matita/matita/contribs/lambdadelta/ground/arith/ynat_lt_le_lminus_plus.ma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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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/arith/ynat_lminus_plus.ma".
  16 include "ground/arith/ynat_lt_le_lminus.ma".
  17
  18 (* STRICT ORDER FOR NON-NEGATIVE INTEGERS WITH INFINITY *********************)
  19
  20 (* Constructions with yle and ylminus and yplus *****************************)
  21
  22 (*** ylt_plus2_to_minus_inj2 *)
  23 lemma ylt_plus_dx_dx_lminus_sn (o) (x) (y):
  24       yinj_nat o ≤ x → x < y + yinj_nat o → x - o < y.
  25 /2 width=1 by ylt_lminus_bi_dx/ qed.
  26
  27 (*** ylt_plus2_to_minus_inj1 *)
  28 lemma ylt_plus_dx_sn_lminus_sn (o) (x) (y):
  29       yinj_nat o ≤ x → x < yinj_nat o + y → x - o < y.
  30 /2 width=1 by ylt_plus_dx_dx_lminus_sn/ qed.