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<b>let </b><font color="Maroon">x</font> be  non <a href="facirc_1.html#V1" target="_self">pair</a>  <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> be  non <a href="facirc_1.html#V1" target="_self">pair</a>  <a href="hidden.html#M1">set</a> , <font color="Maroon">c</font> be  non <a href="facirc_1.html#V1" target="_self">pair</a>  <a href="hidden.html#M1">set</a> ;<br/>

<b>set </b><font color="Maroon">S</font> =  <a href="facirc_1.html#K23" target="_self">BitAdderWithOverflowStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font>;<br/>
<b>set </b><font color="Maroon">S1</font> =  <a href="facirc_1.html#K12" target="_self">2GatesCircStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font>,<a href="facirc_1.html#K1" target="_self">'xor'</a> ;<br/>
<b>set </b><font color="Maroon">S2</font> =  <a href="facirc_1.html#K19" target="_self">MajorityStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font>;<br/>
<a NAME="E1:130"/><i><font color="Green">E33</font></i>: 
( not  <a href="msafree2.html#K2">InputVertices</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K12" target="_self">2GatesCircStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font>,<a href="facirc_1.html#K1" target="_self">'xor'</a> </span>)</span> is <a href="facirc_1.html#V2" target="_self">with_pair</a> &amp;  <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K12" target="_self">2GatesCircStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font>,<a href="facirc_1.html#K1" target="_self">'xor'</a> </span>)</span> is   <a href="relat_1.html#NM1">Relation</a> )
 
<b>by </b><i>, <a class="ref" href="facirc_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E2:130"/><i><font color="Green">E35</font></i>: 
( not  <a href="msafree2.html#K2">InputVertices</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K19" target="_self">MajorityStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span>)</span> is <a href="facirc_1.html#V2" target="_self">with_pair</a> &amp;  <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K19" target="_self">MajorityStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span>)</span> is   <a href="relat_1.html#NM1">Relation</a> )
 
<b>by </b><i><a class="ref" href="facirc_1.html#T9" target="_self">Th9</a>, </i>;<br/>
<a NAME="E3:130"/>
(  <a href="msafree2.html#K2">InputVertices</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K12" target="_self">2GatesCircStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font>,<a href="facirc_1.html#K1" target="_self">'xor'</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span><a href="enumset1.html#K1">}</a></span> &amp;  <a href="msafree2.html#K2">InputVertices</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K19" target="_self">MajorityStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span><a href="enumset1.html#K1">}</a></span> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b> <a href="msafree2.html#K2">InputVertices</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K23" target="_self">BitAdderWithOverflowStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span>)</span> = 
<span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span><a href="enumset1.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span><a href="enumset1.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="facirc_1.html#D4" target="_self">Def4</a>, <a class="ref" href="facirc_1.html#D5" target="_self">Def5</a>, </i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span><a href="enumset1.html#K1">}</a></span>

;<br/><br/>


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