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Proof step 69 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)), 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), i ∈ all_prime_divisors(j / max_prime_divisor(j))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 70:
⊦ j ∈ all_prime_divisors(i) ↔ prime(j) ∧ j | i ∧ 2 ≤ i
Proof step 71:
all_prime_divisors((j / max_prime_divisor(j)) / i) = all_prime_divisors(j / max_prime_divisor(j)), 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), prime(i) ∧ i | j / max_prime_divisor(j) ∧ 2 ≤ j / max_prime_divisor(j)

Rule argument

spec: inst: name: all_prime_divisors-in-01 seq: ⊦ j ∈ all_prime_divisors(i) ↔ prime(j) ∧ j | i ∧ 2 ≤ i subst: [i, j] → [j / max_prime_divisor(j), i] flags: rewrite, current

Additional information

Used terms: j / max_prime_divisor(j), i