File: The_Induction_Scheme_Selected_for_the_App_Example.html

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<html>
<head><title>The_Induction_Scheme_Selected_for_the_App_Example.html  --  ACL2 Version 3.1</title></head>
<body text=#000000 bgcolor="#FFFFFF">
<h2>The Induction Scheme Selected for the App Example</h2>
<p>

<pre>
(AND
   (IMPLIES (AND (NOT (ENDP A))         ; Induction Step: test 
                 (:P (CDR A) B C))      ;  and induction hypothesis
            (:P A B C))                 ;  implies induction conclusion.
   (IMPLIES (ENDP A) (:P A B C)))       ; Base Case 
</pre>
<p>

The formula beginning with this parenthesis is the induction scheme
suggested by <code>(APP A B)</code> applied to <code>(P A B C)</code>.<p>

It is a <b>conjunction</B> (<code><a href="AND.html">AND</a></code> <a href="A_Tiny_Warning_Sign.html"><img src=twarning.gif></a>) of two formulas.<p>

The first is the <b>induction step</B> and the second is the <b>base case</B>.
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