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Proof step 1 from proof modmod-add-02 (conclusion)

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

Rule argument

Additional information

Used simplifier rules: forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs