  Collaborative work on shared documents was revolutionized by web services
like Google Docs or Etherpad. Multiple users can work on the same document in a
comfortable and distributed way. For the synchronization of the changes a
replication system named Operational Transformation is used. Such a system
consists of a control algorithm and a transformation function. In essence, a
transformation function solves the conflicts that arise when multiple users
change the document at the same time. In this work we investigate on the
correctness of such transformation functions. We introduce transformation
functions n-ary trees that we designed especially for the purpose of
synchronization changes on JSON objects. We provide a detailed proof of the
necessary property: the Transformation Property 1.
