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<b>let </b><font color="Maroon" title="c1">A</font> be  <a href="ordinal1.html#V4" title="ORDINAL1:attr.4">being_limit_ordinal</a> <a href="finset_1.html#NV2" title="FINSET_1:NV.2">infinite</a> <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>;<br/><b>let </b><font color="Maroon" title="c2">B1</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>;<br/><b>let </b><font color="Maroon" title="c3">X</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">A</font>;<br/>





<b>assume </b><a NAME="E1:16"/><i><font color="Green" title="E14">A1</font></i>: 
<font color="Maroon" title="c3">X</font> is <a href="card_lar.html#V1" title="CARD_LAR:attr.1">unbounded</a>
 ;<br/>

<b>assume </b><a NAME="E2:16"/>
<font color="Maroon" title="c2">B1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 ;<br/>

<a NAME="E3:16"/><b>then </b>
 <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c2">B1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="ref" href="ordinal1.html#T41" title="ORDINAL1:th.41">ORDINAL1:41</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">B3</font> being   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a><b> such that </b><br/><a NAME="E5:16"/><i><font color="Green" title="E15">A2</font></i>: 
<font color="Maroon" title="c4">B3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font>
 <b>and </b><br/><a NAME="E6:16"/><i><font color="Green" title="E16">A3</font></i>: 
 <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c2">B1</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c4">B3</font>
 <b>by </b><i><a class="txt" href="card_lar.html#E1:16"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="card_lar.html#T7" target="_self" title="CARD_LAR:th.7">Th7</a></i>;<br/>
<a NAME="E7:16"/><i><font color="Green" title="E17">A4</font></i>: 
<font color="Maroon" title="c2">B1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">B3</font>
 
<b>by </b><i><a class="txt" href="card_lar.html#E6:16"><i><font color="Green" title="E16">A3</font></i></a>, <a class="ref" href="ordinal1.html#T33" title="ORDINAL1:th.33">ORDINAL1:33</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">B4</font> = <font color="Maroon" title="c4">B3</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font> <b>by </b><i><a class="txt" href="card_lar.html#E5:16"><i><font color="Green" title="E15">A2</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c5">B4</font>
;<br/>

<b>thus </b><a NAME="E9:16"/>
<font color="Maroon" title="c5">B4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">B2</font> where <font color="Olive" title="b1">B2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font> : ( <font color="Olive" title="b1">B2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font> &amp; <font color="Maroon" title="c2">B1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">B2</font> ) </span>}</span> 
 <b>by </b><i><a class="txt" href="card_lar.html#E5:16"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="card_lar.html#E7:16"><i><font color="Green" title="E17">A4</font></i></a></i>;<br/>


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