Hint Resolve min_not_occ: searchtrees.
(* technical lemmas about some non-leaf search tree *)
Section search_tree_basic_properties.
Variables (n : key) (v : data) (t1 t2 : btree).
Hypothesis se : search_tree (bnode n v t1 t2).

(* Specifications: *)
Lemma search_tree_l : search_tree t1.
Hint Resolve search_tree_l: searchtrees.
Lemma search_tree_r : search_tree t2.
Hint Resolve search_tree_r: searchtrees.
Lemma maj_l : maj n t1.
Hint Resolve maj_l: searchtrees.
Lemma min_r : min n t2.
Hint Resolve min_r: searchtrees.
Lemma not_right : forall (p : key) (v' : data), Key.le p n -> ~ occ v' p t2.
Hint Resolve not_right: searchtrees.
Lemma not_left : forall (p : key) (v' : data), Key.le n p -> ~ occ v' p t1.
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.
Lemma go_right :
forall (p : key) (v' : data),
occ v' p (bnode n v t1 t2) -> Key.lt n p -> occ v' p t2.