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Proof step 2 from proof all_prime_divisors-rec-01 (previous step)

i | j, prime(i), 0 < j ⊦ #oc(i, all_prime_divisors(j)) = #oc(i, all_prime_divisors(j / i)) + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i | j ↔ (∃ i0. i * i0 = j)
Proof step 4:
∃ i0. i * i0 = j, prime(i), 0 < j ⊦ #oc(i, all_prime_divisors(j)) = #oc(i, all_prime_divisors(j / i)) + 1

Rule argument

spec: int-gcd inst: name: divides seq: ⊦ i | j ↔ (∃ i0. i * i0 = j) subst: [j, i] → [j, i] flags: rewrite

Additional information

Used terms: j, i