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Proof step 2 from proof prime-fac-divides-not (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
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) ⊦

Rule argument

Additional information

Used simplifier rules: forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]