<?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   non  <a href="xtuple_0.html#V1" title="XTUPLE_0:attr.1">pair</a>   <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"> ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</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> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</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> &amp; <font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</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> )</span><br/>

<span class="kw">assume </span><a NAME="E1:108"/><span class="lab"><font color="Green" title="E61">A1</font></span>: 
(  not <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</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> or  not <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</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> or  not <font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</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> )
 ; <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"> contradiction</span><br/>

<a NAME="E2:108"/><span class="lab"><font color="Green" title="E62">A2</font></span>: 
<font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T72" target="_self" onmouseover="rs('facirc_1/T72')" onmouseout="rh()">Th72</a></span>;<br/>
<a NAME="E3:108"/><span class="lab"><font color="Green" title="E63">A3</font></span>: 
 <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="ref" href="facirc_1.html#T67" target="_self" onmouseover="rs('facirc_1/T67')" onmouseout="rh()">Th67</a></span>;<br/>
<a NAME="E4:108"/>
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <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> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <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> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T72" target="_self" onmouseover="rs('facirc_1/T72')" onmouseout="rh()">Th72</a></span>;<br/>
<a NAME="E5:108"/><span class="kw">then </span>
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <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> or <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <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> or <font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <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> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:108"><span class="lab"><font color="Green" title="E62">A2</font></span></a>, <a class="txt" href="#E1:108"><span class="lab"><font color="Green" title="E61">A1</font></span></a>, <a class="ref" href="xboole_0.html#D5" onmouseover="rs('xboole_0/D5')" onmouseout="rh()">XBOOLE_0:def 5</a></span>;<br/>
<a NAME="E6:108"/><span class="kw">then </span>
(  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:108"><span class="lab"><font color="Green" title="E63">A3</font></span></a>, <a class="ref" href="relat_1.html#D1" onmouseover="rs('relat_1/D1')" onmouseout="rh()">RELAT_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:108"/>
contradiction
 ; <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>
