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Proof step 20 from proof modmod-add-law-pos (previous step)

(i0 % j + i % j) % j + 2 * j < j, (i0 % j + i % j) % j + 2 * j = (i + i0 % j) % j + j, 0 < j ⊦ j = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: 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%one: ⊦ 1 * i = i; from specification int-mult%numeq-02: ⊦ (* i2) * i + j = i + j0 ↔ (i2 - 1) * i + j = j0; from specification int-mult