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Proof step 1 from proof prime-def-mod (conclusion)

⊦ 1 < j → (prime(j) ↔ (∀ i. 1 < i ∧ i * i ≤ j → j % i ≠ 0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ prime(j) ↔ 2 ≤ j ∧ (∀ i. 1 < i ∧ i < j → ¬ i | j)
Proof step 3:
⊦ 1 < j → (2 ≤ j ∧ (∀ i. 1 < i ∧ i < j → ¬ i | j) ↔ (∀ i. 1 < i ∧ i * i ≤ j → j % i ≠ 0))

Rule argument

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

Additional information

Used terms: j