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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">R</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>;<br/>



<b>assume </b><a NAME="E1:11"/>
<font color="Maroon" title="c2">R</font> <a href="wellord1.html#R2" title="WELLORD1:pred.2">well_orders</a> <font color="Maroon" title="c1">X</font>
 ;<br/>

<a NAME="E2:11"/><b>then </b><i><font color="Green" title="E12">A1</font></i>: 
( <font color="Maroon" title="c2">R</font> <a href="relat_2.html#R1" title="RELAT_2:pred.1">is_reflexive_in</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">R</font> <a href="relat_2.html#R6" title="RELAT_2:pred.6">is_connected_in</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">R</font> <a href="wellord1.html#R1" title="WELLORD1:pred.1">is_well_founded_in</a> <font color="Maroon" title="c1">X</font> )
 
<b>by </b><i><a class="ref" href="wellord1.html#D5" target="_self" title="WELLORD1:def.5">Def5</a></i>;<br/>
<b>let </b><font color="Maroon" title="c3">Y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E3:11"/><i><font color="Green" title="E13">A2</font></i>: 
( <font color="Maroon" title="c3">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c3">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E5:11"/><i><font color="Green" title="E14">A3</font></i>: 
( <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c2">R</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c4">a</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c3">Y</font> )
 <b>by </b><i><a class="txt" href="wellord1.html#E2:11"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="wellord1.html#D3" target="_self" title="WELLORD1:def.3">Def3</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">a</font>
;<br/>

<b>thus </b><a NAME="E6:11"/>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Y</font>
 <b>by </b><i><a class="txt" href="wellord1.html#E5:11"><i><font color="Green" title="E14">A3</font></i></a></i>;<br/>

<b>let </b><font color="Maroon" title="c5">b</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E7:11"/><i><font color="Green" title="E15">A4</font></i>: 
<font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Y</font>
 ;<br/>

<a NAME="E8:11"/><b>then </b>
not <font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">R</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c4">a</font>
 
<b>by </b><i><a class="txt" href="wellord1.html#E5:11"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/>
<a NAME="E9:11"/><b>then </b>
( <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> or  not <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c4">a</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">R</font> )
 
<b>by </b><i><a class="ref" href="wellord1.html#D1" target="_self" title="WELLORD1:def.1">Def1</a></i>;<br/>
<a NAME="E10:11"/><b>then </b>
( <font color="Maroon" title="c4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b</font> implies <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">R</font> )
 
<b>by </b><i><a class="txt" href="wellord1.html#E2:11"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="wellord1.html#E3:11"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="wellord1.html#E5:11"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="wellord1.html#E7:11"><i><font color="Green" title="E15">A4</font></i></a>, <a class="ref" href="relat_2.html#D6" title="RELAT_2:def.6">RELAT_2:def 6</a></i>;<br/>
<b>hence </b><a NAME="E11:11"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">R</font>
 <b>by </b><i><a class="txt" href="wellord1.html#E2:11"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="wellord1.html#E3:11"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="wellord1.html#E5:11"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="relat_2.html#D1" title="RELAT_2:def.1">RELAT_2:def 1</a></i>;<br/>


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