Ready to preorder: an algebraic and general proof

There have been quite a few proposals for behavioural equivalences for concurrent processes, and many of them are presented in Van Glabbeek’s linear time-branching time spectrum. Since their original definitions are based on rather different ideas, proving general properties of them all would seem to require a case-by-case study. However, the use of their axiomatizations allows a uniform treatment that might produce general proofs of those properties. Recently Aceto, Fokkink and Ingólfsdóttir have presented a very interesting result: for any process preorder coarser than the ready simulation in the linear time-branching time spectrum they show how to get an axiomatization of the induced equivalence. Unfortunately, their proof is not uniform and requires a case-by-case analysis. Following the algebraic approach suggested above, in this paper we present a much simpler proof of that result which, in addition, is more general and totally uniform, so that it does not need to consider one by one the different semantics in the spectrum.