update in lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / multiple / llpx_sn_lpx_sn.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/multiple/llpx_sn_lpx_sn.ma b/matita/matita/contribs/lambdadelta/basic_2A/multiple/llpx_sn_lpx_sn.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2A/multiple/llpx_sn_lpx_sn.ma
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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_2A/substitution/lpx_sn_drop.ma".
+include "basic_2A/multiple/llpx_sn.ma".
+
+(* LAZY SN POINTWISE EXTENSION OF A CONTEXT-SENSITIVE REALTION FOR TERMS ****)
+
+(* Properties on pointwise extensions ***************************************)
+
+lemma lpx_sn_llpx_sn: ∀R. (∀L. reflexive … (R L)) →
+                      ∀T,L1,L2,l. lpx_sn R L1 L2 → llpx_sn R l T L1 L2.
+#R #HR #T #L1 @(f2_ind … rfw … L1 T) -L1 -T
+#x #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 #Hx #L2 #l elim (ylt_split i l) 
+  [ -x /3 width=2 by llpx_sn_skip, lpx_sn_fwd_length/ ]
+  #Hli #HL12 elim (drop_O1_lt (Ⓕ) L1 i) //
+  #I #K1 #V1 #HLK1 elim (lpx_sn_drop_conf … HL12 … HLK1) -HL12
+  /4 width=9 by llpx_sn_lref, drop_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.