matita/matita/contribs/lambdadelta/ground/arith/ynat_minus1_plus.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   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/nat_minus_plus.ma".
  16 include "ground/arith/ynat_plus.ma".
  17 include "ground/arith/ynat_minus1_succ.ma".
  18
  19 (* LEFT SUBTRACTION FOR NON-NEGATIVE INTEGERS WITH INFINITY *****************)
  20
  21 (* Constructions with yplus *************************************************)
  22
  23 (*** yplus_minus *)
  24 lemma yminus1_plus_sn_refl_sn (x) (n):
  25       x = x + yinj_nat n - n.
  26 #x @(ynat_split_nat_inf … x) -x //
  27 #n <yplus_inf_sn //
  28 qed.
  29
  30 (*** yminus_plus2 *)
  31 lemma yminus_plus_dx (x:ynat) (n) (o):
  32       x - n - o = x - (n + o).
  33 #x @(ynat_split_nat_inf … x) -x //
  34 qed.