matita/matita/contribs/lambdadelta/ground/relocation/pr_fcla_eq.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 "ground/relocation/pr_isi_eq.ma".
  16 include "ground/relocation/pr_fcla.ma".
  17
  18 (* FINITE COLENGTH ASSIGNMENT FOR PARTIAL RELOCATION MAPS *******************)
  19
  20 (* Constructions with pr_eq *************************************************)
  21
  22 (*** fcla_eq_repl_back *)
  23 lemma pr_fcla_eq_repl_back (n):
  24       pr_eq_repl_back … (λf. 𝐂❨f❩ ≘ n).
  25 #n #f1 #H elim H -f1 -n /3 width=3 by pr_fcla_isi, pr_isi_eq_repl_back/
  26 #f1 #n #_ #IH #g2 #H [ elim (pr_eq_inv_push_sn … H) | elim (pr_eq_inv_next_sn … H) ] -H
  27 /3 width=3 by pr_fcla_push, pr_fcla_next/
  28 qed-.
  29
  30 (*** fcla_eq_repl_fwd *)
  31 lemma fcla_eq_repl_fwd (n):
  32       pr_eq_repl_fwd … (λf. 𝐂❨f❩ ≘ n).
  33 #n @pr_eq_repl_sym /2 width=3 by pr_fcla_eq_repl_back/
  34 qed-.