Definition internal_msg (tag : nat) (from to : nid) : bool :=
  coord_msg tag from to || participant_msg tag from to.

Lemma cn_state_functional d cs1 lg1 cs2 lg2 : valid (loc cn d) -> cn_state d cs1 lg1 -> cn_state d cs2 lg2 -> cs1 = cs2 /\ lg1 = lg2.