Section rm_root.
Variable n p : Z.
Variable t1 t2 t' : Z_btree.
Hypothesis S : search (Z_bnode n (Z_bnode p t1 t2) t').
Variable q : Z.
Variable t0 : Z_btree.
Hypothesis R : RMAX (Z_bnode p t1 t2) t0 q.
Hint Resolve S: searchtrees.
Remark rm_2 : (q < n)%Z.
(********************)
Hint Resolve rm_2: searchtrees.
Remark rm_3 : ~ occ n (Z_bnode q t0 t').
Hint Resolve rm_3: searchtrees.
Remark rm_4 :
forall p0 : Z,
occ p0 (Z_bnode q t0 t') -> occ p0 (Z_bnode n (Z_bnode p t1 t2) t').
Hint Resolve rm_4: searchtrees.
Remark rm_5 :
forall p0 : Z,
occ p0 (Z_bnode n (Z_bnode p t1 t2) t') ->
occ p0 (Z_bnode q t0 t') \/ n = p0.
Hint Resolve rm_5: searchtrees.
Remark rm_6 : search (Z_bnode q t0 t').
Hint Resolve rm_6: searchtrees.

Lemma rm_root_lemma :
RM n (Z_bnode n (Z_bnode p t1 t2) t') (Z_bnode q t0 t').