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Proof step 140 from proof all_prime_divisors-div (previous step)

¬ i ∈ all_prime_divisors(j / max_prime_divisor(j)), all_prime_divisors((j / max_prime_divisor(j)) / i) = all_prime_divisors(j / max_prime_divisor(j)) -1l i, 2 ≤ j / i, 2 ≤ j, 0 < j, prime(i), i | j, 0 ≤ j, 0 < j / i, 0 ≤ j / i, ∀ 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) / max_prime_divisor(j / i)) + max_prime_divisor(j / i) ' = all_prime_divisors(j / max_prime_divisor(j)) + (max_prime_divisor(j) ' -1l i), prime(j), prime(j / i)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 141:
all_prime_divisors((j / max_prime_divisor(j)) / i) = all_prime_divisors(j / max_prime_divisor(j)), 2 ≤ j / i, 2 ≤ j, 0 < j, prime(i), i | j, 0 ≤ j, 0 < j / i, 0 ≤ j / i, ∀ 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) / max_prime_divisor(j / i)) + max_prime_divisor(j / i) ' = all_prime_divisors(j / max_prime_divisor(j)) + (max_prime_divisor(j) ' -1l i), prime(j), prime(j / i), i ∈ all_prime_divisors(j / max_prime_divisor(j))

Rule argument

Additional information

Used simplifier rules: in-02-01: ⊦ ¬ i ∈ ints → ints -1l i = ints; from specification list-del[intlista]