(** Definition of Controlled Bisimulations *)
    Definition bicontrolled R := controlled TX TX R /\ incl R (bisim TX TX).

(* Specifications: *)
Lemma expand_refl: reflexive (expand TX TX).
Lemma expand_trans: transitive (expand TX TX).
Lemma wexpand_refl: reflexive (wexpand TX TX).
Lemma wexpand_trans: transitive (wexpand TX TX).