matita/matita/contribs/lambdadelta/basic_2/static/lfxs_fle.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/syntax/lveq_length.ma". *)
  16 include "basic_2/static/fle.ma".
  17 include "basic_2/static/lfxs_lfxs.ma".
  18
  19 (* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
  20 (*
  21 lemma pippo: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1, n2] L2 →
  22              ∀T,f. L1 ⊢ 𝐅*⦃T⦄ ≡ f → ∃g. ↑*[n1]g = f.
  23 *)
  24 (* Properties with free variables inclusion for restricted closures *********)
  25 (*
  26 lemma fle_lfxs_trans: ∀R,L1,T1,T2. ⦃L1, T1⦄ ⊆ ⦃L1, T2⦄ →
  27                       ∀L2. L1 ⪤*[R, T2] L2 → L1 ⪤*[R, T1] L2.
  28 #R #L1 #T1 #T2 * #x #n #f1 #f2 #Hf1 #Hf2 #Hn #Hf #L2 #HL12
  29 lapply (lveq_inj_length … Hn ?) // #H destruct
  30
  31
  32  Hn : (L1≋ⓧ*[n,n]L1) (L1⊢𝐅*⦃T1⦄≡f1) →
  33
  34 lapply (lfxs_inv_frees … HL12 … Hf2) -HL12 -Hf2 #HL12
  35 @(ex2_intro … Hf1) -Hf1
  36 @(sle_lexs_trans … HL12) -HL12 //
  37
  38 /4 width=5 by lfxs_inv_frees, sle_lexs_trans, ex2_intro/
  39 qed-.
  40 *)