#[global]
Instance merge_ok s1 s2 : forall `(Ok s1, Ok s2)
 `(forall y1 y2 : elt, InT y1 s1 -> InT y2 s2 -> X.lt y1 y2),
 Ok (merge s1 s2).

Lemma remove_spec : forall s x y `{Ok s}, (InT y (remove x s) <-> InT y s /\ ~ X.eq y x).