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Proof step 5 from proof nummult-ls-01 (previous step)

j = i1 * i + j0, 0 < i, j < 0, i * i0 < j, abs(j0) < i, i1 ≤ i0, j0 ≤ 0 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
abs(j0) < i, i * i0 < i1 * i + j0, 0 < i, j0 < i, i1 * i + j0 < 0, i1 ≤ i0, j0 ≤ 0 ⊦

Rule argument

Additional information

Used simplifier rules: 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