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Proof step 9 from proof mod-pred-neg (previous step)

i1 = i2 * j + j1 ∧ j1 ≤ 0 ∧ abs(j1) < j ∧ i2 ≤ 0, i0 * j + j0 = i1 + 1, i0 < j, i0 ≤ 0, j0 < j, j0 ≤ 0, 0 < j, abs(j0) < j, i1 < ~1, i1 < 0 ⊦ 1 = j0 + j, j0 = j1 + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
i0 * j + j0 = (i2 * j + j1) + 1, abs(j1) < j, i0 < j, i0 ≤ 0, j0 < j, j0 ≤ 0, 0 < j, abs(j0) < j, i2 * j + j1 < ~1, j1 ≤ 0, j1 < j, i2 ≤ 0, i2 < j, i2 * j + j1 < 0 ⊦ 1 = j0 + j, j0 = j1 + 1

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