matita/matita/contribs/lambdadelta/ground/relocation/gr_id_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/gr_tl_eq.ma".
  16 include "ground/relocation/gr_id.ma".
  17
  18 (* IDENTITY ELEMENT FOR GENERIC RELOCATION MAPS *****************************)
  19
  20 (* Constructions with gr_eq *************************************************)
  21
  22 corec lemma gr_id_eq (f): ⫯f ≡ f → 𝐢 ≡ f.
  23 cases gr_id_unfold #Hf
  24 cases (gr_eq_inv_push_sn … Hf) [|*: // ] #_ #H
  25 cases H in Hf; -H #Hf
  26 @gr_eq_push [3:|*: // ]
  27 /3 width=5 by gr_eq_inv_push_bi/
  28 qed.
  29
  30 (* Inversions with gr_eq ****************************************************)
  31
  32 (* Note: this has the same proof of the previous *)
  33 corec lemma gr_id_inv_eq (f): 𝐢 ≡ f → ⫯f ≡ f.
  34 cases gr_id_unfold #Hf
  35 cases (gr_eq_inv_push_sn … Hf) [|*: // ] #_ #H
  36 cases H in Hf; -H #Hf
  37 @gr_eq_push [3:|*: // ]
  38 /3 width=5 by gr_eq_inv_push_bi/
  39 qed-.