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Proof step 7 from proof mod-div-zero (previous step)

j < 0, 0 - j ≤ abs(i) % (0 - j) ⊦ j = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
0 ≤ j + abs(i) % j, j < 0 ⊦ j = 0

Rule argument

Additional information

Used simplifier rules: mod-neg: j ≠ 0 ⊦ i % ~ j = i % j;%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%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%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%negle-13: ⊦ ~ i ≤ j ↔ 0 ≤ i + j; from specification int-abs%neg-06: ⊦ 0 - i = ~ i; from specification int-abs