Definition dim_opp(k:dim):dim:=
 match k with zero => one | one => zero end.(*========================================================
          TAGS AS NATS
========================================================*)

Definition tag := nat.(* Decidability of tag equality: *)

Definition eq_tag_dec := eq_nat_dec.(*========================================================
       POINTS AS PAIRS OF REALS
========================================================*)

Definition point := (R * R)%type.(*
Check point.
point : Set
*)

(* Equality of points : *)

Definition eq_point(p q :point):=
  fst p = fst q /\ snd p = snd q.

Lemma eq_point_dec : forall (p q:point), {eq_point p q} + {~eq_point p q}.