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Proof step 2 from proof max_prime_divisor-nle-zero-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < j → (i / j ≤ 0 ↔ i < j)

Rule argument

spec: int-div inst: name: div-lezero seq: ⊦ 0 < j → (i / j ≤ 0 ↔ i < j) subst: [j, i] → [max_prime_divisor(i), i] flags: rewrite

Additional information

Used simplifier rules: max_prime_divisor-nle-zero: ⊦ ¬ prime(i) ∧ 2 ≤ i → ¬ max_prime_divisor(i) ≤ 0;%max_prime_divisor-nls-01: ⊦ ¬ prime(i) ∧ 2 ≤ i → ¬ i < max_prime_divisor(i);%div-zero-06: ⊦ i < j ∧ 0 < j ∧ 0 < i → i / j = 0; from specification int-div%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs Used terms: max_prime_divisor(i), i