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Proof step 2 from proof all_prime_divisors-rec-02 (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < j ∧ i | j ∧ prime(i) → all_prime_divisors(j / i) = all_prime_divisors(j) -1l i
Proof step 4:
0 < i * j ∧ i | i * j ∧ prime(i) → all_prime_divisors((i * j) / i) = all_prime_divisors(i * j) -1l i, prime(i), 0 < j ⊦ #oc(i, all_prime_divisors(i * j)) = #oc(i, all_prime_divisors(j)) + 1

Rule argument

spec: inst: name: all_prime_divisors-div seq: ⊦ 0 < j ∧ i | j ∧ prime(i) → all_prime_divisors(j / i) = all_prime_divisors(j) -1l i subst: [j, i] → [i * j, i] flags: current, []

Additional information

Used terms: i * j, i