matita/matita/contribs/lambdadelta/ground/relocation/pr_isi_pat.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_id.ma".
  16 include "ground/relocation/pr_pat_pat_id.ma".
  17
  18 (* IDENTITY CONDITION FOR PARTIAL RELOCATION MAPS ***************************)
  19
  20 (* Advanced constructions with pr_isi and pr_pat ****************************)
  21
  22 (*** isid_at *)
  23 lemma pr_isi_pat (f): (∀i. @❨i,f❩ ≘ i) → 𝐈❨f❩.
  24 /3 width=1 by pr_eq_id_isi, pr_pat_inv_id/
  25 qed.
  26
  27 (* Inversions with pr_pat ***************************************************)
  28
  29 (*** isid_inv_at *)
  30 lemma pr_isi_inv_pat (f) (i): 𝐈❨f❩ → @❨i,f❩ ≘ i.
  31 /3 width=3 by pr_isi_inv_eq_id, pr_pat_id, pr_pat_eq_repl_back/
  32 qed-.
  33
  34 (* Destructions with pr_pat *************************************************)
  35
  36 (*** isid_inv_at_mono *)
  37 lemma pr_isi_pat_des (f) (i1) (i2): 𝐈❨f❩ → @❨i1,f❩ ≘ i2 → i1 = i2.
  38 /4 width=3 by pr_isi_inv_eq_id, pr_pat_id_des, pr_pat_eq_repl_fwd/
  39 qed-.