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Proof step 29 from proof coef-mult-rec (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ 0 < i → fac(i) = i * fac(i - 1)

Rule argument

spec: int-fac inst: name: fac-rec seq: ⊦ 0 < i → fac(i) = i * fac(i - 1) subst: [i] → [i] flags: rewrite, current

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i