#[local]
Hint Resolve add_Inf : core.

Lemma add_sorted : forall m (Hm:Sort m) x e, Sort (add x e m).
Fixpoint remove (k : key) (s : t elt) {struct s} : t elt :=
match s with
| nil => nil
| (k',x) :: l =>
match X.compare k k' with
| LT _ => s
| EQ _ => l
| GT _ => (k',x) :: remove k l
end
end.