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Proof step 3 from proof modmod-add-04 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
0 < j, 0 ≤ i, 0 ≤ i0 ⊦ (i % j + i0 % j) % j = (i + i0) % j

Rule argument

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs