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Proof step 4 from proof div-nls-01 (previous step)

0 ≤ i ∧ 0 < j ∨ i < 0 ∧ j < 0, i0 < abs(i) / abs(j), abs(i) ≤ i0, i ≤ 0, j < 0, abs(i) < abs(i) / abs(j) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: div-nls seq: ⊦ ¬ i0 < i ∧ 0 ≤ i ∧ 0 < j → ¬ i0 < i / j subst: [j, i, i0] → [abs(j), abs(i), i0] flags: rewrite, current

Additional information

Used simplifier rules: neg: j ≠ 0 ⊦ i / ~ j = ~(i / j);%neg-01: j ≠ 0 ⊦ ~ i / j = ~(i / j);%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs%neg-07: ⊦ i < ~ j ↔ i + j < 0; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%negle-13: ⊦ ~ i ≤ j ↔ 0 ≤ i + j; from specification int-abs%zero-gels-03: ⊦ i < 0 ∧ 0 ≤ j → 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-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%neg-11: ⊦ ~ i + ~ j = ~(i + j); from specification int-abs%neg-05: ⊦ ~ i < 0 ↔ 0 < i; from specification int-abs%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%negle-07: ⊦ i ≤ ~ j ↔ i + j ≤ 0; from specification int-abs%neg: ⊦ 0 < ~ i ↔ i < 0; from specification int-abs Used terms: abs(j), abs(i), i0