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Proof step 8 from proof div-add-pos (previous step)

i0 = i2 * j + j1, j1 = 0, 0 < j, j0 < j, j1 < j, 0 ≤ i1, 0 ≤ j0, 0 ≤ i0, 0 ≤ j1 ⊦ ((i1 * j + j0) + i0) / j = i1 + i2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
j0 < j, 0 < j, 0 ≤ j0, 0 ≤ i1, 0 ≤ i2 ⊦ (j * (i2 + i1) + j0) / j = i1 + i2

Rule argument

Additional information

Used simplifier rules: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); (s)%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; 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% ⊦ i + 0 = i; (s)% ⊦ i * j + i * j0 = i * (j + j0); (s)