1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
|
<html>
<head><title>DEFCONG.html -- ACL2 Version 3.1</title></head>
<body text=#000000 bgcolor="#FFFFFF">
<h2>DEFCONG</h2>prove that one <a href="EQUIVALENCE.html">equivalence</a> relation preserves another in a given
<code> </code> argument position of a given function
<pre>Major Section: <a href="EVENTS.html">EVENTS</a>
</pre><p>
<pre>
Example:
(defcong set-equal iff (memb x y) 2)<p>
is an abbreviation for
(defthm set-equal-implies-iff-memb-2
(implies (set-equal y y-equiv)
(iff (memb x y) (memb x y-equiv)))
:rule-classes (:congruence))
</pre>
See <a href="CONGRUENCE.html">congruence</a> and also see <a href="EQUIVALENCE.html">equivalence</a>.
<p>
<pre>
General Form:
(defcong equiv1 equiv2 term k
:rule-classes rule-classes
:instructions instructions
:hints hints
:otf-flg otf-flg
:event-name event-name
:doc doc)
</pre>
where <code>equiv1</code> and <code>equiv2</code> are known <a href="EQUIVALENCE.html">equivalence</a> relations, <code>term</code> is a
call of a function <code>fn</code> on the correct number of distinct variable
arguments <code>(fn x1 ... xn)</code>, <code>k</code> is a positive integer less than or equal
to the arity of <code>fn</code>, and other arguments are as specified in the
documentation for <code><a href="DEFTHM.html">defthm</a></code>. The <code>defcong</code> macro expands into a call
of <code><a href="DEFTHM.html">defthm</a></code>. The name of the <code><a href="DEFTHM.html">defthm</a></code> event is
<code>equiv1-implies-equiv2-fn-k</code> unless an <code>:event-name</code> keyword argument is
supplied for the name. The term of the theorem is
<pre>
(implies (equiv1 xk yk)
(equiv2 (fn x1... xk ...xn)
(fn x1... yk ...xn))).
</pre>
The rule-class <code>:</code><code><a href="CONGRUENCE.html">congruence</a></code> is added to the <code><a href="RULE-CLASSES.html">rule-classes</a></code> specified,
if it is not already there. All other arguments to the generated
<code><a href="DEFTHM.html">defthm</a></code> form are as specified by the keyword arguments above.
<br><br><br><a href="acl2-doc.html"><img src="llogo.gif"></a> <a href="acl2-doc-index.html"><img src="index.gif"></a>
</body>
</html>
|
