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diff --git a/matita/matita/contribs/lambdadelta/basic_2A/equivalence/cpcs_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2A/equivalence/cpcs_aaa.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_2A/computation/cpxs_aaa.ma".
+include "basic_2A/equivalence/cpcs_cpcs.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
+
+(* Main inversion lemmas about atomic arity assignment on terms *************)
+
+theorem cpcs_aaa_mono: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 →
+                       ∀A1. ⦃G, L⦄ ⊢ T1 ⁝ A1 → ∀A2. ⦃G, L⦄ ⊢ T2 ⁝ A2 →
+                       A1 = A2.
+#G #L #T1 #T2 #HT12 #A1 #HA1 #A2 #HA2
+elim (cpcs_inv_cprs … HT12) -HT12 #T #HT1 #HT2
+lapply (cprs_aaa_conf … HA1 … HT1) -T1 #HA1
+lapply (cprs_aaa_conf … HA2 … HT2) -T2 #HA2
+lapply (aaa_mono … HA1 … HA2) -L -T //
+qed-.