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Proof step 22 from proof mod-add1-negpos-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs name: Abs-neg seq: ⊦ j < 0 → abs(j) = 0 - j subst: [j] → [j1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 0 - i = ~ i; (s)% ⊦ ~ i < j ↔ 0 < j + i; (s)% ⊦ i < j → ¬ j < i; (s)% ⊦ ¬ j < 0 → abs(j) = j; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s)% ⊦ i + 0 = i; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: j1