(defun g (x y a)
  (if (zp x)
      a
      (g (- x 1) y (+ y a))))

(defthm generalized-g-lemma
  (implies (and (natp x)
                (natp y)
                (natp a))
           (equal (g x y a)
                  (+ a (* x y)))))

(defthm g-theorem
  (implies (and (natp x)
                (natp y))
           (equal (g x y 0)
                  (* x y))))