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Proof step 3 from proof prime-mult-not (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ prime(j) ↔ 2 ≤ j ∧ (∀ i. 1 < i ∧ i < j → ¬ i | j)
Proof step 5:
1 < i, 0 < i, 1 < j, 0 < j, 2 ≤ i * j, ∀ i0. 1 < i0 ∧ i0 < i * j → ¬ i0 | i * j ⊦

Rule argument

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

Additional information

Used terms: i * j