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Proof step 2 from proof mod-nle-02 (previous step)

0 < j, i % j ≤ j0, j0 ≤ ~ j ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
0 < j, i % j < 0, j0 < 0, j0 + j ≤ 0, i % j ≤ j0 ⊦

Rule argument

Additional information

Used simplifier rules: forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%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-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%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% ⊦ i ≤ ~ j ↔ i + j ≤ 0; (s)