Liveness analysis is a standard compiler analysis, enabling several optimizations such as deadcode elimination. The SSA form is a popular compiler intermediate language allowing for simple and fast optimizations. Boissinot et al. [7] designed a fast liveness analysis by combining the specific properties of SSA with graph-theoretic ideas such as depth-first search and dominance. We formalize their approach in the Coq proof assistant, inside the CompCertSSA verified C compiler. We also compare experimentally this approach on CompCert's benchmarks with respect to the classic data-flow-based liveness analysis, and observe performance gains.