matita/matita/contribs/lambdadelta/ground/relocation/gr_isi_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/gr_id.ma".
  16 include "ground/relocation/gr_isi_eq.ma".
  17
  18 (* IDENTITY CONDITION FOR GENERIC RELOCATION MAPS ***************************)
  19
  20 (* Constructions with gr_id *************************************************)
  21
  22 (*** id_isid *)
  23 lemma gr_isi_id: 𝐈❪𝐢❫.
  24 /2 width=1 by gr_eq_push_isi/ qed.
  25
  26 (* Alternative definition with gr_id and gr_eq ******************************)
  27
  28 (*** eq_id_isid *)
  29 lemma gr_eq_id_isi (f): 𝐢 ≡ f → 𝐈❪f❫.
  30 /2 width=3 by gr_isi_eq_repl_back/ qed.
  31
  32 (*** eq_id_inv_isid *)
  33 lemma gr_isi_inv_eq_id (f): 𝐈❪f❫ → 𝐢 ≡ f.
  34 /2 width=1 by gr_isi_inv_eq_repl/ qed-.