# A total order on finite subsets of an ordered set

Let $$(A,<)$$ be an ordered set. Then I define an ordering on the set of finite subsets of $$A$$ as follows. I say that $$Xprec Y$$ if and only if the smallest element of $$Xtriangle Y$$ (the symmetric difference) is contained in $$X$$. An easy, but not completely trivial, observation is that $$prec$$ actually defines a total order on the family of finite subsets of $$A$$. My question is whether this construction is well-known.