By reading the documentation of defthm 
(and especially of its
:rule-classes argument) you would learn that when we submitted
the command
(defthm associativity-of-app
(equal (app (app a b) c)
(app a (app b c))))
we not only command the system to prove that app is an associative
function but
* we commanded it to use that fact as a rewrite rule.
That means that every time the system encounters a term of the form
(app (app x y) z)it will replace it with
(app x (app y z))!
