| (fac(j - 1) * fac(i + 1 - j)) * i1 = fac(i), (fac(i - j) * fac(j)) * i0 = fac(i), 0 < j, 0 ≤ i, 0 ≤ j, 0 < i, j ≤ i ⊦ i0 * j = fac(i) / (fac(i + 1 - j) * fac(j - 1)) * (i + 1 - j) |
(fac(j - 1) * fac(i + 1 - j)) * i1 = fac(i), (fac(i - j) * fac(j)) * i0 = (fac(j - 1) * fac(i + 1 - j)) * i1, 0 < j, 0 ≤ i, 0 ≤ j, 0 < i, j ≤ i ⊦ i0 * j = ((fac(j - 1) * fac(i + 1 - j)) * i1) / (fac(i + 1 - j) * fac(j - 1)) * (i + 1 - j)