#[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).
(** ** Splitting *)

Lemma split_spec1 : forall s x y `{Ok s},
(InT y (split x s)#l <-> InT y s /\ X.lt y x).