Proof by computation in the Coq system

This paper presents a method to automati ally prove statements from primitive re ursive arithmeti . The method repla es logi al formulas by boolean expressions. A orre tness proof is onstru ted, whi h states that the original formula is derivable, if and only if the boolean expression equals true. Be ause the boolean expression redu es to true, the onversion rule yields a trivial proof of the equality. By ombining this proof with the orre tness proof, we get a proof for the original statement.