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_dx_sn: ∀L1,L2,V1,V2. ⦃L1, V1⦄ ⊆ ⦃L2, V2⦄ →
  27                       ∀p,I,T2. ⦃L1, V1⦄ ⊆ ⦃L2, ⓑ{p,I}V2.T2⦄.
  28 #L1 #L2 #V1 #V2 * -L1 #f1 #g1 #L1 #n #Hf1 #Hg1 #HL12 #Hfg1 #p #I #T2
  29 elim (frees_total (L2.ⓧ) T2) #g2 #Hg2
  30 elim (sor_isfin_ex g1 (⫱g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
  31 /4 width=8 by fle_intro, frees_bind_void, sor_inv_sle_sn, sle_trans/
  32 qed.
  33 (*
  34 lemma fle_bind_dx_dx: ∀L1,L2,T1,T2. ⦃L1.ⓧ, T1⦄ ⊆ ⦃L2.ⓧ, T2⦄ →
  35                       ∀p,I,V2. ⦃L1.ⓧ, T1⦄ ⊆ ⦃L2, ⓑ{p,I}V2.T2⦄.
  36 #L1 #L2 #T1 #T2 * -L1 #f2 #g2 #L1 #n #Hf2 #Hg2 #HL12 #Hfg2 #p #I #V2
  37 elim (frees_total L2 V2) #g1 #Hg1
  38 elim (sor_isfin_ex g1 (⫱g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
  39 @(fle_intro … g … Hf2) /2 width=5 by frees_bind_void/
  40 @(sle_trans … Hfg1) @(sor_inv_sle_sn … Hg)
  41
  42
  43
  44 /4 width=8 by fle_intro, frees_bind_void, sor_inv_sle_dx, sle_trans/
  45 qed.
  46 *)
  47 lemma fle_flat_dx_sn: ∀L1,L2,V1,V2. ⦃L1, V1⦄ ⊆ ⦃L2, V2⦄ →
  48                       ∀I,T2. ⦃L1, V1⦄ ⊆ ⦃L2, ⓕ{I}V2.T2⦄.
  49 #L1 #L2 #V1 #V2 * -L1 #f1 #g1 #L1 #n #Hf1 #Hg1 #HL12 #Hfg1 #I #T2
  50 elim (frees_total L2 T2) #g2 #Hg2
  51 elim (sor_isfin_ex g1 g2) /2 width=3 by frees_fwd_isfin/ #g #Hg #_
  52 /4 width=8 by fle_intro, frees_flat, sor_inv_sle_sn, sle_trans/
  53 qed.
  54
  55 lemma fle_flat_dx_dx: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄ →
  56                       ∀I,V2. ⦃L1, T1⦄ ⊆ ⦃L2, ⓕ{I}V2.T2⦄.
  57 #L1 #L2 #T1 #T2 * -L1 #f2 #g2 #L1 #n #Hf2 #Hg2 #HL12 #Hfg2 #I #V2
  58 elim (frees_total L2 V2) #g1 #Hg1
  59 elim (sor_isfin_ex g1 g2) /2 width=3 by frees_fwd_isfin/ #g #Hg #_
  60 /4 width=8 by fle_intro, frees_flat, sor_inv_sle_dx, sle_trans/
  61 qed.