matita/matita/contribs/lambdadelta/ground/relocation/rtmap_coafter_uni.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/rtmap_uni.ma".
  16 include "ground/relocation/rtmap_coafter.ma".
  17
  18 (* RELOCATION MAP ***********************************************************)
  19
  20 (* Properties with test for uniform relocations *****************************)
  21
  22 lemma coafter_isuni_isid: ∀f2. 𝐈❪f2❫ → ∀f1. 𝐔❪f1❫ → f1 ~⊚ f2 ≘ f2.
  23 #f #Hf #g #H elim H -g
  24 /3 width=5 by coafter_isid_sn, coafter_eq_repl_back0, coafter_next, eq_push_inv_isid/
  25 qed.
  26
  27 (* Properties with uniform relocations **************************************)
  28
  29 lemma coafter_uni_sn: ∀n,f. 𝐔❨n❩ ~⊚ f ≘ ⫯*[n] f.
  30 #n @(nat_ind_succ … n) -n
  31 /2 width=5 by coafter_isid_sn, coafter_next/
  32 qed.