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Proof step 4 from proof div-add-neg (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
i0 % j = 0, i1 * j + j0 < j, j0 < j, i0 < 0, i0 < j, i0 + 1 < j, i1 * j + j0 < 0, 0 < j, abs(j0) < j, j0 ≤ 0, (i1 * j + j0) + 1 < j ⊦ ((i1 * j + j0) + i0) / j = i1 + i0 / j

Rule argument

Additional information

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