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

Lemma split_ok : forall s x `{Ok s}, Ok (split x s)#l /\ Ok (split x s)#r.