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Proof step 14 from proof div2-add-neg (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 15:
⊦ 0 < j ∧ i < 0 → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j)
Proof step 16:
i0 = i2 * 2 + j0, i0 < 0, abs(j0) < 2, 0 < 2, 0 ≤ i1, ~1 ≤ i0 + i1 * 2, j0 ≤ 0 ⊦ (1 + i0 + i1 * 2) / 2 = i2 + i1

Rule argument

spec: <toplevel> name: div-elim2 seq: ⊦ 0 < j ∧ i < 0 → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j) subst: [i, j, i0, j0] → [i0, 2, i1, j] flags: <rotated> <all paths>

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j; (s) Used terms: i0, 2, i1, j