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(* 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                                 *)
(*                                                                          *)
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(*                               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.

Lemma Alt_u : alt b u.
Section Case1_.