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<b>let </b><font color="Maroon" title="c1">A</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>;<br/><b>let </b><font color="Maroon" title="c2">W</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:8"/><i><font color="Green" title="E7">A1</font></i>: 
for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W</font> &amp; <font color="Olive" title="b2">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">X</font> holds <br/><font color="Olive" title="b2">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W</font>
 <b>and </b><br/><a NAME="E2:8"/><i><font color="Green" title="E8">A2</font></i>: 
for <font color="Olive" title="b1">X</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W</font> holds <br/> <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Olive" title="b1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W</font>
 <b>and </b><br/><a NAME="E3:8"/>
for <font color="Olive" title="b1">X</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive" title="b1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">W</font> or <font color="Olive" title="b1">X</font>,<font color="Maroon" title="c2">W</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a>  or <font color="Olive" title="b1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W</font> )
 <b>and </b><br/><a NAME="E4:8"/><i><font color="Green" title="E9">A3</font></i>: 
<font color="Maroon" title="c1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="classes1.html#D1" title="CLASSES1:def.1">CLASSES1:def 1</a>,<a class="ref" href="classes1.html#D2" title="CLASSES1:def.2">CLASSES1:def 2</a><br/>

<a NAME="E5:8"/>
(  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W</font> &amp;  <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">A</font> )
 
<b>by </b><i><a class="txt" href="classes2.html#E2:8"><i><font color="Green" title="E8">A2</font></i></a>, <a class="txt" href="classes2.html#E4:8"><i><font color="Green" title="E9">A3</font></i></a>, <a class="ref" href="ordinal2.html#T3" title="ORDINAL2:th.3">ORDINAL2:3</a></i>;<br/>
<b>hence </b><a NAME="E6:8"/>
 <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W</font>
 <b>by </b><i><a class="txt" href="classes2.html#E1:8"><i><font color="Green" title="E7">A1</font></i></a></i>;<br/>

<b>let </b><font color="Maroon" title="c3">x</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="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E7:8"/><i><font color="Green" title="E10">A4</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c4">B</font> = <font color="Maroon" title="c3">x</font> as   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a> <b>by </b><i><a class="ref" href="ordinal1.html#T23" title="ORDINAL1:th.23">ORDINAL1:23</a></i>;<br/>
<a NAME="E9:8"/>
<font color="Maroon" title="c4">B</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="txt" href="classes2.html#E7:8"><i><font color="Green" title="E10">A4</font></i></a>, <a class="ref" href="ordinal1.html#D2" title="ORDINAL1:def.2">ORDINAL1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E10:8"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W</font>
 <b>by </b><i><a class="txt" href="classes2.html#E1:8"><i><font color="Green" title="E7">A1</font></i></a>, <a class="txt" href="classes2.html#E4:8"><i><font color="Green" title="E9">A3</font></i></a></i>;<br/>


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