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Proof step 4 from proof mod-add-pos (previous step)

i0 = i1 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j, j0 = 0, 0 < j, 0 ≤ i0, 0 ≤ i ⊦ (i + i0) % j = i % 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-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-zero: ⊦ i + 0 = i; from specification int-basic2