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Proof step 10 from proof all_prime_divisors-rec-02 (previous step)

prime(i), 0 < j, 0 < i ⊦ i ∈ all_prime_divisors(i * j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ j ∈ all_prime_divisors(i) ↔ prime(j) ∧ j | i ∧ 2 ≤ i
Proof step 12:
prime(i), 0 < j, 0 < i ⊦ prime(i) ∧ i | i * j ∧ 2 ≤ i * j

Rule argument

spec: inst: name: all_prime_divisors-in-01 seq: ⊦ j ∈ all_prime_divisors(i) ↔ prime(j) ∧ j | i ∧ 2 ≤ i subst: [i, j] → [i * j, i] flags: rewrite, current

Additional information

Used terms: i * j, i