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<b>let </b><font color="Maroon">c</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>set </b><font color="Maroon">f</font> =  <a href="facirc_1.html#K3" target="_self">'&amp;'</a> ;<br/>
<b>assume </b><a NAME="E1:102"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span><a href="tarski.html#K4">]</a></span>
 ;<br/>

<b>let </b><font color="Maroon">s</font> be   <a href="circuit1.html#NM3">State</a> of <span class="p1">(<span class="default"><a href="facirc_1.html#K14" target="_self">2GatesCircuit</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span>)</span>;<br/><b>let </b><font color="Maroon">a1</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a> , <font color="Maroon">a2</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a> , <font color="Maroon">a3</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a> ;<br/>



<b>assume </b><a NAME="E2:102"/>
( <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> &amp; <font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> &amp; <font color="Maroon">a3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c</font> )
 ;<br/>

<b>hence </b><span class="p1">(<span class="default"><a href="facirc_1.html#K9" target="_self">Following</a> <font color="Maroon">s</font>,2</span>)</span> <a href="facirc_1.html#K15" target="_self">.</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K13" target="_self">2GatesCircOutput</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span>)</span> = 
<a href="facirc_1.html#K3" target="_self">'&amp;'</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="facirc_1.html#K3" target="_self">'&amp;'</a>  <a href="funct_1.html#K1">.</a> <span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">a2</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span></span>)</span>,<font color="Maroon">a3</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>
<b>by </b><i><a class="ref" href="facirc_1.html#T9" target="_self">Th9</a>, <a class="ref" href="facirc_1.html#T6" target="_self">Th6</a></i>
<br/>.= 
<a href="facirc_1.html#K3" target="_self">'&amp;'</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">a2</font></span>)</span>,<font color="Maroon">a3</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">a2</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">a3</font>
<b>by </b><i/>
;<br/><br/>


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