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Proof step 11 from proof max_exp-divides (previous step)

i ^ n→i(#oc(i, all_prime_divisors(j))) * Π(all_prime_divisors(j) -l i) = j, prime(i), 0 < j, i | j, 2 ≤ j, 0 ≤ j ⊦ i ^ n→i(#oc(i, all_prime_divisors(j))) | i ^ n→i(#oc(i, all_prime_divisors(j))) * Π(all_prime_divisors(j) -l i) ∧ ¬ i | (i ^ n→i(#oc(i, all_prime_divisors(j))) * Π(all_prime_divisors(j) -l i)) / i ^ n→i(#oc(i, all_prime_divisors(j)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ i | i * j
Proof step 13:
i ^ n→i(#oc(i, all_prime_divisors(j))) * Π(all_prime_divisors(j) -l i) = j, prime(i), 0 < j, i | j, 2 ≤ j, 0 ≤ j ⊦ true ∧ ¬ i | (i ^ n→i(#oc(i, all_prime_divisors(j))) * Π(all_prime_divisors(j) -l i)) / i ^ n→i(#oc(i, all_prime_divisors(j)))

Rule argument

spec: int-gcd inst: name: div-mult seq: ⊦ i | i * j subst: [j, i] → [Π(all_prime_divisors(j) -l i), i ^ n→i(#oc(i, all_prime_divisors(j)))] flags: rewrite

Additional information

Used terms: Π(all_prime_divisors(j) -l i), i ^ n→i(#oc(i, all_prime_divisors(j)))