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Proof step 12 from proof max_prime_divisor-nls-02 (previous step)

2 ≤ i / j, j < max_prime_divisor(i / j), 2 ≤ i, 0 ≤ i, 0 < i, prime(j), j | i, j < i, ∀ j0. j < j0 ∧ j0 < i ∧ prime(j0) → ¬ j0 | i, 2 ≤ i / j → prime(j0) ∧ j0 | i / j ∧ j0 < i / j ∧ (∀ j1. j0 < j1 ∧ j1 < i / j ∧ prime(j1) → ¬ j1 | i / j) ⊦ prime(i), prime(i / j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
2 ≤ i / j, j < max_prime_divisor(i / j), 2 ≤ i, 0 ≤ i, 0 < i, prime(j), j | i, j < i, prime(j0), j0 | i / j, j0 < i / j, 0 ≤ i / j, 0 < i / j, ∀ j0. j < j0 ∧ j0 < i ∧ prime(j0) → ¬ j0 | i, ∀ j1. j0 < j1 ∧ j1 < i / j ∧ prime(j1) → ¬ j1 | i / j ⊦ prime(i), prime(i / j)

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs%numleledel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j; from specification int-abs