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<html>
<head><title>CASE-SPLIT.html -- ACL2 Version 3.1</title></head>
<body text=#000000 bgcolor="#FFFFFF">
<h2>CASE-SPLIT</h2>like force but immediately splits the top-level goal on the hypothesis
<pre>Major Section: <a href="MISCELLANEOUS.html">MISCELLANEOUS</a>
</pre><p>
When a hypothesis of a conditional rule has the form <code>(case-split hyp)</code>
it is logically equivalent to <code>hyp</code>. However it affects the
application of the rule generated as follows: if ACL2
attempts to apply the rule but cannot establish that the required
instance of <code>hyp</code> holds in the current context, it considers the
hypothesis true anyhow, but (assuming all hypotheses are seen to be true and
the rule is applied) creates a subgoal in which that instance of <code>hyp</code> is
assumed false. (There are exceptions, noted below.)
<p>
For example, given the rule
<pre>
(defthm p1->p2
(implies (case-split (p1 x))
(p2 x)))
</pre>
then an attempt to prove
<pre>
(implies (p3 x) (p2 (car x)))
</pre>
can give rise to a single subgoal:
<pre>
(IMPLIES (AND (NOT (P1 (CAR X))) (P3 X))
(P2 (CAR X))).
</pre>
Unlike <code><a href="FORCE.html">force</a></code>, <code>case-split</code> does not delay the ``false case'' to
a forcing round but tackles it more or less immediately.<p>
The special ``split'' treatment of <code>case-split</code> can be disabled by
disabling forcing: see <a href="FORCE.html">force</a> for a discussion of disabling forcing, and
also see <a href="DISABLE-FORCING.html">disable-forcing</a>. Finally, we should mention that the rewriter is
never willing to split when there is an <code><a href="IF.html">if</a></code> term present in the goal
being simplified. Since <code><a href="AND.html">and</a></code> terms and <code><a href="OR.html">or</a></code> terms are merely
abbreviations for <code><a href="IF.html">if</a></code> terms, they also prevent splitting. Note that
<code><a href="IF.html">if</a></code> terms are ultimately eliminated using the ordinary flow of the proof
(but see <a href="SET-CASE-SPLIT-LIMITATIONS.html">set-case-split-limitations</a>), so <code>case-split</code> will ultimately
function as intended.<p>
When in the proof checker, <code>case-split</code> behaves like <code>force</code>.
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