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Proof step 10 from proof mod-add1-negpos-neg (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%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%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs