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Proof step 10 from proof all_prime_divisors-in-01 (previous step)

2 ≤ i, 0 < i, 0 ≤ i, ∀ i0, j. i→n(i0) < i→n(i) → true → (j ∈ all_prime_divisors(i0) ↔ prime(j) ∧ j | i0 ∧ 2 ≤ i0) ⊦ j = max_prime_divisor(i), j ∈ all_prime_divisors(i / max_prime_divisor(i)) ∨ j = max_prime_divisor(i) ↔ prime(j) ∧ j | i, prime(i)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
2 ≤ i, 0 < i, 0 ≤ i, ∀ i0, j. i→n(i0) < i→n(i) → true → (j ∈ all_prime_divisors(i0) ↔ prime(j) ∧ j | i0 ∧ 2 ≤ i0) ⊦ j = max_prime_divisor(i), j ∈ all_prime_divisors(i / max_prime_divisor(i)) ↔ prime(j) ∧ j | i, prime(i)

Proof step 10 from proof all_prime_divisors-in-01 (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information