update in static_2

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

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_tweq.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_tweq.ma
deleted file mode 100644 (file)
index 45f8a38..0000000
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_tweq.ma
+++ /dev/null
@@ -1,105 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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".
-include "static_2/relocation/lifts_lifts.ma".
-
-(* GENERIC RELOCATION FOR TERMS *********************************************)
-
-(* Properties with sort-irrelevant whd equivalence for terms ****************)
-
-lemma tweq_lifts_sn: liftable2_sn tweq.
-#T1 #T2 #H elim H -T1 -T2
-[ #s1 #s2 #f #X #H >(lifts_inv_sort1 … H) -H
-  /3 width=3 by lifts_sort, tweq_sort, ex2_intro/
-| #i #f #X #H elim (lifts_inv_lref1 … H) -H
-  /3 width=3 by lifts_lref, tweq_lref, ex2_intro/
-| #l #f #X #H >(lifts_inv_gref1 … H) -H
-  /2 width=3 by lifts_gref, tweq_gref, ex2_intro/
-| #p #V1 #V2 #T1 #T2 #_ #IHT #f #X #H
-  elim (lifts_inv_bind1 … H) -H #W1 #U1 #HVW1 #HTU1 #H destruct
-  elim (lifts_total V2 f) #W2 #HVW2
-  elim (true_or_false p) #H destruct
-  [ elim (IHT … HTU1) -T1 [| // ] #U2 #HTU2 #HU12
-  | elim (lifts_total T2 (⫯f)) #U2 #HTU2
-  ]
-  /3 width=4 by tweq_abbr_pos, lifts_bind, ex2_intro/
-| #p #V1 #V2 #T1 #T2 #f #X #H
-  elim (lifts_inv_bind1 … H) -H #W1 #U1 #HVW1 #HTU1 #H destruct
-  elim (lifts_total V2 f) #W2 #HVW2
-  elim (lifts_total T2 (⫯f)) #U2 #HTU2
-  /3 width=3 by lifts_bind, ex2_intro/
-| #V1 #V2 #T1 #T2 #_ #IHT #f #X #H
-  elim (lifts_inv_flat1 … H) -H #W1 #U1 #HVW1 #HTU1 #H destruct
-  elim (lifts_total V2 f) #W2 #HVW2
-  elim (IHT … HTU1) -T1 #U2 #HTU2 #HU12
-  /3 width=4 by lifts_flat, tweq_appl, ex2_intro/
-| #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 #W2 #HVW2 #HW12
-  elim (IHT … HTU1) -T1 #U2 #HTU2 #HU12
-  /3 width=5 by lifts_flat, tweq_cast, ex2_intro/
-]
-qed-.
-
-lemma tweq_lifts_dx: liftable2_dx tweq.
-/3 width=3 by tweq_lifts_sn, liftable2_sn_dx, tweq_sym/ qed-.
-
-lemma tweq_lifts_bi: liftable2_bi tweq.
-/3 width=6 by tweq_lifts_sn, liftable2_sn_bi/ qed-.
-
-(* Inversion lemmas with sort-irrelevant whd equivalence for terms **********)
-
-lemma tweq_inv_lifts_bi: deliftable2_bi tweq.
-#U1 #U2 #H elim H -U1 -U2
-[ #s1 #s2 #f #X1 #H1 #X2 #H2
-  >(lifts_inv_sort2 … H1) -H1 >(lifts_inv_sort2 … H2) -H2
-  /1 width=1 by tweq_sort/
-| #j #f #X1 #H1 #X2 #H2
-  elim (lifts_inv_lref2 … H1) -H1 #i1 #Hj1 #H destruct
-  elim (lifts_inv_lref2 … H2) -H2 #i2 #Hj2 #H destruct
-  <(at_inj … Hj2 … Hj1) -j -f -i1
-  /1 width=1 by tweq_lref/
-| #l #f #X1 #H1 #X2 #H2
-  >(lifts_inv_gref2 … H1) -H1 >(lifts_inv_gref2 … H2) -H2
-  /1 width=1 by tweq_gref/
-| #p #W1 #W2 #U1 #U2 #_ #IH #f #X1 #H1 #X2 #H2
-  elim (lifts_inv_bind2 … H1) -H1 #V1 #T1 #_ #HTU1 #H destruct -W1
-  elim (lifts_inv_bind2 … H2) -H2 #V2 #T2 #_ #HTU2 #H destruct -W2
-  elim (true_or_false p) #H destruct
-  [ /3 width=3 by tweq_abbr_pos/
-  | /1 width=1 by tweq_abbr_neg/
-  ]
-| #p #W1 #W2 #U1 #U2 #f #X1 #H1 #X2 #H2
-  elim (lifts_inv_bind2 … H1) -H1 #V1 #T1 #_ #_ #H destruct -W1 -U1
-  elim (lifts_inv_bind2 … H2) -H2 #V2 #T2 #_ #_ #H destruct -W2 -U2
-  /1 width=1 by tweq_abst/
-| #W1 #W2 #U1 #U2 #_ #IH #f #X1 #H1 #X2 #H2
-  elim (lifts_inv_flat2 … H1) -H1 #V1 #T1 #_ #HTU1 #H destruct -W1
-  elim (lifts_inv_flat2 … H2) -H2 #V2 #T2 #_ #HTU2 #H destruct -W2
-  /3 width=3 by tweq_appl/
-| #W1 #W2 #U1 #U2 #_ #_ #IHW #IHU #f #X1 #H1 #X2 #H2
-  elim (lifts_inv_flat2 … H1) -H1 #V1 #T1 #HVW1 #HTU1 #H destruct
-  elim (lifts_inv_flat2 … H2) -H2 #V2 #T2 #HVW2 #HTU2 #H destruct
-  /3 width=3 by tweq_cast/
-]
-qed-.
-
-lemma tweq_inv_abbr_pos_x_lifts_y_y (T) (f):
-      ∀V,U. +ⓓV.U ≅ T → ⇧*[f]T ≘ U → ⊥.
-@(f_ind … tw) #n #IH #T #Hn #f #V #U #H1 #H2 destruct
-elim (tweq_inv_abbr_pos_sn … H1) -H1 #X1 #X2 #HX2 #H destruct -V
-elim (lifts_inv_bind1 … H2) -H2 #Y1 #Y2 #_ #HXY2 #H destruct
-/2 width=7 by/
-qed-.