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Proof step 4 from proof modmod-ma (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%zero-ge-02: ⊦ 0 ≤ i → (0 ≤ i * j ↔ ¬ ¬(i = 0 ∨ 0 ≤ j)); from specification int-mult