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Proof step 29 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, j / i ≤ 0, j / i < j, 2 ≤ j, 0 < j, prime(i), i | j, 0 ≤ 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) ') -1l i, prime(j)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: div-lezero seq: ⊦ 0 < j → (i / j ≤ 0 ↔ i < j) subst: [j, i] → [i, j] flags: rewrite

Additional information

Used simplifier rules: div-zero-05: ⊦ i < j ∧ 0 < j ∧ 0 ≤ i → i / j = 0; from specification int-div%div-not-ls: ⊦ i < j ∧ 0 < i → ¬ j | i; from specification int-gcd%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%prime-not-neg-01: ⊦ j ≤ 0 → ¬ prime(j); from specification int-gcd Used terms: i, j