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Proof step 4 from proof div2-add-neg (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 5:
⊦ 0 < j ∧ 0 ≤ i → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j)
Proof step 6:
j % 2 = 0, ~1 ≤ i0 + j, i0 < 0 ⊦ 0 < 2 ∧ 0 ≤ j, ((i0 + 1) + j) / 2 = i0 / 2 + j / 2
Proof step 12:
j = i1 * 2 + j0 ∧ 0 ≤ j0 ∧ j0 < 2 ∧ 0 < 2 ∧ 0 ≤ j, j0 = 0, ~1 ≤ i0 + j, i0 < 0 ⊦ ((i0 + 1) + j) / 2 = i0 / 2 + i1

Rule argument

spec: int-div inst: name: div-elim-pos seq: ⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j) subst: [i, j, i0, j0] → [j, 2, i, j0] flags: rewrite, current

Additional information

Used terms: j, 2, i, j0