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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="subset_1.html#NM2">Subset</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="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> =  <a href="setlim_1.html#K2">superior_setsequence</a> <font color="Maroon">c<sub>3</sub></font> as   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> =  <a href="setlim_1.html#K2">superior_setsequence</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="setlim_2.html#K5" target="_self">(/\)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> as   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E3:83"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="setlim_2.html#K5" target="_self">(/\)</a> <font color="Maroon">c<sub>4</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="83_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="83_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>thus </b><font color="Maroon">c<sub>5</sub></font> <a href="prob_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> = 
<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prob_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="setlim_2.html#T55" target="_self">Th55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="setlim_2.html#K5" target="_self">(/\)</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="prob_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="ref" href="setlim_2.html#D5" target="_self">Def5</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:83_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="setlim_2.html#K5" target="_self">(/\)</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:83"/><b>then </b>
 <a href="prob_1.html#K4">Intersection</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="prob_1.html#K4">Intersection</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="setlim_2.html#T33" target="_self">Th33</a></i>;<br/>
<a NAME="E5:83"/><b>then </b>
 <a href="kurato_2.html#K5">lim_sup</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="setlim_2.html#K5" target="_self">(/\)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="prob_1.html#K4">Intersection</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="setlim_1.html#D5">SETLIM_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E6:83"/>
 <a href="kurato_2.html#K5">lim_sup</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="setlim_2.html#K5" target="_self">(/\)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="kurato_2.html#K5">lim_sup</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="setlim_1.html#D5">SETLIM_1:def 5</a></i>;<br/>


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