Fixpoint ndN (m:fmap):nat:=
 match m with
    V => 0%nat
  | I m0 x _ _ => 
       if exd_dec m0 x then ndN m0
       else (1 + ndN m0)%nat
  | L m0 _ _ _ => ndN m0
 end.

(* Specifications: *)
Lemma nd_card:forall(m:fmap), ndN m = card (fmap_to_set m).