Section search_tree_basic_properties.
Variable n : Z.
Variable t1 t2 : Z_btree.
Hypothesis se : search (Z_bnode n t1 t2).
Hint Resolve search_l: searchtrees.
Hint Resolve search_r: searchtrees.
Hint Resolve maj_l: searchtrees.
Hint Resolve min_r: searchtrees.
Hint Resolve not_right: searchtrees.

Lemma not_left : forall p : Z, (p >= n)%Z -> ~ occ p t1.