update in ground_2 and basic_2 (partial commit)

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / relocation / lex_lex.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lex_lex.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lex_lex.ma
new file mode 100644 (file)
index 0000000..e8b30f2
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lex_lex.ma
@@ -0,0 +1,52 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "basic_2/relocation/lex.ma".
+
+(* GENERIC ENTRYWISE EXTENSION OF CONTEXT-SENSITIVE REALTIONS FOR TERMS *****)
+
+(* Main properties **********************************************************)
+
+(* Basic_2A1: was: lpx_sn_trans *)
+theorem lex_trans (R): lex_transitive R R → Transitive … (lex R).
+#R #HR #L1 #L #H @(lex_ind … H) -L1 -L //
+[ #I #K1 #K #HK1 #IH #Y #H
+  elim (lex_inv_unit_sn … H) -H #K2 #K2 #H destruct
+  /3 width=1 by lex_unit/
+| #I #K1 #L #V1 #V #HK1 #IH #HV1 #X #H
+  elim (lex_inv_pair_sn … H) -H #K2 #V2 #HK2 #HV2 #H destruct
+  /3 width=5 by lex_pair/
+]
+qed-.
+
+(* Basic_2A1: was: lpx_sn_conf *)
+theorem lex_conf (R1) (R2): lex_confluent R1 R2 → confluent2 … (lex R1) (lex R2).
+#R1 #R2 #HR12 #L0 elim L0 -L0 [| #K0 * ]
+[ #Y1 #H1 #Y2 #H2
+  >(lex_inv_atom_sn … H1) -Y1
+  >(lex_inv_atom_sn … H2) -Y2
+  /2 width=3 by lex_atom, ex2_intro/
+| #I #IH #Y1 #H1 #Y2 #H2
+  elim (lex_inv_unit_sn … H1) -H1 #K1 #HK01 #H destruct
+  elim (lex_inv_unit_sn … H2) -H2 #K2 #HK02 #H destruct
+  elim (IH … HK01 … HK02) -K0 #K #HK1 #HK2
+  /3 width=3 by lex_unit, ex2_intro/
+| #I #V0 #IH #Y1 #H1 #Y2 #H2
+  elim (lex_inv_pair_sn … H1) -H1 #K1 #V1 #HK01 #HV01 #H destruct
+  elim (lex_inv_pair_sn … H2) -H2 #K2 #V2 #HK02 #HV02 #H destruct
+  elim (HR12 … HV01 … HV02 … HK01 … HK02) -V0 #V #HV1 #HV2
+  elim (IH … HK01 … HK02) -K0 #K #HK1 #HK2
+  /3 width=5 by lex_pair, ex2_intro/
+]
+qed-.