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Proof step 149 from proof all_prime_divisors-div (previous step)

max_prime_divisor(j) ≠ i, all_prime_divisors((j / max_prime_divisor(j)) / i) = all_prime_divisors(j / max_prime_divisor(j)), 2 ≤ j / i, 2 ≤ j, 0 < j, prime(i), i | j, 0 ≤ j, 0 < j / i, 0 ≤ j / i, ∀ 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) / max_prime_divisor(j / i)) + max_prime_divisor(j / i) ' = all_prime_divisors(j / max_prime_divisor(j)) + max_prime_divisor(j) ', prime(j), prime(j / i), i ∈ all_prime_divisors(j / max_prime_divisor(j))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 150:
all_prime_divisors((j / max_prime_divisor(j)) / i) = all_prime_divisors(j / max_prime_divisor(j)), 0 ≤ j / i, 0 < j / i, 0 ≤ j, i | j, prime(i), 0 < j, 2 ≤ j, 2 ≤ j / i, ∀ 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, all_prime_divisors((j / i) / max_prime_divisor(j / i)) + max_prime_divisor(j / i) ' = all_prime_divisors(j / max_prime_divisor(j)) + max_prime_divisor(j) ', i ∈ all_prime_divisors(j / max_prime_divisor(j)), prime(j / i), prime(j)

Proof step 149 from proof all_prime_divisors-div (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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