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Proof step 143 from proof all_prime_divisors-div (previous step)

¬ max_prime_divisor(j) ≠ i, 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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ 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%max_prime_divisor-divides: ⊦ ¬ prime(i) ∧ 2 ≤ i → max_prime_divisor(i) | i; from specification int-gcd%max_prime_divisor-prime: ⊦ ¬ prime(i) ∧ 2 ≤ i → prime(max_prime_divisor(i)); from specification int-gcd%max_prime_divisor-ge2: ⊦ ¬ prime(i) ∧ 2 ≤ i → 2 ≤ i / max_prime_divisor(i); from specification int-gcd%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%app: ⊦ ints + [] = ints; from specification list[intlista]%one-01: ⊦ i ' -1l i = []; from specification list-del[intlista]