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Proof step 29 from proof mod-ls-same-01 (previous step)

(i0 * j + j0) + j < 0, j < 0, 0 < i0 * j + j0, j0 + j < 0, i0 < i0 * j + j0, i0 < 0, i0 ≤ 0, 0 ≤ j0 ⊦ i0 * j + j0 = 0, ~1 = j, j = 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
i0 * j + j < 0, i0 < 0, i0 < i0 * j + j0, j0 + j < 0, 0 < i0 * j + j0, j < 0, (i0 * j + j0) + j < 0, 0 ≤ j0 ⊦ i0 * j + j0 = 0, ~1 = j, j = 1

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i + j < j ↔ i < 0; (s)%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% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; (s)