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Proof step 12 from proof div-le-pos (previous step)

i0 / j < j, abs(j1) < j, 0 < j, i0 / j < j0, i1 * j + j1 ≤ i0, j0 ≤ i1, (i1 * j + j1) + 1 < j, j1 ≤ 0, j1 < j, i1 ≤ 0, i1 < j, i1 * j + j1 < 0, i1 * j + j1 < j, i0 / j < 0, i0 / j < i1, j0 ≤ 0, j0 < j, i0 / j + 1 < j ⊦ 0 < j ∧ 0 ≤ i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
i0 < j, i0 < 0, i0 / j + 1 < j, j0 < j, j0 ≤ 0, i0 / j < i1, i0 / j < 0, i1 * j + j1 < j, i1 * j + j1 < 0, i1 < j, i1 ≤ 0, j1 < j, j1 ≤ 0, (i1 * j + j1) + 1 < j, j0 ≤ i1, i1 * j + j1 ≤ i0, i0 / j < j0, 0 < j, abs(j1) < j, i0 / j < j, i0 + 1 < j ⊦

Rule argument

Additional information

Used simplifier rules: succ-01: ⊦ i +1 = i + 1; from specification int-basic2%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs