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Proof step 1 from proof modmod-add-03 (conclusion)

j ≠ 0 ⊦ i < 0 ∧ i0 < 0 → (i % j + i0 % j) % j = (i + i0) % j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
i < 0, i0 < 0 ⊦ (i % j + i0 % j) % j = (i + i0) % j, j = 0

Rule argument

Additional information

Used simplifier rules: forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs