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Proof step 7 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 | j, i | fac(j - 1)

User applied rule apply induction

And obtained the following new goals

Proof step 8:
0 < j, i < j, prime(i), ∀ j0, i. i→n(j0) < i→n(j) → prime(i) ∧ i < j0 ∧ 0 < j0 → i | fac(j0) ⊦ prime(i) ∧ i < j - 1 ∧ 0 < j - 1, i | j, i | fac(j - 1)

Rule argument

subst: [j0, i] → [j - 1, i]

Additional information

Used simplifier rules: abs-pred: ⊦ i→n(i - 1) < i→n(i) ↔ 0 < i; from specification intnat%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used terms: j - 1, i