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<b>let </b><font color="Maroon">E</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">d'</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font>;<br/><b>let </b><font color="Maroon">d</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font>;<br/>







<b>assume </b><a NAME="E1:7"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">d'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">d</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#R2">in</a>  <a href="zf_colla.html#K1" target="_self">Collapse</a> <font color="Maroon">E</font>,<font color="Maroon">A</font> )
 ;<br/>

<a NAME="E2:7"/><b>then </b>
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">d1</font> where <font color="Olive">d1</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font> : for <font color="Olive">d</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font>  st <font color="Olive">d</font> <a href="hidden.html#R2">in</a> <font color="Olive">d1</font> holds <br/> ex <font color="Olive">B</font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <br/>( <font color="Olive">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Olive">d</font> <a href="hidden.html#R2">in</a>  <a href="zf_colla.html#K1" target="_self">Collapse</a> <font color="Maroon">E</font>,<font color="Olive">B</font> ) </span>}</span> 
 
<b>by </b><i/>;<br/>
<a NAME="E3:7"/><b>then </b>
 ex <font color="Olive">d1</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font> st <br/>( <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">d1</font> &amp; ( for <font color="Olive">d</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font>  st <font color="Olive">d</font> <a href="hidden.html#R2">in</a> <font color="Olive">d1</font> holds <br/> ex <font color="Olive">B</font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <br/>( <font color="Olive">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Olive">d</font> <a href="hidden.html#R2">in</a>  <a href="zf_colla.html#K1" target="_self">Collapse</a> <font color="Maroon">E</font>,<font color="Olive">B</font> ) ) )
 
;<br/>
<b>then consider </b><font color="Maroon">B</font> being   <a href="ordinal1.html#NM2">Ordinal</a><b> such that </b><br/><a NAME="E5:7"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">d'</font> <a href="hidden.html#R2">in</a>  <a href="zf_colla.html#K1" target="_self">Collapse</a> <font color="Maroon">E</font>,<font color="Maroon">B</font> )
 <b>by </b><i/>;<br/>
<a NAME="E6:7"/>
<font color="Maroon">B</font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="ref" href="ordinal1.html#D2">ORDINAL1:def 2</a></i>;<br/>
<a NAME="E7:7"/><b>then </b>
 <a href="zf_colla.html#K1" target="_self">Collapse</a> <font color="Maroon">E</font>,<font color="Maroon">B</font> <a href="tarski.html#R1">c=</a>  <a href="zf_colla.html#K1" target="_self">Collapse</a> <font color="Maroon">E</font>,<font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E8:7"/>
<font color="Maroon">d'</font> <a href="hidden.html#R2">in</a>  <a href="zf_colla.html#K1" target="_self">Collapse</a> <font color="Maroon">E</font>,<font color="Maroon">A</font>
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E9:7"/>
 ex <font color="Olive">B</font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <br/>( <font color="Olive">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">d'</font> <a href="hidden.html#R2">in</a>  <a href="zf_colla.html#K1" target="_self">Collapse</a> <font color="Maroon">E</font>,<font color="Olive">B</font> )
 <b>by </b><i/>;<br/>


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