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We provide a framework consisting of tools and metatheorems for the end-to-end verification of security protocols, which bridges the gap between automated protocol verification and code-level proofs. We automatically translate a Tamarin protocol model into a set of I/O specifications expressed in separation logic. Each such specification describes a protocol role's intended I/O behavior against which the role's implementation is then verified. Our soundness result guarantees that the verified implementation inherits all security (trace) properties proved for the Tamarin model. Our framework thus enables us to leverage the substantial body of prior verification work in Tamarin to verify new and existing implementations. The possibility to use any separation logic code verifier provides flexibility regarding the target language. To validate our approach and show that it scales to real-world protocols, we verify a substantial part of the official Go implementation of the WireGuard VPN key exchange protocol.