update in static_2 and basic_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
new file mode 100644 (file)
index 0000000..3802cb1
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_tweq.ma
@@ -0,0 +1,105 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_sn_X_lifts_Y_Y (T) (f:rtmap):
+      ∀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-.