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Proof step 4 from proof modmod-add-03 (previous step)

0 ≠ j ∧ i ≤ 0 ∧ i0 % j ≤ 0, i < 0, i0 < 0 ⊦ (i + i0 % j) % j = (i + i0) % j, j = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
i < 0, i0 < 0, i0 % j ≤ 0 ⊦ (i + i0 % j) % j = (i + i0) % j, 0 = j

Rule argument

Additional information

Used simplifier rules: forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%zero-gels-03: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs