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Proof step 17 from proof all_prime_divisors-div (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
2 ≤ j, 0 < j, prime(i), i | j, 0 ≤ j, 0 < j / max_prime_divisor(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) = all_prime_divisors(j / max_prime_divisor(j)) + (max_prime_divisor(j) ' -1l i), prime(j), i | j / max_prime_divisor(j), i ∈ all_prime_divisors(j / max_prime_divisor(j))

Rule argument

Additional information

Used simplifier rules: a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%app-01: ⊦ ¬ i ∈ ints → (ints + ints0) -1l i = ints + (ints0 -1l i); from specification list-del[intlista]