We report on our experience in using the Isabelle/HOL theorem prover to mechanize proofs of observation equivalence for systems with infinitely many states, and for parameterized systems. We follow the direct approach: An infinite relation containing the pair of systems to be shown equivalent is defined, and then proved to be a weak bisimulation. The weak bisimilarity proof is split into many cases, corresponding to the derivatives of the pairs in the relation. Isabelle/HOL automatically proves simple cases, and guarantees that no case is forgotten. The strengths and weaknesses of the approach are discussed.

Observation equivalence is a well-known technique for proving that a concurrent system satises its specication. We report on our experience in the mechanization of observation equivalence proofs with the help of a general-purpose theorem prover. Several case-studies are considered, incluiding an sliding window and a cache-coherence protocol. In all cases the system has an innite number of states, and sometimes also an arbitrarily large number of components. We show how compositionality and bisimulation-up-to techniques can be applied to reduce the size of the proofs. 1 Introduction One of the main goals of the A3 Teilprojekt within the Sonderforschungsbereich 342 is the development of verication techniques for distributed systems. Since 1995, special emphasis has been put on automatic (model-checking) and semi-automatic techniques, and in the period 1998-2000, A3 has devoted special attention and resources to the development of machine support for the analysis of systems ...