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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">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="E1:27"/><i><font color="Green" title="E22">A1</font></i>: 
<font color="Maroon" title="c2">X</font> is <a href="card_lar.html#V3" title="CARD_LAR:attr.3">stationary</a>
 ;<br/>

<b>assume </b><a NAME="E2:27"/>
not <font color="Maroon" title="c2">X</font> is <a href="card_lar.html#V1" title="CARD_LAR:attr.1">unbounded</a>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c3">B1</font> being   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a><b> such that </b><br/><a NAME="E4:27"/><i><font color="Green" title="E23">A2</font></i>: 
<font color="Maroon" title="c3">B1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 <b>and </b><br/><a NAME="E5:27"/><i><font color="Green" title="E24">A3</font></i>: 
<font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">B1</font>
 <b>by </b><i><a class="ref" href="card_lar.html#T5" target="_self" title="CARD_LAR:th.5">Th5</a></i>;<br/>
<a NAME="E6:27"/><i><font color="Green" title="E25">A4</font></i>: 
( <font color="Maroon" title="c1">A</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">B1</font> is <a href="card_lar.html#V2" title="CARD_LAR:attr.2">closed</a> &amp; <font color="Maroon" title="c1">A</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">B1</font> is <a href="card_lar.html#V1" title="CARD_LAR:attr.1">unbounded</a> )
 
<b>by </b><i><a class="txt" href="card_lar.html#E4:27"><i><font color="Green" title="E23">A2</font></i></a>, <a class="ref" href="card_lar.html#T13" target="_self" title="CARD_LAR:th.13">Th13</a></i>;<br/>
<a NAME="E7:27"/>
<font color="Maroon" title="c1">A</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">B1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c3">B1</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T79" title="XBOOLE_1:th.79">XBOOLE_1:79</a></i>;<br/>
<a NAME="E8:27"/><b>then </b>
<font color="Maroon" title="c1">A</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">B1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c2">X</font>
 
<b>by </b><i><a class="txt" href="card_lar.html#E5:27"><i><font color="Green" title="E24">A3</font></i></a>, <a class="ref" href="xboole_1.html#T63" title="XBOOLE_1:th.63">XBOOLE_1:63</a></i>;<br/>
<a NAME="E9:27"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">B1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/>
<b>hence </b><a NAME="E10:27"/>
contradiction
 <b>by </b><i><a class="txt" href="card_lar.html#E1:27"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="card_lar.html#E6:27"><i><font color="Green" title="E25">A4</font></i></a>, <a class="ref" href="card_lar.html#D7" target="_self" title="CARD_LAR:def.7">Def7</a></i>;<br/>


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