milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / lpx_sn / lpx_sn_lpx_sn.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lpx_sn/lpx_sn_lpx_sn.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lpx_sn/lpx_sn_lpx_sn.etc
deleted file mode 100644 (file)
index bd72cf6..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lpx_sn/lpx_sn_lpx_sn.etc
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-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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/lpx_sn.ma".
-
-(* SN POINTWISE EXTENSION OF A CONTEXT-SENSITIVE REALTION FOR TERMS *********)
-
-definition lpx_sn_confluent: relation (relation3 lenv term term) ≝ λR1,R2.
-                             ∀L0,T0,T1. R1 L0 T0 T1 → ∀T2. R2 L0 T0 T2 →
-                             ∀L1. lpx_sn (λ_.R1) L0 L1 → ∀L2. lpx_sn (λ_.R2) L0 L2 →
-                             ∃∃T. R2 L1 T1 T & R1 L2 T2 T.
-
-definition lpx_sn_transitive: relation (relation3 lenv term term) ≝ λR1,R2.
-                              ∀L1,T1,T. R1 L1 T1 T → ∀L2. lpx_sn (λ_.R1) L1 L2 →
-                              ∀T2. R2 L2 T T2 → R1 L1 T1 T2.
-
-(* Main properties **********************************************************)
-
-theorem lpx_sn_trans: ∀R. lpx_sn_transitive R R → Transitive … (lpx_sn (λ_.R)).
-#R #HR #L1 #L #H elim H -L1 -L //
-#I #L1 #L #V1 #V #HL1 #HV1 #IHL1 #X #H
-elim (lpx_sn_inv_pair1 … H) -H #L2 #V2 #HL2 #HV2 #H destruct /3 width=5 by lpx_sn_pair/
-qed-.
-
-theorem lpx_sn_conf: ∀R1,R2. lpx_sn_confluent R1 R2 →
-                     confluent2 … (lpx_sn (λ_.R1)) (lpx_sn (λ_.R2)).
-#R1 #R2 #HR12 #L0 @(f_ind … length … L0) -L0 #n #IH *
-[ #_ #X1 #H1 #X2 #H2 -n
-  >(lpx_sn_inv_atom1 … H1) -X1
-  >(lpx_sn_inv_atom1 … H2) -X2 /2 width=3 by lpx_sn_atom, ex2_intro/
-| #L0 #I #V0 #Hn #X1 #H1 #X2 #H2 destruct
-  elim (lpx_sn_inv_pair1 … H1) -H1 #L1 #V1 #HL01 #HV01 #H destruct
-  elim (lpx_sn_inv_pair1 … H2) -H2 #L2 #V2 #HL02 #HV02 #H destruct
-  elim (IH … HL01 … HL02) -IH normalize // #L #HL1 #HL2
-  elim (HR12 … HV01 … HV02 … HL01 … HL02) -L0 -V0 /3 width=5 by lpx_sn_pair, ex2_intro/
-]
-qed-.