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Proof step 26 from proof coef-mult-rec-lower (previous step)

(fac(i - j) * fac(j)) * i0 = fac(i), fac(i) = (fac(j - 1) * fac(i + 1 - j)) * i1, 0 < j, 0 ≤ i, 0 ≤ j, 0 < i, j ≤ i ⊦ i0 * j = i1 * (i + 1 - j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ 0 < i → fac(i) = i * fac(i - 1)
Proof step 28:
0 < j, (fac(i - j) * j * fac(j - 1)) * i0 = fac(i), fac(i) = (fac(j - 1) * fac(i + 1 - j)) * i1, 0 < j, 0 ≤ i, 0 ≤ j, 0 < i, j ≤ i ⊦ i0 * j = i1 * (i + 1 - j)

Rule argument

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

Additional information

Used terms: j