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<html>
<head><title>Overview_of_the_Proof_of_a_Trivial_Consequence.html -- ACL2 Version 3.1</title></head>
<body text=#000000 bgcolor="#FFFFFF">
<h2>Overview of the Proof of a Trivial Consequence</h2>
<p>
<img src=green-line.gif><p>
<pre>
ACL2 !><b>(defthm trivial-consequence</B>
<b>(equal (app (app (app (app x1 x2) (app x3 x4)) (app x5 x6)) x7)</B>
<b>(app x1 (app (app x2 x3) (app (app x4 x5) (app x6 x7))))))</B><p>
<a href="The_WARNING_about_the_Trivial_Consequence.html">ACL2 Warning</a> [Subsume] in ( DEFTHM TRIVIAL-CONSEQUENCE ...): The previously
added rule ASSOCIATIVITY-OF-APP subsumes the newly proposed :REWRITE
rule TRIVIAL-CONSEQUENCE, in the sense that the old rule rewrites a
more general target. Because the new rule will be tried first, it
may nonetheless find application.<p>
By the simple :rewrite rule <a href="The_First_Application_of_the_Associativity_Rule.html">ASSOCIATIVITY-OF-APP</a> we reduce the conjecture
to<p>
Goal'
(EQUAL (APP X1
(APP X2
(APP X3 (APP X4 (APP X5 (APP X6 X7))))))
(APP X1
(APP X2
(APP X3 (APP X4 (APP X5 (APP X6 X7))))))).<p>
But we reduce the conjecture to T, by primitive type reasoning.<p>
Q.E.D.<p>
Summary
Form: ( DEFTHM TRIVIAL-CONSEQUENCE ...)
Rules: ((:REWRITE ASSOCIATIVITY-OF-APP)
(:FAKE-RUNE-FOR-TYPE-SET NIL))
Warnings: <a href="The_Summary_of_the_Proof_of_the_Trivial_Consequence.html">Subsume</a>
Time: 0.20 seconds (prove: 0.02, print: 0.00, other: 0.18)
TRIVIAL-CONSEQUENCE
</pre>
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