Section search_tree_basic_properties.
Variable n : Z.
Variable t1 t2 : Z_btree.
Hypothesis se : search (Z_bnode n t1 t2).

(* Specifications: *)
Lemma search_l : search t1.
Hint Resolve search_l: searchtrees.
Lemma search_r : search t2.
Hint Resolve search_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 : Z, (p <= n)%Z -> ~ occ p t2.
Hint Resolve not_right: searchtrees.
Lemma not_left : forall p : Z, (p >= n)%Z -> ~ occ p t1.
Hint Resolve not_left: searchtrees.
Lemma go_left :
forall p : Z, occ p (Z_bnode n t1 t2) -> (p < n)%Z -> occ p t1.
Lemma go_right :
forall p : Z, occ p (Z_bnode n t1 t2) -> (p > n)%Z -> occ p t2.