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Proof step 26 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, 0 ≤ j, i | j, prime(i), 0 < j, 2 ≤ j, j / i < 2, j / 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 / max_prime_divisor(j)) + max_prime_divisor(j) ') -1l i, prime(j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ 0 < j → (j < 2 ↔ j = 1)
Proof step 28:
¬ 0 < j / i, all_prime_divisors((j / max_prime_divisor(j)) / i) = all_prime_divisors(j / max_prime_divisor(j)) -1l i, 0 ≤ j, i | j, prime(i), 0 < j, 2 ≤ j, j / i < 2, j / 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 / max_prime_divisor(j)) + max_prime_divisor(j) ') -1l i, prime(j)
Proof step 31:
0 < j / i, all_prime_divisors((j / max_prime_divisor(j)) / i) = all_prime_divisors(j / max_prime_divisor(j)) -1l i, 0 ≤ j, i | j, prime(i), 0 < j, 2 ≤ j, j / i = 1, j / 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 / max_prime_divisor(j)) + max_prime_divisor(j) ') -1l i, prime(j)

Rule argument

spec: int-basic1 inst: name: two-ls seq: ⊦ 0 < j → (j < 2 ↔ j = 1) subst: [j] → [j / i] flags: rewrite

Additional information

Used terms: j / i