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Proof step 17 from proof mod-add1-posneg-pos (previous step)

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

User applied rule cut formula

And obtained the following new goals

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

Rule argument

fma: 2 * j + j0 < j

Additional information

Used formulas: 2 * j + j0 < j