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diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpmhe.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpmhe.ma
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--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpmhe.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/cpms_cnh.ma".
-include "basic_2/rt_computation/cpmhe_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_cpmhe_trans (a) (h) (G) (L):
-      ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] →
-      ∀T2,n. ⦃G,L⦄ ⊢ T1 ➡*[h,n] 𝐍*⦃T2⦄ → ⦃G,L⦄ ⊢ T2 ![a,h].
-/3 width=4 by cpmhe_fwd_cpms, cnv_cpms_trans/ qed-.
-
-lemma cnv_R_cpmhe_total (a) (h) (G) (L):
-      ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] → ∃n. R_cpmhe h G L T1 n.
-/4 width=2 by cnv_fwd_fsb, fsb_inv_csx, R_cpmhe_total_csx/ qed-.
-
-axiom cnv_R_cpmhe_dec (a) (h) (G) (L):
-      ∀T. ⦃G,L⦄ ⊢ T ![a,h] → ∀n. Decidable (R_cpmhe h G L T n).
-
-(* Main inversions with head evaluation for t-bound rt-transition on terms **)
-
-theorem cnv_cpmhe_mono (a) (h) (G) (L):
-        ∀T0. ⦃G,L⦄ ⊢ T0 ![a,h] → ∀T1,n1. ⦃G,L⦄ ⊢ T0 ➡*[h,n1] 𝐍*⦃T1⦄ →
-        ∀T2,n2. ⦃G,L⦄ ⊢ T0 ➡*[h,n2] 𝐍*⦃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=8 by cpms_div, cpms_inv_cnh_sn, theq_canc_dx, conj/
-qed-.