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(* 02110-1301 USA                                                     *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
(* -----                          log2_spec.v                          ---- *)
(*                                                                          *)
(* Author: Pierre Casteran.                                                 *)
(*    LABRI, URA CNRS 1304,                                                 *)
(*    Departement d'Informatique, Universite Bordeaux I,                    *)
(*    33405 Talence CEDEX,                                                  *)
(*    e-mail:  casteran@labri.u-bordeaux.fr                                 *)
(* specification of logarithm (base 2) *)
(***************************************)
Definition log2_spec (n0 : nat) :=
{l : nat &
{n0 = two_power l} + {two_power l < n0 /\ n0 < two_power (S l)}}.
Section applications.
Variable log2 : forall n : nat, 0 < n -> log2_spec n.
(* logarithm by excess *)
(***********************)

Lemma ceiling_log2 :
forall n : nat,
one < n -> {l : nat | two_power (pred l) < n /\ n <= two_power l}.