This slide explains more clearly this concept and as you see the least fixed point and the greatest fixed point can be seen in one case as the least such object and in this case as the greatest such object. So in order to show that something belongs to a greatest fixed point we just need to show that it belongs to some post fixed-point. In order to show that something belongs to some least fixed-point we just need to show that it belongs to some pre fixed-point.

---