update in ground_2 and basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/fid/fle_fid.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/fid/fle_fid.etc
new file mode 100644 (file)
index 0000000..310b1d8
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc/fid/fle_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/static/fid.ma".
+include "basic_2/static/fle_fqup.ma".
+
+(* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
+
+(* Properties with free variables identity for restricted closures **********)
+
+lemma fle_fid_sn: ∀L1,L2. |L1| = |L2| →
+                  ∀T1,T2. 𝐈⦃L1, T1⦄ → ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄.
+#L1 #L2 #HL #T1 #T2 #HT1
+elim (frees_total L1 T1) #f1 #Hf1
+elim (frees_total L2 T2) #f2 #Hf2
+/4 width=8 by lveq_length_eq, sle_isid_sn, ex4_4_intro/
+qed.
+
+(* Inversion lemmas with free variables identity for restricted closures ****)
+
+lemma fle_inv_fid_dx: ∀L1,L2. |L1| = |L2| →
+                      ∀T1,T2. ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄ →  𝐈⦃L2, T2⦄ → 𝐈⦃L1, T1⦄.
+#L1 #L2 #HL #T1 #T2
+* #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HL12 #Hf12 #HT2 #g1 #Hg1
+elim (lveq_inj_length … HL12) // -HL -HL12 #H1 #H2 destruct
+lapply (frees_mono … Hf1 … Hg1) -Hg1 #Hfg1
+/4 width=5 by sle_inv_isid_dx, isid_eq_repl_back/
+qed-.