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Proof step 2 from proof prime-fac-divides (previous step)

prime(i), i < j, 0 < j ⊦ i | fac(j)

User applied rule induction

And obtained the following new goals

Proof step 3:
prime(i) ∧ i < j ∧ 0 < j, ∀ j0, i. i→n(j0) < i→n(j) → prime(i) ∧ i < j0 ∧ 0 < j0 → i | fac(j0) ⊦ i | fac(j)

Rule argument

indvar: i→n(j) wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: i→n(j)