matita/matita/contribs/lambdadelta/ground/relocation/pr_isi_nat.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_nat.ma".
  16 include "ground/relocation/pr_isi_pat.ma".
  17
  18 (* IDENTITY CONDITION FOR PARTIAL RELOCATION MAPS ***************************)
  19
  20 (* Advanced constructions with pr_isi and pr_nat ****************************)
  21
  22 lemma pr_isi_nat (f): (∀l. @↑❨l,f❩ ≘ l) → 𝐈❨f❩.
  23 /2 width=1 by pr_isi_pat/ qed.
  24
  25 (* Inversions with pr_nat ***************************************************)
  26
  27 lemma pr_isi_inv_nat (f) (l): 𝐈❨f❩ → @↑❨l,f❩ ≘ l.
  28 /2 width=1 by pr_isi_inv_pat/ qed-.
  29
  30 (* Destructions with pr_nat *************************************************)
  31
  32 lemma pr_isi_nat_des (f) (l1) (l2): 𝐈❨f❩ → @↑❨l1,f❩ ≘ l2 → l1 = l2.
  33 /3 width=3 by pr_isi_pat_des, eq_inv_npsucc_bi/ qed-.