Keith - nice! Just one nitpick: I think you mean to use \$$f(c) = [c \lt \infty]\$$, not \$$[c \gt \infty]\$$... unless you are playing a sneaky trick and defining \$$\lt\$$ to mean the usual \$$\gt\$$. Of course, this is all very confusing, given the strange way we are making \$$\mathbf{Cost}\$$ into a poset.