matita/matita/contribs/lambdadelta/basic_2/i_static/rexs_rexs.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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   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/rex_fsle.ma".
  16 include "basic_2/i_static/rexs.ma".
  17
  18 (* ITERATED EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ***)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 lemma rexs_sym: ∀R. rex_fsge_compatible R →
  23                 (∀L1,L2,T1,T2. R L1 T1 T2 → R L2 T2 T1) →
  24                 ∀T. symmetric … (rexs R T).
  25 #R #H1R #H2R #T #L1 #L2 #H elim H -L2
  26 /4 width=3 by rex_sym, rexs_step_sn, inj/
  27 qed-.
  28
  29 (* Main properties **********************************************************)
  30
  31 theorem rexs_trans: ∀R,T. Transitive … (rexs R T).
  32 #R #T #L1 #L #HL1 #L2 #HL2 @(trans_TC … HL1 HL2) (**) (* auto fails *)
  33 qed-.