matita/matita/contribs/lambdadelta/ground/relocation/pr_isu_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/pr_isi_uni.ma".
  16 include "ground/relocation/pr_isu.ma".
  17
  18 (* UNIFORMITY CONDITION FOR PARTIAL RELOCATION MAPS *************************)
  19
  20 (* Constructions with pr_uni ************************************************)
  21
  22 (*** isuni_uni *)
  23 lemma pr_isu_uni (n): 𝐔❪𝐮❨n❩❫.
  24 #n @(nat_ind_succ … n) -n
  25 /3 width=3 by pr_isu_isi, pr_isu_next/
  26 qed.
  27
  28 (*** uni_inv_isuni *)
  29 lemma pr_isu_eq_repl_back:
  30       pr_eq_repl_back … pr_isu.
  31 #f1 #H elim H -f1
  32 [ /3 width=3 by pr_isu_isi, pr_isi_eq_repl_back/
  33 | #f1 #_ #g1 * #IH #f2 #H -g1
  34   elim (pr_eq_inv_next_sn … H) -H
  35   /3 width=3 by pr_isu_next/
  36 ]
  37 qed-.
  38
  39 lemma pr_isu_eq_repl_fwd:
  40       pr_eq_repl_fwd … pr_isu.
  41 /3 width=3 by pr_isu_eq_repl_back, pr_eq_repl_sym/ qed-.
  42
  43 (* Inversions with pr_uni ***************************************************)
  44
  45 (*** uni_isuni *)
  46 lemma pr_isu_inv_uni (f): 𝐔❪f❫ → ∃n. 𝐮❨n❩ ≡ f.
  47 #f #H elim H -f
  48 [ /3 width=2 by pr_isi_inv_uni, ex_intro/
  49 | #f #_ #g #H * /3 width=6 by pr_eq_next, ex_intro/
  50 ]
  51 qed-.