matita/matita/contribs/lambdadelta/ground/arith/ynat_lt_le_lminus.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/arith/nat_lt_minus.ma".
  16 include "ground/arith/ynat_lminus.ma".
  17 include "ground/arith/ynat_le.ma".
  18 include "ground/arith/ynat_lt.ma".
  19
  20 (* STRICT ORDER FOR NON-NEGATIVE INTEGERS WITH INFINITY *********************)
  21
  22 (* Constructions with yle and ylminus ***************************************)
  23
  24 (*** monotonic_ylt_minus_dx *)
  25 lemma ylt_lminus_bi_dx (o) (x) (y):
  26       x < y → yinj_nat o ≤ x → x - o < y - o.
  27 #o #x #y * -x -y
  28 /4 width=1 by ylt_inj, yle_inv_inj_bi, nlt_minus_bi_dx/
  29 qed.