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Proof step 6 from proof mod-rec (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: mod-zero: ⊦ 0 < j ∧ 0 ≤ i → 0 ≤ i % j; from specification int-div%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%mod-add: ⊦ 0 < i ∧ 0 ≤ j → (i + j) % i = j % i; from specification int-div