update in ground_2 static_2 basic_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / etc / tueq / lifts_tueq.etc

diff --git a/matita/matita/contribs/lambdadelta/static_2/etc/tueq/lifts_tueq.etc b/matita/matita/contribs/lambdadelta/static_2/etc/tueq/lifts_tueq.etc
new file mode 100644 (file)
index 0000000..a9805a9
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/static_2/etc/tueq/lifts_tueq.etc
@@ -0,0 +1,80 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/tueq.ma".
+include "static_2/relocation/lifts_lifts.ma".
+
+(* GENERIC RELOCATION FOR TERMS *********************************************)
+
+(* Properties with tail sort-irrelevant equivalence for terms ***************)
+
+lemma tueq_lifts_sn: liftable2_sn tueq.
+#T1 #T2 #H elim H -T1 -T2
+[ #s1 #s2 #f #X #H >(lifts_inv_sort1 … H) -H
+  /3 width=3 by lifts_sort, tueq_sort, ex2_intro/
+| #i #f #X #H elim (lifts_inv_lref1 … H) -H
+  /3 width=3 by lifts_lref, tueq_lref, ex2_intro/
+| #l #f #X #H >(lifts_inv_gref1 … H) -H
+  /2 width=3 by lifts_gref, tueq_gref, ex2_intro/
+| #p #I #V #T1 #T2 #_ #IHT #f #X #H elim (lifts_inv_bind1 … H) -H
+  #W1 #U1 #HVW1 #HTU1 #H destruct
+  elim (IHT … HTU1) -T1
+  /3 width=3 by lifts_bind, tueq_bind, ex2_intro/
+| #V #T1 #T2 #_ #IHT #f #X #H elim (lifts_inv_flat1 … H) -H
+  #W1 #U1 #HVW1 #HTU1 #H destruct
+  elim (IHT … HTU1) -T1
+  /3 width=3 by lifts_flat, tueq_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 elim (IHT … HTU1) -T1
+  /3 width=5 by lifts_flat, tueq_cast, ex2_intro/  
+]
+qed-.
+
+lemma tueq_lifts_dx: liftable2_dx tueq.
+/3 width=3 by tueq_lifts_sn, liftable2_sn_dx, tueq_sym/ qed-.
+
+lemma tueq_lifts_bi: liftable2_bi tueq.
+/3 width=6 by tueq_lifts_sn, liftable2_sn_bi/ qed-.
+
+(* Inversion lemmas with tail sort-irrelevant equivalence for terms *********)
+
+lemma tueq_inv_lifts_sn: deliftable2_sn tueq.
+#U1 #U2 #H elim H -U1 -U2
+[ #s1 #s2 #f #X #H >(lifts_inv_sort2 … H) -H
+  /3 width=3 by lifts_sort, tueq_sort, ex2_intro/
+| #i #f #X #H elim (lifts_inv_lref2 … H) -H
+  /3 width=3 by lifts_lref, tueq_lref, ex2_intro/
+| #l #f #X #H >(lifts_inv_gref2 … H) -H
+  /2 width=3 by lifts_gref, tueq_gref, ex2_intro/
+| #p #I #W #U1 #U2 #_ #IHU #f #X #H elim (lifts_inv_bind2 … H) -H
+  #V1 #T1 #HVW1 #HTU1 #H destruct
+  elim (IHU … HTU1) -U1
+  /3 width=3 by lifts_bind, tueq_bind, ex2_intro/
+| #W #U1 #U2 #_ #IHU #f #X #H elim (lifts_inv_flat2 … H) -H
+  #V1 #T1 #HVW1 #HTU1 #H destruct
+  elim (IHU … HTU1) -U1
+  /3 width=3 by lifts_flat, tueq_appl, ex2_intro/
+| #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, tueq_cast, ex2_intro/
+]
+qed-.
+
+lemma tueq_inv_lifts_dx: deliftable2_dx tueq.
+/3 width=3 by tueq_inv_lifts_sn, deliftable2_sn_dx, tueq_sym/ qed-.
+
+lemma tueq_inv_lifts_bi: deliftable2_bi tueq.
+/3 width=6 by tueq_inv_lifts_sn, deliftable2_sn_bi/ qed-.