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Proof step 4 from proof all_prime_divisors-rec-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
prime(i), 0 < i * i0 ⊦ #oc(i, all_prime_divisors(i * i0)) = #oc(i, all_prime_divisors(i0)) + 1

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%div-mult-03: j ≠ 0 ⊦ (i * j) / j = i; from specification int-div%prime-not-neg-01: ⊦ j ≤ 0 → ¬ prime(j); from specification int-gcd