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

<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">M</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/>
<b>set </b><font color="Maroon">MI</font> =  <a href="facirc_1.html#K18" target="_self">MajorityIStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font>;<br/>
<b>set </b><font color="Maroon">S</font> =  <a href="circcomb.html#K7">1GateCircStr</a> <span class="p1"><a href="facirc_1.html#K7" target="_self">&lt;*</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><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>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">c</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>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">x</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></span><a href="facirc_1.html#K7" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K4" target="_self">or3</a> ;<br/>
<a NAME="E1:109"/><i><font color="Green">E33</font></i>: 
( not  <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">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>)</span> is <a href="facirc_1.html#V2" target="_self">with_pair</a> &amp; not  <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</font>,<font color="Maroon">x</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span>)</span> is <a href="facirc_1.html#V2" target="_self">with_pair</a> &amp; not  <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">y</font>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span>)</span> is <a href="facirc_1.html#V2" target="_self">with_pair</a> )
 
<b>by </b><i><a class="ref" href="facirc_1.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E2:109"/><b>then </b>
not  <a href="msafree2.html#K2">InputVertices</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p3"><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>)</span> <a href="circcomb.html#K3">+*</a> <span class="p2">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span>)</span></span>)</span> is <a href="facirc_1.html#V2" target="_self">with_pair</a>
 
<b>by </b><i/>;<br/>
<a NAME="E3:109"/><b>then </b><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#K18" target="_self">MajorityIStr</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>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:109"/>
 <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K7" target="_self">&lt;*</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4"><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>,<span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">c</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>,<span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">x</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></span><a href="facirc_1.html#K7" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K4" target="_self">or3</a> </span>)</span> is   <a href="relat_1.html#NM1">Relation</a>
 
<b>by </b><i/>;<br/>
<a NAME="E5:109"/><b>then </b><i><font color="Green">E54</font></i>: 
 <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">(<span class="default"><a href="msafree2.html#K2">InputVertices</a> <span class="p2">(<span class="default"><a href="facirc_1.html#K18" target="_self">MajorityIStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K2">InputVertices</a> <span class="p3">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p4"><a href="facirc_1.html#K7" target="_self">&lt;*</a><span class="default"><span class="p5"><a href="tarski.html#K4">[</a><span class="default"><span class="p0"><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>,<span class="p5"><a href="tarski.html#K4">[</a><span class="default"><span class="p0"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">c</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>,<span class="p5"><a href="tarski.html#K4">[</a><span class="default"><span class="p0"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">x</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></span><a href="facirc_1.html#K7" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K4" target="_self">or3</a> </span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><a href="msafree2.html#K4">InnerVertices</a> <span class="p3">(<span class="default"><a href="facirc_1.html#K18" target="_self">MajorityIStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>given </b><font color="Maroon">xx</font> being  <a href="facirc_1.html#V1" target="_self">pair</a>  <a href="hidden.html#M1">set</a> <b> such that </b><a NAME="E6:109"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">xx</font> <a href="hidden.html#R2">in</a>  <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>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="facirc_1.html#D2" target="_self">FACIRC_1:def 2</a><br/>

<a NAME="E7:109"/><i><font color="Green">E56</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#K7" target="_self">&lt;*</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4"><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>,<span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">c</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>,<span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">x</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></span><a href="facirc_1.html#K7" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K4" target="_self">or3</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><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>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">c</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>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">x</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></span><a href="enumset1.html#K1">}</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E8:109"/><i><font color="Green">E57</font></i>: 
(  <a href="msafree2.html#K4">InnerVertices</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">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>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><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></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="msafree2.html#K4">InnerVertices</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">y</font>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">c</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></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="msafree2.html#K4">InnerVertices</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</font>,<font color="Maroon">x</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">x</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></span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="circcomb.html#T49">CIRCCOMB:49</a></i>;<br/>
<a NAME="E9:109"/><i><font color="Green">E138</font></i>: 
(  <a href="circcomb.html#K7">1GateCircStr</a> <span class="p1"><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>  <a href="circcomb.html#R1">tolerates</a>  <a href="circcomb.html#K7">1GateCircStr</a> <span class="p1"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a>  &amp;  <a href="circcomb.html#K7">1GateCircStr</a> <span class="p1"><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>  <a href="circcomb.html#R1">tolerates</a>  <a href="circcomb.html#K7">1GateCircStr</a> <span class="p1"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">x</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a>  &amp;  <a href="circcomb.html#K7">1GateCircStr</a> <span class="p1"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a>  <a href="circcomb.html#R1">tolerates</a>  <a href="circcomb.html#K7">1GateCircStr</a> <span class="p1"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">x</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a>  )
 
<b>by </b><i><a class="ref" href="circcomb.html#T51">CIRCCOMB:51</a></i>;<br/>
<a NAME="E10:109"/><b>then </b><i><font color="Green">E139</font></i>: 
 <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p3"><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>)</span> <a href="circcomb.html#K3">+*</a> <span class="p2">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><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></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">c</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></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i>, <a class="ref" href="circcomb.html#T15">CIRCCOMB:15</a></i>;<br/>
<a NAME="E11:109"/>
<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">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>)</span> <a href="circcomb.html#K3">+*</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">y</font>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span>)</span> <a href="circcomb.html#R1">tolerates</a>  <a href="circcomb.html#K7">1GateCircStr</a> <span class="p1"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">x</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> 
 
<b>by </b><i>, <a class="ref" href="circcomb.html#T7">CIRCCOMB:7</a></i>;<br/>
<b>then </b> <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K18" target="_self">MajorityIStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4"><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></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">c</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></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">x</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></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i>, , <a class="ref" href="circcomb.html#T15">CIRCCOMB:15</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><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>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">c</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></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">x</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></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T41">ENUMSET1:41</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><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>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">c</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>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">x</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></span><a href="enumset1.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T43">ENUMSET1:43</a></i>
;<br/>
<a NAME="E13:109"/><b>then </b>
<span class="p1">(<span class="default"><a href="msafree2.html#K2">InputVertices</a> <span class="p2">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K7" target="_self">&lt;*</a><span class="default"><span class="p4"><a href="tarski.html#K4">[</a><span class="default"><span class="p5"><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>,<span class="p4"><a href="tarski.html#K4">[</a><span class="default"><span class="p5"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">c</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>,<span class="p4"><a href="tarski.html#K4">[</a><span class="default"><span class="p5"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">x</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></span><a href="facirc_1.html#K7" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K4" target="_self">or3</a> </span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4">InnerVertices</a> <span class="p2">(<span class="default"><a href="facirc_1.html#K18" target="_self">MajorityIStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T37">XBOOLE_1:37</a></i>;<br/>
<b>hence </b><a NAME="E14:109"/>
contradiction
 <b>by </b><i>, , , </i>;<br/>


</div>
