matita/matita/contribs/lambdadelta/ground/relocation/tr_pap_pat.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "ground/relocation/pr_pat_pat.ma".
  16 include "ground/relocation/tr_pat.ma".
  17 include "ground/relocation/tr_pap.ma".
  18
  19 (* POSITIVE APPLICATION FOR TOTAL RELOCATION MAPS ***************************)
  20
  21 (* Constructions with pr_pat ***********************************************)
  22
  23 (*** at_total *)
  24 lemma tr_pat_total: ∀i1,f. @❨i1,𝐭❨f❩❩ ≘ f@❨i1❩.
  25 #i1 elim i1 -i1
  26 [ * // | #i #IH * /3 width=1 by tr_pat_succ_sn/ ]
  27 qed.
  28
  29 (* Inversions with pr_pat ***************************************************)
  30
  31 (*** at_inv_total *)
  32 lemma tr_pat_inv_total (f):
  33       ∀i1,i2. @❨i1, 𝐭❨f❩❩ ≘ i2 → f@❨i1❩ = i2.
  34 /2 width=6 by pr_pat_mono/ qed-.