(* ========================================================== 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.