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Proof step 10 from proof all_prime_divisors-div (previous step)

prime(j), i | j, prime(i), 0 < 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) = j ' -1l i

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-gcd inst: name: divides-prime seq: ⊦ prime(j) → (i | j ↔ abs(i) = j ∨ abs(i) = 1) subst: [j, i] → [j, i] flags: rewrite

Additional information

Used simplifier rules: all_prime_divisors-prime: ⊦ prime(i) → all_prime_divisors(i) = i ';%all_prime_divisors-base: ⊦ i < 2 → all_prime_divisors(i) = [];%prime-abs: ⊦ prime(j) → abs(j) = j; from specification int-gcd%one: ⊦ i / 1 = i; from specification int-div%prime-one: ⊦ i ≤ 1 → ¬ prime(i); from specification int-gcd%div-same: i ≠ 0 ⊦ i / i = 1; from specification int-div%one-01: ⊦ i ' -1l i = []; from specification list-del[intlista] Used terms: j, i