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Proof step 28 from proof le-abs-numerator (previous step)

0 < j, abs(i) / j * j ≤ abs(i), abs(i) + abs(i) / j < 0, abs(i) / j < 0 ⊦ j = 0, i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
0 < j ⊦ i / (* j) < 0 ↔ i + j ≤ 0

Rule argument

spec: int-div inst: name: div-ls-zero seq: 0 < j ⊦ i / (* j) < 0 ↔ i + j ≤ 0 subst: [j, i] → [j, abs(i)] flags: rewrite, current

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2%absls: ⊦ ¬ abs(i) < 0; 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 Used terms: j, abs(i)