Developed a formal proof component for the HEPLean/PhysLean repository, focusing on the Harmonic Oscillator model within the domain of classical mechanics. Leveraging Lean for formal verification and mathematical proof, the work established that a trajectory’s velocity is zero if and only if its position matches a magnitude derived from initial conditions, grounded in energy conservation principles. This lemma was integrated into the model to enhance simulation validation and reliability, enabling more robust scenario testing. The contribution included updates to model checks and documentation, improving traceability and supporting future audits and maintenance without introducing any bug fixes during the development period.