(* ==========================================================
          RELATIONSHIPS BETWEEN sets AND fmaps
===========================================================*)

(* fmap to set *)

Fixpoint fmap_to_set(m:fmap):set:=
 match m with
     V => Vs
   | I m0 x _ _ => Is (fmap_to_set m0) x
   | L m0 _ _ _ => (fmap_to_set m0)
 end.

Lemma exd_exds:forall(m:fmap)(z:dart), exd m z <-> exds (fmap_to_set m) z.