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(*                                                                    *)
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(*                                                                    *)
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(* 02110-1301 USA                                                     *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
(*                     --- shift.v ---                                      *)
(*                                                                          *)
(* Author: Pierre Casteran.                                                 *)
(*    LABRI, URA CNRS 1304,                                                 *)
(*    Departement d'Informatique, Universite Bordeaux I,                    *)
(*    33405 Talence CEDEX,                                                  *)
(*    e-mail:  casteran@labri.u-bordeaux.fr                                 *)
(* Many programmers use left and right shifts in their code; so we found useful to provide some definitions and lemmas about these operations. *)
(* machine arithmetics *)
(* Left shift *)
Definition shift (n : nat) := two * n.
(************************************)
(* Right shift (and information on parity) *)
(*************************************************************)

Lemma half_lt :
forall a b : nat, 0 < b -> b = shift a \/ b = S (shift a) -> a < b.