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Proof step 74 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) / 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 75:
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)

Rule argument

Additional information

Used simplifier rules: forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs