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<b>let </b><font color="Maroon">D</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">pd</font> be   <a href="afinsq_1.html#NM2">XFinSequence</a> of <font color="Maroon">D</font>;<br/>





<b>consider </b><font color="Maroon">q'</font> being   <a href="afinsq_1.html#NM1">XFinSequence</a><b> such that </b><br/><a NAME="E2:5"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">pd</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">pd</font> <a href="card_fin.html#K4">|</a> <font color="Maroon">n</font></span>)</span> <a href="ordinal4.html#K1">^</a> <font color="Maroon">q'</font>
 <b>by </b><i/>;<br/>
<a NAME="E3:5"/>
(  <a href="relat_1.html#K2">rng</a> <font color="Maroon">q'</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">pd</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">pd</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D</font> )
 
<b>by </b><i>, <a class="ref" href="afinsq_1.html#T28">AFINSQ_1:28</a>, <a class="ref" href="ordinal1.html#D8">ORDINAL1:def 8</a></i>;<br/>
<a NAME="E4:5"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">q'</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E5:5"/><b>then </b>
<font color="Maroon">q'</font> is   <a href="afinsq_1.html#NM2">XFinSequence</a> of <font color="Maroon">D</font>
 
<b>by </b><i><a class="ref" href="ordinal1.html#D8">ORDINAL1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E6:5"/>
 ex <font color="Olive">qd</font> being  <a href="afinsq_1.html#NM2">XFinSequence</a> of <font color="Maroon">D</font> st <font color="Maroon">pd</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">pd</font> <a href="card_fin.html#K4">|</a> <font color="Maroon">n</font></span>)</span> <a href="afinsq_1.html#K5">^</a> <font color="Olive">qd</font>
 <b>by </b><i/>;<br/>


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