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Proof step 11 from proof prime-def-prime (previous step)

0 < i, 1 < i, ∀ j. prime(j) ∧ j * j ≤ i → ¬ j | i, ∀ i0. i→n(i0) < i→n(i) → 0 < i0 ∧ 1 < i0 ∧ (∀ j. prime(j) ∧ j * j ≤ i0 → ¬ j | i0) → prime(i0) ⊦ prime(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-gcd inst: name: prime-def seq: ⊦ prime(j) ↔ 2 ≤ j ∧ (∀ i. 1 < i ∧ i < j → ¬ i | j) subst: [j] → [i] flags: rewrite, current

Additional information

Used terms: i