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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="prob_1.html#NM2">SetSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:95"/><i><font color="Green">E56</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">c<sub>2</sub></font> <a href="kurato_2.html#K7" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>thus </b><a NAME="E2:95"/>
 <a href="kurato_2.html#K8" target="_self">Lim_inf</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="kurato_2.html#K9" target="_self">Lim_sup</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="kurato_2.html#T68" target="_self">Th68</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<b>thus </b><a NAME="E3:95"/>
 <a href="kurato_2.html#K9" target="_self">Lim_sup</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="kurato_2.html#K8" target="_self">Lim_inf</a> <font color="Maroon">c<sub>2</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="95_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:95_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="kurato_2.html#K9" target="_self">Lim_sup</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="kurato_2.html#M1" target="_self">subsequence</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E3:95_1"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="kurato_2.html#K8" target="_self">Lim_inf</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="kurato_2.html#D12" target="_self">Def12</a></i>;<br/>
<b>thus </b><a NAME="E4:95_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="kurato_2.html#K8" target="_self">Lim_inf</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="kurato_2.html#E1:95"><i><font color="Green">E56</font></i></a>, <a class="txt" href="kurato_2.html#E3:95_1"><i><font color="Green">E57</font></i></a>, <a class="ref" href="kurato_2.html#T47" target="_self">Th47</a></i>;<br/>


</div><b>end;</b></div>


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