--- /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/relocation/lifts_teqx.ma".
+include "static_2/static/rex_drops.ma".
+include "static_2/static/reqx.ma".
+
+(* SORT-IRRELEVANT EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ***)
+
+(* Properties with generic slicing for local environments *******************)
+
+lemma reqx_lifts_sn: f_dedropable_sn cdeq.
+/3 width=5 by rex_liftable_dedropable_sn, teqx_lifts_sn/ qed-.
+
+(* Inversion lemmas with generic slicing for local environments *************)
+
+lemma reqx_inv_lifts_sn: f_dropable_sn cdeq.
+/2 width=5 by rex_dropable_sn/ qed-.
+
+lemma reqx_inv_lifts_dx: f_dropable_dx cdeq.
+/2 width=5 by rex_dropable_dx/ qed-.
+
+lemma reqx_inv_lifts_bi: โL1,L2,U. L1 โ[U] L2 โ โb,f. ๐โฆfโฆ โ
+ โK1,K2. โฉ*[b,f] L1 โ K1 โ โฉ*[b,f] L2 โ K2 โ
+ โT. โง*[f] T โ U โ K1 โ[T] K2.
+/2 width=10 by rex_inv_lifts_bi/ qed-.
+
+lemma reqx_inv_lref_pair_sn: โL1,L2,i. L1 โ[#i] L2 โ โI,K1,V1. โฉ*[i] L1 โ K1.โ{I}V1 โ
+ โโK2,V2. โฉ*[i] L2 โ K2.โ{I}V2 & K1 โ[V1] K2 & V1 โ V2.
+/2 width=3 by rex_inv_lref_pair_sn/ qed-.
+
+lemma reqx_inv_lref_pair_dx: โL1,L2,i. L1 โ[#i] L2 โ โI,K2,V2. โฉ*[i] L2 โ K2.โ{I}V2 โ
+ โโK1,V1. โฉ*[i] L1 โ K1.โ{I}V1 & K1 โ[V1] K2 & V1 โ V2.
+/2 width=3 by rex_inv_lref_pair_dx/ qed-.
+
+lemma reqx_inv_lref_pair_bi (L1) (L2) (i):
+ L1 โ[#i] L2 โ
+ โI1,K1,V1. โฉ*[i] L1 โ K1.โ{I1}V1 โ
+ โI2,K2,V2. โฉ*[i] L2 โ K2.โ{I2}V2 โ
+ โงโง K1 โ[V1] K2 & V1 โ V2 & I1 = I2.
+/2 width=6 by rex_inv_lref_pair_bi/ qed-.