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diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpmuwe.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpmuwe.ma
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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 "basic_2/rt_computation/cpmuwe_csx.ma".
+include "basic_2/rt_equivalence/cpes.ma".
+include "basic_2/dynamic/cnv_preserve.ma".
+
+(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
+
+(* Properties with head evaluation for t-bound rt-transition on terms *******)
+
+lemma cnv_cpmuwe_trans (a) (h) (G) (L):
+      ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] →
+      ∀T2,n. ⦃G,L⦄ ⊢ T1 ➡*𝐍𝐖*[h,n] T2 → ⦃G,L⦄ ⊢ T2 ![a,h].
+/3 width=4 by cpmuwe_fwd_cpms, cnv_cpms_trans/ qed-.
+
+lemma cnv_R_cpmuwe_total (a) (h) (G) (L):
+      ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] → ∃n. R_cpmuwe h G L T1 n.
+/4 width=2 by cnv_fwd_fsb, fsb_inv_csx, R_cpmuwe_total_csx/ qed-.
+
+axiom cnv_R_cpmuwe_dec (a) (h) (G) (L):
+      ∀T. ⦃G,L⦄ ⊢ T ![a,h] → ∀n. Decidable (R_cpmuwe h G L T n).
+
+(* Main inversions with head evaluation for t-bound rt-transition on terms **)
+
+theorem cnv_cpmuwe_mono (a) (h) (G) (L):
+        ∀T0. ⦃G,L⦄ ⊢ T0 ![a,h] → ∀T1,n1. ⦃G,L⦄ ⊢ T0 ➡*𝐍𝐖*[h,n1] T1 →
+        ∀T2,n2. ⦃G,L⦄ ⊢ T0 ➡*𝐍𝐖*[h,n2] T2 →
+        ∧∧ ⦃G,L⦄ ⊢ T1 ⬌*[h,n2-n1,n1-n2] T2 & T1 ≅ T2.
+#a #h #G #L #T0 #HT0 #T1 #n1 * #HT01 #HT1 #T2 #n2 * #HT02 #HT2
+elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 #T0 #HT10 #HT20
+/4 width=4 by cpms_div, tweq_canc_dx, conj/
+qed-.