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Proof step 4 from proof all_prime_divisors-div (previous step)

0 < j, prime(i), i | 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 / i) = all_prime_divisors(j) -1l i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 2 ≤ i ∧ ¬ prime(i) → all_prime_divisors(i) = all_prime_divisors(i / max_prime_divisor(i)) + max_prime_divisor(i) '
Proof step 6:
¬(2 ≤ j ∧ ¬ prime(j)), 0 < j, prime(i), i | 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 / i) = all_prime_divisors(j) -1l i
Proof step 12:
2 ≤ j ∧ ¬ prime(j), 0 < j, prime(i), i | 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 / i) = (all_prime_divisors(j / max_prime_divisor(j)) + max_prime_divisor(j) ') -1l i

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] flags: rewrite, current

Additional information

Used terms: j