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Proof step 2 from proof mod-mult-neg-03 (previous step)

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

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: mod-mult-neg-02: ⊦ 0 < j ∧ i ≤ 0 ∧ i0 ≤ 0 → (j * i + i0) % j = i0 % j;%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult