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Proof step 2 from proof mod2-add-neg (previous step)

j % 2 = 0, i ≤ 0, abs(i) ≤ j ⊦ (i + j) % 2 = ~ i % 2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
j % 2 = 0, abs(i) ≤ j, i ≤ 0 ⊦ i % 2 + (i + j) % 2 = 0

Rule argument

Additional information

Used simplifier rules: mod-neg-01: j ≠ 0 ⊦ ~ i % j = ~(i % j);%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs% ⊦ ~ i = j ↔ i + j = 0; (s)