It is desirable to augment rewrite rules in two ways:

1. Add a predicate to perform tests on the input; only perform the transformation if the test succeeds:
   (and (numberp ?n) (> ?n 0))

2. Create new variables by running a program on existing variables:

   
   (transf '((intersection
              (subset (function (lambda (?x) ?p))
                      ?s)
              (subset (function (lambda (?y) ?q))
                      ?s))
             (subset (function (lambda (?x)
                       (and ?p ?qq)))
                     ?s)
             t
             ((?qq (subst ?x ?y ?q))) )
     '(intersection
        (subset #'(lambda (w) (rich w)) people)
        (subset #'(lambda (z) (famous z)) people)))
   
   (SUBSET #'(LAMBDA (W) (AND (RICH W) (FAMOUS W)))
           PEOPLE))
   

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