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Proof step 18 from proof all_prime_divisors-div (previous step)

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))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-del inst: intlista name: one-01-01 seq: ⊦ i ≠ i0 → i ' -1l i0 = i ' subst: [i0, i] → [i, max_prime_divisor(j)] flags: rewrite

Additional information

Used simplifier rules: max_prime_divisor-divides-03: ⊦ ¬ prime(i) ∧ 2 ≤ i ∧ prime(j) ∧ j | i ∧ j ≠ max_prime_divisor(i) → j | i / max_prime_divisor(i); from specification int-gcd%one-01: ⊦ i ' -1l i = []; from specification list-del[intlista]%app: ⊦ ints + [] = ints; from specification list[intlista]%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista] Used terms: i, max_prime_divisor(j)