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Proof step 14 from proof div-ls-mone (previous step)

0 < j + j0, j0 < 0, i0 < j + j0, i0 * j + j0 < 0, j0 < j, i0 < j, 0 < j, i0 < 0, i0 < ~1, i0 ≤ 0 ⊦ i0 < ~1 ↔ j * (2 + i0) + j0 ≤ 0, i0 = ~1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
i0 < ~1, 0 < j, i0 < j, j0 < j, i0 < j + j0, j0 < 0, 0 < j + j0, i0 < 0 ⊦ i0 = ~1, j * (2 + i0) + j0 ≤ 0

Rule argument

Additional information

Used simplifier rules: forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%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% ⊦ i < 0 ∧ j0 < j ∧ 0 < j → i * j + j0 < 0; (s)% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; (s)%j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0); (s)