matita/matita/contribs/lambdadelta/ground/relocation/pr_pat_pat_id.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_pat_id.ma".
  16 include "ground/relocation/pr_pat_pat.ma".
  17
  18 (* POSITIVE APPLICATION FOR PARTIAL RELOCATION MAPS *************************)
  19
  20 (* Advanced destructions with pr_id *****************************************)
  21
  22 (*** at_id_fwd *)
  23 lemma pr_pat_id_des (i1) (i2):
  24       @❨i1,𝐢❩ ≘ i2 → i1 = i2.
  25 /2 width=4 by pr_pat_mono/ qed-.
  26
  27 (* Main constructions with pr_id ********************************************)
  28
  29 (*** at_div_id_dx *)
  30 theorem pr_pat_div_id_dx (f):
  31         H_pr_pat_div f 𝐢 𝐢 f.
  32 #f #jf #j0 #j #Hf #H0
  33 lapply (pr_pat_id_des … H0) -H0 #H destruct
  34 /2 width=3 by ex2_intro/
  35 qed-.
  36
  37 (*** at_div_id_sn *)
  38 theorem pr_pat_div_id_sn (f):
  39         H_pr_pat_div 𝐢 f f 𝐢.
  40 /3 width=6 by pr_pat_div_id_dx, pr_pat_div_comm/ qed-.