update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / lfeq_fsle.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfeq_fsle.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfeq_fsle.ma
new file mode 100644 (file)
index 0000000..0f80c97
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfeq_fsle.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/lfxs_length.ma".
+include "basic_2/static/lfxs_fsle.ma".
+include "basic_2/static/lfeq.ma".
+
+(* SYNTACTIC EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES *********)
+
+(* Properties with free variables inclusion for restricted closures *********)
+
+lemma lfeq_fsle_comp: lfxs_fsle_compatible ceq.
+#L1 #L2 #T #HL12
+elim (frees_total L1 T)
+/4 width=8 by frees_lfeq_conf, lfxs_fwd_length, lveq_length_eq, sle_refl, ex4_4_intro/
+qed.
+
+(* Forward lemmas with free variables inclusion for restricted closures *****)
+
+lemma lfeq_lfxs_trans: ∀R. lfeq_transitive R →
+                       ∀L1,L,T. L1 ≡[T] L → ∀L2. L ⪤*[R, T] L2 → L1 ⪤*[R, T] L2.
+/4 width=16 by lfeq_fsle_comp, lfxs_trans_fsle, lfxs_trans_next/ qed-.