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Proof step 38 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, i | 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 ⊦ (j / i)' = (all_prime_divisors(j / max_prime_divisor(j)) -1l i) + max_prime_divisor(j) ', prime(j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 39:
⊦ i | j ↔ (∃ i0. i * i0 = j)
Proof step 40:
all_prime_divisors((j / max_prime_divisor(j)) / i) = all_prime_divisors(j / max_prime_divisor(j)) -1l i, prime(j / i), 0 ≤ j, ∃ i0. i * i0 = j, prime(i), 0 < j, 2 ≤ j, i | 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 ⊦ (j / i)' = (all_prime_divisors(j / max_prime_divisor(j)) -1l i) + max_prime_divisor(j) ', prime(j)

Rule argument

spec: int-gcd inst: name: divides seq: ⊦ i | j ↔ (∃ i0. i * i0 = j) subst: [j, i] → [j, i] flags: rewrite

Additional information

Used terms: j, i