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Proof step 1 from proof modmod-ma (conclusion)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
0 ≤ i, 0 ≤ i0, 0 ≤ j0, 0 < j ⊦ (i % j * i0 % j + j0) % j = (i * i0 + j0) % j

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs