update for the article

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / relocation / lifts_tdeq.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_tdeq.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_tdeq.ma
deleted file mode 100644 (file)
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--- a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_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".
-include "static_2/relocation/lifts_lifts.ma".
-
-(* GENERIC RELOCATION FOR TERMS *********************************************)
-
-(* Properties with sort-irrelevant equivalence for terms ********************)
-
-lemma tdeq_lifts_sn: liftable2_sn tdeq.
-#T1 #T2 #H elim H -T1 -T2 [||| * ]
-[ #s1 #s2 #f #X #H >(lifts_inv_sort1 … H) -H
-  /3 width=3 by lifts_sort, tdeq_sort, ex2_intro/
-| #i #f #X #H elim (lifts_inv_lref1 … H) -H
-  /3 width=3 by lifts_lref, tdeq_lref, ex2_intro/
-| #l #f #X #H >(lifts_inv_gref1 … H) -H
-  /2 width=3 by lifts_gref, tdeq_gref, ex2_intro/
-| #p #I #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT #f #X #H elim (lifts_inv_bind1 … H) -H
-  #W1 #U1 #HVW1 #HTU1 #H destruct
-  elim (IHV … HVW1) -V1 elim (IHT … HTU1) -T1
-  /3 width=5 by lifts_bind, tdeq_pair, ex2_intro/
-| #I #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT #f #X #H elim (lifts_inv_flat1 … H) -H
-  #W1 #U1 #HVW1 #HTU1 #H destruct
-  elim (IHV … HVW1) -V1 elim (IHT … HTU1) -T1
-  /3 width=5 by lifts_flat, tdeq_pair, ex2_intro/
-]
-qed-.
-
-lemma tdeq_lifts_dx: liftable2_dx tdeq.
-/3 width=3 by tdeq_lifts_sn, liftable2_sn_dx, tdeq_sym/ qed-.
-
-lemma tdeq_lifts_bi: liftable2_bi tdeq.
-/3 width=6 by tdeq_lifts_sn, liftable2_sn_bi/ qed-.
-
-(* Inversion lemmas with sort-irrelevant equivalence for terms **************)
-
-lemma tdeq_inv_lifts_sn: deliftable2_sn tdeq.
-#U1 #U2 #H elim H -U1 -U2 [||| * ]
-[ #s1 #s2 #f #X #H >(lifts_inv_sort2 … H) -H
-  /3 width=3 by lifts_sort, tdeq_sort, ex2_intro/
-| #i #f #X #H elim (lifts_inv_lref2 … H) -H
-  /3 width=3 by lifts_lref, tdeq_lref, ex2_intro/
-| #l #f #X #H >(lifts_inv_gref2 … H) -H
-  /2 width=3 by lifts_gref, tdeq_gref, ex2_intro/
-| #p #I #W1 #W2 #U1 #U2 #_ #_ #IHW #IHU #f #X #H elim (lifts_inv_bind2 … H) -H
-  #V1 #T1 #HVW1 #HTU1 #H destruct
-  elim (IHW … HVW1) -W1 elim (IHU … HTU1) -U1
-  /3 width=5 by lifts_bind, tdeq_pair, ex2_intro/
-| #I #W1 #W2 #U1 #U2 #_ #_ #IHW #IHU #f #X #H elim (lifts_inv_flat2 … H) -H
-  #V1 #T1 #HVW1 #HTU1 #H destruct
-  elim (IHW … HVW1) -W1 elim (IHU … HTU1) -U1
-  /3 width=5 by lifts_flat, tdeq_pair, ex2_intro/
-]
-qed-.
-
-lemma tdeq_inv_lifts_dx: deliftable2_dx tdeq.
-/3 width=3 by tdeq_inv_lifts_sn, deliftable2_sn_dx, tdeq_sym/ qed-.
-
-lemma tdeq_inv_lifts_bi: deliftable2_bi tdeq.
-/3 width=6 by tdeq_inv_lifts_sn, deliftable2_sn_bi/ qed-.
-
-lemma tdeq_lifts_inv_pair_sn (I) (f:rtmap):
-                             ∀X,T. ⇧*[f]X ≘ T → ∀V. ②{I}V.T ≛ X → ⊥.
-#I #f #X #T #H elim H -f -X -T
-[ #f #s #V #H
-  elim (tdeq_inv_pair1 … H) -H #X1 #X2 #_ #_ #H destruct
-| #f #i #j #_ #V #H
-  elim (tdeq_inv_pair1 … H) -H #X1 #X2 #_ #_ #H destruct
-| #f #l #V #H
-  elim (tdeq_inv_pair1 … H) -H #X1 #X2 #_ #_ #H destruct
-| #f #p #J #X1 #T1 #X2 #T2 #_ #_ #_ #IH2 #V #H
-  elim (tdeq_inv_pair1 … H) -H #Z1 #Z2 #_ #HZ2 #H destruct
-  /2 width=2 by/
-| #f #J #X1 #T1 #X2 #T2 #_ #_ #_ #IH2 #V #H
-  elim (tdeq_inv_pair1 … H) -H #Z1 #Z2 #_ #HZ2 #H destruct
-  /2 width=2 by/
-]
-qed-.