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<b>let </b><font color="Maroon" title="c1">Q</font> be  <a href="rewrite1.html#V1" title="REWRITE1:attr.1">co-well_founded</a> <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</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="E1:66"/><i><font color="Green" title="E56">A1</font></i>: 
<font color="Maroon" title="c2">R</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">Q</font>
 ;<br/>

<a NAME="E2:66"/><b>then </b><i><font color="Green" title="E57">A2</font></i>: 
 <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c2">R</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c1">Q</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T31" title="RELAT_1:th.31">RELAT_1:31</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> ; <i><font color="Red">:: according to </font></i><a class="ref" href="rewrite1.html#D16" target="_self" title="REWRITE1:def.16">REWRITE1:def 16</a><br/>

<b>assume </b><a NAME="E3:66"/><i><font color="Green" title="E58">A3</font></i>: 
( <font color="Maroon" title="c3">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c2">R</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/>

<a NAME="E4:66"/><b>then </b>
<font color="Maroon" title="c3">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c1">Q</font>
 
<b>by </b><i><a class="txt" href="rewrite1.html#E2:66"><i><font color="Green" title="E57">A2</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<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="E6:66"/><i><font color="Green" title="E59">A4</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>
 <b>and </b><br/><a NAME="E7:66"/><i><font color="Green" title="E60">A5</font></i>: 
for <font color="Olive" title="b1">b</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">b</font> holds <br/> not <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="Olive" title="b1">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="c1">Q</font>
 <b>by </b><i><a class="txt" href="rewrite1.html#E3:66"><i><font color="Green" title="E58">A3</font></i></a>, <a class="ref" href="rewrite1.html#D16" target="_self" title="REWRITE1:def.16">Def16</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">a</font>
;<br/>

<b>thus </b><a NAME="E8:66"/>
<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="rewrite1.html#E6:66"><i><font color="Green" title="E59">A4</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="E9:66"/>
( <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> &amp; <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> )
 ;<br/>

<b>hence </b><a NAME="E10:66"/>
not <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="rewrite1.html#E1:66"><i><font color="Green" title="E56">A1</font></i></a>, <a class="txt" href="rewrite1.html#E7:66"><i><font color="Green" title="E60">A5</font></i></a></i>;<br/>


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