During February 2026, Hanbyul Yoo contributed to leanprover-community/mathlib4 by implementing the Focal Subgroup Theorem within the group theory module. Using Lean and formal verification techniques, Hanbyul defined the focal subgroup, constructed the transfer homomorphism, and formally proved the relationship between Sylow p-subgroups and commutator subgroups in finite groups. This work required deep mathematical insight and careful formalization, enhancing the library’s foundation for future group theory research. Hanbyul also updated documentation to improve source citation. The contribution focused on expanding mathlib4’s mathematical tooling, providing a rigorous basis for downstream formal proofs and further development in abstract algebra.