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Proof step 4 from proof ls-02 (previous step)

j < i0, i + 1 < i0, j < 0, i / i0 < j / i0, j ≤ i, 0 < i0, i < 0, i < i0, j + 1 < i0 ⊦

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: ls-01 seq: i0 ≠ 0, j0 ≠ 0, 0 ≤ i, 0 ≤ i0, i ≤ j, i0 ≤ j0 ⊦ i / j0 ≤ j / i0 subst: [i0, j0, i, j] → [i0, i0, ~ i, ~ j] flags: current, []

Additional information

Used simplifier rules: neg-01: j ≠ 0 ⊦ ~ i / j = ~(i / j);%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%numls-03: ⊦ i + (* j) < (* j0) ↔ i < j0 - 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-13: ⊦ ~ i ≤ j ↔ 0 ≤ i + j; from specification int-abs%neg-15: ⊦ i + ~ j = i - j; from specification int-abs%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%negle-07: ⊦ i ≤ ~ j ↔ i + j ≤ 0; from specification int-abs%zero-gels-03: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%ler: ⊦ i ≤ i; from specification int-abs%lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1 Used terms: i0, i0, ~ i, ~ j