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<b>let </b><font color="Maroon">C</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/>



<b>assume </b><a NAME="E1:33"/><i><font color="Green">E13</font></i>: 
( 1 <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">A</font> <a href="ordinal1.html#NR2" target="_self">is_limit_ordinal</a>  )
 ;<br/>

<b>let </b><font color="Maroon">fi</font> be   <a href="ordinal2.html#NM1">Ordinal-Sequence</a>;<br/>

<b>assume </b><a NAME="E2:33"/><i><font color="Green">E25</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">fi</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> &amp; ( for <font color="Olive">B</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Olive">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/><font color="Maroon">fi</font> <a href="funct_1.html#K1">.</a> <font color="Olive">B</font> <a href="hidden.html#R1">=</a>  <a href="ordinal2.html#K12">exp</a> <font color="Maroon">C</font>,<font color="Olive">B</font> ) )
 ;<br/>

<a NAME="E3:33"/><b>then </b>
<font color="Maroon">fi</font> is <a href="ordinal2.html#V2">increasing</a>
 
<b>by </b><i>, <a class="txt" href="ordinal4.html#E2:33"><i><font color="Green">E25</font></i></a></i>;<br/>
<a NAME="E4:33"/><b>then </b>
 <a href="ordinal2.html#K8">lim</a> <font color="Maroon">fi</font> <a href="hidden.html#R1">=</a>  <a href="ordinal2.html#K4">sup</a> <font color="Maroon">fi</font>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E5:33"/>
 <a href="ordinal2.html#K12">exp</a> <font color="Maroon">C</font>,<font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="ordinal2.html#K4">sup</a> <font color="Maroon">fi</font>
 <b>by </b><i>, , <a class="ref" href="ordinal2.html#T62">ORDINAL2:62</a></i>;<br/>


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