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Proof step 5 from proof div-gcd-is-neg-01 (previous step)

i0 / gcd(i, i0) ≤ 0, i0 < i0 / gcd(i, i0), i0 < 0, 0 < i0 / gcd(i, i0), i0 + 1 < i0 / gcd(i, i0) ⊦

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 6:
⊦ i ≤ j ∧ 0 < i → 0 < j

Rule argument

spec: int-abs inst: name: forward-le seq: ⊦ i ≤ j ∧ 0 < i → 0 < j subst: [i, j] → [i0 / gcd(i, i0), 0] flags:

Additional information

Used simplifier rules: div-gcd-is-neg: ⊦ i0 < 0 → i0 / gcd(i, i0) ≤ 0; Used terms: i0 / gcd(i, i0), 0