SET (Secure Electronic Transaction) is a suite of protocols proposed by a consortium of credit card companies and software corporations to secure e-commerce transactions. The Purchase part of the suite is intended to guarantee the integrity and authenticity of the payment transaction while keeping the Cardholder’s account details secret from the Merchant and his choice of goods secret from the Bank. This paper details the first verification results for the complete Purchase protocols of SET. Using Isabelle and the inductive method, we show that their primary goal is indeed met. However, a lack of explicitness in the dual signature makes some agreement properties fail: it is impossible to prove that the Cardholder meant to send his credit card details to the very payment gateway that receives them. A major effort in the verification went into digesting the SET documentation to produce a realistic model. The protocol’s complexity and size make verification difficult, compared with other protocols. However, our effort has yielded significant insights.