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Proof step 2 from proof all_prime_divisors-div (previous step)

i | j, prime(i), 0 < j ⊦ all_prime_divisors(j / i) = all_prime_divisors(j) -1l i

User applied rule induction

And obtained the following new goals

Proof step 3:
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

Rule argument

indvar: i→n(j) wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: i→n(j)