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Proof step 4 from proof div-gcd-is-neg (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: int-gcd inst: name: gcd-pos seq: ⊦ 0 ≤ gcd(i, j) subst: [i, j] → [i, i0] flags: current, []

Additional information

Used simplifier rules: lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%div-ls-same: ⊦ 0 < j → (i < i / j ↔ i < 0 ∧ 1 < j); from specification int-div%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%div-zero-ngr: ⊦ i < 0 ∧ 0 < j → ¬ 0 < i / j; from specification int-div Used terms: i, i0