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.

Lemma go_left :
forall (p : key) (v' : data),
occ v' p (bnode n v t1 t2) -> Key.lt p n -> occ v' p t1.