(** * Bisimilarity is an equivalence relation, Expansion and Weak expansion are preorders *)
Section Properties.
Variable X: Type.
Variable TX: reduction_t A X.

(* Specifications: *)
(** Symmetry of Bisimilarity *)
Lemma bisim_sym: symmetric (bisim TX TX).
(** Reflexivity of Bisimilarity *)
Lemma bisim_refl: reflexive (bisim TX TX).
(** Transitivity of Bisimilarity *)
Lemma bisim_trans: transitive (bisim TX TX).
Definition bicontrolled R := controlled TX TX R /\ incl R (bisim TX TX).