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Proof step 23 from proof div-ls-mone (previous step)

0 < j ⊦ i / j < ~1 ↔ i + 2 * j ≤ 0, i < 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
0 < j, i / j < ~1, i / j < 0, 0 ≤ i ⊦ i + 2 * j ≤ 0

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j; (s)%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%numlsf: ⊦ i < (* j) ∧ j < 0 → i < 0; (forward) from specification int-basic1% ⊦ i < j → (j ≤ i ↔ false); (as)% ⊦ 0 < i → (i * j ≤ 0 ↔ j ≤ 0); (s)% ⊦ i + j ≤ i ↔ j ≤ 0; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ 1 * i = i; (s)% ⊦ (* i1) * j + i < j ↔ (i1 - 1) * j + i < 0; (s)%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs% ⊦ i < j ↔ ¬ j ≤ i; (ss)