(** * Application to the bisimulation case *)
Require Export Settings.
Set Implicit Arguments.
Section Modular.
Variables A X: Type.
Variable TX: reduction_t A X.
Let F  := Comp (chaining_l (expand TX TX)) (chaining_r (bisim TX TX)).
Let G  := Comp (star (X:=X)) (Union2 (identity (X:=X) (Y:=X)) (constant (bisim TX TX))).

(* Specifications: *)
Lemma F_mon: monotonic TX TX F.
Lemma G_wmon: wmonotonic TX TX G.
Lemma FG: contains F G.
Lemma G_reverse: forall R, eeq (trans (G R)) (G (trans R)).
intros R; unfold G, Comp, Union2, identity, constant.