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Proof step 144 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) ∈ all_prime_divisors(j / max_prime_divisor(j))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 145:
⊦ j ∈ all_prime_divisors(i) ↔ prime(j) ∧ j | i ∧ 2 ≤ i
Proof step 146:
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)), prime(max_prime_divisor(j)) ∧ max_prime_divisor(j) | 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), max_prime_divisor(j)] flags: rewrite, current

Additional information

Used terms: j / max_prime_divisor(j), max_prime_divisor(j)