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<b>let </b><font color="Maroon" title="c1">A</font> be  <a href="ordinal1.html#V4" title="ORDINAL1:attr.4">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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">X</font> <a href="card_lar.html#R4" title="CARD_LAR:pred.4">is_stationary_in</a> <font color="Maroon" title="c1">A</font> &amp; <font color="Olive" title="b1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">Y</font> &amp; <font color="Olive" title="b2">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">A</font> holds <br/><font color="Olive" title="b2">Y</font> <a href="card_lar.html#R4" title="CARD_LAR:pred.4">is_stationary_in</a> <font color="Maroon" title="c1">A</font></span><br/><b>let </b><font color="Maroon" title="c2">X</font>, <font color="Maroon" title="c3">Y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">X</font> <a href="card_lar.html#R4" title="CARD_LAR:pred.4">is_stationary_in</a> <font color="Maroon" title="c1">A</font> &amp; <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c3">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">A</font> implies <font color="Maroon" title="c3">Y</font> <a href="card_lar.html#R4" title="CARD_LAR:pred.4">is_stationary_in</a> <font color="Maroon" title="c1">A</font> )</span><br/>



<b>assume </b><a NAME="E1:25"/><i><font color="Green" title="E22">A1</font></i>: 
<font color="Maroon" title="c2">X</font> <a href="card_lar.html#R4" title="CARD_LAR:pred.4">is_stationary_in</a> <font color="Maroon" title="c1">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">Y</font> or  not <font color="Maroon" title="c3">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">A</font> or <font color="Maroon" title="c3">Y</font> <a href="card_lar.html#R4" title="CARD_LAR:pred.4">is_stationary_in</a> <font color="Maroon" title="c1">A</font> )</span><br/>

<b>assume </b><a NAME="E2:25"/><i><font color="Green" title="E23">A2</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">Y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">A</font> or <font color="Maroon" title="c3">Y</font> <a href="card_lar.html#R4" title="CARD_LAR:pred.4">is_stationary_in</a> <font color="Maroon" title="c1">A</font> )</span><br/>

<b>assume </b><a NAME="E3:25"/>
<font color="Maroon" title="c3">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">Y</font> <a href="card_lar.html#R4" title="CARD_LAR:pred.4">is_stationary_in</a> <font color="Maroon" title="c1">A</font></span><br/>

<b>then reconsider </b><font color="Maroon" title="c4">Y1</font> = <font color="Maroon" title="c3">Y</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">A</font> ;<br/>
<a NAME="E5:25"/><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="c1">A</font> &amp; ( for <font color="Olive" title="b1">Z</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">A</font>  st <font color="Olive" title="b1">Z</font> is <a href="card_lar.html#V2" title="CARD_LAR:attr.2">closed</a> &amp; <font color="Olive" title="b1">Z</font> is <a href="card_lar.html#V1" title="CARD_LAR:attr.1">unbounded</a> holds <br/> not <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b1">Z</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E1:25"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="card_lar.html#D8" target="_self" title="CARD_LAR:def.8">Def8</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">X1</font> = <font color="Maroon" title="c2">X</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">A</font> <b>by </b><i><a class="txt" href="#E1:25"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="card_lar.html#D8" target="_self" title="CARD_LAR:def.8">Def8</a></i>;<br/>
<a NAME="E7:25"/>
<font color="Maroon" title="c5">X1</font> is <a href="card_lar.html#V3" title="CARD_LAR:attr.3">stationary</a>
 
<b>by </b><i><a class="txt" href="#E5:25"><i><font color="Green" title="E24">A3</font></i></a>, <a class="ref" href="card_lar.html#D7" target="_self" title="CARD_LAR:def.7">Def7</a></i>;<br/>
<a NAME="E8:25"/><b>then </b>
<font color="Maroon" title="c4">Y1</font> is <a href="card_lar.html#V3" title="CARD_LAR:attr.3">stationary</a>
 
<b>by </b><i><a class="txt" href="#E2:25"><i><font color="Green" title="E23">A2</font></i></a>, <a class="ref" href="card_lar.html#T14" target="_self" title="CARD_LAR:th.14">Th14</a></i>;<br/>
<a NAME="E9:25"/><b>then </b>
for <font color="Olive" title="b1">Z</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">A</font>  st <font color="Olive" title="b1">Z</font> is <a href="card_lar.html#V2" title="CARD_LAR:attr.2">closed</a> &amp; <font color="Olive" title="b1">Z</font> is <a href="card_lar.html#V1" title="CARD_LAR:attr.1">unbounded</a> holds <br/> not <font color="Maroon" title="c4">Y1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b1">Z</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 
<b>by </b><i><a class="ref" href="card_lar.html#D7" target="_self" title="CARD_LAR:def.7">Def7</a></i>;<br/>
<b>hence </b><a NAME="E10:25"/>
<font color="Maroon" title="c3">Y</font> <a href="card_lar.html#R4" title="CARD_LAR:pred.4">is_stationary_in</a> <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="ref" href="card_lar.html#D8" target="_self" title="CARD_LAR:def.8">Def8</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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