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Proof step 102 from proof all_prime_divisors-div (previous step)

¬ prime(j) ∧ 2 ≤ j → (∃ j0. prime(j0) ∧ j0 | j ∧ j0 < j ∧ (∀ j1. j0 < j1 ∧ j1 < j ∧ prime(j1) → ¬ j1 | j)), all_prime_divisors((j / max_prime_divisor(j)) / i) = all_prime_divisors(j / max_prime_divisor(j)) -1l i, 2 ≤ j / i, 2 ≤ j, 0 < j, prime(i), i | j, 0 ≤ j, 0 < j / i, 0 ≤ j / i, i | j / max_prime_divisor(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 ⊦ max_prime_divisor(j / i) = max_prime_divisor(j), all_prime_divisors((j / i) / max_prime_divisor(j / i)) + max_prime_divisor(j / i) ' = all_prime_divisors((j / max_prime_divisor(j)) / i) + max_prime_divisor(j) ', prime(j), prime(j / i)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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