Представить множество с использованием бинарных деревьев - Prolog

DOMAINS
tree=empty;tr(integer,tree,tree);
tr(tree,integer,tree);
tr(tree,tree,integer)
X,L,R,K,R1,L1=integer
 
PREDICATES       
 
tree_member(integer,tr(integer,tree,tree))
tree_member(integer,tr(tree,integer,tree))
tree_member(integer,tr(tree,tree,integer))
tree_insert(integer,empty,tr(integer,empty,empty))
tree_insert(integer,tr(integer,integer,integer),tr(integer,integer,integer))
tree_del_min(tr(integer,empty,integer), integer, integer)
tree_delete(integer,tr(integer,empty,integer), integer)
tree_delete (integer,tr(integer,integer,empty), integer)    
tree_delete (integer,tr(integer,integer,integer), tr(integer,integer,integer))

CLAUSES
tree_member(X,tr(X,_,_)):-!. 
tree_member(X,tr(_,L,_)):-tree_member(X,L),!. 
tree_member(X,tr(_,_,R)):-tree_member(X,R). 
 
tree_member2(X,tr(X,_,_)):-!. 
tree_member2(X,tr(K,L,_)):-X<K,!,tree_member2(X,L).  
tree_member2(X,tr(K,_,R)):-X>K,!,tree_member2(X,R). 
 
tree_insert(X,empty,tr(X,empty,empty)). 
    
tree_insert(X,tr(X,L,R),tr(X,L,R)):-!. 
     
tree_insert(X,tr(K,L,R),tr(K,L1,R)):-
        X<K,!, 
        tree_insert(X,L,L1). 
        
tree_insert(X,tr(K,L,R),tr(K,L,R1)):-
        tree_insert(X,R,R1). 

tree_del_min(tr(X,empty,R), R, X). 
        
tree_del_min(tr(K,L,R), tr(K,L1,R), X):- 
        tree_del_min(L, L1, X). 

tree_delete(X,tr(X,empty,R), R):-!. 
        
tree_delete (X,tr(X,L,empty), L):-!. 
       
tree_delete (X,tr(X,L,R), tr(Y,L,R1)):- 
        tree_del_min(R,R1, Y). 
          
tree_delete (X,tr(K,L,R), tr(K,L1,R)):-
        X<K,!, 
        tree_delete (X,L,L1). 
        
tree_delete (X,tr(K,L,R), tr(K,L,R1)):-
        tree_delete (X,R,R1).