i0 * j + j0 < i0 * j, i0 * i1 = i0 * j + j0, 0 ≤ i1, 0 ≤ i0, 0 ≤ j0, j0 < j, 1 < j, 0 < j, 0 < i1, 0 < i0, i1 < j, i0 < j ⊦