(* This program is free software; you can redistribute it and/or      *)
(* modify it under the terms of the GNU Lesser General Public License *)
(* as published by the Free Software Foundation; either version 2.1   *)
(* of the License, or (at your option) any later version.             *)
(*                                                                    *)
(* This program is distributed in the hope that it will be useful,    *)
(* but WITHOUT ANY WARRANTY; without even the implied warranty of     *)
(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU Lesser General Public License for more details.                *)
(*                                                                    *)
(* You should have received a copy of the GNU Lesser General Public   *)
(* License along with this program; if not, write to the Free         *)
(* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA *)
(* 02110-1301 USA                                                     *)
(********************************************************************** Proof of Huffman algorithm: Aux.v  Auxillary functions & Theorems  Definitions: le_bool, map2, first_n, skip_n find_min find_max  Theorems: minus, map, app  Laurent.Thery@inria.fr (2003) **********************************************************************)
Require Export List.
Require Export Arith.
From Huffman Require Export sTactic.
(* Some facts about the minus operator *)
Section Minus.

(* Specifications: *)
Theorem lt_minus_O : forall n m, m < n -> 0 < n - m.
Proof using.