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Proof step 15 from proof div2-add-neg (previous step)

i0 = i2 * 2 + j0 ∧ j0 ≤ 0 ∧ abs(j0) < 2 ∧ 0 < 2, 0 ≤ i1, ~1 ≤ i0 + i1 * 2, i0 < 0 ⊦ (1 + i0 + i1 * 2) / 2 = i2 + i1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
j0 ≤ 0, i2 * 2 + j0 < 0, ~1 ≤ 2 * (i1 + i2) + j0, 0 ≤ i1, abs(j0) < 2 ⊦ (2 * (i1 + i2) + 1 + j0) / 2 = i2 + i1

Rule argument

Additional information

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