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Proof step 10 from proof div-le-pos (previous step)

i = i1 * j + j1, i < 0, i0 / j < i1, 0 < j, i0 / j < j0, abs(j1) < j, j0 ≤ i1, i ≤ i0, j1 ≤ 0, i1 ≤ 0 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
i1 * j + j1 < 0, i0 / j < 0, i0 / j < i1, j1 < j, i1 < j, 0 < j, i0 / j < j0, abs(j1) < j, j0 < j, j0 ≤ 0, j0 ≤ i1, i1 * j + j1 ≤ i0, j1 ≤ 0, i1 ≤ 0 ⊦

Rule argument

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%forward-lsle: ⊦ 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