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Proof step 7 from proof all_prime_divisors-div (previous step)

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) = all_prime_divisors(j) -1l i, 2 ≤ j ∧ ¬ prime(j)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: all_prime_divisors-prime seq: ⊦ prime(i) → all_prime_divisors(i) = i ' subst: [i] → [j] flags: rewrite, current

Additional information

Used simplifier rules: all_prime_divisors-base: ⊦ i < 2 → all_prime_divisors(i) = [];%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%two-ls: ⊦ 0 < j → (j < 2 ↔ j = 1); from specification int-basic1%del1-e: ⊦ [] -1l i = []; from specification list-del[intlista]%prime-divides-one: ⊦ prime(i) → ¬ i | 1; from specification int-gcd Used terms: j