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Proof step 6 from proof mod-neg (previous step)

i % j < 0, i < 0, i < j, 0 < j ⊦ i % j + j = 0, j = (i % j + j) + ~ i |%| j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
i % j < 0, 0 < j, i < j, i < 0 ⊦ i % j + ~ i |%| j = 0

Rule argument

Additional information

Used simplifier rules: mod-less-01: ⊦ 0 < j → i % j < j; from specification int-div%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]%eq: ⊦ i = i + j ↔ j = 0; from specification int-basic2%mod-neq-01: j ≠ 0 ⊦ i % j + j ≠ 0; from specification int-div%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; 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%ax-04: ⊦ i + 0 = i; from specification int-basic2