  As an experiment to the application of proof assistant for logic research, we
formalize the model and proof system for multi-agent modal logic S5 with
PAL-style dynamic modality in Lean theorem prover. We provide a formal proof
for the reduction axiom of public announcement, and the soundness and
completeness of modal logic S5, which can be typechecked with Lean 3.19.0. The
complete proof is now available at Github.
