  This paper presents experiments on common knowledge logic, conducted with the
help of the proof assistant Coq. The main feature of common knowledge logic is
the eponymous modality that says that a group of agents shares a knowledge
about a certain proposition in a inductive way. This modality is specified by
using a fixpoint approach. Furthermore, from these experiments, we discuss and
compare the structure of theorems that can be proved in specific theories that
use common knowledge logic. Those structures manifests the interplay between
the theory (as implemented in the proof assistant Coq) and the metatheory.
