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Proof step 35 from proof all_prime_divisors-div (previous step)

all_prime_divisors((j / max_prime_divisor(j)) / i) = all_prime_divisors(j / max_prime_divisor(j)) -1l i, prime(j / i), 0 ≤ j, i | j, prime(i), 0 < j, 2 ≤ j, ∀ j0, i. i→n(j0) < i→n(j) → i | j0 ∧ prime(i) ∧ 0 < j0 → all_prime_divisors(j0 / i) = all_prime_divisors(j0) -1l i ⊦ (j / i)' = (all_prime_divisors(j / max_prime_divisor(j)) + max_prime_divisor(j) ') -1l i, prime(j)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-del inst: intlista name: app-01 seq: ⊦ ¬ i ∈ ints → (ints + ints0) -1l i = ints + (ints0 -1l i) subst: [i, ints0, ints] → [i, max_prime_divisor(j) ', all_prime_divisors(j / max_prime_divisor(j))] flags: rewrite

Additional information

Used terms: i, max_prime_divisor(j) ', all_prime_divisors(j / max_prime_divisor(j))