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Proof step 16 from proof coef-fac-divides-h (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ 0 < i → fac(i) = i * fac(i - 1)
Proof step 18:
0 < j, fac(j - 1) * fac(i - j) | fac(i - 1), (j * fac(j - 1)) * fac(i - 1 + j) | fac(i - 1), 0 < j, j < i, 0 ≤ j, 1 < i, 0 < i ⊦ (j * fac(j - 1)) * fac(i - j) | j * fac(i - 1), (j * fac(j - 1)) * fac(i - j) | fac(i)

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