(************************************************************************)
(*  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        *)
(************************************************************************)
(*i 	$Id$	 i*)
Section MapCanon.
Variable A : Type.
Inductive mapcanon : Map A -> Prop :=
| M0_canon : mapcanon (M0 A)
| M1_canon : forall (a:ad) (y:A), mapcanon (M1 A a y)
| M2_canon :
forall m1 m2:Map A,
mapcanon m1 ->
mapcanon m2 -> 2 <= MapCard A (M2 A m1 m2) -> mapcanon (M2 A m1 m2).

Lemma mapcanon_M2_1 :
forall m1 m2:Map A, mapcanon (M2 A m1 m2) -> mapcanon m1.