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Proof step 10 from proof div-ls-mone (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
0 < j, i0 < j, j0 < j, i0 * j + j0 < 0, 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-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs% ⊦ ~ i < j ↔ 0 < j + i; (s)% ⊦ 0 - i = ~ i; (s)% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; (s)