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Proof step 9 from proof mod-add-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
i * (i0 + 1) + j0 = i1 * i + j1, abs(j1) < i, i0 < i, i0 ≤ 0, j0 < i, j0 ≤ 0, i0 * i + j0 < 0, abs(j0) < i, 0 < i, j1 ≤ 0, j1 < i, i1 ≤ 0, i1 < i, i1 * i + j1 < 0 ⊦ j1 = j0

Rule argument

Additional information

Used simplifier rules: forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%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%zero-gels-03: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs