# Abstract

We use the interactive theorem prover Isabelle to prove that the

algebraic axiomatization of bisimulation equivalence in the

pi-calculus is sound and complete. This is thefirst proof of

its kind to be wholly machine checked. Although the

result has been known for some time the proof had parts which needed

careful attention to detail to become completely formal. It is not

that the result was ever in doubt; rather, our contribution lies in

the methodology to prove completeness and get absolute certainty

that the proof is correct, while at the same time following the

intuitive lines of reasoning of the original proof. Completeness of

axiomatizations is relevant for many variants of the calculus, so

our method has applications beyond this single result. We build on

our previous effort of implementing a framework for the pi-calculus

in Isabelle using the nominal data type package, and strengthen our

claim that this framework is well suited to represent the theory of

the pi-calculus, especially in the smooth treatment of bound names.