matita/matita/contribs/lambdadelta/ground/arith/ynat_lt_pred.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_pred.ma".
  16 include "ground/arith/ynat_pred.ma".
  17 include "ground/arith/ynat_lt.ma".
  18
  19 (* STRICT ORDER FOR NON-NEGATIVE INTEGERS WITH INFINITY *********************)
  20
  21 (* Constructions with ypred *************************************************)
  22
  23 (*** ylt_pred *)
  24 lemma ylt_pred_bi (x) (y):
  25       x < y → 𝟎 < x → ↓x < ↓y.
  26 #x #y * -x -y
  27 /4 width=1 by ylt_inv_inj_bi, ylt_inj, nlt_pred_bi/
  28 qed.