(* Specifications: *)
Theorem wexpansion1_ctrl: wexpansion1 TX TX B -> controlled TX TY B.
Theorem plus_wf_controlled: controlled TX TY B.
Theorem star_wf_controlled: controlled TX TY B.
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)).
Theorem upto: incl R (bisim TX TX).
Theorem upto_ctrl: incl R (bisim TX TX).
Theorem monotonic_correct: simulation TX TY (UIter F R).
Lemma wmonotonic_correct_t: simulation_t TX TY (UIter F R).
Theorem wmonotonic_correct: simulation TX TY (UIter F R).
Theorem unified_correct: simulation TX TY (UIter (UIter G) R).
Theorem controlled_correct: simulation TX TY (UIter (UIter G) R).
Lemma monotonic_wmonotonic: forall F, monotonic TX TY F -> wmonotonic TX TY F.
Lemma star_wmon: wmonotonic TX TX (star (X:=X)).
Lemma Comp_wmon: wmonotonic TX TY (Comp G F).
Lemma Union2_wmon: wmonotonic TX TY (Union2 F G).
Lemma Union_wmon: wmonotonic TX TY (Union H).
Lemma UExp_wmon: forall n, wmonotonic TX TY (fun R => UExp F R n).
Lemma UIter_wmon: wmonotonic TX TY (UIter F).
Lemma Chaining_wmon: wmonotonic TX TX (Chain F G).
Lemma chaing_l_wmon: wmonotonic TY TX (chaining_l L).
Lemma identity_mon: monotonic TX TY (identity (X:=X) (Y:=Y)).
Lemma constant_mon: simulation TX TY R -> monotonic TX TY (constant R).
Lemma chaining_r_mon: simulation TY TY T -> monotonic TX TY (chaining_r T).
Lemma chaining_l_mon: expansion1 TX TX E -> monotonic TX TY (chaining_l E).
Lemma Comp_mon: monotonic TX TY (Comp G F).
Lemma Union2_mon: monotonic TX TY (Union2 F G).
Lemma Union_mon: monotonic TX TY (Union H).
Lemma UExp_mon: forall n, monotonic TX TY (fun R => UExp F R n).
Lemma UIter_mon: monotonic TX TY (UIter F).