#[local]
Hint Resolve bal_bst : core.

(* Specifications: *)
Lemma bal_in : forall l x e r y,
In y (bal l x e r) <-> X.eq y x \/ In y l \/ In y r.
Lemma bal_mapsto : forall l x e r y e',
MapsTo y e' (bal l x e r) <-> MapsTo y e' (create l x e r).
Lemma bal_find : forall l x e r y,
bst l -> bst r -> lt_tree x l -> gt_tree x r ->
find y (bal l x e r) = find y (create l x e r).