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Proof step 13 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 ⊦ 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)))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: div-mult seq: j ≠ 0 ⊦ (j * i) / j = i subst: [i, j] → [Π(all_prime_divisors(j) -l i), i ^ n→i(#oc(i, all_prime_divisors(j)))] flags: rewrite

Additional information

Used simplifier rules: all_prime_divisors-product-del: ⊦ prime(i) → ¬ i | Π(all_prime_divisors(j) -l i); from specification intlist%lel: ⊦ i < i0 ∧ i = i1 → i1 < i0; (forward) from specification oelem[intlista]%Mult-zero: ⊦ i * 0 = 0; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%all_prime_divisors-base: ⊦ i < 2 → all_prime_divisors(i) = []; from specification intlist%oc-e: ⊦ #oc(i, []) = 0; from specification list-perm[intlista]%Pot-zero: ⊦ j ^ 0 = 1; from specification int-pot Used terms: Π(all_prime_divisors(j) -l i), i ^ n→i(#oc(i, all_prime_divisors(j)))