Section search_tree_basic_properties.
Variables (n : key) (v : data) (t1 t2 : btree).
Hypothesis se : search_tree (bnode n v t1 t2).
Hint Resolve search_tree_l: searchtrees.
Hint Resolve search_tree_r: searchtrees.
Hint Resolve maj_l: searchtrees.
Hint Resolve min_r: searchtrees.
Hint Resolve not_right: searchtrees.
Hint Resolve not_left: searchtrees.
End search_tree_basic_properties.
Hint Resolve go_left go_right not_left not_right search_tree_l search_tree_r
maj_l min_r: searchtrees.
(* each key occurs at most once *)

Lemma occ_unicity :
forall t : btree,
search_tree t ->
forall (k : key) (v v' : data), occ v k t -> occ v' k t -> v = v'.