(*======================================================== DARTS AS NATURALS ========================================================*)
(* For simplicity, dart is nat, but it could be a deferred type: *)
Definition dart := nat.
(* Decidability of dart equality: *)
Definition eq_dart_dec := eq_nat_dec.
(* Nil dart: *)
Definition nil := 0%nat.
(*======================================================== FREE MAPS, CONSTRUCTORS, OBSERVERS AND DESTRUCTORS ========================================================*)
Open Scope Z_scope.
(* Free maps: *)
Inductive fmap:Set :=
V : fmap
| I : fmap->dart->tag->point->fmap
| L : fmap->dim->dart->dart->fmap.
(* Map emptiness: *)
Definition empty(m:fmap): Prop:=
match m with
V => True
|  _ => False
end.
(* Map emptiness is decidable: *)

Lemma empty_dec: forall (m:fmap),
{empty m}+{~empty m}.