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Proof step 14 from proof modeq-neg-02 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 15:
j * (i1 + i0) + j1 = i2 * j + j0, j0 + j < j1, j0 ≤ j1, i2 * j + j0 < 0, j0 < j1, j0 < j, j0 ≤ 0, j1 < j, i0 < 0, 0 < j1, 1 < j, 0 < j, 0 ≤ i1 * j + j1, abs(j0) < j, j0 + j ≤ j1, 2 * j + j0 ≤ j1, j0 + j < j, 2 * j + j0 < j ⊦ j0 = 0, j1 = 0, j1 = j0 + j

Rule argument

fma: j0 = 0

Additional information

Used simplifier rules: add-zero: ⊦ i + 0 = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used formulas: j0 = 0