(define (delete-node T v)
  (if (not (is-member? T v)) T
      (cond ((null? T) (list))
            ((< v (value T))
             (make-tree (value T) (delete-node (left T) v) (right T)))
            ((> v (value T))
             (make-tree (value T) (left T) (delete-node (right T) v)))
            (else
             (cond ((and (null? (right T)) (and null? (left T)))
                   (list))
                   ((and (null? (right T)) (not (null? (left T))))
                    (left T))
                   ((and (null? (left T)) (not (null? (right T))))
                    (right T))
                   (else
                    (let ((rep-value (find-largest (left T))))
                      (let ((new-left (delete-node (left T) rep-value)))
                        (make-tree rep-value
                                   new-left (right T))))))))))


(define t6 '(5 (2 (1 () ()) (3 () ())) (11 (8 (6 () ()) (9 () ())) (15 () (17 () ())))))

;;outputs:
;;> (delete-node t6 11) --> from problem set pdf examples
;;(5 (2 (1 () ()) (3 () ())) (9 (8 (6 () ()) ()) (15 () (17 () ()))))
;;> (delete-node t5 6)
;;(5 (4 (3 () ()) ()) (7 () ()))
;;> (delete-node t1 4)
;;(3 (1 () ()) ())