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Proof step 33 from proof div-div-pred-01 (previous step)

i1 < 0, 8 * i1 + j0 + j1 * 2 < 0, 8 * i1 + j0 + j1 * 2 < ~7, abs(j0) < 2, abs(j1) < 4, i1 * 4 + j1 < 0, i1 * 4 < j1 + j0, 0 ≤ j0 + j1 * 2, i1 * 4 + j1 ≤ ~3, j0 ≤ 0, j1 ≤ 0 ⊦ i1 = (8 * i1 + j0 + j1 * 2) / 8, i1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ i < 0 ∧ j < 0 → ¬ 0 ≤ i + j
Proof step 35:
i1 * 4 < j1 + j0, i1 * 4 + j1 < 0, abs(j1) < 4, abs(j0) < 2, 8 * i1 + j0 + j1 * 2 < ~7, 8 * i1 + j0 + j1 * 2 < 0, i1 < 0, j1 ≤ 0, j0 ≤ 0, i1 * 4 + j1 ≤ ~3, 0 ≤ j0 + j1 * 2 ⊦ i1 = 0, i1 = (8 * i1 + j0 + j1 * 2) / 8, j0 < 0 ∧ j1 * 2 < 0

Rule argument

spec: int-abs name: zero-ge-01 seq: ⊦ i < 0 ∧ j < 0 → ¬ 0 ≤ i + j subst: [j, i] → [j1 * 2, j0] flags: <all paths>

Additional information

Used terms: j1 * 2, j0