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Proof step 23 from proof max_prime_divisor-nls-02 (previous step)

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) ⊦ 2 ≤ i / j, prime(i), prime(i / j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
i / j < i, i / j < 2, j < i, j | i, prime(j), 0 < i, 0 ≤ i, 2 ≤ i, j < max_prime_divisor(i / j), ∀ j0. j < j0 ∧ j0 < i ∧ prime(j0) → ¬ j0 | i ⊦ prime(i)

Rule argument

Additional information

Used simplifier rules: prime-small: ⊦ j < 2 → ¬ prime(j);%numlelsdel: j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0); from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs