(** * [remove] *)
Fixpoint remove (k : key) (s : t elt) {struct s} : t elt :=
match s with
| nil => nil
| (k',x) :: l => if X.eq_dec k k' then l else (k',x) :: remove k l
end.

Lemma remove_NoDup : forall m (Hm:NoDupA m) x, NoDupA (remove x m).
Definition elements (m: t elt) := m.