--- /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/unfold/delift_lift.ma".
+include "basic_2/unfold/delift_delift.ma".
+include "basic_2/computation/cprs_delift.ma".
+include "basic_2/equivalence/cpcs_cpcs.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
+
+(* Properties on inverse basic term relocation ******************************)
+
+lemma cpcs_zeta_delift_comm: ∀L,V,T1,T2. L.ⓓV ⊢ ▼*[O, 1] T1 ≡ T2 →
+ L ⊢ T2 ⬌* +ⓓV.T1.
+/3 width=1/ qed.
+
+(* Basic_1: was only: pc3_gen_cabbr *)
+lemma thin_cpcs_delift_mono: ∀L,U1,U2. L ⊢ U1 ⬌* U2 →
+ ∀K,d,e. ▼*[d, e] L ≡ K → ∀T1. L ⊢ ▼*[d, e] U1 ≡ T1 →
+ ∀T2. L ⊢ ▼*[d, e] U2 ≡ T2 → K ⊢ T1 ⬌* T2.
+#L #U1 #U2 #H #K #d #e #HLK #T1 #HTU1 #T2 #HTU2
+elim (cpcs_inv_cprs … H) -H #U #HU1 #HU2
+elim (thin_cprs_delift_conf … HU1 … HLK … HTU1) -U1 #T #HT1 #HUT
+elim (thin_cprs_delift_conf … HU2 … HLK … HTU2) -U2 -HLK #X #HT2 #H
+lapply (delift_mono … H … HUT) -L #H destruct /2 width=3/
+qed.