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Proof step 32 from proof all_prime_divisors-div (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
⊦ i | j ∧ i ≠ 0 → (j / i = 1 ↔ j = i)

Rule argument

spec: int-gcd inst: name: div-eq-one seq: ⊦ i | j ∧ i ≠ 0 → (j / i = 1 ↔ j = i) subst: [i, j] → [i, j] flags: rewrite

Additional information

Used simplifier rules: lel: ⊦ i < i0 ∧ i = i1 → i1 < i0; (forward) from specification oelem[intlista]%div-zero-zero: ⊦ 0 | i ↔ i = 0; from specification int-gcd Used terms: i, j