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<b>let </b><font color="Maroon">B</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>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="ordinal1.html#NM2">Ordinal</a>) <b>-&gt; </b>  <a href="ordinal1.html#NM2">Ordinal</a> = <font color="Maroon">a<sub>1</sub></font> <a href="ordinal2.html#K11" target="_self">*^</a> <font color="Maroon">A</font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(  <a href="ordinal1.html#NM2">Ordinal</a>,  <a href="ordinal1.html#NM3">T-Sequence</a>) <b>-&gt; </b>   <a href="hidden.html#M1">set</a>  =  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="ordinal2.html#K4" target="_self">sup</a> <font color="Maroon">a<sub>2</sub></font></span>)</span>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>3</sub></font>(  <a href="ordinal1.html#NM2">Ordinal</a>,  <a href="ordinal1.html#NM2">Ordinal</a>) <b>-&gt; </b>  <a href="ordinal1.html#NM2">Ordinal</a> = <font color="Maroon">a<sub>2</sub></font> <a href="ordinal2.html#K10" target="_self">+^</a> <font color="Maroon">A</font>;<br/>
<a NAME="E1:71"/><i><font color="Green">E6</font></i>: 
for <font color="Olive">B</font>, <font color="Olive">C</font> being  <a href="ordinal1.html#NM2">Ordinal</a> holds <br/> ( <font color="Olive">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">B</font>) iff  ex <font color="Olive">fi</font> being  <a href="ordinal2.html#NM1">Ordinal-Sequence</a> st <br/>( <font color="Olive">C</font> <a href="hidden.html#R1">=</a>  <a href="ordinal2.html#K1" target="_self">last</a> <font color="Olive">fi</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Olive">fi</font> <a href="hidden.html#R1">=</a>  <a href="ordinal1.html#K1">succ</a> <font color="Olive">B</font> &amp; <font color="Olive">fi</font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; ( for <font color="Olive">C</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st  <a href="ordinal1.html#K1">succ</a> <font color="Olive">C</font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K1">succ</a> <font color="Olive">B</font> holds <br/><font color="Olive">fi</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ordinal1.html#K1">succ</a> <font color="Olive">C</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">C</font>,<font color="Olive">fi</font> <a href="funct_1.html#K1">.</a> <font color="Olive">C</font>) ) &amp; ( for <font color="Olive">C</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Olive">C</font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K1">succ</a> <font color="Olive">B</font> &amp; <font color="Olive">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Olive">C</font> <a href="ordinal1.html#NR2" target="_self">is_limit_ordinal</a>  holds <br/><font color="Olive">fi</font> <a href="funct_1.html#K1">.</a> <font color="Olive">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">C</font>,<font color="Olive">fi</font> <a href="ordinal1.html#K2">|</a> <font color="Olive">C</font>) ) ) )
 
<b>by </b><i/>;<br/>
<a NAME="E2:71"/>
for <font color="Olive">B</font> being  <a href="ordinal1.html#NM2">Ordinal</a> holds  <font color="Maroon">H<sub>1</sub></font>( <a href="ordinal1.html#K1">succ</a> <font color="Olive">B</font>) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">B</font>,<font color="Maroon">H<sub>1</sub></font>(<font color="Olive">B</font>))
 
<b>from </b><i><a class="ref" href="ordinal2.html#S15" target="_self">ORDINAL2:sch 15</a>();<br/></i>
<b>hence </b><a NAME="E3:71"/>
<span class="p1">(<span class="default"><a href="ordinal1.html#K1">succ</a> <font color="Maroon">B</font></span>)</span> <a href="ordinal2.html#K11" target="_self">*^</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="ordinal2.html#K11" target="_self">*^</a> <font color="Maroon">A</font></span>)</span> <a href="ordinal2.html#K10" target="_self">+^</a> <font color="Maroon">A</font>
 ;<br/>


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