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Proof step 10 from proof div-div-pred (previous step)

i0 < 0, j0 ≤ 0, abs(j0) < 2, 2 * i0 + j0 < ~3, 2 * i0 + j0 < 0 ⊦ i0 / 2 = (2 * i0 + j0) / 4

User applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
⊦ 0 < j ∧ i < 0 → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j ∧ i0 ≤ 0)
Proof step 12:
i0 = i1 * 2 + j1 ∧ j1 ≤ 0 ∧ abs(j1) < 2 ∧ i1 ≤ 0 ∧ 0 < 2, i0 < 0, j0 ≤ 0, abs(j0) < 2, 2 * i0 + j0 < ~3, 2 * i0 + j0 < 0 ⊦ i1 = (2 * i0 + j0) / 4

Rule argument

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

Additional information

Used simplifier rules: zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs Used terms: i0, 2, i, j