We introduce a formal framework for analyzing trades in financial markets. These days, all big exchanges use computer algorithms to match buy and sell requests and these algorithms must abide by certain regulatory guidelines. For example, market regulators enforce that a matching produced by exchanges should be \emph{fair}, \emph{uniform}, and \emph{individual rational}. To verify these properties of trades, we first formally define these notions in a theorem prover and then develop many important results about matching demand and supply. Finally, we use this framework to verify the properties of two important classes of double sided auction mechanisms. All the definitions and results presented in this work are completely formalized in the Coq proof assistant without adding any additional axioms to it.