matita/matita/contribs/lambdadelta/basic_2/static/lfxs_lfxs.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/relocation/lexs_lexs.ma".
  16 include "basic_2/static/lfxs.ma".
  17
  18 (* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
  19
  20 (* Main properties ******************************************************)
  21
  22 theorem lfxs_bind: ∀R,p,I,L1,L2,V1,V2,T.
  23                    L1 ⦻*[R, V1] L2 → L1.ⓑ{I}V1 ⦻*[R, T] L2.ⓑ{I}V2 →
  24                    L1 ⦻*[R, ⓑ{p,I}V1.T] L2.
  25 #R #p #I #L1 #L2 #V1 #V2 #T * #f1 #HV #Hf1 * #f2 #HT #Hf2
  26 elim (lexs_fwd_pair … Hf2) -Hf2 #Hf2 #_ elim (sor_isfin_ex f1 (⫱f2))
  27 /3 width=7 by frees_fwd_isfin, frees_bind, lexs_join, isfin_tl, ex2_intro/
  28 qed.
  29
  30 theorem lfxs_flat: ∀R,I,L1,L2,V,T.
  31                    L1 ⦻*[R, V] L2 → L1 ⦻*[R, T] L2 →
  32                    L1 ⦻*[R, ⓕ{I}V.T] L2.
  33 #R #I #L1 #L2 #V #T * #f1 #HV #Hf1 * #f2 #HT #Hf2 elim (sor_isfin_ex f1 f2)
  34 /3 width=7 by frees_fwd_isfin, frees_flat, lexs_join, ex2_intro/
  35 qed.