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Proof step 8 from proof max_prime_divisor-nls (previous step)

0 < i / j, 2 < i / j, j < i / j, j + 1 < i / j, i < i / j, 2 ≤ i, 0 ≤ i, 0 < i, prime(j), j | i, j < 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 9:
⊦ 0 < j → (i < i / j ↔ i < 0 ∧ 1 < j)

Rule argument

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

Additional information

Used simplifier rules: prime-not-neg-01: ⊦ j ≤ 0 → ¬ prime(j);%div-zero-ngr: ⊦ i < 0 ∧ 0 < j → ¬ 0 < i / j; from specification int-div%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs Used terms: j, i