The term shared dataspace refers to the general class of programming languages in which the principal means of communication among the concurrent components of programs is a common, content-addressable data structure called a dataspace. In the programming language and artificial intelligence communities, there is considerable interest in such languages, e.g., logic-based languages, production rule systems, and the Linda language. However, these languages have not been the subject of extensive program verification research. This paper specifies a proof system for a shared dataspace programming notation called Swarm-a programming logic similar in style to that of UNITY. The paper then uses the proof system to reason about a Swarm program to label the equal-intensity regions of a digital image.