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<b>let </b><font color="Maroon">fi</font> be   <a href="ordinal2.html#NM1">Ordinal-Sequence</a>;<br/><b>let </b><font color="Maroon">C</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/>



<a NAME="E1:46"/><i><font color="Green">E19</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">fi</font> <a href="ordinal3.html#K4" target="_self">*^</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">fi</font>
 
<b>by </b><i><a class="ref" href="ordinal3.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E2:46"/>
for <font color="Olive">A</font>, <font color="Olive">B</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Olive">A</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">fi</font> &amp; <font color="Olive">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fi</font> <a href="funct_1.html#K1">.</a> <font color="Olive">A</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon">fi</font> <a href="ordinal3.html#K4" target="_self">*^</a> <font color="Maroon">C</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <font color="Olive">B</font> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="ordinal3.html#T10" target="_self">Th10</a></i>;<br/>
<b>hence </b><a NAME="E3:46"/>
(  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">fi</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="ordinal2.html#K4">sup</a> <font color="Maroon">fi</font> <a href="ordinal1.html#NR2" target="_self">is_limit_ordinal</a>  implies  <a href="ordinal2.html#K4">sup</a> <span class="p1">(<span class="default"><font color="Maroon">fi</font> <a href="ordinal3.html#K4" target="_self">*^</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ordinal2.html#K4">sup</a> <font color="Maroon">fi</font></span>)</span> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">C</font> )
 <b>by </b><i><a class="ref" href="ordinal3.html#T26" target="_self">Th26</a>, <a class="ref" href="ordinal3.html#T22" target="_self">Th22</a></i>;<br/>


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