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Proof step 1 from proof max_prime_divisor-nle-zero-01 (conclusion)

⊦ ¬ prime(i) ∧ 2 ≤ i → ¬ i / max_prime_divisor(i) ≤ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
i / max_prime_divisor(i) < i, 2 ≤ i, i / max_prime_divisor(i) ≤ 0, 0 ≤ i, 0 < i ⊦ prime(i)

Rule argument

Additional information

Used simplifier rules: max_prime_divisor-not-zero: ⊦ ¬ prime(i) ∧ 2 ≤ i → max_prime_divisor(i) ≠ 0;%zero-07: j ≠ 0 ⊦ 0 < i → i / j ≤ i; from specification int-div%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%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