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Proof step 1 from proof mod-zero-neg (conclusion)

⊦ i < 0 ∧ abs(i) < j ∧ 0 < j → i |%| j = i + j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
0 < j + i, i < j, i < 0, 0 < j ⊦ i |%| j = i + j

Rule argument

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-less: ⊦ 0 < i → i1 < i1 + i; from specification int-basic2%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]%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%neg-13: ⊦ ~ i < j ↔ 0 < j + i; from specification int-abs%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs