We present a mechanized proof of security for an efficient Searchable Symmetric Encryption (SSE) scheme completed in the Foundational Cryptography Framework (FCF). FCF is a Coq library for reasoning about cryptographic schemes in the computational model that features a small trusted computing base and an extensible design. Through this effort, we provide the first mechanized proof of security for an efficient SSE scheme, and we demonstrate that FCF is well-suited to reasoning about such complex protocols.