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diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/tdeq_tdeq.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/tdeq_tdeq.ma
new file mode 100644
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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/tdeq.ma".
+
+(* DEGREE-BASED EQUIVALENCE ON TERMS ****************************************)
+
+(* Main properties **********************************************************)
+
+theorem tdeq_trans: ∀h,o. Transitive … (tdeq h o).
+#h #o #T1 #T #H elim H -T1 -T
+[ #s1 #s #d #Hs1 #Hs #X #H
+  elim (tdeq_inv_sort1_deg … H … Hs) -s /2 width=3 by tdeq_sort/
+| #i1 #i #H <(tdeq_inv_lref1 … H) -H //
+| #l1 #l #H <(tdeq_inv_gref1 … H) -H //
+| #I #V1 #V #T1 #T #_ #_ #IHV #IHT #X #H
+  elim (tdeq_inv_pair1 … H) -H /3 width=1 by tdeq_pair/
+]
+qed-.
+
+theorem tdeq_canc_sn: ∀h,o. left_cancellable … (tdeq h o).
+/3 width=3 by tdeq_trans, tdeq_sym/ qed-.
+
+theorem tdeq_canc_dx: ∀h,o. right_cancellable … (tdeq h o).
+/3 width=3 by tdeq_trans, tdeq_sym/ qed-.
+
+theorem tdeq_repl: ∀h,o,T1,T2. T1 ≛[h, o] T2 →
+                   ∀U1. T1 ≛[h, o] U1 → ∀U2. T2 ≛[h, o] U2 → U1 ≛[h, o] U2.
+/3 width=3 by tdeq_canc_sn, tdeq_trans/ qed-.
+
+(* Negated main properies ***************************************************)
+
+theorem tdeq_tdneq_trans: ∀h,o,T1,T. T1 ≛[h, o] T → ∀T2. (T ≛[h, o] T2 → ⊥) →
+                          T1 ≛[h, o] T2 → ⊥.
+/3 width=3 by tdeq_canc_sn/ qed-.
+
+theorem tdneq_tdeq_canc_dx: ∀h,o,T1,T. (T1 ≛[h, o] T → ⊥) → ∀T2. T2 ≛[h, o] T →
+                            T1 ≛[h, o] T2 → ⊥.
+/3 width=3 by tdeq_trans/ qed-.