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Proof step 41 from proof all_prime_divisors-div (previous step)

all_prime_divisors(((i * i0) / max_prime_divisor(i * i0)) / i) = all_prime_divisors((i * i0) / max_prime_divisor(i * i0)) -1l i, prime(i), 2 ≤ i * i0, i | (i * i0) / max_prime_divisor(i * i0), prime(i0), 0 < i * i0, 0 ≤ i * i0, ∀ j0, i1. i→n(j0) < i→n(i * i0) → i1 | j0 ∧ prime(i1) ∧ 0 < j0 → all_prime_divisors(j0 / i1) = all_prime_divisors(j0) -1l i1 ⊦ i0 ' = (all_prime_divisors((i * i0) / max_prime_divisor(i * i0)) -1l i) + max_prime_divisor(i * i0) ', prime(i * i0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-gcd inst: name: max_prime_divisor-def seq: ⊦ j | i ∧ prime(j) ∧ j < i ∧ (∀ j0. j < j0 ∧ j0 < i ∧ prime(j0) → ¬ j0 | i) → max_prime_divisor(i) = j subst: [j, i] → [i, i * i0] flags: rewrite

Additional information

Used terms: i, i * i0