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Proof step 1 from proof prime-fac-divides-not (conclusion)

⊦ prime(i) ∧ j < i ∧ 0 < j → ¬ i | fac(j)

User applied rule induction

And obtained the following new goals

Proof step 2:
true, ∀ j0, i. i→n(j0) < i→n(j) → true → prime(i) ∧ j0 < i ∧ 0 < j0 → ¬ i | fac(j0) ⊦ prime(i) ∧ j < i ∧ 0 < j → ¬ i | fac(j)

Rule argument

indvar: i→n(j) wfpred: <

Additional information

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