--- /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 "basic_2/static/rex_rex.ma".
+include "basic_2/rt_transition/rpx.ma".
+
+(* UNBOUND PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS ***********)
+
+(* Main properties **********************************************************)
+
+theorem rpx_bind: ∀h,G,L1,L2,V1. ⦃G, L1⦄ ⊢ ⬈[h, V1] L2 →
+ ∀I,V2,T. ⦃G, L1.ⓑ{I}V1⦄ ⊢ ⬈[h, T] L2.ⓑ{I}V2 →
+ ∀p. ⦃G, L1⦄ ⊢ ⬈[h, ⓑ{p,I}V1.T] L2.
+/2 width=2 by rex_bind/ qed.
+
+theorem rpx_flat: ∀h,G,L1,L2,V. ⦃G, L1⦄ ⊢ ⬈[h, V] L2 →
+ ∀I,T. ⦃G, L1⦄ ⊢ ⬈[h, T] L2 → ⦃G, L1⦄ ⊢ ⬈[h, ⓕ{I}V.T] L2.
+/2 width=1 by rex_flat/ qed.
+
+theorem rpx_bind_void: ∀h,G,L1,L2,V. ⦃G, L1⦄ ⊢ ⬈[h, V] L2 →
+ ∀T. ⦃G, L1.ⓧ⦄ ⊢ ⬈[h, T] L2.ⓧ →
+ ∀p,I. ⦃G, L1⦄ ⊢ ⬈[h, ⓑ{p,I}V.T] L2.
+/2 width=1 by rex_bind_void/ qed.