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Proof step 1 from proof modeqp-02 (conclusion)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
i * j + j0 = i0 * j + j1, j1 + j < 0, 0 ≤ j1, j0 + j < 0, 0 ≤ j0, j < 0 ⊦ i = i0 ∧ j0 = j1

Rule argument

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (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%neg-07: ⊦ i < ~ j ↔ i + j < 0; from specification int-abs%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs