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Proof step 8 from proof all_prime_divisors-rec-02 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
all_prime_divisors(j) = all_prime_divisors(i * j), prime(i), 0 < j, 0 < i ⊦ i ∈ all_prime_divisors(j)

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%notin: ⊦ ¬ i ∈ ints → #oc(i, ints) = 0; from specification list-perm[intlista]%in-02-01: ⊦ ¬ i ∈ ints → ints -1l i = ints; from specification list-del[intlista]