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Proof step 14 from proof coef-mult-rec (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-fac inst: name: fac-divides seq: ⊦ i ≤ j ∧ 0 ≤ i → fac(j - i) * fac(i) | fac(j) subst: [i, j] → [j, i] flags: rewrite, current

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j, i