matita/matita/contribs/lambdadelta/ground/relocation/fr2_nat_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/fr2_nat.ma".
  16
  17 (* NON-NEGATIVE APPLICATION FOR FINITE RELOCATION MAPS WITH PAIRS ***********)
  18
  19 (* Main constructions *******************************************************)
  20
  21 (*** at_mono *)
  22 theorem fr2_nat_mono (f) (l):
  23         ∀l1. @❨l, f❩ ≘ l1 → ∀l2. @❨l, f❩ ≘ l2 → l1 = l2.
  24 #f #l #l1 #H elim H -f -l -l1
  25 [ #l #x #H <(fr2_nat_inv_empty … H) -x //
  26 | #f #d #h #l #l1 #Hld #_ #IH #x #H
  27   lapply (fr2_nat_inv_lcons_lt … H Hld) -H -Hld /2 width=1 by/
  28 | #f #d #h #l #l1 #Hdl #_ #IH #x #H
  29   lapply (fr2_nat_inv_lcons_ge … H Hdl) -H -Hdl /2 width=1 by/
  30 ]
  31 qed-.