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Proof step 17 from proof mod-add1-negpos-neg (previous step)

j * (i2 + i1) + j0 = i0 * j + j1, j1 + j < j0, j1 ≤ j0, i0 * j + j1 < 0, i0 < j0, i0 < j, i0 ≤ 0, j1 < j0, j1 < j, j1 ≤ 0, i1 < 0, j0 < j, 0 ≤ i2 * j + j0, 0 < j0, 1 < j, 0 < j, 0 ≤ i2, abs(j1) < j, j1 + j ≤ j0, 2 * j + j1 ≤ j0, j1 + j < j, 2 * j + j1 < j ⊦ j0 = 0, j0 = j1 + j

User applied rule cut formula

And obtained the following new goals

Proof step 18:
2 * j + j1 < j, j * (i2 + i1) + j0 = i0 * j + j1, j1 + j < j0, j1 ≤ j0, i0 * j + j1 < 0, i0 < j0, i0 < j, i0 ≤ 0, j1 < j0, j1 < j, j1 ≤ 0, i1 < 0, j0 < j, 0 ≤ i2 * j + j0, 0 < j0, 1 < j, 0 < j, 0 ≤ i2, abs(j1) < j, j1 + j ≤ j0, 2 * j + j1 ≤ j0, j1 + j < j, 2 * j + j1 < j ⊦ j0 = 0, j0 = j1 + j

Rule argument

fma: 2 * j + j1 < j

Additional information

Used formulas: 2 * j + j1 < j