--- /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_tdeq.ma".
+include "basic_2/rt_transition/cpr_drops_basic.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL R-TRANSITION FOR TERMS ************************)
+
+(* Properties with context-free sort-irrelevant equivalence *****************)
+
+lemma cpr_abbr_pos_tdneq (h) (G) (L) (V) (T1):
+ ∃∃T2. ⦃G,L⦄ ⊢ +ⓓV.T1 ➡[h] T2 & (+ⓓV.T1 ≛ T2 → ⊥).
+#h #G #L #V #U1
+elim (cpr_subst h G (L.ⓓV) U1 … 0) [|*: /2 width=4 by drops_refl/ ] #U2 #T2 #HU12 #HTU2
+elim (tdeq_dec U1 U2) [ -HU12 #HU12 | -HTU2 #HnU12 ]
+[ elim (tdeq_inv_lifts_dx … HU12 … HTU2) -U2 #T1 #HTU1 #_ -T2
+ /3 width=9 by cpm_zeta, tdeq_lifts_inv_pair_sn, ex2_intro/
+| @(ex2_intro … (+ⓓV.U2)) [ /2 width=1 by cpm_bind/ ] -HU12 #H
+ elim (tdeq_inv_pair … H) -H #_ #_ /2 width=1 by/
+]
+qed-.