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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></font> =  <a href="facirc_1.html#K23" target="_self">BitAdderWithOverflowStr</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="facirc_1.html#K12" target="_self">2GatesCircStr</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<a href="facirc_1.html#K1" target="_self">'xor'</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="facirc_1.html#K19" target="_self">MajorityStr</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>
<a NAME="E1:130"/><i><font color="Green">E75</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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></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#T58" target="_self">Th58</a>, <a class="ref" href="facirc_1.html#T59" target="_self">Th59</a></i>;<br/>
<a NAME="E2:130"/><i><font color="Green">E76</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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> is   <a href="relat_1.html#NM1">Relation</a> )
 
<b>by </b><i><a class="ref" href="facirc_1.html#T67" target="_self">Th67</a>, <a class="ref" href="facirc_1.html#T68" target="_self">Th68</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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="enumset1.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="facirc_1.html#T57" target="_self">Th57</a>, <a class="ref" href="facirc_1.html#T75" target="_self">Th75</a></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="enumset1.html#K1">}</a></span>
<b>by </b><i><a class="txt" href="facirc_1.html#E1:130"><i><font color="Green">E75</font></i></a>, <a class="txt" href="facirc_1.html#E2:130"><i><font color="Green">E76</font></i></a>, <a class="ref" href="facirc_1.html#T7" target="_self">Th7</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="enumset1.html#K1">}</a></span>

;<br/><br/>


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