - 1)