- free variables innclusion (fle) encapsulates some complexity

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/fle_fqup.ma b/matita/matita/contribs/lambdadelta/basic_2/static/fle_fqup.ma
new file mode 100644 (file)
index 0000000..23e4603
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/fle_fqup.ma
@@ -0,0 +1,48 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_fqup.ma".
+include "basic_2/static/fle.ma".
+
+(* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
+
+(* Advanced properties ******************************************************)
+
+lemma fle_refl: bi_reflexive … fle.
+#L #T elim (frees_total L T) /2 width=5 by sle_refl, ex3_2_intro/
+qed.
+
+lemma fle_bind_sn: ∀p,I,L,V,T. ⦃L, V⦄ ⊆ ⦃L, ⓑ{p,I}V.T⦄.
+#p #I #L #V #T
+elim (frees_total L V) #f1 #Hf1
+elim (frees_total (L.ⓑ{I}V) T) #f2 #Hf2
+elim (sor_isfin_ex f1 (⫱f2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #f #Hf #_
+/3 width=6 by frees_bind, sor_inv_sle_sn, ex3_2_intro/
+qed.
+
+lemma fle_flat_sn: ∀I,L,V,T. ⦃L, V⦄ ⊆ ⦃L, ⓕ{I}V.T⦄.
+#I #L #V #T
+elim (frees_total L V) #f1 #Hf1
+elim (frees_total L T) #f2 #Hf2
+elim (sor_isfin_ex f1 f2) /2 width=3 by frees_fwd_isfin/ #f #Hf #_
+/3 width=6 by frees_flat, sor_inv_sle_sn, ex3_2_intro/
+qed.
+
+lemma fle_flat_dx: ∀I,L,V,T. ⦃L, T⦄ ⊆ ⦃L, ⓕ{I}V.T⦄.
+#I #L #V #T
+elim (frees_total L V) #f1 #Hf1
+elim (frees_total L T) #f2 #Hf2
+elim (sor_isfin_ex f1 f2) /2 width=3 by frees_fwd_isfin/ #f #Hf #_
+/3 width=6 by frees_flat, sor_inv_sle_dx, ex3_2_intro/
+qed.