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Proof step 1 from proof mult-split-mod-02 (conclusion)

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

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: mult-split-mod: ⊦ 0 ≤ i ∧ 0 ≤ i0 ∧ 0 < j → i / j * i0 + (i0 * i % j) / j = (i0 * i) / j;%add-in: ⊦ i + j = i + i0 ↔ j = i0; from specification int-basic2%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