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Proof step 1 from proof modlsp-06 (conclusion)

j * i + j0 < j * i0 + j1, j < j1, j1 ≤ 0, abs(j0) < abs(j) ⊦ i0 ≤ i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
j < j1, j * i + j0 < j * i0 + j1, j1 ≤ 0, j < 0, i < i0, abs(j0) + j < 0 ⊦

Rule argument

Additional information

Used simplifier rules: forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%neg-07: ⊦ i < ~ j ↔ i + j < 0; from specification int-abs%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs%forward-lsle: ⊦ 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%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs