update for the article

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / syntax / tdeq_tdeq.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/tdeq_tdeq.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/tdeq_tdeq.ma
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--- a/matita/matita/contribs/lambdadelta/static_2/syntax/tdeq_tdeq.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/tdeq.ma".
-
-(* SORT-IRRELEVANT EQUIVALENCE ON TERMS *************************************)
-
-(* Main properties **********************************************************)
-
-theorem tdeq_trans: Transitive … tdeq.
-#T1 #T #H elim H -T1 -T
-[ #s1 #s #X #H
-  elim (tdeq_inv_sort1 … H) -s /2 width=1 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: left_cancellable … tdeq.
-/3 width=3 by tdeq_trans, tdeq_sym/ qed-.
-
-theorem tdeq_canc_dx: right_cancellable … tdeq.
-/3 width=3 by tdeq_trans, tdeq_sym/ qed-.
-
-theorem tdeq_repl: ∀T1,T2. T1 ≛ T2 →
-                   ∀U1. T1 ≛ U1 → ∀U2. T2 ≛ U2 → U1 ≛ U2.
-/3 width=3 by tdeq_canc_sn, tdeq_trans/ qed-.
-
-(* Negated main properies ***************************************************)
-
-theorem tdeq_tdneq_trans: ∀T1,T. T1 ≛ T → ∀T2. (T ≛ T2 → ⊥) → T1 ≛ T2 → ⊥.
-/3 width=3 by tdeq_canc_sn/ qed-.
-
-theorem tdneq_tdeq_canc_dx: ∀T1,T. (T1 ≛ T → ⊥) → ∀T2. T2 ≛ T → T1 ≛ T2 → ⊥.
-/3 width=3 by tdeq_trans/ qed-.