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.