milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / etc / lpx_sn / llpx_sn_lpx_sn.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/lpx_sn/llpx_sn_lpx_sn.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/lpx_sn/llpx_sn_lpx_sn.etc
new file mode 100644 (file)
index 0000000..21a88ca
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2A/etc/lpx_sn/llpx_sn_lpx_sn.etc
@@ -0,0 +1,38 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_ldrop.ma".
+include "basic_2/substitution/llpx_sn.ma".
+
+(* LAZY SN POINTWISE EXTENSION OF A CONTEXT-SENSITIVE REALTION FOR TERMS ****)
+
+(* Properties on pointwise extensions ***************************************)
+
+lemma lpx_sn_llpx_sn: ∀R. (∀I,L. reflexive … (R I L)) →
+                      ∀T,L1,L2,d. lpx_sn R L1 L2 → llpx_sn R d T L1 L2.
+#R #HR #T #L1 @(f2_ind … rfw … L1 T) -L1 -T
+#n #IH #L1 * *
+[ -HR -IH /4 width=2 by lpx_sn_fwd_length, llpx_sn_sort/
+| -HR #i elim (lt_or_ge i (|L1|))
+  [2: -IH /4 width=4 by lpx_sn_fwd_length, llpx_sn_free, le_repl_sn_conf_aux/ ]
+  #Hi #Hn #L2 #d elim (ylt_split i d) 
+  [ -n /3 width=2 by llpx_sn_skip, lpx_sn_fwd_length/ ]
+  #Hdi #HL12 elim (ldrop_O1_lt (Ⓕ) L1 i) //
+  #I #K1 #V1 #HLK1 elim (lpx_sn_ldrop_conf … HL12 … HLK1) -HL12
+  /4 width=9 by llpx_sn_lref, ldrop_fwd_rfw/
+| -HR -IH /4 width=2 by lpx_sn_fwd_length, llpx_sn_gref/
+| /4 width=1 by llpx_sn_bind, lpx_sn_pair/
+| -HR /3 width=1 by llpx_sn_flat/
+]
+qed.