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Proof step 7 from proof div2-add-neg (previous step)

j % 2 = 0, ~1 ≤ i0 + j, i0 < 0, j < 0 ⊦ ((i0 + 1) + j) / 2 = i0 / 2 + j / 2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ i + 1 ≠ 0 → (~1 ≤ i ↔ 0 ≤ i)
Proof step 9:
¬ (i0 + j) + 1 ≠ 0, j % 2 = 0, ~1 ≤ i0 + j, i0 < 0, j < 0 ⊦ ((i0 + 1) + j) / 2 = i0 / 2 + j / 2

Rule argument

spec: int-abs inst: name: mone-07 seq: ⊦ i + 1 ≠ 0 → (~1 ≤ i ↔ 0 ≤ i) subst: [i] → [i0 + j] flags: rewrite

Additional information

Used simplifier rules: numadd-01: ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%zero-ge-01: ⊦ i < 0 ∧ j < 0 → ¬ 0 ≤ i + j; from specification int-abs Used terms: i0 + j