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Proof step 8 from proof modmod-add-04 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
j0 < j, 0 < j, 0 ≤ i0, 0 ≤ j0, 0 ≤ i1 ⊦ (j0 + i0 % j) % j = ((i1 * j + j0) + 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