#[global]
Instance join_ok : forall l x r `(Ok l, Ok r, lt_tree x l, gt_tree x r),
Ok (join l x r).
(** ** Extraction of minimum element *)

Lemma remove_min_spec : forall l x r y h,
InT y (Node h l x r) <->
X.eq y (remove_min l x r)#2 \/ InT y (remove_min l x r)#1.