+(**************************************************************************)
+(* ___ *)
+(* ||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/rex_drops.ma".
+include "basic_2/rt_transition/cpx_drops.ma".
+include "basic_2/rt_transition/rpx.ma".
+
+(* UNBOUND PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS ***********)
+
+(* Properties with generic slicing for local environments *******************)
+
+lemma rpx_lifts_sn (h) (G): f_dedropable_sn (cpx h G).
+/3 width=6 by rex_liftable_dedropable_sn, cpx_lifts_sn/ qed-.
+
+(* Inversion lemmas with generic slicing for local environments *************)
+
+lemma rpx_inv_lifts_sn (h) (G): f_dropable_sn (cpx h G).
+/2 width=5 by rex_dropable_sn/ qed-.
+
+lemma rpx_inv_lifts_dx (h) (G): f_dropable_dx (cpx h G).
+/2 width=5 by rex_dropable_dx/ qed-.
+
+lemma rpx_inv_lifts_bi (h) (G):
+ ∀L1,L2,U. ⦃G,L1⦄ ⊢ ⬈[h,U] L2 → ∀b,f. 𝐔⦃f⦄ →
+ ∀K1,K2. ⬇*[b,f] L1 ≘ K1 → ⬇*[b,f] L2 ≘ K2 →
+ ∀T. ⬆*[f]T ≘ U → ⦃G,K1⦄ ⊢ ⬈[h,T] K2.
+/2 width=10 by rex_inv_lifts_bi/ qed-.