Definition getSt_server d (C : LockCoh d) : server_state :=
match find st (getLocal server d) as f return _ = f -> _ with
Some v => fun epf => icast (sym_eq (getLocal_server_st_tp C epf)) (dyn_val v)
| _ => fun epf => ServerState [::] 0 None
end (erefl _).

Lemma getSt_server_K d (C : LockCoh d) m :
getLocal server d = st :-> m -> getSt_server C = m.