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Proof step 16 from proof coef-mult-rec (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j