--- /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/cpx_drops_basic.ma".
+include "basic_2/rt_transition/cnx.ma".
+
+(* NORMAL TERMS FOR UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION ********)
+
+(* Advanced inversion lemmas ************************************************)
+
+lemma cnx_inv_abbr_pos (h) (G) (L): ∀V,T. ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃+ⓓV.T⦄ → ⊥.
+#h #G #L #V #U1 #H
+elim (cpx_subst h G (L.ⓓV) U1 … 0) [|*: /2 width=4 by drops_refl/ ] #U2 #T2 #HU12 #HTU2
+elim (tdeq_dec U1 U2) #HnU12 [ -HU12 | -HTU2 ]
+[ elim (tdeq_inv_lifts_dx … HnU12 … HTU2) -U2 #T1 #HTU1 #_ -T2
+ lapply (H T1 ?) -H [ /2 width=3 by cpx_zeta/ ] #H
+ /2 width=9 by tdeq_lifts_inv_pair_sn/
+| lapply (H (+ⓓV.U2) ?) -H [ /2 width=1 by cpx_bind/ ] -HU12 #H
+ elim (tdeq_inv_pair … H) -H #_ #_ /2 width=1 by/
+]
+qed-.