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(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
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(*i 	$Id$	 i*)
Section AdAlloc.
Variable A : Set.
(** Allocator: returns an address not in the domain of [m]. This allocator is optimal in that it returns the lowest possible address, in the usual ordering on integers. It is not the most efficient, however. *)
Fixpoint ad_alloc_opt (m:Map A) : ad :=
match m with
| M0 => N0
| M1 a _ => if Neqb a N0 then Npos 1 else N0
| M2 m1 m2 =>
Nmin (Ndouble (ad_alloc_opt m1))
(Ndouble_plus_one (ad_alloc_opt m2))
end.

Lemma ad_alloc_opt_allocates_1 :
forall m:Map A, MapGet A m (ad_alloc_opt m) = None.