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Proof step 5 from proof prime-def-prime (previous step)

0 < i, 1 < i, prime(i), prime(j), j | i, j * j ≤ i ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ prime(j) ↔ 2 ≤ j ∧ (∀ i. 1 < i ∧ i < j → ¬ i | j)
Proof step 7:
1 < i, 0 < i, prime(j), j | i, j * j ≤ i, 2 ≤ i, ∀ i0. 1 < i0 ∧ i0 < i → ¬ i0 | i ⊦

Rule argument

spec: <toplevel> name: prime-def seq: ⊦ prime(j) ↔ 2 ≤ j ∧ (∀ i. 1 < i ∧ i < j → ¬ i | j) subst: [j] → [i] flags: <all paths>

Additional information

Used terms: i