#[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_spec2 : forall s x y `{Ok s}, (InT y (split x s)#r <-> InT y s /\ X.lt x y).