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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>, <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>assume </b><a NAME="E1:75"/><i><font color="Green">E66</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="kurato_2.html#V3">convergent</a> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="kurato_2.html#V3">convergent</a> )
 ;<br/>

<b>thus </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#K4" target="_self">(\+\)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
 <a href="kurato_2.html#K5">lim_sup</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="setlim_2.html#K2" target="_self">(\/)</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="setlim_2.html#T3" target="_self">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="kurato_2.html#K5">lim_sup</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="kurato_2.html#K5">lim_sup</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="setlim_2.html#T68" target="_self">Th68</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="kurato_2.html#K5">lim_sup</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><a href="kurato_2.html#K5">lim_sup</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="kurato_2.html#K5">lim_sup</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="setlim_2.html#E1:75"><i><font color="Green">E66</font></i></a>, <a class="ref" href="setlim_2.html#T72" target="_self">Th72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="kurato_2.html#K5">lim_sup</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><a href="kurato_2.html#K5">lim_sup</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="kurato_2.html#K5">lim_sup</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><a href="kurato_2.html#K5">lim_sup</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="setlim_2.html#E1:75"><i><font color="Green">E66</font></i></a>, <a class="ref" href="setlim_2.html#T72" target="_self">Th72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="kurato_2.html#K5">lim_sup</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K5">\+\</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>

;<br/>


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