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Proof step 2 from proof zero-07 (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: zero-05 seq: j ≠ 0 ⊦ i < 0 → i ≤ i / j subst: [j, i] → [j, ~ i] flags: current, []

Additional information

Used simplifier rules: Div-left: ⊦ j ≠ 0 → ~ i / j = ~(i / j);%neg-05: ⊦ ~ i < 0 ↔ 0 < i; from specification int-abs%negle-13: ⊦ ~ i ≤ j ↔ 0 ≤ i + j; from specification int-abs%neg-15: ⊦ i + ~ 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%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; 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: j, ~ i