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Proof step 9 from proof modmod-add-04 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
0 < j, j0 < j, 0 ≤ i0, 0 ≤ j0, 0 ≤ i1 ⊦ (j0 + i0 % j) % j = ((i1 * j + j0) + i0) % j

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)