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Proof step 8 from proof mod2-add-neg (previous step)

0 < i0, i < i0, 0 ≤ i0, i < i0 * 2, i ≤ 0, abs(i) ≤ i0 * 2 ⊦ i = 0, i % 2 + (i + i0 * 2) % 2 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
0 ≤ i + i0 * 2, i < 0, i < i0 * 2, 0 ≤ i0, 0 < i0 ⊦ i % 2 + (i + i0 * 2) % 2 = 0, i = 0

Rule argument

Additional information

Used simplifier rules: forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%negle-13: ⊦ ~ i ≤ j ↔ 0 ≤ i + j; from specification int-abs%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs