0 < j, i < (i0 + i1) * j, 0 ≤ i1, 0 ≤ i, 0 ≤ i0, i0 * j ≤ i ⊦ ∃ i0. i0 * j ≤ i ∧ i < (i0 + 1) * j ∧ 0 ≤ i0