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Proof step 9 from proof max_prime_divisor-nls (previous step)

j < i, 0 < i, i < i / j, 2 < i / j, 0 < i / j, 1 < i / j, prime(j), j | i, 0 ≤ i, 2 ≤ i, ∀ j0. j < j0 ∧ j0 < i ∧ prime(j0) → ¬ j0 | i ⊦ prime(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ 0 < j → (i < i / j ↔ i < 0 ∧ 1 < j)

Rule argument

spec: int-div name: div-ls-same seq: ⊦ 0 < j → (i < i / j ↔ i < 0 ∧ 1 < j) subst: [j, i] → [j, i] flags: <all paths>

Additional information

Used simplifier rules: prime-not-neg-01: ⊦ j ≤ 0 → ¬ prime(j);% ⊦ i < 0 ∧ 0 < j → ¬ 0 < i / j; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss) Used terms: j, i