(** * [add] *)

Fixpoint add (k : key) (x : elt) (s : t elt) {struct s} : t elt :=
 match s with
  | nil => (k,x) :: nil
  | (k',y) :: l =>
     match X.compare k k' with
      | LT _ => (k,x)::s
      | EQ _ => (k,x)::l
      | GT _ => (k',y) :: add k x l
     end
 end.

Lemma add_sorted : forall m (Hm:Sort m) x e, Sort (add x e m).