+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||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-.