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<b>reconsider </b><font color="Maroon" title="c3">X</font> = <font color="Maroon" title="c2">X</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font> ;<br/>
<div><i><font color="Green" title="E49">A1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="106_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">Y</font> be  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font>;<br/><a NAME="E1:106_1_1_1"/>
<font color="Maroon" title="c4">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><b>hence </b><a NAME="E2:106_1_1_1"/>
( <font color="Maroon" title="c4">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c4">Y</font>,<font color="Maroon" title="c1">L</font> )
 <b>by </b><i><a class="ref" href="yellow_0.html#T55" title="YELLOW_0:th.55">YELLOW_0:55</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E50">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="106_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/><b>assume </b><a NAME="E1:106_1_1_2"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel_0.html#K12" title="WAYBEL_0:func.12">fininfs</a> <font color="Maroon" title="c3">X</font>
 ;<br/><a NAME="E2:106_1_1_2"/><b>then </b>
 ex <font color="Olive" title="b1">Y</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> st <br/>( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Olive" title="b1">Y</font>,<font color="Maroon" title="c1">L</font> &amp;  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Olive" title="b1">Y</font>,<font color="Maroon" title="c1">L</font> )
 ;<br/><b>hence </b><a NAME="E3:106_1_1_2"/>
 ex <font color="Olive" title="b1">Y</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> st <br/>(  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Olive" title="b1">Y</font>,<font color="Maroon" title="c1">L</font> &amp; <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Olive" title="b1">Y</font>,<font color="Maroon" title="c1">L</font> )
 ;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="106_1_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">Y</font> be  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font>;<br/><b>reconsider </b><font color="Maroon" title="c5">Z</font> = <font color="Maroon" title="c4">Y</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><b>assume </b><a NAME="E2:106_1_1_3"/>
<font color="Maroon" title="c4">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><a NAME="E3:106_1_1_3"/><b>then </b>
 <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c5">Z</font>,<font color="Maroon" title="c1">L</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T55" title="YELLOW_0:th.55">YELLOW_0:55</a></i>;<br/><b>hence </b><a NAME="E4:106_1_1_3"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Maroon" title="c4">Y</font>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel_0.html#K12" title="WAYBEL_0:func.12">fininfs</a> <font color="Maroon" title="c3">X</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:106_1_1"/>
 <a href="waybel_0.html#K12" title="WAYBEL_0:func.12">fininfs</a> <font color="Maroon" title="c2">X</font> is <a href="waybel_0.html#V2" title="WAYBEL_0:attr.2">filtered</a>
 <b>by </b><i><a class="txt" href="waybel_0.html#E2:106_1_1"><i><font color="Green" title="E49">A1</font></i></a>, <a class="txt" href="waybel_0.html#E3:106_1_1"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="waybel_0.html#T56" target="_self" title="WAYBEL_0:th.56">Th56</a></i>;<br/>


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