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Proof step 1 from proof pnls-posneg (conclusion)

i0 ≤ i, j ≤ j0, 0 ≤ i0, j0 ≤ 0 ⊦ ¬ i0 * j0 < i * j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
i0 * j0 < i * j, i0 ≤ i, j ≤ j0, j ≤ 0, 0 ≤ i, 0 ≤ i0, j0 ≤ 0 ⊦

Rule argument

Additional information

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