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Proof step 3 from proof modeqp-01 (previous step)

i * j + j0 = i0 * j + j1, j0 ≤ 0, abs(j0) < j, j1 ≤ 0, abs(j1) < j ⊦ i * j + ~ j1 = i0 * j + ~ j0 ∧ 0 ≤ ~ j1 ∧ ~ j1 < j ∧ 0 ≤ ~ j0 ∧ ~ j0 < j, i = i0 ∧ j0 = j1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
i * j + j0 = i0 * j + j1, abs(j0) < j, abs(j1) < j, j0 ≤ 0, j1 ≤ 0 ⊦ i = i0 ∧ j0 = j1, 0 < j + j1 ∧ 0 < j + j0

Rule argument

Additional information

Used simplifier rules: forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%neg-13: ⊦ ~ i < j ↔ 0 < j + i; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%negle-07: ⊦ i ≤ ~ j ↔ i + j ≤ 0; from specification int-abs%sub-add-01: ⊦ i + (j - i0) = i + j - i0; from specification int-abs%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%neg-15: ⊦ i + ~ j = i - j; from specification int-abs