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diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/tweq_tweq.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/tweq_tweq.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/tweq.ma".
+
+(* SORT-IRRELEVANT WHD EQUIVALENCE ON TERMS *********************************)
+
+(* Main properties **********************************************************)
+
+theorem tweq_trans: Transitive … tweq.
+#T1 #T #H elim H -T1 -T
+[ #s1 #s #X #H
+  elim (tweq_inv_sort_sn … H) -s #s2 destruct
+  /2 width=1 by tweq_sort/
+| #i1 #i #H //
+| #l1 #l #H //
+| #p #V1 #V #T1 #T #_ #IHT #X #H
+  elim (tweq_inv_abbr_sn … H) -H #V2 #T2 #HT #H destruct
+  /4 width=1 by tweq_abbr/
+| #p #V1 #V #T1 #T #X #H
+  elim (tweq_inv_abst_sn … H) -H #V2 #T2 #H destruct
+  /2 width=1 by tweq_abst/
+| #V1 #V #T1 #T #_ #IHT #X #H
+  elim (tweq_inv_appl_sn … H) -H #V2 #T2 #HT #H destruct
+  /3 width=1 by tweq_appl/
+| #V1 #V #T1 #T #_ #_ #IHV #IHT #X #H
+  elim (tweq_inv_cast_sn … H) -H #V2 #T2 #HV #HT #H destruct
+  /3 width=1 by tweq_cast/
+]
+qed-.
+
+theorem tweq_canc_sn: left_cancellable … tweq.
+/3 width=3 by tweq_trans, tweq_sym/ qed-.
+
+theorem tweq_canc_dx: right_cancellable … tweq.
+/3 width=3 by tweq_trans, tweq_sym/ qed-.
+
+theorem tweq_repl:
+        ∀T1,T2. T1 ≅ T2 → ∀U1. T1 ≅ U1 → ∀U2. T2 ≅ U2 → U1 ≅ U2.
+/3 width=3 by tweq_canc_sn, tweq_trans/ qed-.