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Proof step 31 from proof all_prime_divisors-div (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: numlsledel-01: i0 ≠ 0, i0 < i ⊦ (* i) ≤ j → (* i0) < j; from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1