I have this kind of exercise:

Let < be the partial order in the set A and define function by determining , when .

Let . Show that F is the isomorphism between structures and .

Okey, my problem is how to mark function between A and S. I think I can't do it like , because I have already defined F before.

Rest of the exercise I can handle, I just have to show that the function between A and S is bijection and that .