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Proof step 5 from proof all_prime_divisors-rec-01 (previous step)

prime(i), 0 < i * i0 ⊦ #oc(i, all_prime_divisors(i * i0)) = #oc(i, all_prime_divisors(i0)) + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: all_prime_divisors-rec-02 seq: ⊦ prime(i) ∧ 0 < j → #oc(i, all_prime_divisors(i * j)) = #oc(i, all_prime_divisors(j)) + 1 subst: [j, i] → [i0, i] flags: rewrite, current

Additional information

Used simplifier rules: lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%zero-gr-03: ⊦ i ≤ 0 → (0 < i * j ↔ ¬ ¬(j < 0 ∧ i ≠ 0)); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%prime-not-neg: ⊦ j < 0 → ¬ prime(j); from specification int-gcd Used terms: i0, i