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(* 02110-1301 USA                                                     *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
(*  ---                        two_power.v                             ---  *)
(*                                                                          *)
(* Author: Pierre Casteran.                                                 *)
(*    LABRI, URA CNRS 1304,                                                 *)
(*    Departement d'Informatique, Universite Bordeaux I,                    *)
(*    33405 Talence CEDEX,                                                  *)
(*    e-mail:  casteran@labri.u-bordeaux.fr                                 *)
(* The integer powers of 2 are fundamental in computer science; so we wrote this module, the results of which are used mainly in the "log2_spec" module. *)
(* 2 at the n *)
(**************)
Fixpoint two_power (m : nat) : nat :=
match m with
| O => 1
| S n => two * two_power n
end.
(********************************************)
Hint Resolve zero_lt_pow: arith.
(**************************************************)
(***************************************************************)
(*************************************************************)

Lemma two_power_le : forall n p : nat, n <= p -> two_power n <= two_power p.