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Proof step 5 from proof modmod-ma (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
0 < j, 0 ≤ j0, 0 ≤ i0, 0 ≤ i ⊦ (i % j * i0 % j + j0) % j = ((i * i0) % j + j0) % j

Rule argument

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s)% ⊦ 0 ≤ i → (0 ≤ i * j ↔ i = 0 ∨ 0 ≤ j); (s)