  We present a series of definitions and theorems demonstrating how to reduce
the requirements for proving system refinements ensuring containment of fair
stuttering runs. A primary result of the work is the ability to reduce the
requisite proofs on runs of a system of interacting state machines to a set of
definitions and checks on single steps of a small number of state machines
corresponding to the intuitive notions of freedom from starvation and deadlock.
We further refine the definitions to afford an efficient explicit-state
checking procedure in certain finite state cases. We demonstrate the proof
reduction on versions of the Bakery Algorithm.
