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<html>
<head><title>DEFTHM.html -- ACL2 Version 3.1</title></head>
<body text=#000000 bgcolor="#FFFFFF">
<h2>DEFTHM</h2>prove and name a theorem
<pre>Major Section: <a href="EVENTS.html">EVENTS</a>
</pre><p>
<pre>
Examples:
(defthm assoc-of-app
(equal (app (app a b) c)
(app a (app b c))))
</pre>
The following nonsensical example illustrates all the optional
arguments but is illegal because not all combinations are permitted.
See <a href="HINTS.html">hints</a> for a complete list of <a href="HINTS.html">hints</a>.
<pre>
(defthm main
(implies (hyps x y z) (concl x y z))
:rule-classes (:REWRITE :GENERALIZE)
:instructions (induct prove promote (dive 1) x
(dive 2) = top (drop 2) prove)
:hints (("Goal"
:do-not '(generalize fertilize)
:in-theory (set-difference-theories
(current-theory :here)
'(assoc))
:induct (and (nth n a) (nth n b))
:use ((:instance assoc-of-append
(x a) (y b) (z c))
(:functional-instance
(:instance p-f (x a) (y b))
(p consp)
(f assoc)))))
:otf-flg t
:doc "#0[one-liner/example/details]")
<p>
General Form:
(defthm name term
:rule-classes rule-classes
:instructions instructions
:hints hints
:otf-flg otf-flg
:doc doc-string)
</pre>
where <code>name</code> is a new symbolic name (see <a href="NAME.html">name</a>), <code>term</code> is a
term alleged to be a theorem, and <code><a href="RULE-CLASSES.html">rule-classes</a></code>, <code><a href="INSTRUCTIONS.html">instructions</a></code>,
<code><a href="HINTS.html">hints</a></code>, <code><a href="OTF-FLG.html">otf-flg</a></code> and <code><a href="DOC-STRING.html">doc-string</a></code> are as described in their
respective <a href="DOCUMENTATION.html">documentation</a>. The five keyword arguments above are
all optional, however you may not supply both <code>:</code><code><a href="INSTRUCTIONS.html">instructions</a></code>
and <code>:</code><code><a href="HINTS.html">hints</a></code>, since one drives the proof checker and the other
drives the theorem prover. If <code>:</code><code><a href="RULE-CLASSES.html">rule-classes</a></code> is not specified,
the list <code>(:rewrite)</code> is used; if you wish the theorem to generate
no rules, specify <code>:</code><code><a href="RULE-CLASSES.html">rule-classes</a></code> <code>nil</code>.<p>
When ACL2 processes a <code>defthm</code> event, it first tries to prove the
<a href="TERM.html">term</a> using the indicated hints (see <a href="HINTS.html">hints</a>) or <a href="INSTRUCTIONS.html">instructions</a>
(see <a href="PROOF-CHECKER.html">proof-checker</a>). If it is successful, it stores the rules
described by the rule-classes (see <a href="RULE-CLASSES.html">rule-classes</a>), proving the
necessary corollaries.
<br><br><br><a href="acl2-doc.html"><img src="llogo.gif"></a> <a href="acl2-doc-index.html"><img src="index.gif"></a>
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