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Proof step 22 from proof all_prime_divisors-div (previous step)

¬(2 ≤ j / i ∧ ¬ prime(j / i)), all_prime_divisors((j / max_prime_divisor(j)) / i) = all_prime_divisors(j / max_prime_divisor(j)) -1l i, 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 / i) = (all_prime_divisors(j / max_prime_divisor(j)) + max_prime_divisor(j) ') -1l i, prime(j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
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, ∀ 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 / i) = (all_prime_divisors(j / max_prime_divisor(j)) + max_prime_divisor(j) ') -1l i, prime(j), 2 ≤ j / i ∧ ¬ prime(j / i)

Proof step 22 from proof all_prime_divisors-div (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information