The unique solution of contractions is a proof technique for (weak) bisimilarity that overcomes certain syntactic limitations of Milner's “unique solution of equations” theorem. This paper presents an overview of a comprehensive formalisation of Milner's Calculus of Communicating Systems (CCS) in the HOL theorem prover (HOL4), with a focus towards the theory of unique solutions of equations and contractions. The formalisation consists of about 24,000 lines (1MB) of code in total. Some refinements of the “unique solution of contractions” theory itself are obtained. In particular we remove the constraints on summation, which must be guarded, by moving from contraction to rooted contraction. We prove the “unique solution of rooted contractions” theorem and show that rooted contraction is the coarsest precongruence contained in the contraction preorder.

收缩的唯一解是（弱）双相似性的证明技术，它克服了米尔纳“方程的唯一解”定理的某些句法限制。本文介绍了HOL定理证明者（HOL4）中米尔纳通信系统微积分（CCS）的全面形式化的概述，重点是方程和收缩的唯一解的理论。正式形式总共包含大约24,000行（1MB）代码。获得了“收缩的唯一解”理论本身的一些改进。特别是，我们从收缩转变为有根收缩，从而消除了必须加以保护的求和约束。。我们证明了“有根收缩的唯一解”定理，并证明了有根收缩是收缩前序中包含的最粗糙的前同余。