renaming in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / i_static / rexs_rexs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/i_static/rexs_rexs.ma b/matita/matita/contribs/lambdadelta/basic_2/i_static/rexs_rexs.ma
new file mode 100644 (file)
index 0000000..7b0b83d
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/i_static/rexs_rexs.ma
@@ -0,0 +1,33 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/static/rex_fsle.ma".
+include "basic_2/i_static/rexs.ma".
+
+(* ITERATED EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ***)
+
+(* Advanced properties ******************************************************)
+
+lemma rexs_sym: ∀R. rex_fsge_compatible R →
+                (∀L1,L2,T1,T2. R L1 T1 T2 → R L2 T2 T1) →
+                ∀T. symmetric … (rexs R T).
+#R #H1R #H2R #T #L1 #L2 #H elim H -L2
+/4 width=3 by rex_sym, rexs_step_sn, inj/
+qed-.
+
+(* Main properties **********************************************************)
+
+theorem rexs_trans: ∀R,T. Transitive … (rexs R T).
+#R #T #L1 #L #HL1 #L2 #HL2 @(trans_TC … HL1 HL2) (**) (* auto fails *)
+qed-.