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Proof step 8 from proof int-simp-04 (previous step)

0 < i0, i0 + i3 < i2, ∃ i0. i3 = i2 + i0 ∧ 0 < i0 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
i0 + i < 0, 0 < i, 0 < i0 ⊦

Rule argument

Additional information

Used simplifier rules: forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0;%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j;%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j;%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)