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Proof step 12 from proof modmod-add-zero (previous step)

i0 = i1 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j ∧ i1 ≤ 0, (i + j0) % j = 0, i0 < 0, 0 < j ⊦ 0 = j, (i + i0) % j = 0, 0 ≤ i0, i ≤ 0 ∧ i0 ≤ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
(i + j0) % j = 0, abs(j0) < j, 0 < j, j0 ≤ 0, j0 < j, i1 ≤ 0, i1 < j, i1 * j + j0 < 0 ⊦ 0 = j, (i + i1 * j + j0) % j = 0, 0 ≤ i1 * j + j0, i ≤ 0 ∧ i1 * j + j0 ≤ 0

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