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Proof step 20 from proof mod-add1-negpos-neg (previous step)

(2 - 1) * j + j1 < 0, 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 - 1) * j + j1 < 0 ⊦ j0 = 0, j0 = j1 + j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
j * (i2 + i1) + j0 = i0 * j + j1, j + j1 < 0, j1 + j < j, 2 * j + j1 ≤ j0, j1 + j ≤ j0, abs(j1) < j, 0 ≤ i2, 0 < j, 1 < j, 0 < j0, 0 ≤ i2 * j + j0, j0 < j, i1 < 0, j1 ≤ 0, j1 < j, j1 < j0, i0 ≤ 0, i0 < j, i0 < j0, i0 * j + j1 < 0, j1 ≤ j0, j1 + j < j0 ⊦ j0 = j1 + j, j0 = 0

Rule argument

Additional information

Used simplifier rules: zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult