#[local]
Hint Resolve create_bst : core.

(* Specifications: *)
Lemma create_in :
forall l x e r y,
In y (create l x e r) <-> X.eq y x \/ In y l \/ In y r.
Lemma bal_bst : forall l x e r, bst l -> bst r ->
lt_tree x l -> gt_tree x r -> bst (bal l x e r).