<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">c</font>, <font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>





<b>set </b><font color="Maroon" title="c4">f</font> =  <a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> ;<br/>
<b>assume </b><a NAME="E1:98"/><i><font color="Green" title="E60">A1</font></i>: 
<font color="Maroon" title="c1">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ;<br/>

<b>let </b><font color="Maroon" title="c5">s</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><a href="facirc_1.html#K14" title="FACIRC_1:func.14">2GatesCircuit</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">c</font>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span>)</span>;<br/><b>let </b><font color="Maroon" title="c6">a1</font>, <font color="Maroon" title="c7">a2</font>, <font color="Maroon" title="c8">a3</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="circcomb.html#K9" title="CIRCCOMB:func.9">BOOLEAN</a> ;<br/>



<b>assume </b><a NAME="E2:98"/>
( <font color="Maroon" title="c6">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c7">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c8">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">c</font> )
 ;<br/>

<b>hence </b><span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c5">s</font>,2</span>)</span> <a href="facirc_1.html#K15" title="FACIRC_1:func.15">.</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K13" title="FACIRC_1:func.13">2GatesCircOutput</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">c</font>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a> </span>)</span> = 
<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c6">a1</font>,<font color="Maroon" title="c7">a2</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c8">a3</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>
<b>by </b><i><a class="txt" href="facirc_1.html#E1:98"><i><font color="Green" title="E60">A1</font></i></a>, <a class="ref" href="facirc_1.html#T62" target="_self" title="FACIRC_1:th.62">Th62</a></i>
<br/>.= 
<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">a1</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c7">a2</font></span>)</span>,<font color="Maroon" title="c8">a3</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>
<b>by </b><i><a class="ref" href="facirc_1.html#D6" target="_self" title="FACIRC_1:def.6">Def6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">a1</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c7">a2</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c8">a3</font>
<b>by </b><i><a class="ref" href="facirc_1.html#D6" target="_self" title="FACIRC_1:def.6">Def6</a></i>
;<br/><br/>


</div>
