- degree-based equivalene for terms

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lpx_sn/llpx_sn_tc.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lpx_sn/llpx_sn_tc.etc
new file mode 100644 (file)
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--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lpx_sn/llpx_sn_tc.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/substitution/llpx_sn_ldrop.ma".
+
+(* LAZY SN POINTWISE EXTENSION OF A CONTEXT-SENSITIVE REALTION FOR TERMS ****)
+
+(* Properties about transitive closure **************************************)
+
+lemma llpx_sn_TC_pair_dx: ∀R. (∀I,L. reflexive … (R I L)) →
+                          ∀I,L,V1,V2,T. LTC … (R I) L V1 V2 →
+                          LTC … (llpx_sn R 0) T (L.ⓑ{I}V1) (L.ⓑ{I}V2).
+#R #HR #I #L #V1 #V2 #T #H @(TC_star_ind … V2 H) -V2
+/4 width=9 by llpx_sn_bind_repl_O, llpx_sn_refl, step, inj/
+qed.