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diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_acle.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_acle.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 "static_2/syntax/acle.ma".
+include "basic_2/dynamic/cnv_aaa.ma".
+
+(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
+
+(* Properties with preorder for applicability domains ***********************)
+
+lemma cnv_acle_trans (h) (a1) (a2):
+      a1 ⊆ a2 → ∀G,L,T. ⦃G,L⦄ ⊢ T ![h,a1] → ⦃G,L⦄ ⊢ T ![h,a2].
+#h #a1 #a2 #Ha12 #G #L #T #H elim H -G -L -T
+[ /1 width=1 by cnv_sort/
+| /3 width=1 by cnv_zero/
+| /3 width=1 by cnv_lref/
+| /3 width=1 by cnv_bind/
+| #n1 #p #G #L #V #W #T #U #Hn1 #_ #_ #HVW #HTU #IHV #IHT
+  elim (Ha12 … Hn1) -a1 #n2 #Hn2 #Hn12
+  /3 width=11 by cnv_appl_ge/
+| /3 width=3 by cnv_cast/
+]
+qed-.
+
+lemma cnv_acle_omega (h) (a):
+      ∀G,L,T. ⦃G,L⦄ ⊢ T ![h,a] → ⦃G,L⦄ ⊢ T ![h,𝛚].
+/3 width=3 by cnv_acle_trans, acle_omega/ qed-.
+
+lemma cnv_acle_one (h) (a) (n):
+      ∀G,L,T. ⦃G,L⦄ ⊢ T ![h,𝟏] → ad a n → ⦃G,L⦄ ⊢ T ![h,a].
+/3 width=3 by cnv_acle_trans, acle_one/ qed-.