- free variables innclusion (fle) encapsulates some complexity

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/fle_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/static/fle_drops.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/frees_drops.ma".
+include "basic_2/static/fle.ma".
+
+(* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
+
+(* Advanced properties ******************************************************)
+
+lemma fle_bind_dx: ∀T,U. ⬆*[1] T ≡ U →
+                   ∀p,I,L,V. ⦃L, T⦄ ⊆ ⦃L, ⓑ{p,I}V.U⦄.
+#T #U #HTU #p #I #L #V
+elim (frees_total L V) #f1 #Hf1
+elim (frees_total L T) #f2 #Hf2
+elim (sor_isfin_ex f1 f2) /3 width=3 by frees_fwd_isfin, isfin_tl/ #f #H #_
+lapply (sor_inv_sle_dx … H) #Hf0
+>(tl_push_rew f) in H; #Hf
+/6 width=6 by frees_lifts_SO, frees_bind, drops_refl, drops_drop, ex3_2_intro/
+qed.