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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_simple_toeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_simple_toeq.ma
new file mode 100644
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+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_simple_toeq.ma
@@ -0,0 +1,49 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/toeq_simple.ma".
+include "static_2/syntax/toeq_toeq.ma".
+include "basic_2/rt_transition/cpx_simple.ma".
+include "basic_2/rt_computation/cpxs.ma".
+include "basic_2/rt_computation/csx_csx.ma".
+
+(* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
+
+(* Properties with outer equivalence for terms ******************************)
+
+(* Basic_1: was just: sn3_appl_appl *)
+(* Basic_2A1: was: csx_appl_simple_tsts *)
+lemma csx_appl_simple_toeq (h) (G) (L):
+      ∀V. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ → ∀T1. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ →
+      (∀T2. ⦃G,L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ⩳ T2 → ⊥) → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV.T2⦄) →
+      𝐒⦃T1⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV.T1⦄.
+#h #G #L #V #H @(csx_ind … H) -V
+#V #_ #IHV #T1 #H @(csx_ind … H) -T1
+#T1 #H1T1 #IHT1 #H2T1 #H3T1
+@csx_intro #X #HL #H
+elim (cpx_inv_appl1_simple … HL) -HL //
+#V0 #T0 #HLV0 #HLT10 #H0 destruct
+elim (tdneq_inv_pair … H) -H
+[ #H elim H -H //
+| -IHT1 #HV0
+  @(csx_cpx_trans … (ⓐV0.T1)) /2 width=1 by cpx_flat/ -HLT10
+  @IHV -IHV /4 width=3 by csx_cpx_trans, cpx_pair_sn/
+| -IHV -H1T1 #H1T10
+  @(csx_cpx_trans … (ⓐV.T0)) /2 width=1 by cpx_flat/ -HLV0
+  elim (toeq_dec T1 T0) #H2T10
+  [ @IHT1 -IHT1 /4 width=5 by cpxs_strap2, cpxs_strap1, toeq_canc_sn, simple_toeq_repl_dx/
+  | -IHT1 -H3T1 -H1T10 /3 width=1 by cpx_cpxs/
+  ]
+]
+qed.