(* 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 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                                                     *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
(****************************************************************************)
(*                 The Calculus of Inductive Constructions                  *)
(*                                                                          *)
(*                                Projet Coq                                *)
(*                                                                          *)
(*                     INRIA                        ENS-CNRS                *)
(*              Rocquencourt                        Lyon                    *)
(*                                                                          *)
(*                                Coq V5.10                                 *)
(*                                                                          *)
(****************************************************************************)
(*                               Gilbreath.v                                 *)
(****************************************************************************)
(* G. Huet - V5.8  Nov. 1994 *)
(*    ported V5.10 June 1995 *)
(****************************)
(* The Gilbreath card trick *)
(****************************)
Section Context.
Variable x : word.
Hypothesis Even_x : even x.
Variable b : bool. (* witness for (alternate x) *)
Hypothesis A : alt b x.
Variable u v : word.
Hypothesis C : conc u v x.
Variable w : word.
Hypothesis S : shuffle u v w.

(* Specifications: *)
Lemma Alt_u : alt b u.
Section Case1_.