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Proof step 24 from proof div-div-pred-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
j0 ≤ 0, i1 * 4 + j1 ≤ ~3, i1 * 4 + j1 < 0, abs(j0) < 2, abs(j1) < 4, i1 ≤ 0, j1 ≤ 0, j0 + 8 * i1 + j1 * 2 < ~7, j0 + 8 * i1 + j1 * 2 < 0 ⊦ i1 = (j0 + 8 * i1 + j1 * 2) / 8

Rule argument

Additional information

Used simplifier rules: forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult