matita/matita/contribs/lambdadelta/basic_2/static/fle_fqup.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "basic_2/static/frees_fqup.ma".
  16 include "basic_2/static/fle.ma".
  17
  18 (* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 lemma fle_refl: bi_reflexive … fle.
  23 #L #T elim (frees_total L T) /2 width=5 by sle_refl, ex3_2_intro/
  24 qed.
  25
  26 lemma fle_bind_sn: ∀p,I,L,V,T. ⦃L, V⦄ ⊆ ⦃L, ⓑ{p,I}V.T⦄.
  27 #p #I #L #V #T
  28 elim (frees_total L V) #f1 #Hf1
  29 elim (frees_total (L.ⓑ{I}V) T) #f2 #Hf2
  30 elim (sor_isfin_ex f1 (⫱f2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #f #Hf #_
  31 /3 width=6 by frees_bind, sor_inv_sle_sn, ex3_2_intro/
  32 qed.
  33
  34 lemma fle_flat_sn: ∀I,L,V,T. ⦃L, V⦄ ⊆ ⦃L, ⓕ{I}V.T⦄.
  35 #I #L #V #T
  36 elim (frees_total L V) #f1 #Hf1
  37 elim (frees_total L T) #f2 #Hf2
  38 elim (sor_isfin_ex f1 f2) /2 width=3 by frees_fwd_isfin/ #f #Hf #_
  39 /3 width=6 by frees_flat, sor_inv_sle_sn, ex3_2_intro/
  40 qed.
  41
  42 lemma fle_flat_dx: ∀I,L,V,T. ⦃L, T⦄ ⊆ ⦃L, ⓕ{I}V.T⦄.
  43 #I #L #V #T
  44 elim (frees_total L V) #f1 #Hf1
  45 elim (frees_total L T) #f2 #Hf2
  46 elim (sor_isfin_ex f1 f2) /2 width=3 by frees_fwd_isfin/ #f #Hf #_
  47 /3 width=6 by frees_flat, sor_inv_sle_dx, ex3_2_intro/
  48 qed.