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Proof step 2 from proof zero-02 (previous step)

j < i / j, j < i, j < 0, 0 < i, 0 < i / j, j + 1 < i / j, j + 1 < i ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < i ∧ 0 < j → 0 ≤ i / j

Rule argument

spec: int-div inst: name: zero-03 seq: ⊦ 0 < i ∧ 0 < j → 0 ≤ i / j subst: [i, j] → [i, ~ j] flags: current, []

Additional information

Used simplifier rules: neg: j ≠ 0 ⊦ i / ~ j = ~(i / j);%neg: ⊦ 0 < ~ i ↔ i < 0; from specification int-abs%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%negle-07: ⊦ i ≤ ~ j ↔ i + j ≤ 0; from specification int-abs%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used terms: i, ~ j