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Proof step 40 from proof div-div-pred-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
i1 < 0, j0 + j1 * 2 < 0, 8 * i1 + j0 + j1 * 2 < 0, 8 * i1 + j0 + j1 * 2 < ~7, abs(j0) < 2, abs(j1) < 4, i1 * 4 + j1 < 0, j0 + j1 * 2 ≤ ~8, j0 ≤ 0, j1 ≤ 0, i1 * 4 + j1 ≤ ~3 ⊦ (j0 + j1 * 2) / 8 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; (s)%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; (s)% ⊦ ~ i < j ↔ 0 < j + i; (s)% ⊦ i < 0 → abs(i) = ~ i; (s)