--- /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_tweq.ma".
+include "basic_2/rt_computation/cpms_drops.ma".
+include "basic_2/rt_computation/cnuw.ma".
+
+(* NORMAL TERMS FOR T-UNUNBOUND WHD RT-TRANSITION ***************************)
+
+(* Properties with generic relocation ***************************************)
+
+lemma cnuw_lifts (h) (G): d_liftable1 … (cnuw h G).
+#h #G #K #T #HT #b #f #L #HLK #U #HTU #n #U0 #H
+elim (cpms_inv_lifts_sn … H … HLK … HTU) -b -L #T0 #HTU0 #HT0
+lapply (HT … HT0) -G -K /2 width=6 by tweq_lifts_bi/
+qed-.
+
+(* Inversion lemmas with generic relocation *********************************)
+
+lemma cnuw_inv_lifts (h) (G): d_deliftable1 … (cnuw h G).
+#h #G #L #U #HU #b #f #K #HLK #T #HTU #n #T0 #H
+elim (cpms_lifts_sn … H … HLK … HTU) -b -K #U0 #HTU0 #HU0
+lapply (HU … HU0) -G -L /2 width=6 by tweq_inv_lifts_bi/
+qed-.
+
+(* Advanced properties ******************************************************)
+
+lemma cnuw_lref (h) (I) (G) (L):
+ ∀i. ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] #i → ⦃G,L.ⓘ{I}⦄ ⊢ ➡𝐍𝐖*[h] #↑i.
+#h #I #G #L #i #Hi #n #X2 #H
+elim (cpms_inv_lref_sn … H) -H *
+[ #H #_ destruct //
+| #T2 #HT2 #HTX2
+ lapply (Hi … HT2) -Hi -HT2 #H
+ lapply (tweq_inv_lref_sn … H) -H #H destruct
+ lapply (lifts_inv_lref1_uni … HTX2) -HTX2 #H destruct //
+]
+qed.
+
+lemma cnuw_atom_drops (h) (b) (G) (L):
+ ∀i. ⬇*[b,𝐔❴i❵] L ≘ ⋆ → ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] #i.
+#h #b #G #L #i #Hi #n #X #H
+elim (cpms_inv_lref1_drops … H) -H * [ // || #m ] #K #V1 #V2 #HLK
+lapply (drops_gen b … HLK) -HLK #HLK
+lapply (drops_mono … Hi … HLK) -L #H destruct
+qed.
+
+lemma cnuw_unit_drops (h) (I) (G) (L):
+ ∀K,i. ⬇*[i] L ≘ K.ⓤ{I} → ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] #i.
+#h #I #G #L #K #i #HLK #n #X #H
+elim (cpms_inv_lref1_drops … H) -H * [ // || #m ] #Y #V1 #V2 #HLY
+lapply (drops_mono … HLK … HLY) -L #H destruct
+qed.