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Proof step 4 from proof mod-abs-neg-neg (previous step)

i % j < 0, i < 0, j < 0 ⊦ i % j = 0, i % j + j = i |%| ~ j + 2 * j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
i < 0, j < 0, i % j < 0 ⊦ 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%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult%numeq-02: ⊦ (* i2) * i + j = i + j0 ↔ (i2 - 1) * i + j = j0; from specification int-mult