| 0 < i, prime(j), j | i, 2 ≤ i, 0 ≤ i, ¬ prime(i) ∧ 2 ≤ i → (∃ i0. max_prime_divisor(i) * i0 = i) ⊦ j = max_prime_divisor(i), prime(i), j | i / max_prime_divisor(i) |
max_prime_divisor(i) * i0 = i, 0 < i, prime(j), j | i, 0 ≤ i, 2 ≤ i ⊦ j = max_prime_divisor(i), prime(i), j | i / max_prime_divisor(i)