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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cwhx_rdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cwhx_rdeq.ma
new file mode 100644
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/static/rdeq_fqup.ma".
+include "basic_2/rt_transition/cwhx.ma".
+
+(* WHD NORMAL TERMS FOR UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION ****)
+
+(* Properties with degree-based equivalence *********************************)
+
+lemma rdeq_tdeq_cwhx_trans (h) (o) (G):
+                           ∀L2,T2. ⦃G,L2⦄ ⊢ ⬈[h] 𝐖𝐇⦃T2⦄ →
+                           ∀T1. T1 ≛[h,o] T2 →
+                           ∀L1. L1 ≛[h,o,T1] L2 → ⦃G,L1⦄ ⊢ ⬈[h] 𝐖𝐇⦃T1⦄.
+#h #o #G #L2 #T2 #H elim H -L2 -T2
+[ #L2 #s2 #X1 #HX #L1 #HL
+  elim (tdeq_inv_sort2 … HX) -HX #s1 #d #_ #_ #H destruct -s2 -d //
+| #p #L2 #W2 #T2 #X1 #HX #L1 #HL
+  elim (tdeq_inv_pair2 … HX) -HX #W1 #T1 #_ #_ #H destruct -W2 -T2 //
+| #L2 #V2 #T2 #_ #IH #X1 #HX #L1 #HL
+  elim (tdeq_inv_pair2 … HX) -HX #V1 #T1 #HV12 #HT12 #H destruct
+  elim (rdeq_inv_bind … HL) -HL #HV1 #HT1
+  /5 width=2 by cwhx_ldef, rdeq_bind_repl_dx, ext2_pair/
+]
+qed-.
+
+lemma tdeq_cwhx_trans (h) (o) (G) (L):
+                      ∀T2. ⦃G,L⦄ ⊢ ⬈[h] 𝐖𝐇⦃T2⦄ →
+                      ∀T1. T1 ≛[h,o] T2 → ⦃G,L⦄ ⊢ ⬈[h] 𝐖𝐇⦃T1⦄.
+/3 width=6 by rdeq_tdeq_cwhx_trans/ qed-.