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Proof step 7 from proof modeq-neg-02 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
j * (i1 + i0) + j1 = i2 * j + j0, i2 * j + j0 < 0, j0 < j1, j0 < j, j0 ≤ 0, j1 < j, i0 < 0, 0 < j1, 1 < j, 0 < j, 0 ≤ i1 * j + j1, abs(j0) < j ⊦ j1 = 0, j1 = j0 + j

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