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diff --git a/matita/matita/contribs/lambda_delta/basic_2/equivalence/fpcs_aaa.ma b/matita/matita/contribs/lambda_delta/basic_2/equivalence/fpcs_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_2/computation/fprs_aaa.ma".
+include "basic_2/equivalence/fpcs_fpcs.ma".
+
+(* CONTEXT-FREE PARALLEL EQUIVALENCE ON CLOSURES ****************************)
+
+(* Main properties about atomic arity assignment on terms *******************)
+
+theorem aaa_fpcs_mono: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⬌* ⦃L2, T2⦄ →
+                       ∀A1. L1 ⊢ T1 ⁝ A1 → ∀A2. L2 ⊢ T2 ⁝ A2 →
+                       A1 = A2.
+#L1 #L2 #T1 #T2 #H12 #A1 #HT1 #A2 #HT2
+elim (fpcs_inv_fprs … H12) -H12 #L #T #H1 #H2
+lapply (aaa_fprs_conf … HT1 … H1) -L1 -T1 #HT1
+lapply (aaa_fprs_conf … HT2 … H2) -L2 -T2 #HT2
+lapply (aaa_mono … HT1 … HT2) -L -T //
+qed-.