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diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/toeq_toeq.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/toeq_toeq.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/toeq.ma".
+
+(* SORT-IRRELEVANT OUTER EQUIVALENCE FOR TERMS ******************************)
+
+(* Main properties **********************************************************)
+
+(* Basic_1: was: iso_trans *)
+(* Basic_2A1: was: tsts_trans *)
+theorem toeq_trans: Transitive … toeq.
+#T1 #T * -T1 -T
+[ #s1 #s #X #H
+  elim (toeq_inv_sort1 … H) -s /2 width=1 by toeq_sort/
+| #i1 #i #H <(toeq_inv_lref1 … H) -H //
+| #l1 #l #H <(toeq_inv_gref1 … H) -H //
+| #I #V1 #V #T1 #T #X #H
+  elim (toeq_inv_pair1 … H) -H #V2 #T2 #H destruct //
+]
+qed-.
+
+(* Basic_2A1: was: tsts_canc_sn *)
+theorem toeq_canc_sn: left_cancellable … toeq.
+/3 width=3 by toeq_trans, toeq_sym/ qed-.
+
+(* Basic_2A1: was: tsts_canc_dx *)
+theorem toeq_canc_dx: right_cancellable … toeq.
+/3 width=3 by toeq_trans, toeq_sym/ qed-.