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Proof step 1 from proof div-addthree-rew (conclusion)

⊦ 0 ≤ i ∧ 0 ≤ i0 ∧ 0 ≤ i1 ∧ 0 < j → (i + i0 + i1) / j = i / j + i0 / j + i1 / j + (i % j + i0 % j + i1 % j) / j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
0 ≤ i, 0 ≤ i0, 0 ≤ i1, 0 < j ⊦ (i + i0 + i1) / j = i / j + i0 / j + i1 / j + (i % j + i0 % j + i1 % j) / j

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs