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Proof step 6 from proof mod2-add-neg (previous step)

j = i0 * 2 + j0 ∧ 0 ≤ j0 ∧ j0 < 2 ∧ 0 < 2 ∧ 0 ≤ j, j0 = 0, abs(i) ≤ j, i ≤ 0, 0 < j, i < j ⊦ i % 2 + (i + j) % 2 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
0 < i0, i < i0, 0 ≤ i0, i < i0 * 2, i ≤ 0, abs(i) ≤ i0 * 2 ⊦ i % 2 + (i + i0 * 2) % 2 = 0

Rule argument

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-zero: ⊦ i + 0 = i; from specification int-basic2