update in ground_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / lsubv_lsubv.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubv_lsubv.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubv_lsubv.ma
new file mode 100644 (file)
index 0000000..d416b5f
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubv_lsubv.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/dynamic/lsubv_cnv.ma".
+
+(* LOCAL ENVIRONMENT REFINEMENT FOR NATIVE VALIDITY *************************)
+
+(* Main properties **********************************************************)
+
+(* Note: not valid in Basic_2A1 *)
+theorem lsubv_trans (a) (h) (G): Transitive … (lsubv a h G).
+#a #h #G #L1 #L #H elim H -L1 -L //
+[ #I #K1 #K #HK1 #IH #Y #H
+  elim (lsubv_inv_bind_sn … H) -H *
+  [ #K2 #HK2 #H destruct /3 width=1 by lsubv_bind/
+  | #K2 #W #V #HWV #HK2 #H1 #H2 destruct /3 width=3 by lsubv_cnv_trans, lsubv_beta/
+  ]
+| #K1 #K #W #V #HWV #_ #IH #Y #H
+  elim (lsubv_inv_abst_sn … H) -H
+  #K2 #HK2 #H1 destruct /3 width=1 by lsubv_beta/
+]
+qed-.