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Proof step 4 from proof mod-pred-neg (previous step)

i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j ∧ i0 ≤ 0, i < 0, 0 < j ⊦ j0 = (i - 1) % j + 1, 1 = j0 + j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
abs(j0) < j, 0 < j, j0 ≤ 0, j0 < j, i0 ≤ 0, i0 < j, i0 * j + j0 < 0 ⊦ j0 = (i0 * j + j0 - 1) % j + 1, 1 = j0 + j

Rule argument

Additional information

Used simplifier rules: forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs