(** * [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_1 : forall m (Hm:NoDupA m) x y, X.eq x y -> ~ In y (remove x m).