traverse a list recursively and find specific elements

trav.lisp

(defun traverse (lst elt)
  (defun traverse-and-count (lst elt cnt)
    (if (= 0 (length lst))
        cnt
      (progn
        (if (equal elt (car lst))
            (traverse-and-count (cdr lst) elt (+ 1 cnt))
          (traverse-and-count (cdr lst) elt cnt)))))
  (traverse-and-count lst elt 0))

(traverse '(1 3 4 5 6 1 4 1) 1)  ;; 3                                                                                                                         
(traverse '("a" "b" 2 5 "b" 8 0) "b") ;; 2