To express message authentication of A to B, we describe B's process so that it sends out an end(B) event within session, modeling the fact that B has finished a Simple network session. Similarly, A's process is modified to send a begin(B) event directly after public keys are exchanged, modeling the fact that A has started a communication with B[11]. In our syntax (based on that of ProVerif), we express this correspondence assertion that follows the pattern: