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Proof step 5 from proof div-elim-posneg (previous step)

i1 * j + j1 = i0 * j + j0, i0 ≤ 0, j0 + j < 0, 0 ≤ j0, i1 ≤ 0, 0 ≤ i0 * j + j0, j < 0, 0 ≤ j1, j1 + j < 0 ⊦ i0 = i1 ∧ j0 = j1

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: modeqp-02 seq: i * j + j0 = i0 * j + j1, j < 0, 0 ≤ j0, j0 < abs(j), 0 ≤ j1, j1 < abs(j) ⊦ i = i0 ∧ j0 = j1 subst: [i, j, j0, i0, j1] → [i1, j, j1, i0, j0] flags:

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs%neg-07: ⊦ i < ~ j ↔ i + j < 0; from specification int-abs Used terms: i1, j, j1, i0, j0