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Machine-checked cryptography aims to reinforce confidence in the primitives and protocols that underpin all digital security. However, machine-checked proof techniques remain in practice difficult to apply to real-world constructions. A particular challenge is structured reasoning about complex constructions at different levels of abstraction. The State-Separating Proofs (SSP) methodology for guiding cryptographic proofs by Brzuska, Delignat-Lavaud, Fournet, Kohbrok and Kohlweiss (ASIACRYPT'18) is a promising contestant to support such reasoning. In this work, we explore how SSPs can guide EasyCrypt formalisations of proofs for modular constructions. Concretely, we propose a mapping from SSP to EasyCrypt concepts which enables us to enhance cryptographic proofs with SSP insights while maintaining compatibility with existing EasyCrypt proof support. To showcase our insights, we develop a formal security proof for the cryptobox family of public-key authenticated encryption schemes based on non-interactive key exchange and symmetric authenticated encryption. As a side effect, we obtain the first formal security proof for NaCl's instantiation of cryptobox. Finally we discuss changes to the practice of SSP on paper and potential implications for future tool designers.