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Proof step 22 from proof div-div-pred (previous step)

2 * (i1 * 2 + j1) + j0 = i0 * 4 + j2, abs(j2) < abs(2 * j1 + j0), 4 ≤ abs(2 * j1 + j0), i0 * 4 + j2 < 0, i0 ≤ 0, j2 ≤ 0, i1 * 2 + j1 < 0, i1 ≤ 0, j1 ≤ 0, i0 * 4 + j2 < ~3, abs(j0) < 2, j0 ≤ 0, abs(j1) < 2, abs(j2) < 4 ⊦ i1 = i0, 2 * j1 + j0 = 0

User applied rule cut formula

And obtained the following new goals

Proof step 23:
j0 = ~1, 2 * (i1 * 2 + j1) + j0 = i0 * 4 + j2, abs(j2) < abs(2 * j1 + j0), 4 ≤ abs(2 * j1 + j0), i0 * 4 + j2 < 0, i0 ≤ 0, j2 ≤ 0, i1 * 2 + j1 < 0, i1 ≤ 0, j1 ≤ 0, i0 * 4 + j2 < ~3, abs(j0) < 2, j0 ≤ 0, abs(j1) < 2, abs(j2) < 4 ⊦ i1 = i0, 2 * j1 + j0 = 0
Proof step 28:
2 * (i1 * 2 + j1) + j0 = i0 * 4 + j2, abs(j2) < abs(2 * j1 + j0), 4 ≤ abs(2 * j1 + j0), i0 * 4 + j2 < 0, i0 ≤ 0, j2 ≤ 0, i1 * 2 + j1 < 0, i1 ≤ 0, j1 ≤ 0, i0 * 4 + j2 < ~3, abs(j0) < 2, j0 ≤ 0, abs(j1) < 2, abs(j2) < 4 ⊦ j0 = ~1, i1 = i0, 2 * j1 + j0 = 0

Rule argument

fma: j0 = ~1

Additional information

Used formulas: j0 = ~1