update in ground_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc / fid / lfeq_fid.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/fid/lfeq_fid.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/fid/lfeq_fid.etc
new file mode 100644 (file)
index 0000000..c735f95
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc/fid/lfeq_fid.etc
@@ -0,0 +1,39 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/relocation/lexs_length.ma".
+include "basic_2/static/frees_fqup.ma".
+include "basic_2/static/fid.ma".
+include "basic_2/static/lfeq.ma".
+
+(* SYNTACTIC EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES *********)
+
+(* properties with free variables identity for restricted closures **********)
+
+lemma fid_lfeq: ∀L1,L2. |L1| = |L2| → ∀T. 𝐈⦃L1, T⦄ → L1 ≡[T] L2.
+#L1 #L2 #HL1 #T #HT
+elim (frees_total L1 T) #f #Hf
+/4 width=3 by lexs_length_isid, ex2_intro/
+qed.
+
+(* Advanced properties with free variables identity for restricted closures *)
+
+lemma fid_length: ∀L1,L2. |L1| = |L2| → ∀T. 𝐈⦃L1, T⦄ → 𝐈⦃L2, T⦄.
+#L1 #L2 #HL #T #HT #g #Hg
+elim (frees_total L1 T) #f #Hf
+lapply (frees_mono f … Hg) -Hg
+[ /3 width=4 by fid_lfeq, frees_lfeq_conf/
+| /3 width=3 by isid_eq_repl_back/
+]
+qed-. 
\ No newline at end of file