--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "static_2/static/feqg_fqu.ma".
+include "basic_2/rt_transition/fpb_fqup.ma".
+include "basic_2/rt_transition/fpbc.ma".
+
+(* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
+
+(* Advanced properties ******************************************************)
+
+(* Basic_2A1: uses: fpb_cpx *)
+lemma cpx_fpbc (G) (L):
+ ∀T1,T2. ❪G,L❫ ⊢ T1 ⬈ T2 → (T1 ≅ T2 → ⊥) → ❪G,L,T1❫ ≻ ❪G,L,T2❫.
+/4 width=5 by fpbc_intro, cpx_fpb, feqg_fwd_teqg/ qed.
+
+(* Basic_2A1: uses: fpb_fqu *)
+lemma fqu_fpbc (G1) (G2) (L1) (L2) (T1) (T2):
+ ❪G1,L1,T1❫ ⬂ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫.
+/4 width=10 by fpbc_intro, fquq_fpb, fqu_fquq, fqu_fneqg/ qed.