matita/matita/contribs/lambdadelta/basic_2A/multiple/mr2_mr2.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 "basic_2A/multiple/mr2.ma".
  16
  17 (* MULTIPLE RELOCATION WITH PAIRS *******************************************)
  18
  19 (* Main properties **********************************************************)
  20
  21 theorem at_mono: ∀cs,i,i1. @⦃i, cs⦄ ≡ i1 → ∀i2. @⦃i, cs⦄ ≡ i2 → i1 = i2.
  22 #cs #i #i1 #H elim H -cs -i -i1
  23 [ #i #x #H <(at_inv_nil … H) -x //
  24 | #cs #l #m #i #i1 #Hil #_ #IHi1 #x #H
  25   lapply (at_inv_cons_lt … H Hil) -H -Hil /2 width=1 by/
  26 | #cs #l #m #i #i1 #Hli #_ #IHi1 #x #H
  27   lapply (at_inv_cons_ge … H Hli) -H -Hli /2 width=1 by/
  28 ]
  29 qed-.