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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><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> = <span class="p1"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>;<br/>
<a NAME="E1:73"/><i><font color="Green">E46</font></i>: 
 <a href="msafree2.html#K2">InputVertices</a> <span class="p1">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="facirc_1.html#T40" target="_self">Th40</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>5</sub></font> be  <a href="facirc_1.html#V1" target="_self">pair</a>  <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="facirc_1.html#D2" target="_self">FACIRC_1:def 2</a><br/>

<b>assume </b><a NAME="E2:73"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K2">InputVertices</a> <span class="p1">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/>

<b>hence </b><a NAME="E3:73"/>
contradiction
 <b>by </b><i><a class="txt" href="facirc_1.html#E1:73"><i><font color="Green">E46</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>


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