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

<span class="kw">let </span><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font>, <font color="Maroon" title="c3">c</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K15" title="FACIRC_1:func.15">MajorityStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font>)</span>)</span> is   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a></span><br/>





<a NAME="E1:99"/><span class="lab"><font color="Green" title="E57">A1</font></span>: 
 <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <span class="p1">(<span class="default"><a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<span class="p2"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>,<a href="facirc_1.html#K4" title="FACIRC_1:func.4">or3</a>)</span>)</span> is   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T38" target="_self" onmouseover="rs('facirc_1/T38')" onmouseout="rh()">Th38</a></span>;<br/>
<a NAME="E2:99"/>
(  <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <span class="p1">(<span class="default"><a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a>)</span>)</span> is   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a> &amp;  <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <span class="p1">(<span class="default"><a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a>)</span>)</span> is   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T38" target="_self" onmouseover="rs('facirc_1/T38')" onmouseout="rh()">Th38</a></span>;<br/>
<a NAME="E3:99"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A2</font></span>: 
 <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a>)</span>)</span> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</a> <span class="p2">(<span class="default"><a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a>)</span>)</span></span>)</span> is   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T2" target="_self" onmouseover="rs('facirc_1/T2')" onmouseout="rh()">Th2</a>, <a class="ref" href="circcomb.html#T47" onmouseover="rs('circcomb/T47')" onmouseout="rh()">CIRCCOMB:47</a></span>;<br/>
<a NAME="E4:99"/>
 <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <span class="p1">(<span class="default"><a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> (<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">x</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<a href="facirc_1.html#K3" title="FACIRC_1:func.3">'&amp;'</a>)</span>)</span> is   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T38" target="_self" onmouseover="rs('facirc_1/T38')" onmouseout="rh()">Th38</a></span>;<br/>
<a NAME="E5:99"/><span class="kw">then </span>
 <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K14" title="FACIRC_1:func.14">MajorityIStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font>)</span>)</span> is   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:99"><span class="lab"><font color="Green" title="E58">A2</font></span></a>, <a class="ref" href="facirc_1.html#T2" target="_self" onmouseover="rs('facirc_1/T2')" onmouseout="rh()">Th2</a>, <a class="ref" href="circcomb.html#T47" onmouseover="rs('circcomb/T47')" onmouseout="rh()">CIRCCOMB:47</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:99"/>
 <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K15" title="FACIRC_1:func.15">MajorityStr</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font>)</span>)</span> is   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:99"><span class="lab"><font color="Green" title="E57">A1</font></span></a>, <a class="ref" href="facirc_1.html#T2" target="_self" onmouseover="rs('facirc_1/T2')" onmouseout="rh()">Th2</a>, <a class="ref" href="circcomb.html#T47" onmouseover="rs('circcomb/T47')" onmouseout="rh()">CIRCCOMB:47</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
