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Proof step 32 from proof div-div-pred-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
⊦ i < 0 ∧ j < 0 → ¬ 0 ≤ i + j
Proof step 34:
¬(j0 < 0 ∧ j1 * 2 < 0), abs(j1) < 4, abs(j0) < 2, i1 * 4 + j1 < 0, i1 * 4 + j1 ≤ ~3, j0 ≤ 0, 8 * i1 + j0 + j1 * 2 < 0, 8 * i1 + j0 + j1 * 2 < ~7, j1 ≤ 0, 0 ≤ j0 + j1 * 2, i1 < 0, i1 * 4 < j1 + j0 ⊦ i1 = (8 * i1 + j0 + j1 * 2) / 8, i1 = 0

Rule argument

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

Additional information

Used terms: j1 * 2, j0