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Rewrite Rules are Generated from DEFTHM Events

Rewrite Rules are Generated from DEFTHM Events

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))!