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Proof step 1 from proof mod-neg (conclusion)

⊦ i < 0 ∧ 0 < j ∧ i |%| j ≠ 0 → i |%| j = ~(~ i |%| j - j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: 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%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs%minus-sub: ⊦ ~(i - j) = j - i; from specification int-abs