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Proof step 147 from proof all_prime_divisors-div (previous step)

all_prime_divisors((j / max_prime_divisor(j)) / max_prime_divisor(j)) = all_prime_divisors(j / max_prime_divisor(j)), 2 ≤ j, 0 < j, 0 ≤ j, 0 < j / max_prime_divisor(j), 0 ≤ j / max_prime_divisor(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 ⊦ all_prime_divisors((j / max_prime_divisor(j)) / max_prime_divisor(j / max_prime_divisor(j))) + max_prime_divisor(j / max_prime_divisor(j)) ' = all_prime_divisors(j / max_prime_divisor(j)), prime(j), prime(j / max_prime_divisor(j)), max_prime_divisor(j) | j / max_prime_divisor(j)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: all_prime_divisors-rec seq: ⊦ 2 ≤ i ∧ ¬ prime(i) → all_prime_divisors(i) = all_prime_divisors(i / max_prime_divisor(i)) + max_prime_divisor(i) ' subst: [i] → [j / max_prime_divisor(j)] flags: rewrite, current

Additional information

Used simplifier rules: max_prime_divisor-ge2: ⊦ ¬ prime(i) ∧ 2 ≤ i → 2 ≤ i / max_prime_divisor(i); from specification int-gcd Used terms: j / max_prime_divisor(j)