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

<a NAME="E1:22_1_1"/><i><font color="Green">E37</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T71">RELAT_1:71</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">xi</font> =  <a href="relat_1.html#K6">id</a> <font color="Maroon">A</font> as   <a href="ordinal1.html#NM3">T-Sequence</a> <b>by </b><i><a class="ref" href="ordinal1.html#D7">ORDINAL1:def 7</a></i>;<br/>
<b>reconsider </b><font color="Maroon">xi</font> = <font color="Maroon">xi</font> as   <a href="ordinal2.html#NM1">Ordinal-Sequence</a> <b>by </b><i>, <a class="ref" href="ordinal2.html#D8">ORDINAL2:def 8</a></i>;<br/>
<b>take </b>
<font color="Maroon">xi</font>
;<br/>

<b>thus </b><a NAME="E4:22_1_1"/>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">xi</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">xi</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> )
 <b>by </b><i><a class="ref" href="relat_1.html#T71">RELAT_1:71</a></i>;<br/>

<b>thus </b><a NAME="E5:22_1_1"/>
<font color="Maroon">xi</font> is <a href="ordinal2.html#V2">increasing</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">B</font> be   <a href="ordinal1.html#NM2">Ordinal</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="ordinal2.html#D16">ORDINAL2:def 16</a><br/><b>let </b><font color="Maroon">C</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/>



<b>assume </b><a NAME="E1:22_1_1_1"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">xi</font> )
 ;<br/>

<a NAME="E2:22_1_1_1"/><b>then </b>
( <font color="Maroon">B</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">xi</font> &amp; <font color="Maroon">xi</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> )
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T35">FUNCT_1:35</a>, <a class="ref" href="ordinal1.html#T19">ORDINAL1:19</a></i>;<br/>
<b>hence </b><a NAME="E3:22_1_1_1"/>
<font color="Maroon">xi</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">xi</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T35">FUNCT_1:35</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E6:22_1_1"/>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="ordinal2.html#K4">sup</a> <font color="Maroon">xi</font>
 <b>by </b><i>, <a class="ref" href="ordinal2.html#T26">ORDINAL2:26</a></i>;<br/>


</div>
