helm/software/matita/contribs/RELATIONAL/NLE/dec.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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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 set "baseuri" "cic:/matita/RELATIONAL/NLE/dec".
  16
  17 include "NLE/props.ma".
  18
  19 theorem nat_dec_lt_ge: \forall x,y. x < y \lor y <= x.
  20  intros 2; elim y; clear y;
  21  [ auto
  22  | decompose;
  23    [ lapply linear nle_inv_succ_1 to H1. decompose.
  24      subst. auto depth=4
  25    | lapply linear nle_lt_or_eq to H1; decompose;
  26      subst; auto
  27    ]
  28  ].
  29 qed.