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Proof step 3 from proof prime-fac-divides-not (previous step)

i | fac(j), prime(i), j < i, 1 < i, 0 < i, 0 < j, ∀ j0, i. i→n(j0) < i→n(j) → true → prime(i) ∧ j0 < i ∧ 0 < j0 → ¬ i | fac(j0) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 0 < i → fac(i) = i * fac(i - 1)
Proof step 5:
0 < j, i | j * fac(j - 1), prime(i), j < i, 1 < i, 0 < i, 0 < j, ∀ j0, i. i→n(j0) < i→n(j) → true → prime(i) ∧ j0 < i ∧ 0 < j0 → ¬ i | fac(j0) ⊦

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