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Proof step 28 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 < 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: zero-07: j ≠ 0 ⊦ 0 < i → i / j ≤ i; from specification int-div%prime-not-neg-01: ⊦ j ≤ 0 → ¬ prime(j); from specification int-gcd%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%numlsledel: j0 ≠ 0, j < j0 ⊦ i ≤ (* j) → i < (* j0); from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs