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Proof step 55 from proof all_prime_divisors-div (previous step)

prime(j), all_prime_divisors(((i * i0) / max_prime_divisor(i * i0)) / i) = all_prime_divisors((i * i0) / max_prime_divisor(i * i0)) -1l i, i0 < i * i0, i0 < i, i < i * i0, prime(j), j < i * i0, i < j, j | i ∨ j | i0, 0 ≤ i * i0, 0 < i * i0, prime(i0), i | (i * i0) / max_prime_divisor(i * i0), 2 ≤ i * i0, prime(i), i0 < j, ∀ 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 ⊦ i = 1, i0 ' = (all_prime_divisors((i * i0) / max_prime_divisor(i * i0)) -1l i) + max_prime_divisor(i * i0) ', prime(i * i0)

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: left 9

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