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Proof step 4 from proof max_prime_divisor-nls (previous step)

¬ prime(i) ∧ 2 ≤ i → (∃ j. prime(j) ∧ j | i ∧ j < i ∧ (∀ j0. j < j0 ∧ j0 < i ∧ prime(j0) → ¬ j0 | i)), 0 < i / max_prime_divisor(i), i < i / max_prime_divisor(i), 2 ≤ i, 0 ≤ i, 2 < i / max_prime_divisor(i), 0 < i ⊦ prime(i)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
j < i / max_prime_divisor(i), j < i, j | i, prime(j), 0 < i, 2 < i / max_prime_divisor(i), 0 ≤ i, 2 ≤ i, i < i / max_prime_divisor(i), 0 < i / max_prime_divisor(i), j + 1 < i / max_prime_divisor(i), ∀ j0. j < j0 ∧ j0 < i ∧ prime(j0) → ¬ j0 | i ⊦ prime(i)

Rule argument

Additional information

Used simplifier rules: succ-01: ⊦ i +1 = i + 1; from specification int-basic2%trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1