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Proof step 18 from proof div-add1-negpos-neg-01 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 19:
j * (i2 + i1) + j0 = i0 * j + j1, 2 * j + j1 < j, j1 < j, j1 < j0, i0 < j, i0 < j0, 0 < j, 0 < j0, j0 < j, i1 < 0, i0 * j + j1 < 0, 1 < j, 0 < j + j1, j1 < 0, i0 < j + j1, 2 * j + j1 ≤ j0, j1 + j ≤ j0, j1 ≤ j0, 0 ≤ i2, 0 ≤ i2 * j + j0, i0 ≤ 0 ⊦ i0 = i1 + i2 + 1, j0 = 0, 2 * j + ~ j ≤ j0

Rule argument

fma: 2 * j + ~ j ≤ j0

Additional information

Used simplifier rules: ⊦ i + ~ j = i - j; (s)% ⊦ i * j - i = i * (j - 1); (s)% ⊦ 1 * i = i; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i < j → (j ≤ i ↔ false); (as) Used formulas: 2 * j + ~ j ≤ j0