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Proof step 4 from proof prime-fac-divides (previous step)

0 < j, i < j, prime(i), ∀ j0, i. i→n(j0) < i→n(j) → prime(i) ∧ i < j0 ∧ 0 < j0 → i | fac(j0) ⊦ i | fac(j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 0 < i → fac(i) = i * fac(i - 1)
Proof step 6:
0 < j, 0 < j, i < j, prime(i), ∀ j0, i. i→n(j0) < i→n(j) → prime(i) ∧ i < j0 ∧ 0 < j0 → i | fac(j0) ⊦ i | j * fac(j - 1)

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